Springer Handbook of Condensed Matter and Materials Data

Springer Handbook of Condensed Matter and Materials Data

Springer Handbook provides a concise compilation of approved key information on methods of research, general principles, and functional relationships in physics and engineering. The world’s leading experts in the fields of physics and engineering will be assigned by one or several renowned editors to write the chapters comprising each volume. The content is selected by these experts from Springer sources (books, journals, online content) and other systematic and approved recent publications of physical and technical information. The volumes will be designed to be useful as readable desk reference book to give a fast and comprehensive overview and easy retrieval of essential reliable key information, including tables, graphs, and bibliographies. References to extensive sources are provided.

Springer

Handbook of Condensed Matter and Materials Data W. Martienssen and H. Warlimont (Eds.) With 1025 Figures and 914 Tables

123

Professor Werner Martienssen Universität Frankfurt Fachbereich 13, Physik Robert-Mayer-Str. 2 – 4 60325 Frankfurt Germany Professor Hans Warlimont IWF Dresden Helmholzstr. 20 01069 Dresden Germany Library of Congress Control Number:

2004116537

ISBN 3-540-44376-2 Spinger Berlin Heidelberg New York This work is subject to copyright. All rights reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September, 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com c
Springer Berlin Heidelberg 2005 Printed in Germany The use of designations, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Product liability: The publisher cannot guarantee the accuracy of any information about dosage and application contained in this book. In every individual case the user must check such information by consulting the relevant literature. Production and typesetting: LE-TeX GbR, Leipzig Handbook coordinator: Dr. W. Skolaut, Heidelberg Typography, layout and illustrations: schreiberVIS, Seeheim Cover design: eStudio Calamar Steinen, Barcelona Cover production: design&production GmbH, Heidelberg Printing and binding: Stürtz GmbH, Würzburg Printed on acid-free paper SPIN 10678245 62/3141/ 5 4 3 2 1 0

V

Preface

The Springer Handbook of Condensed Matter and Materials Data is the realization of a new concept in reference literature, which combines introductory and explanatory texts with a compilation of selected data and functional relationships from the fields of solidstate physics and materials in a single volume. The data have been extracted from various specialized and more comprehensive data sources, in particular the Landolt– Börnstein data collection, as well as more recent publications. This Handbook is designed to be used as a desktop reference book for fast and easy finding of essential information and reliable key data. References to more extensive data sources are provided in each section. The main users of this new Handbook are envisaged to be students, scientists, engineers, and other knowledgeseeking persons interested and engaged in the fields of solid-state sciences and materials technologies. The editors have striven to find authors for the individual sections who were experienced in the full breadth of their subject field and ready to provide succinct accounts in the form of both descriptive text and representative data. It goes without saying that the sections represent the individual approaches of the authors to their subject and their understanding of this task. Accordingly, the sections vary somewhat in character. While some editorial influence was exercised, the flexibility that we have shown is deliberate. The editors are grateful to all of the authors for their readiness to provide a contribution, and to cooperate in delivering their manuscripts and by accepting essentially all alterations which the editors requested to achieve a reasonably coherent presentation. An onerous task such as this could not have been completed without encouragement and support from the

publisher. Springer has entrusted us with this novel project, and Dr. Hubertus von Riedesel has been a persistent but patient reminder and promoter of our work throughout. Dr. Rainer Poerschke has accompanied and helped the editors constantly with his professional attitude and very personable style during the Prof. Werner Martienssen process of developing the concept, soliciting authors, and dealing with technical matters. In the later stages, Dr. Werner Skolaut became a relentless and hard-working member of our team with his painstaking contribution to technically editing the authors’ manuscripts and linking the editors’ work with the copy editing Prof. Hans Warlimont and production of the book. We should also like to thank our families for having graciously tolerated the many hours we have spent in working on this publication. We hope that the users of this Handbook, whose needs we have tried to anticipate, will find it helpful and informative. In view of the novelty of the approach and any possible inadvertent deficiencies which this first edition may contain, we shall be grateful for any criticisms and suggestions which could help to improve subsequent editions so that they will serve the expectations of the users even better and more completely.

September 2004 Frankfurt am Main, Dresden

Werner Martienssen, Hans Warlimont

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VII

List of Authors

Wolf Assmus Johann Wolfgang Goethe-University Physics Department Robert-Mayer-Str. 2 – 4 60054 Frankfurt am Main, Germany e-mail: [email protected] Stefan Brühne Johann Wolfgang Goethe-University Physics Department Robert-Mayer-Str. 2 – 4 60054 Frankfurt am Main, Germany e-mail: [email protected] Fabrice Charra Commissariat à l’Énergie Atomique, Saclay Département de Recherche sur l’État Condensé, les Atomes et les Molécules DRECAM-SPCSI, Centre d’Études de Saclay 91191 Gif-sur-Yvette, France e-mail: [email protected] Gianfranco Chiarotti University of Rome “Tor Vergata“ Department of Physics Via della Ricerca Scientifica 1 00133 Roma, Italy e-mail: [email protected] Claus Fischer Formerly Institute of Solid State and Materials Research (IFW) Georg-Schumann-Str. 20 01187 Dresden, Germany e-mail: [email protected] Günter Fuchs Leibniz Institute for Solid State and Materials Research (IFW) Dresden Magnetism and Superconductivity in the Institute of Metallic Materials Helmholtzstraße 20 01171 Dresden, Germany e-mail: [email protected]

Frank Goodwin International Lead Zinc Research Organization, Inc. PO BOX 12036 Research Triangle Parc, NC 27709, USA e-mail: [email protected] Susana Gota-Goldmann Commissariat à l’Energie Atomique (CEA) Direction de la Recherche Technologique (DRT) Centre de Fontenay aux Roses BP 6 92265 Fontenay aux Roses Cédex, France e-mail: [email protected] Sivaraman Guruswamy University of Utah Metallurgical Engineering 135 South 1460 East RM 412 Salt Lake City, UT 84112-0114, USA e-mail: [email protected] Gagik G. Gurzadyan Technical University of Munich Institute for Physical and Theoretical Chemistry Lichtenbergstrasse 4 85748 Garching, Germany e-mail: [email protected] Hideki Harada High Tech Association Ltd. 3730-30 Higashikaya, Fukaya,Saitama, Japan e-mail: [email protected] Bernhard Holzapfel Leibniz Institute for Solid State and Materials Research Dresden – Institute of Metallic Materials Superconducting Materials Helmholtzstr. 20 01069 Dresden, Germany e-mail: [email protected]

VIII

List of Authors

Karl U. Kainer GKSS Research Center Geesthacht Institute for Materials Research Max-Planck-Str. 1 21502 Geesthacht, Germany e-mail: [email protected]

Werner Martienssen Universität Frankfurt/Main Physikalisches Institut Robert-Mayer-Strasse 2 – 4 60054 Frankfurt/Main, Germany e-mail: [email protected]

Catrin Kammer METALL – Intl. Journal for Metallurgy Kielsche Straße 43B 38642 Goslar, Germany e-mail: [email protected]

Toshio Mitsui Osaka University Nakasuji-Yamate, 3-6-24 665-0875 Takarazuka, Japan e-mail: [email protected]

Wolfram Knabl Plansee AG Technology Center 6600 Reutte, Austria e-mail: [email protected]

Manfred Müller Dresden University of Technology Institute of Materials Science Leubnitzer Straße 26 01069 Dresden, Germany e-mail: [email protected]

Alfred Koethe Leibniz-Institut für Festkörper- und Werkstoffforschung Institut für Metallische Werkstoffe (retired) Lessingstrasse 11 01099 Dresden, Germany e-mail: [email protected] Dieter Krause Schott AG Research and Technology-Development PO BOX 2480 55014 Mainz, Germany e-mail: [email protected] Manfred D. Lechner Universität Osnabrück Institut für Chemie – Physikalische Chemie Barbarastraße 7 46069 Osnabrück, Germany e-mail: [email protected] Gerhard Leichtfried Plansee AG Technology Center 6600 Reutte, Austria e-mail: [email protected]

Sergei Pestov Moscow State Academy of Fine Chemical Technology Department of Inorganic Chemistry Vernadsky pr., 86 119571 Moscow, Russia e-mail: [email protected] Günther Schlamp Metallgesellschaft Ffm and Degussa Demetron (retired) Stettinerstr. 25 61449 Steinbach/Ts, Germany e-mail: Barbara Schüpp-Niewa Leibniz-Institute for Solid State and Materials Research Dresden Institute for Metallic Materials Helmholtzstraße 20 01069 Dresden, Germany e-mail: [email protected] Roland Stickler University of Vienna Department of Chemistry Währingerstr. 42 1090 Vienna, Austria e-mail: [email protected]

List of Authors

Pancho Tzankov Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy Max-Born-Str. 2A 12489 Berlin, Germany e-mail: [email protected] Volkmar Vill University of Hamburg Department of Chemistry, Institute of Organic Chemistry Martin-Luther-King-Platz 6 20146 Hamburg, Germany e-mail: [email protected]

Hans Warlimont DSL Dresden Material-Innovation GmbH Helmholtzstrasse 20 01069 Dresden, Germany e-mail: [email protected]

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List of Authors

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XI

Contents

List of Abbreviations .................................................................................

XV

Part 1 General Tables 1 The Fundamental Constants Werner Martienssen .................................................................................. 1.1 What are the Fundamental Constants and Who Takes Care of Them? ........................................................... 1.2 The CODATA Recommended Values of the Fundamental Constants ....... References................................................................................................

3 3 4 9

2 The International System of Units (SI), Physical Quantities,

and Their Dimensions Werner Martienssen .................................................................................. 2.1 The International System of Units (SI) ................................................ 2.2 Physical Quantities ........................................................................... 2.3 The SI Base Units .............................................................................. 2.4 The SI Derived Units .......................................................................... 2.5 Decimal Multiples and Submultiples of SI Units .................................. 2.6 Units Outside the SI .......................................................................... 2.7 Some Energy Equivalents .................................................................. References................................................................................................

11 11 12 13 16 19 20 24 25

3 Rudiments of Crystallography Wolf Assmus, Stefan Brühne ...................................................................... 3.1 Crystalline Materials ......................................................................... 3.2 Disorder ........................................................................................... 3.3 Amorphous Materials........................................................................ 3.4 Methods for Investigating Crystallographic Structure .......................... References................................................................................................

27 28 38 39 39 41

Part 2 The Elements 1 The Elements Werner Martienssen .................................................................................. 1.1 Introduction .................................................................................... 1.2 Description of Properties Tabulated ................................................... 1.3 Sources ............................................................................................ 1.4 Tables of the Elements in Different Orders ......................................... 1.5 Data ................................................................................................ References................................................................................................

45 45 46 49 49 54 158

XII

Contents

Part 3 Classes of Materials 1 Metals Frank Goodwin, Sivaraman Guruswamy, Karl U. Kainer, Catrin Kammer, Wolfram Knabl, Alfred Koethe, Gerhard Leichtfried, Günther Schlamp, Roland Stickler, Hans Warlimont ............................................................... 1.1 Magnesium and Magnesium Alloys.................................................... 1.2 Aluminium and Aluminium Alloys ..................................................... 1.3 Titanium and Titanium Alloys............................................................ 1.4 Zirconium and Zirconium Alloys ........................................................ 1.5 Iron and Steels ................................................................................. 1.6 Cobalt and Cobalt Alloys ................................................................... 1.7 Nickel and Nickel Alloys .................................................................... 1.8 Copper and Copper Alloys ................................................................. 1.9 Refractory Metals and Alloys ............................................................. 1.10 Noble Metals and Noble Metal Alloys ................................................. 1.11 Lead and Lead Alloys ........................................................................ References................................................................................................

161 162 171 206 217 221 272 279 296 303 329 407 422

2 Ceramics Hans Warlimont ....................................................................................... 2.1 Traditional Ceramics and Cements ..................................................... 2.2 Silicate Ceramics............................................................................... 2.3 Refractory Ceramics .......................................................................... 2.4 Oxide Ceramics ................................................................................. 2.5 Non-Oxide Ceramics ......................................................................... References................................................................................................

431 432 433 437 437 451 476

3 Polymers Manfred D. Lechner ................................................................................... 3.1 Structural Units of Polymers .............................................................. 3.2 Abbreviations................................................................................... 3.3 Tables and Figures............................................................................ References................................................................................................

477 480 482 483 522

4 Glasses Dieter Krause ............................................................................................ 4.1 Properties of Glasses – General Comments ........................................ 4.2 Composition and Properties of Glasses .............................................. 4.3 Flat Glass and Hollowware................................................................ 4.4 Technical Specialty Glasses................................................................ 4.5 Optical Glasses ................................................................................. 4.6 Vitreous Silica .................................................................................. 4.7 Glass-Ceramics................................................................................. 4.8 Glasses for Miscellaneous Applications .............................................. References................................................................................................

523 526 527 528 530 543 556 558 559 572

Contents

Part 4 Functional Materials 1 Semiconductors Werner Martienssen .................................................................................. 1.1 Group IV Semiconductors and IV–IV Compounds................................. 1.2 III–V Compounds .............................................................................. 1.3 II–VI Compounds .............................................................................. References................................................................................................

575 578 604 652 691

2 Superconductors Claus Fischer, Günter Fuchs, Bernhard Holzapfel, Barbara Schüpp-Niewa, Hans Warlimont ....................................................................................... 2.1 Metallic Superconductors .................................................................. 2.2 Non-Metallic Superconductors .......................................................... References................................................................................................

695 696 711 749

3 Magnetic Materials Hideki Harada, Manfred Müller, Hans Warlimont ....................................... 3.1 Basic Magnetic Properties ................................................................. 3.2 Soft Magnetic Alloys ......................................................................... 3.3 Hard Magnetic Alloys ........................................................................ 3.4 Magnetic Oxides ............................................................................... References................................................................................................

755 755 758 794 811 814

4 Dielectrics and Electrooptics Gagik G. Gurzadyan, Pancho Tzankov........................................................ 4.1 Dielectric Materials: Low-Frequency Properties .................................. 4.2 Optical Materials: High-Frequency Properties .................................... 4.3 Guidelines for Use of Tables .............................................................. 4.4 Tables of Numerical Data for Dielectrics and Electrooptics ................... References................................................................................................

817 822 824 826 828 890

5 Ferroelectrics and Antiferroelectrics Toshio Mitsui ............................................................................................ 5.1 Definition of Ferroelectrics and Antiferroelectrics ............................... 5.2 Survey of Research on Ferroelectrics .................................................. 5.3 Classification of Ferroelectrics ........................................................... 5.4 Physical Properties of 43 Representative Ferroelectrics ....................... References................................................................................................

903 903 904 906 912 936

Part 5 Special Structures 1 Liquid Crystals Sergei Pestov, Volkmar Vill ........................................................................ 1.1 Liquid Crystalline State ..................................................................... 1.2 Physical Properties of the Most Common Liquid Crystalline Substances

941 941 946

XIII

XIV

Contents

1.3 Physical Properties of Some Liquid Crystalline Mixtures ...................... References................................................................................................

975 977

2 The Physics of Solid Surfaces Gianfranco Chiarotti ................................................................................. 2.1 The Structure of Ideal Surfaces .......................................................... 2.2 Surface Reconstruction and Relaxation .............................................. 2.3 Electronic Structure of Surfaces ......................................................... 2.4 Surface Phonons .............................................................................. 2.5 The Space Charge Layer at the Surface of a Semiconductor.................. 2.6 Most Frequently Used Acronyms ........................................................ References................................................................................................

979 979 986 996 1012 1020 1026 1029

3 Mesoscopic and Nanostructured Materials Fabrice Charra, Susana Gota-Goldmann .................................................... 3.1 Introduction and Survey ................................................................... 3.2 Electronic Structure and Spectroscopy................................................ 3.3 Electromagnetic Confinement ........................................................... 3.4 Magnetic Nanostructures .................................................................. 3.5 Preparation Techniques .................................................................... References................................................................................................

1031 1031 1035 1044 1048 1063 1066

Acknowledgements ................................................................................... About the Authors ..................................................................................... Detailed Contents...................................................................................... Subject Index.............................................................................................

1073 1075 1081 1091

XV

List of Abbreviations

2D-BZ 2P-PES

2-dimensional Brillouin zone 2-photon photoemission spectroscopy

FEM FIM

A AES AFM AISI APS ARUPS ARXPS ASTM ATR

Auger electron spectroscopy atomic force microscope American Iron and Steel Institute appearance potential spectroscopy angle-resolved ultraviolet photoemission spectroscopy angle-resolved X-ray photoemission spectroscopy American Society for Testing and Materials attenuated total reflection

B BBZ BIPM BZ

bulk Brillouin zone Bureau International des Poids et Mesures Brillouin zone

C CB CBM CISS CITS CMOS CODATA CVD

conduction band conduction band minimum collision ion scattering spectroscopy current imaging tunneling spectroscopy complementary metal–oxide–semiconductor Committee on Data for Science and Technology chemical vapour deposition

D DFB DFG DOS DSC DTA

distributed-feedback difference frequency generation density of states differential scanning calorimetry differential thermal analysis

E EB ECS EELS ELEED ESD EXAFS

F

electron-beam melting electron capture spectroscopy electron-energy loss spectroscopy elastic low-energy electron diffraction electron-stimulated desorption extended X-ray absorption fine structure

field emission microscope/microscopy field ion microscope/microscopy

G GMR

giant magnetoresistance

H HAS HATOF HB HEED HEIS

helium atom scattering helium atom time-of-flight spectroscopy Brinell hardness number high-energy electron diffraction high-energy ion scattering/high-energy ion scattering spectroscopy HK Knoop hardness HOPG highly oriented pyrolytic graphite HPDC high-pressure die casting HR-EELS high-resolution electron energy loss spectroscopy HR-LEED high-resolution LEED HR-RHEED high-resolution RHEED HREELS high-resolution electron energy loss spectroscopy HRTEM high-resolution transition electron microscopy HT high temperature HTSC high-temperature superconductor HV Vicker’s Hardness

I IACS IB IBAD ICISS ICSU IPE IPES ISO ISS IUPAC

International Annealed Copper Standard ion bombardment ion-beam-assisted deposition impact ion scattering spectroscopy International Council of the Scientific Unions inverse photoemission inverse photoemission spectroscopy International Organization for Standardization ion scattering spectroscopy International Union of Pure and Applied Chemistry

J JDOS

joint density of states

XVI

List of Abbreviations

K KRIPES

R K-resolved inverse photoelectron spectroscopy

L LAPW LB LCM LCP LCs LDA LDOS LEED LEIS LPE

linearized augmented-plane-wave method Langmuir–Blodgett liquid crystal material liquid crystal polymer liquid crystals local-density approximation local density of states low-energy electron diffraction low-energy ion scattering/low-energy ion scattering spectroscopy liquid phase epitaxy

M MBE MD MEED MEIS MFM ML MOCVD MOKE MOSFET MQW

molecular-beam epitaxy molecular dynamics medium-energy electron diffraction medium-energy ion scattering/medium-energy ion scattering spectroscopy magnetic force microscopy monolayer metal-organic chemical vapor deposition magneto-optical Kerr effect MOS field-effect transistor multiple quantum well

NIMs

neutral impact collision ion scattering spectroscopy National Institutes for Metrology

O OPO

reflectance anisotropy spectroscopy rare earth reflection electron microscope/ microscopy reflection high-energy electron diffraction reactive ion etching random-phase approximation room temperature room temperaure and standard pressure

S SAM SAM SARS SAW SBZ SCLS SDR SEM SEXAFS SFG SH SHG SI SIMS SNR SPARPES SPIPES

SS STM STS SXRD

self-assembled monolayer scanning Auger microscope/microscopy scattering and recoiling ion spectroscopy surface acoustic wave surface Brillouin zone surface core level shift surface differential reflectivity scanning electron microscope surface-sensitive EXAFS sum frequency generation second harmonic second-harmonic generation Système International d’Unités secondary-ion mass spectroscopy signal-to-noise ratio spin polarized angle-resolved photoemission spectroscopy spin-polarized inverse photoemission spectroscopy spin-polarized surface photovoltage spectroscopy superconducting quantum interference devices surface state scanning tunneling microscope/ microscopy scanning tunneling spectroscopy surface X-ray diffraction

optical parametric oscillation

T

P PDS PED PES PLAP PLD PSZ PZT

RHEED RIE RPA RT RTP

SPLEED SPV SQUIDS

N NICISS

RAS RE REM

photothermal displacement spectroscopy photoelectron diffraction photoemission spectroscopy pulsed laser atom probe pulsed laser deposition stabilized zirconia piezoelectric material

TAFF TEM TFT TMR TMT TOF TOM

thermally activated flux flow transmission electron microscope/microscopy thin-film transistor tunnel magnetoresistance thermomechanical treatment time of flight torsion oscillation magnetometry

List of Abbreviations

TRS TTT

truncation rod scattering time-temperature-transformation

VBM VLEED

U UHV UPS UV

V

ultra-high vacuum ultraviolet photoemission spectroscopy ultraviolet

valence band maximum very low-energy electron diffraction

X XPS

X-ray photoemission spectroscopy

XVII

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1

Part 1

General Ta Part 1 General Tables

1 The Fundamental Constants 2 The International System of Units (SI), Physical Werner Martienssen, Frankfurt/Main, Germany Quantities, and Their Dimensions Werner Martienssen, Frankfurt/Main, Germany 3 Rudiments of Crystallography Wolf Assmus, Frankfurt am Main, Germany Stefan Brühne, Frankfurt am Main, Germany

2

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3

In the quantitative description of physical phenomena and physical relationships, we find constant parameters which appear to be independent of the scale of the phenomena, independent of the place where the phenomena happen, and independent of the time when the phenomena is observed. These parameters are called fundamental constants. In Sect. 1.1.1, we give a qualitative description of these basic parameters and explain how “recommended values” for the numerical values of the fundamental constants are found. In Sect. 1.1.2, we present tables of the most recently determined recommended numerical values for a large number of those fundamental constants which play a role in solid-state physics and chemistry and in materials science.

1.1.1 1.1.2

What are the Fundamental Constants and Who Takes Care of Them?.............. The CODATA Recommended Values of the Fundamental Constants............. 1.1.2.1 The Most Frequently Used Fundamental Constants ........... 1.1.2.2 Detailed Lists of the Fundamental Constants in Different Fields of Application 1.1.2.3 Constants from Atomic Physics and Particle Physics .................

References ..................................................

3 4 4

5 7 9

1.1.1 What are the Fundamental Constants and Who Takes Care of Them? The fundamental constants are constant parameters in the laws of nature. They determine the size and strength of the phenomena in the natural and technological worlds. We conclude from observation that the numerical values of the fundamental constants are independent of space and time; at least, we can say that if there is any dependence of the fundamental constants on space and time, then this dependence must be an extremely weak one. Also, we observe that the numerical values are independent of the scale of the phenomena observed; for example, they seem to be the same in astrophysics and in atomic physics. In addition, the numerical values are quite independent of the environmental conditions. So we have confidence in the idea that the numerical values of the fundamental constants form a set of numbers which are the same everywhere in the world, and which have been the same in the past and will be the same in the future. Whereas the properties of all material objects in nature are more or less subject to continuous change, the fundamental constants seem to represent a constituent of the world which is absolutely permanent. On the basis of this expected invariance of the fundamental constants in space and time, it appears reasonable to relate the units of measurement for physical quanti-

ties to fundamental constants as far as possible. This would guarantee that also the units of measurement become independent of space and time and of environmental conditions. Within the frame work of the International System of Units (Système International d’Unités, abbreviated to SI), the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM) has succeeded in relating a large number of units of measurement for physical quantities to the numerical values of selected fundamental constants; however, several units for physical quantities are still represented by prototypes. For example, the unit of length 1 meter, is defined as the distance light travels in vacuum during a fixed time; so the unit of length is related to the fundamental constant c, i. e. the speed of light, and the unit of time, 1 second. The unit of mass, 1 kilogram, however, is still represented by a prototype, the mass of a metal cylinder made of a platinum–iridium alloy, which is carefully stored at the International Office for Weights and Measures (Bureau International des Poids et Mesures, BIPM), at Sèvres near Paris. In a few years, however, it might become possible also to relate the unit of mass to one or more fundamental constants.

Part 1 1

The Fundame 1.1. The Fundamental Constants

4

Part 1

General Tables

Part 1 1.2

The fundamental constants play an important role in basic physics as well as in applied physics and technology; in fact, they have a key function in the development of a system of reproducible and unchanging units for physical quantities. Nevertheless, there is, at present, no theory which would allow us to calculate the numerical values of the fundamental constants. Therefore, national institutes for metrology (NIMs), together with research institutes and university laboratories, are making efforts worldwide to determine the fundamental constants experimentally with the greatest possible accuracy and reliability. This, of course, is a continuous process, with hundreds of new publications every year. The Committee on Data for Science and Technology (CODATA), established in 1966 as an interdisciplinary, international committee of the International Council of the Scientific Unions (ICSU), has taken the responsibility for improving the quality, reliability, processing, management, and accessibility of data of importance to science and technology. The CODATA task group on fundamental constants, established in 1969, has taken on the job of periodically providing the scientific and technological community with a self-consistent set of internationally recommended values of the fundamental constants based on all relevant data available at given points in time. What is the meaning of “recommended values” of the fundamental constants? Many fundamental constants are not independent of one another; they are related to one another by equations which allow one to calculate a numerical value for one

particular constant from the numerical values of other constants. In consequence, the numerical value of a constant can be determined either by measuring it directly or by calculating it from the measured values of other constants related to it. In addition, there are usually several different experimental methods for measuring the value of any particular fundamental constant. This allows one to compute an adjustment on the basis of a least-squares fit to the whole set of experimental data in order to determine a set of best-fitting fundamental constants from the large set of all experimental data. Such an adjustment is done today about every four years by the CODATA task group mentioned above. The resulting set of best-fit values is then called the “CODATA recommended values of the fundamental constants” based on the adjustment of the appropriate year. The tables in Sect. 1.1.2 show the CODATA recommended values of the fundamental constants of science and technology based on the 2002 adjustment. This adjustment takes into account all data that became available before 31 December 2002. A detailed description of the adjustment has been published by Mohr and Taylor of the National Institute of Standards and Technology, Gaithersburg, in [1.1]. The editors of this Handbook, H. Warlimont and W. Martienssen, would like to express their sincere thanks to Mohr and Taylor for kindly putting their data at our disposal prior to publication in Reviews of Modern Physics. These data first became available in December 2003 on the web site of the NIST fundamental constants data center [1.2].

1.1.2 The CODATA Recommended Values of the Fundamental Constants 1.1.2.1 The Most Frequently Used Fundamental Constants Tables 1.1-1 – 1.1-9 list the CODATA recommended values of the fundamental constants based on the 2002 adjustment. Table 1.1-1 Brief list of the most frequently used fundamental constants Quantity

Symbol and relation

Numerical value

Units

Relative standard uncertainty

Speed of light in vacuum Magnetic constant Electric constant Newtonian constant of gravitation Planck constant Reduced Planck constant Elementary charge

c µ0 = 4π × 10−7 ε0 = 1/(µ0 c2 ) G

299 792 458 12.566370614 . . . × 10−7 8.854187817 . . . × 10−12 6.6742(10) × 10−11

m/s N/A2 F/m m3 /(kg s2 )

Fixed by definition Fixed by definition Fixed by definition 1.5 × 10−4

h

4.13566743(35) × 10−15 6.58211915(56) × 10−16 1.60217653(14) × 10−19

eV s eV s C

8.5 × 10−8 8.5 × 10−8 8.5 × 10−8

~ = h/2π e

The Fundamental Constants

1.2 The CODATA Recommended Values of the Fundamental Constants

Quantity

Symbol and relation

Numerical value

Fine-structure constant

α = (1/4πε0 )(e2 /~c)

7.297352568(24) × 10−3

Magnetic flux quantum

Φ0 = h/2e

2.06783372(18) × 10−15

Wb

8.5 × 10−8

Conductance quantum

G 0 = 2e2 /h

7.748091733(26) × 10−5

S

3.3 × 10−9

10 973 731.568525(73)

1/m

6.6 × 10−12

me

9.1093826(16) × 10−31

kg

1.7 × 10−7

Proton mass

mp

1.67262171(29) × 10−27

kg

1.7 × 10−7

Proton–electron mass ratio

m p /m e

1836.15267261(85)

4.6 × 10−10

Avogadro number

NA , L

6.0221415(10) × 1023

1.7 × 10−7

Faraday constant

F = NA e

96 485.3383(83)

C

8.6 × 10−8

Molar gas constant

R

8.314472(15)

J/K

1.7 × 10−6

Boltzmann constant

k = R/NA

1.3806505(24) × 10−23 8.617343(15) × 10−5

J/K eV/K

1.8 × 10−6 1.8 × 10−6

Stefan–Boltzmann constant

σ = (π 2 /60)(k4 /(~3 c2 ))

5.670400(40) × 10−8

W/(m2 K4 )

7.0 × 10−6

Rydberg constant Electron mass

R∞

= α2 m

e c/2h

Units

Relative standard uncertainty 3.3 × 10−9

1.1.2.2 Detailed Lists of the Fundamental Constants in Different Fields of Application Table 1.1-2 Universal constants Quantity

Symbol and relation

Numerical value

Units

Relative standard uncertainty

Speed of light in vacuum

c

299 792 458

m/s

Fixed by definition

Magnetic constant

µ0 = 4π × 10−7

12.566370614 . . . × 10−7

N/A2

Fixed by definition

Electric constant

ε0 = 1/(µ0 c2 )

8.854187817 . . . × 10−12

F/m

Fixed by definition

Characteristic impedance of vacuum

Z 0 = (µ0 /ε0 )1/2 = µ0 c

376.730313461 . . .

Ω

Fixed by definition

Newtonian constant of gravitation

G

6.6742(10) × 10−11

m3 /(kg s2 )

1.5 × 10−4

Reduced Planck constant

G/~c

6.7087(10) × 10−39

(GeV/c2 )−2

1.5 × 10−4

Planck constant

h

6.6260693(11) × 10−34

4.13566743(35) × 10−15

Js eV s

1.7 × 10−7 8.5 × 10−8

(Ratio)

~ = h/2π

1.05457168(18) × 10−34 6.58211915(56) × 10−16

Js eV s

1.7 × 10−7 8.5 × 10−8

(Product)

~c

197.326968(17)

MeV fm

8.5 × 10−8

3.74177138(64) × 10−16

W m2

1.7 × 10−7

= 2πhc2

(Product)

c1

(Product)

(1/π)c1 = 2hc2

1.19104282(20) × 10−16

W m2 /sr

1.7 × 10−7

(Product)

c2 = h(c/k)

1.4387752(25) × 10−2

mK

1.7 × 10−6

5.670400(40) × 10−8

W/(m2 K4 )

7.0 × 10−6

mK

1.7 × 10−6

Stefan–Boltzmann constant

σ

= (π 2 /60)(k4 /(~3 c2 ))

Wien displacement law constant

b = λmax T = c2 /4.965114231

2.8977685(51) × 10−3

Planck mass

m P = (~c/G)1/2

2.17645(16) × 10−8

kg

7.5 × 10−5

Planck temperature

TP = (1/k)(~c5 /G)1/2

1.41679(11) × 1032

K

7.5 × 10−5

Planck length

lP = ~/m P c = (~G/c3 )1/2

1.61624(12) × 10−35

m

7.5 × 10−5

Planck time

tP = lP /c = (~G/c5 )1/2

5.39121(40) × 10−44

s

7.5 × 10−5

Part 1 1.2

Table 1.1-1 Brief list of the most frequently used fundamental constants, cont.

5

6

Part 1

General Tables

Part 1 1.2

Table 1.1-3 Electromagnetic constants Quantity

Symbol and relation

Numerical value

Units

Relative standard uncertainty

Elementary charge (Ratio) Fine-structure constant Inverse fine-structure constant Magnetic flux quantum Conductance quantum Inverse of conductance quantum Josephson constant a von Klitzing constant b Bohr magneton

e e/h α = (1/4πε0 )(e2 /~c) 1/α Φ0 = h/2e G 0 = 2e2 /h 1/G 0

1.60217653(14) × 10−19 2.41798940(21) × 1014 7.297352568(24) × 10−3 137.03599911(46) 2.06783372(18) × 10−15 7.748091733(26) × 10−5 12 906.403725(43)

C A/J

Wb S Ω

8.5 × 10−8 8.5 × 10−8 3.3 × 10−9 3.3 × 10−9 8.5 × 10−8 3.3 × 10−9 3.3 × 10−9

K J = 2e/h RK = h/e2 = µ0 c/2α µB = e~/2m e

(Ratio) (Ratio) (Ratio) Nuclear magneton

µB /h µB /hc µB /k µN = e~/2m p

(Ratio) (Ratio) (Ratio)

µN /h µN /hc µN /k

483 597.879(41) × 109 25 812.807449(86) 927.400949(80) × 10−26 5.788381804(39) × 10−5 13.9962458(12) × 109 46.6864507(40) 0.6717131(12) 5.05078343(43) × 10−27 3.152451259(21) × 10−8 7.62259371(65) 2.54262358(22) × 10−2 3.6582637(64) × 10−4

Hz/V Ω J/T eV/T Hz/T 1/(m T) K/T J/T eV/T MHz/T 1/(m T) K/T

8.5 × 10−8 3.3 × 10−9 8.6 × 10−8 6.7 × 10−9 8.6 × 10−8 8.6 × 10−8 1.8 × 10−6 8.6 × 10−8 6.7 × 10−9 8.6 × 10−8 8.6 × 10−8 1.8 × 10−6

a b

See Table 1.2-16 for the conventional value adopted internationally for realizing representations of the volt using the Josephson effect. See Table 1.2-16 for the conventional value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

Table 1.1-4 Thermodynamic constants Quantity

Symbol and relation

Numerical value

Avogadro number Atomic mass constant

NA , L u = (1/12)m(12 C) = (1/NA ) × 10−3 kg m u c2

6.0221415(10) × 1023 1.66053886(28) × 10−27

kg

1.7 × 10−7 1.7 × 10−7

1.49241790(26) × 10−10 931.494043(80) 96 485.3383(83) 3.990312716(27) × 10−10 0.11962656572(80) 8.314472(15) 1.3806505(24) × 10−23 8.617343(15) × 10−5 2.0836644(36) × 1010 69.50356(12) 22.413996(39) × 10−3

J MeV C Js Jm J/K J/K eV/K Hz/K 1/(m K) m3

1.7 × 10−7 8.6 × 10−8 8.6 × 10−8 6.7 × 10−9 6.7 × 10−9 1.7 × 10−6 1.8 × 10−6 1.8 × 10−6 1.7 × 10−6 1.7 × 10−6 1.7 × 10−6

2.6867773(47) × 1025 5.670400(40) × 10−8

1/m3 W/(m2 K4 )

1.8 × 10−6 7.0 × 10−6

2.8977685(51) × 10−3

mK

1.7 × 10−6

Energy equivalent of atomic mass constant Faraday constant Molar Planck constant (Product) Molar gas constant Boltzmann constant (Ratio) (Ratio) Molar volume of ideal gas at STP Loschmidt constant Stefan–Boltzmann constant Wien displacement law constant

F = NA e NA h NA hc R k = R/NA k/h k/hc Vm = RT/ p at T = 273.15 K and p = 101.325 kPa n 0 = NA /Vm σ = (π 2 /60)(k4 /(~3 c2 )) b = λmax T = c2 /4.965114231

Units

Relative standard uncertainty

The Fundamental Constants

1.2 The CODATA Recommended Values of the Fundamental Constants

Table 1.1-5 Constants from atomic physics Quantity

Symbol and relation

Numerical value

Units

Relative standard uncertainty

Rydberg constant

R∞ = α2 m e c/2h

10 973 731.568525(73)

1/m

6.6 × 10−12

R∞ c

3.289841960360(22) × 1015

Hz

6.6 × 10−12

(Product)

R∞ hc

2.17987209(37) × 10−18 13.6056923(12)

J eV

1.7 × 10−7 8.5 × 10−8

Bohr radius

a0 = α/4πR∞ = 4πε0 ~2 /m e e2

0.5291772108(18) × 10−10

m

3.3 × 10−9

Hartree energy

E H = e2 /4πε0 a0 = 2R∞ hc = α2 m e c2

4.35974417(75) × 10−18 27.2113845(23)

J eV

1.7 × 10−7 8.5 × 10−8

Quantum of circulation

h/2m e

3.636947550(24) × 10−4

m2 /s

6.7 × 10−9

(Product)

h/m e

7.273895101(48) × 10−4

m2 /s

6.7 × 10−9

(Product)

Table 1.1-6 Properties of the electron Quantity

Symbol and relation

Numerical value

Units

Relative standard uncertainty

Electron mass

me

9.1093826(16) × 10−31 5.4857990945(24) × 10−4

kg u

1.7 × 10−7 4.4 × 10−10

Energy equivalent of electron mass

m e c2

8.1871047(14) × 10−14 0.510998918(44)

J MeV

1.7 × 10−7 8.6 × 10−8

Electron–proton mass ratio

m e /m p

5.4461702173(25) × 10−4

4.6 × 10−10

m e /m n

5.4386734481(38) × 10−4

7.0 × 10−10

m e /m µ

4.83633167(13) × 10−3

2.6 × 10−8

Electron molar mass

M(e) = NA m e

5.4857990945(24) × 10−7

kg

4.4 × 10−10

Charge-to-mass ratio

−e/m e

− 1.75882012(15) × 1011

C/kg

8.6 × 10−8

Compton wavelength

λC = h/m e c

2.426310238(16) × 10−12

m

6.7 × 10−9

386.1592678(26) × 10−15

Electron–neutron mass ratio Electron–muon mass ratio

(Ratio)

λC /2π = αa0

m

6.7 × 10−9

Classical electron radius

re = α2 a0

2.817940325(28) × 10−15

m

1.0 × 10−8

Thomson cross section

σe = (8π/3)re2

0.665245873(13) × 10−28

m2

2.0 × 10−8

Magnetic moment

µe

− 928.476412(80) × 10−26

J/T

8.6 × 10−8

Ratio of magnetic moment to Bohr magneton

µe /µB

− 1.0011596521859(38)

3.8 × 10−12

Ratio of magnetic moment to nuclear magneton

µe /µN

− 1838.28197107(85)

4.6 × 10−10

Ratio of magnetic moment to proton magnetic moment

µe /µp

− 658.2106862(66)

1.0 × 10−8

Ratio of magnetic moment to neutron magnetic moment

µe /µn

960.92050(23)

2.4 × 10−7

Electron magnetic-moment anomaly

ae = |µe |/(µB − 1)

1.1596521859(38) × 10−3

3.2 × 10−9

g-factor

ge = −2(1 + ae )

− 2.0023193043718(75)

3.8 × 10−12

Gyromagnetic ratio

γe = 2|µe |/~

1.76085974(15) × 1011

1/(s T)

8.6 × 10−8

(Ratio)

γe /2π

28 024.9532(24)

MHz/T

8.6 × 10−8

= α2 /(4πR

∞)

Part 1 1.2

1.1.2.3 Constants from Atomic Physics and Particle Physics

7

8

Part 1

General Tables

Part 1 1.2

Table 1.1-7 Properties of the proton Quantity

Symbol and relation

Numerical value

Units

Relative standard uncertainty

Proton mass

mp

Energy equivalent of proton mass Proton–electron mass ratio Proton–neutron mass ratio Proton molar mass Charge-to-mass ratio Compton wavelength (Ratio) rms charge radius Magnetic moment Ratio of magnetic moment to Bohr magneton Ratio of magnetic moment to nuclear magneton Ratio of magnetic moment to neutron magnetic moment g-factor Gyromagnetic ratio (Ratio)

m p c2

kg u J MeV

m p /m e m p /m n M(p) = NA m p e/m p λC,p = h/m p c (1/2π)λC,p Rp µp µp /µB

1.67262171(29) × 10−27 1.00727646688(13) 1.50327743(26) × 10−10 938.272029(80) 1836.15267261(85) 0.99862347872(58) 1.00727646688(13) × 10−3 9.57883376(82) × 107 1.3214098555(88) × 10−15 0.2103089104(14) × 10−15 0.8750(68) × 10−15 1.41060671(12) × 10−26 1.521032206(15) × 10−3

1.7 × 10−7 1.3 × 10−10 1.7 × 10−7 8.6 × 10−8 4.6 × 10−10 5.8 × 10−10 1.3 × 10−10 8.6 × 10−8 6.7 × 10−9 6.7 × 10−9 7.8 × 10−3 8.7 × 10−8 1.0 × 10−8

µp /µN

2.792847351(28)

1.0 × 10−8

µp /µn

−1.45989805(34)

2.4 × 10−7

gp = 2µp /µN γp = 2µp /~ (1/2π)γp

5.585694701(56) 2.67522205(23) × 108 42.5774813(37)

1/(s T) MHz/T

1.0 × 10−8 8.6 × 10−8 8.6 × 10−8

kg C/kg m m m J/T

Table 1.1-8 Properties of the neutron Quantity

Symbol and relation

Numerical value

Units

Relative standard uncertainty

Neutron mass

mn

Energy equivalent

m n c2

kg u J MeV

Neutron–electron mass ratio Neutron–proton mass ratio Molar mass Compton wavelength (Ratio) Magnetic moment Ratio of magnetic moment to Bohr magneton Ratio of magnetic moment to nuclear magneton Ratio of magnetic moment to electron magnetic moment Ratio of magnetic moment to proton magnetic moment g-factor Gyromagnetic ratio (Ratio)

m n /m e m n /m p M(n) = NA m n λC,n = h/(m n c) (1/2π)λC,n µn µn /µB

1.67492728(29) × 10−27 1.00866491560(55) 1.50534957(26) × 10−10 939.565360(81) 1838.6836598(13) 1.00137841870(58) 1.00866491560(55) × 10−3 1.3195909067(88) × 10−15 0.2100194157(14) × 10−15 −0.96623645(24) × 10−26 −1.04187563(25) × 10−3

1.7 × 10−7 5.5 × 10−10 1.7 × 10−7 8.6 × 10−8 7.0 × 10−10 5.8 × 10−10 5.5 × 10−10 6.7 × 10−9 6.7 × 10−9 2.5 × 10−7 2.4 × 10−7

µn /µN

−1.91304273(45)

2.4 × 10−7

µn /µe

1.04066882(25) × 10−3

2.4 × 10−7

µn /µp

−0.68497934(16)

2.4 × 10−7

gn = 2µn /µN γn = 2|µn |/~ (1/2π)γn

−3.82608546(90) 1.83247183(46) × 108 29.1646950(73)

2.4 × 10−7 2.5 × 10−7 2.5 × 10−7

kg m m J/T

1/(s T) MHz/T

The Fundamental Constants

References

Quantity

Symbol and relation

Numerical value

Units

Relative standard uncertainty

Alpha particle mass a

mα

Energy equivalent of alpha particle mass Ratio of alpha particle mass to electron mass Ratio of alpha particle mass to proton mass Alpha particle molar mass

m α c2

kg u J MeV

m α /m e

6.6446565(11) × 10−27 4.001506179149(56) 5.9719194(10) × 10−10 3727.37917(32) 7294.2995363(32)

1.7 × 10−7 1.4 × 10−11 1.7 × 10−7 8.6 × 10−8 4.4 × 10−10

m α /m p

3.97259968907(52)

M(α) = NA m α

4.001506179149(56) × 10−3

a

1.3 × 10−10 kg/mol

1.4 × 10−11

The mass of the alpha particle in units of the atomic mass unit u is given by m α = Ar (α) u; in words, the alpha particle mass is given by the relative atomic mass Ar (α) of the alpha particle, multiplied by the atomic mass unit u

References 1.1

P. J. Mohr, B. N. Taylor: CODATA recommended values of the fundamental physical constants, Rev. Mod. Phys. (2004) (in press)

1.2

NIST Physics Laboratory: Web pages of the Fundamental Constants Data Center, http:/ /physics.nist.gov/constants

Part 1 1

Table 1.1-9 Properties of the alpha particle

9

10

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11

1.2. The International System of Units (SI), Physical Quantities, and Their Dimensions

The Internatio 1.2.1

The International System of Units (SI) ...

11

1.2.2 Physical Quantities .............................

12

1.2.3 The SI Base Units ................................ 1.2.3.1 Unit of Length: the Meter ......... 1.2.3.2 Unit of Mass: the Kilogram ....... 1.2.3.3 Unit of Time: the Second .......... 1.2.3.4 Unit of Electric Current: the Ampere ............................ 1.2.3.5 Unit of (Thermodynamic) Temperature: the Kelvin .......... 1.2.3.6 Unit of Amount of Substance: the Mole ................................ 1.2.3.7 Unit of Luminous Intensity: the Candela ............................

13 13 14 14

15

1.2.4 The SI Derived Units ............................

16

1.2.5 Decimal Multiples and Submultiples of SI Units................

19

1.2.6 Units Outside the SI ............................ 1.2.6.1 Units Used with the SI.............. 1.2.6.2 Other Non-SI Units ..................

20 20 20

1.2.7 Some Energy Equivalents.....................

24

References ..................................................

25

14 14 14

1.2.1 The International System of Units (SI) All data in this handbook are given in the International System of Units (Système International d’Unités), abbreviated internationally to SI, which is the modern metric system of measurement and is acknowledged worldwide. The system of SI units was introduced by the General Conference of Weights and Measures (Conférence Générale des Poids et Mesures), abbreviated internationally to CGPM, in 1960. The system not only is used in science, but also is dominant in technology, industrial production, and international commerce and trade. Who takes care of this system of SI units? The Bureau International des Poids et Mesures (BIPM), which has its headquarters in Sèvres near Paris, has taken on a commitment to ensure worldwide unifi-

cation of physical measurements. Its function is thus to:

• • • •

establish fundamental standards and scales for the measurement of the principal physical quantities and maintain the international prototypes; carry out comparison of national and international standards; ensure the coordination of the corresponding measuring techniques; carry out and coordinate measurements of the fundamental physical constants relevant to those activities.

The BIPM operates under the exclusive supervision of the Comité International des Poids et Mesures (CIPM), which itself comes under the authority of the

Part 1 2

In this chapter, we introduce the International System of Units (SI) on the basis of the SI brochure “Le Système international d’unités (SI)” [2.1], supplemented by [2.2]. We give a short review of how the SI was worked out and who is responsible for the further development of the system. Following the above-mentioned publications, we explain the concepts of base physical quantities and derived physical quantities on which the SI is founded, and present a detailed description of the SI base units and of a large selection of SI derived units. We also discuss a number of non-SI units which still are in use, especially in some specialized fields. A table (Table 1.2-17) presenting the values of various energy equivalents closes the section.

12

Part 1

General Tables

Part 1 2.2

Conférence Générale des Poids et Mesures and reports to it on the work accomplished by the BIPM. The BIPM itself was set up by the Convention du Mètre signed in Paris in 1875 by 17 states during the final session of the Conference on the Meter. The convention was amended in 1921. Delegates from all member states of the Convention du Mètre attend the Conférence Générale, which, at present, meets every four years. The function of these meetings is to:

• • •

discuss and initiate the arrangements required to ensure the propagation and improvement of the International System of Units confirm the results of new fundamental metrological determinations and confirm various scientific resolutions with international scope take all major decisions concerning the finance, organization, and development of the BIPM.

The CIPM has 18 members, each from a different state; at present, it meets every year. The officers of this

committee present an annual report on the administrative and financial position of the BIPM to the governments of the member states of the Convention du Mètre. The principal task of the CIPM is to ensure worldwide uniformity in units of measurement. It does this by direct action or by submitting proposals to the CGPM. The BIPM publishes monographs on special metrological subjects and the brochure Le Système international d’unités (SI) [2.1,2], which is periodically updated and in which all decisions and recommendations concerning units are collected together. The scientific work of the BIPM is published in the open scientific literature, and an annual list of publications appears in the Procès-Verbaux of the CIPM. Since 1965, Metrologica, an international journal published under the auspices of the CIPM, has printed articles dealing with scientific metrology, improvements in methods of measurements, and work on standards and units, as well as reports concerning the activities, decisions, and recommendations of the various bodies created under the Convention du Mètre.

1.2.2 Physical Quantities Physical quantities are tools which allow us to specify and quantify the properties of physical objects and to model the events, phenomena, and patterns of behavior of objects in nature and in technology. The system of physical quantities used with the SI units is dealt by Technical Committee 12 of the International Organization for Standardization (ISO/TC 12). Since 1955, ISO/TC 12 has published a series of international standards on quantities and their units, in which the use of SI units is strongly recommended. How are Physical Quantities Defined? It turns out that it is possible to divide the system of all known physical quantities into two groups:

• •

a small number of base quantities; a much larger number of other quantities, which are called derived quantities.

The derived quantities are introduced into physics unambiguously by a defining equation in terms of the base quantities; the relationships between the derived quantities and the base quantities are expressed in a series of equations, which contain a good deal of our knowledge of physics but are used in this system as the defining equations for new physical quantities. One

might say that, in this system, physics is described in the rather low-dimensional space of a small number of base quantities. Base quantities, on the other hand, cannot be introduced by a defining equation; they cannot be traced back to other quantities; this is what we mean by calling them “base”. How can base quantities then be introduced unambiguously into physics at all? Base physical quantities are introduced into physics in three steps:

• • •

We borrow the qualitative meaning of the word for a base quantity from the meaning of the corresponding word in everyday language. We specify this meaning by indicating an appropriate method for measuring the quantity. For example, length is measured by a measuring rule, and time is measured by a clock. We fix a unit for this quantity, which allows us to communicate the result of a measurement. Length, for example, is measured in meters; time is measured in seconds.

On the basis of these three steps, it is expected that everyone will understand what is meant when the name of a base quantity is mentioned.

The International System of Units (SI), Physical Quantities, and Their Dimensions

Table 1.2-1 The ISO recommended base quantities Name of quantity

Symbol

Measured by

Length Time Mass Electrical current Temperature Particle number Luminous intensity

l t m I T N Iv

A measuring rule A clock A balance A balance A thermometer Counting A photometer

All other physical quantities can then be defined as derived quantities; this means they can be defined by equations in terms of the seven base quantities. Within this “conventional system”, the set of all defining equations for the derived physical quantities also defines the units for the derived quantities in terms of the units of the base quantities. This is the great advantage of the “conventional system”. The quantity velocity v, for example, is defined by the equation dl v= . dt In this way, velocity is traced back to the two base quantities length l and time t. On the right-hand side of this equation, we have a differential of length dl divided by a differential of time dt. The algebraic combination of the base quantities in the defining equation for a derived quantity is called the dimensions of the derived quantity. So velocity has the dimensions length/time, acceleration has the dimensions length/time squared, and so on. Data for a physical quantity are always given as a product of a number (the numerical value of the physical quantity) and a unit in which the quantity has been measured.

1.2.3 The SI Base Units Formal definitions of the seven SI base units have to be approved by the CGPM. The first such definition was approved in 1889. These definitions have been modified, however, from time to time as techniques of measurement have evolved and allowed more accurate realizations of the base units. Table 1.2-2 summarizes the present status of the SI base units and their symbols. In the following, the current definitions of the base units adopted by the CGPM are shown in detail, together with some explanatory notes. Related decisions which clarify these definitions but are not formally part of them are also shown indented, but in a font of normal weight.

1.2.3.1 Unit of Length: the Meter The unit of length, the meter, was defined in the first CGPM approval in 1889 by an international prototype: the length of a bar made of a platinum–iridium alloy defined a length of 1 m. In 1960 this definition was replaced

Table 1.2-2 The seven SI base units and their symbols Base quantity

Symbol for quantity

Unit

Symbol for unit

Length Time Mass Electrical current Temperature Particle number Luminous intensity

l t m I T n Iv

metre second kilogram ampere kelvin mole candela

m s kg A K mol cd

by a definition based upon a wavelength of krypton-86 radiation. Since 1983 (17th CGPM), the meter has been defined as: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. As a result of this definition, the fundamental constant “speed of light in vacuum c” is fixed at exactly 299 792 458 m/s.

13

Part 1 2.3

In fact, the number of base quantities chosen and the selection of the quantities which are considered as base quantities are a matter of expediency; in different fields and applications of physics, it might well be expedient to use different numbers of base quantities and different selections of base quantities. It should be kept in mind, however, that the number and selection of base quantities are only a matter of different representations of physics; physics itself is not affected by the choice that is made. Today, many scientists therefore prefer to use the conventional system recommended by ISO. This system uses seven base quantities, which are selected according to the seven base units of the SI system. Table 1.2-1 shows the recommended names, symbols, and measuring devices for the conventional seven base quantities.

2.3 The SI Base Units

14

Part 1

General Tables

1.2.3.2 Unit of Mass: the Kilogram

Part 1 2.3

Since the first CGPM in 1889, the unit of mass, the kilogram, has been defined by an international prototype, a metal block made of a platinum–iridium alloy, kept at the BIPM at Sèvres. The relevant declaration was modified slightly at the third CGPM in 1901 to confirm that: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per meter of length. As a result of this definition, the fundamental constant “magnetic field constant µ0 ” (also known as the permeability of free space) is fixed at exactly 4π × 10−7 N/A2 .

1.2.3.5 Unit of (Thermodynamic) Temperature: the Kelvin

1.2.3.3 Unit of Time: the Second The unit of time, the second, was originally considered to be the fraction 1/86 400 of the mean solar day. Measurements, however, showed that irregularities in the rotation of the Earth could not be taken into account by theory, and these irregularities have the effect that this definition does not allow the required accuracy to be achieved. The same turned out to be true for other definitions based on astronomical data. Experimental work, however, had already shown that an atomic standard of time interval, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more precisely. Therefore, the 13th CGPM (1967 – 1968) replaced the definition of the second by: The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. At its 1997 meeting, the CIPM affirmed that: This definition refers to a caesium atom at rest at a temperature of 0 K. This note was intended to make it clear that the definition of the SI second is based on a Cs atom unperturbed by black-body radiation, that is, in an environment whose temperature is 0 K.

The definition of the unit of (thermodynamic) temperature was given in substance by the 10th CGPM in 1954, which selected the triple point of water as the fundamental fixed point and assigned to it the temperature 273.16 K, so defining the unit. After smaller amendments, made at the 13th CGPM in 1967–1968, the definition of the unit of (thermodynamic) temperature reads The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. Because of the way temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T , in terms of its difference from the reference temperature T0 = 273.15 K, the ice point. This temperature difference is called the Celsius temperature, symbol t, and is defined by the equation t = T − T0 . The unit of Celsius temperature is the degree Celsius, symbol ◦ C, which is, by definition, equal in magnitude to the kelvin. A difference or interval of temperature may therefore be expressed either in kelvin or in degrees Celsius. The numerical value of a Celsius temperature t expressed in degrees Celsius is given by t (◦ C) = T (K) − 273.15.

1.2.3.4 Unit of Electric Current: the Ampere

1.2.3.6 Unit of Amount of Substance: the Mole

“International” electrical units for current and resistance were introduced by the International Electrical Congress in Chicago as early as in 1893 and were confirmed by an international conference in London in 1908. They were replaced by an “absolute” definition of the ampere as the unit for electric current at the 9th CGPM in 1948, which stated: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular

The “amount of substance” of a sample is understood as a measure of the number of elementary entities (for example atoms or molecules) that the sample consists of. Owing to the fact that on macroscopic scales this number cannot be counted directly in most cases, one has to relate this quantity “amount of substance” to a more easily measurable quantity, the mass of a sample of that substance. On the basis of an agreement between the International Union of Pure and Applied Physics (IUPAP) and

The International System of Units (SI), Physical Quantities, and Their Dimensions

1.2.3.7 Unit of Luminous Intensity: the Candela The base unit candela allows one to establish a quantitative relation between radiometric and photometric measurements of light intensities. In physics and chemistry, the intensities of radiation fields of various natures are normally determined by radiometry; in visual optics, in lighting engineering, and in the physiology of the visual system, however, it is necessary to assess the intensity of the radiation field by photometric means. There are, in fact, three different ways to quantify the intensity of a radiation beam. One way is to measure the “radiant intensity” Ie , defined as the radiant flux ∆Φe per unit solid angle ∆Ω of the beam. The subscript “e”

stands for “energetic”. Here, the radiant flux Φe is defined as the energy of the radiation per unit time, and is accordingly measured in units of watts (W). The radiant intensity Ie , therefore, has the dimensions of energy per time per solid angle, and is measured in the derived unit “watt per steradian” (W/sr). Another way to quantify the intensity of a beam of radiation is to measure the “particle intensity” Ip , which is defined as the particle flux Φp divided by the solid angle ∆Ω of the beam. The subscript “p” stands for “particle”. The particle flux Φp itself is measured by counting the number of particles per unit time in the beam; in the case of a light beam, for example, the particles are photons. The corresponding SI unit for the particle flux is seconds−1 (1/s). The quantity particle intensity Ip therefore has the dimensions of number per time per solid angle; the corresponding derived SI unit for the particle intensity Ip is “seconds−1 times steradian−1 ” (1/(s sr)). In addition to these two radiometric assessments of the beam intensity, for beams of visible light there is a third possibility, which is to quantify the intensity of the beam by the intensity of visual perception by the human eye. Physical quantities connected with this physiological type of assessment are called photometric quantities, in contrast to the two radiometric quantities described above. In photometry, the intensity of the beam is called the “luminous intensity” Iv . The subscript “v” stands for “visual”. The luminous intensity Iv is an ISO recommended base quantity; the corresponding SI base unit is the candela (cd). The luminous flux Φv is determined as the product of the luminous intensity and the solid angle. Its dimensions therefore are luminous intensity times solid angle, so that the SI unit of the luminous flux Φv turns out to be “candela times steradian” (cd sr). A derived unit, the lumen (lm), such that 1 lm = 1 cd sr, has been introduced for this product. Table 1.2-3 summarizes the names, definitions, and SI units for the most frequently used radiometric and photometric quantities in radiation physics. The history of the base unit candela is as follows. Before 1948, the units for photometric measurements were be based on flame or incandescent-filament standards. They were replaced initially by the “new candle” based on the luminance of a Planckian radiator (a blackbody radiator) at the temperature of freezing platinum. This modification was ratified in 1948 by the 9th CGPM, which also adopted the new international name for the base unit of luminous intensity, the candela, and its symbol cd. The 13th CGPM gave an amended version of the 1948 definition in 1967.

15

Part 1 2.3

the International Union of Pure and Applied Chemistry (IUPAC) in 1959/1960, physicists and chemists have ever since agreed to assign, by definition, the value 12, exactly, to the relative atomic mass (formerly called “atomic weight”) of the isotope of carbon with mass number 12 (carbon-12, 12 C). The scale of the masses of all other atoms and isotopes based on this agreement has been called, since then, the scale of relative atomic masses. It remains to define the unit of the “amount of substance” in terms of the mass of the corresponding amount of the substance. This is done by fixing the mass of a particular amount of carbon-12; by international agreement, this mass has been fixed at 0.012 kg. The corresponding unit of the quantity “amount of substance” has been given the name “mole” (symbol mol). On the basis of proposals by IUPAC, IUPAP, and ISO, the CIPM formulated a definition of the mole in 1967 and confirmed it in 1969. This definition was adopted by the 14th CGPM in 1971 in two statements: 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12; its symbol is “mol”. 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In 1980, the CIPM approved the report of the Comité Consultatif des Unités (CCU), which specified that: In this definition, it is understood that unbound atoms of carbon-12, at rest and in their ground state, are referred to.

2.3 The SI Base Units

16

Part 1

General Tables

Table 1.2-3 Radiometric and photometric quantities in radiation physics Quantity

Symbol and definition

Radiant flux Φe = ∆E/∆t a Particle flux, activity Φp = ∆Np /∆t Luminous flux Φv = Iv Ω b

Part 1 2.4

Radiant intensity Particle intensity Luminous intensity Radiance c

Ie = ∆Φe /∆Ω Ip = ∆Φp /∆Ω Iv , basic quantity L e = ∆Ie (ϕ)/[∆A1 g(ϕ)] d

Particle radiance c

L p = ∆Ip (ϕ)/[∆A1 g(ϕ)] d

Luminance c Irradiance Particle irradiance

L v = ∆Iv (ϕ)/[∆A1 g(ϕ)] d E e = ∆Φe /∆A2e E p = ∆Φp /∆A2e

Illuminance

E v = ∆Φv /∆A2e

a b c

d e

Dimensions

SI unit

Symbol for unit

Power = energy/time 1/time Luminous intensity times solid angle Power/solid angle (Time times solid angle)−1 Luminous intensity Power per source area and solid angle (Time times area times solid angle)−1 Luminous intensity/source area Power/area Number of particles per (time times area) Luminous flux per area

watt second−1 lumen

W = J/s 1/s lm = cd sr

watt/steradian (second times steradian)−1 candela watt/(meter2 times steradian)

W/sr 1/(s sr) cd W/(m2 sr) = kg/(s3 sr)

1/(second times meter2 times steradian) candela/meter2 watt/meter2 1/(second times meter2 )

1/(s m2 sr)

lux = lumen/meter2

lx = lm/m2 = cd sr/m2

cd/m2 W/m2 1/(s m2 )

The symbol E stands for the radiant energy (see Table 1.2-5). Iv stands for the luminous intensity, and Ω stands for the solid angle (see Table 1.2-5). The radiance L e , particle radiance L p , and luminance L v are important characteristic properties of sources, not radiation fields. For a blackbody source, the radiance L e , for example, is dependent only on the frequency of the radiation and the temperature of the black body. The dependence is given by Planck’s radiation law. In optical imaging, the radiance L e of an object turns out to show an invariant property. In correct imaging, the image always radiates with the same radiance L e as the object, independent of the magnification. ϕ is the angle between the direction of the beam axis and the direction perpendicular to the source area; A1 indicates the area of the source; and g(ϕ) is the directional characteristic of the source. A2 indicates the irradiated area or the area of the detector.

Because of experimental difficulties in realizing a Planckian radiator at high temperatures and because of new possibilities in the measurement of optical radiation power, the 16th CGPM in 1979 adopted a new definition of the candela as follows:

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/ 683 watt per steradian.

1.2.4 The SI Derived Units The SI derived units are the SI units for derived physical quantities. In accordance with the defining equations for derived physical quantities in terms of the base physical quantities, the units for derived quantities can be expressed as products or ratios of the units for the base quantities. Table 1.2-4 shows some examples of SI derived units in terms of SI base units. For convenience, certain derived units, which are listed in Table 1.2-5, have been given special names and symbols. Among these, the last four entries in Table 1.2-5 are of particular note, since they were accepted by the 15th (1975), 16th (1979), and 21st (1999)

CGPMs specifically with a view to safeguarding human health. In Tables 1.2-5 and 1.2-6, the final column shows how the SI units concerned may be expressed in terms of SI base units. In this column, factors such as m0 and kg0 , etc., which are equal to 1, are not shown explicitly. The special names and symbols for derived units listed in Table 1.2-5 may themselves be used to express other derived units: Table 1.2-6 shows some examples. The special names and symbols provide a compact form for the expression of units which are used frequently.

The International System of Units (SI), Physical Quantities, and Their Dimensions

2.4 The SI Derived Units

17

Table 1.2-4 Examples of SI derived units (for derived physical quantities) in terms of base units Defining equation

Name of SI derived unit

Symbol for unit

Area

A = l1 l2

square meter

m2

Volume

V = l1 l2 l3

cubic meter

m3

Velocity

v = dl/ dt

meter per second

m/s

Acceleration

a=

meter per second squared

m/s2

Angular momentum

L = Θω

meter squared kilogram/second

m2 kg/s

Wavenumber

k = 2π/λ

reciprocal meter

1/m

Density

= m/V

kilogram per cubic meter

kg/m3

Concentration (of amount of substance)

Concentration = amount/V

mole per cubic meter

mol/m3

Current density

j = I/A

ampere per square meter

A/m2

Magnetic exciting field

H = I/l

ampere per meter

A/m

Radiance (of a radiation source)

L e = ∆Ie (ϕ)/[∆A1 g(ϕ)] a

watt per (square meter × steradian)

W/(m2 sr) = kg/(s3 sr)

Luminance (of a light source)

L v = ∆Iv (ϕ)/[∆A1 g(ϕ)] b

candela per square meter

cd/m2

Refractive index

n = cmat /c

(number one)

1

a b

d 2 l/ dt 2

ϕ is the angle between the direction of the beam axis and the direction perpendicular to the source area; Ie (ϕ) is the radiant intensity emitted in the direction ϕ; A1 is the radiating area of the source; and g(ϕ) is the directional characteristic of the source. ϕ is the angle between the direction of the beam axis and the direction perpendicular to the source area; Iv (ϕ) is the luminous intensity emitted in the direction ϕ; A1 is the radiating area of the light source; and g(ϕ) is the directional characteristic of the source.

Table 1.2-5 SI derived units with special names and symbols Derived quantity

SI derived unit

Name

Symbol

Name

Symbol

Expressed in terms of other SI units

Expressed in terms of SI base units

Plane angle

α, ∆α

radian a

rad

m/m = 1 b

Solid angle

Ω, ∆Ω

steradian a

sr c

m2 /m2 = 1 b

Frequency

ν

hertz

Hz

1/s

Force

F

newton

N

m kg/s2 (1/m) kg/s2

Pressure, stress

P

pascal

Pa

N/m2

Energy, work, quantity of heat

E, A, Q

joule

J

Nm

m2 kg/s2

Power, radiant flux

P, Φe

watt

W

J/s

m2 kg/s3

Electric charge, quantity of electricity

q, e

coulomb

C

Electric potential difference, electromotive force

V

volt

V

W/A

(1/A) m2 kg/s3

Capacitance

C

farad

F

C/V

A2 (1/(m2 kg)) s4

Electrical resistance

R

ohm

Ω

V/A

(1/A2 ) m2 kg/s3

Electrical conductance

1/R

siemens

S

A/V

A2 (1/(m2 kg))s3

Magnetic flux

Φ

weber

Wb

Vs

(1/A) m2 kg(1/s2 )

Magnetic field strength

B

tesla

T

Wb/m2

(1/A) kg/s2

Inductance

L

henry

H

Wb/A

(1/A2 ) m2 kg/s2

degree Celsius

◦C

Celsius temperature

t

Luminous flux

Φv

lumen

lm

As

K; T/K = t/◦ C + 273.15 cd sr c

(m2 /m2 ) cd = cd

Part 1 2.4

Derived quantity

18

Part 1

General Tables

Table 1.2-5 SI derived units with special names and symbols, cont. Derived quantity

SI derived unit

Part 1 2.4

Name

Symbol

Name

Symbol

Expressed in terms of other SI units

Expressed in terms of SI base units

Illuminance

E v = ∆Φv /∆A

lux

lx

lm/m2

(m2 /m4 ) cd = cd/m2

Activity (referred to a radionuclide)

A

becquerel

Bq

Absorbed dose

D

gray

Gy

J/kg

m2 /s2

Dose equivalent

H

sievert

Sv

J/kg

m2 /s2

katal

kat

Catalytic activity a b c

1/s

(1/s) mol

The units radian and steradian may be used with advantage in expressions for derived units to distinguish between quantities of different nature but the same dimensions. Some examples of their use in forming derived units are given in Tables 1.2-5 and 1.2-6. In practice, the symbols rad and sr are used where appropriate, but the derived unit “1” is generally omitted in combination with a numerical value. In photometry, the name steradian and the symbol sr are frequently retained in expressions for units.

Table 1.2-6 Examples of SI derived units whose names and symbols include SI derived units with special names and

symbols Derived quantity

SI derived unit

Name

Symbol

Name

Symbol

Expressed in terms of SI base units

Dynamic viscosity

η

pascal second

Pa s

(1/m) kg/s

Moment of force

M

newton meter

Nm

m2 kg/s2

Surface tension

σ

newton per meter

N/m

kg/s2

Angular velocity

ω

radian per second

rad/s

m/(m s) = 1/s

Angular acceleration

dω/ dt

radian per second squared

rad/s2

m/(m s2 ) = 1/s2 kg/s3

Heat flux density

qth

watt per square meter

W/m2

Heat capacity, entropy

C, S

joule per kelvin

J/K

m2 kg/(s2 K)

Specific heat capacity, specific entropy

Cmass , Smass

joule per (kilogram kelvin)

J/(kg K)

m2 /(s2 K)

joule per kilogram

J/kg

m2 /s2 (1/m) kg/s2

Specific energy Energy density

w

joule per cubic meter

J/m3

Thermal conductivity

λ

watt per (meter kelvin)

W/(m K)

m kg/(s3 K)

Electric charge density

ρ

coulomb per cubic meter

C/m3

(1/m3 ) s A

Electric field strength

E

volt per meter

V/m

m kg/(s3 A)

D

coulomb per square meter

C/m2

(1/m2 ) s A

Molar energy

E mol

joule per mole

J/mol

m2 kg/(s2 mol)

Molar heat capacity, molar entropy

Cmol , Smol

joule per (mole kelvin)

J/(mol K)

m2 kg/(s2 K mol)

Exciting electric

field b

Exposure (X- and γ -rays)

coulomb per kilogram

C/kg

(1/kg) s A

Absorbed dose rate

dD/ dt

gray per second

Gy/s

m2 /s3

Radiant intensity

Iε

watt per steradian

W/sr

(m4 /m2 ) kg/s3 = m2 kg/s3

watt per (square meter steradian)

W/(m2

katal per cubic meter

kat/m3

Radiance a Catalytic (activity) concentration a b

Le

sr)

(m2 /m2 ) kg/s3 = kg/s3 (1/(m3 s)) mol

The radiance is a property of the source of the radiation, not of the radiation field (see footnote c to Table 1.2-3). also called “electric flux density”

The International System of Units (SI), Physical Quantities, and Their Dimensions

second rather than the reciprocal second (in this case, retaining the word “radian” emphasizes that the angular velocity is equal to 2π times the rotational frequency). Similarly, the SI unit of moment of force is called the newton meter rather than the joule. In the field of ionizing radiation, the SI unit of activity is called the becquerel rather than the reciprocal second, and the SI units of absorbed dose and dose equivalent are called the gray and the sievert, respectively, rather than the joule per kilogram. In the field of catalysis, the SI unit of catalytic activity is called the katal rather than the mole per second. The special names becquerel, gray, sievert, and katal were specifically introduced because of the dangers to human health which might arise from mistakes involving the units reciprocal second, joule per kilogram, and mole per second.

1.2.5 Decimal Multiples and Submultiples of SI Units The 11th CGPM adopted, in 1960, a series of prefixes and prefix symbols for forming the names and symbols of the decimal multiples and submultiples of SI units ranging from 1012 to 10−12 . Prefixes for 10−15 and 10−18 were added by the 12th CGPM in 1964, and for 1015 and 1018 by the 15th CGPM in 1975. The 19th CGPM extended the scale in 1991 from 10−24 to 1024 . Table 1.2-7 lists all approved prefixes and symbols.

Table 1.2-7 SI prefixes and their symbols Factor

Name

Symbol

1024 1021 1018 1015 1012 109 106 103 102 101 10−1 10−2 10−3 10−6 10−9 10−12 10−15 10−18 10−21 10−24

yotta zeta exa peta tera giga mega kilo hecto deca deci centi milli micro nano pico femto atto zepto yocto

Y Z E P T G M k h da d c m µ n p f a z y

19

Part 1 2.5

A derived unit can often be expressed in several different ways by combining the names of base units with special names for derived units. This, however, is an algebraic freedom whose use should be limited by common-sense physical considerations. The joule, for example, may formally be written “newton meter” or even “kilogram meter squared per second squared”, but in a given situation some forms may be more helpful than others. In practice, with certain quantities, preference is given to the use of certain special unit names or combinations of unit names, in order to facilitate making a distinction between different quantities that have the same dimensions. For example, the SI unit of frequency is called the hertz rather than the reciprocal second, and the SI unit of angular velocity is called the radian per

2.5 Decimal Multiples and Submultiples of SI Units

20

Part 1

General Tables

1.2.6 Units Outside the SI

Part 1 2.6

The SI base units and SI derived units, including those with special names, have the important advantage of forming a coherent set, with the effect that unit conversions are not required when one is inserting particular values for quantities into equations involving quantities. Nonetheless, it is recognized that some non-SI units still appear widely in the scientific, technical, and commercial literature, and some will probably continue to be used for many years. Other non-SI units, such as the units of time, are so widely used in everyday life and are so deeply embedded in the history and culture of human beings that they will continue to be used for the foreseeable future. For these reasons, some of the more important non-SI units are listed.

of commercial, legal, and specialized scientific interests. These units should be defined in relation to SI units in every document in which they are used. Their use is not encouraged.

1.2.6.2 Other Non-SI Units Certain other non-SI units are still occasionally used. Some are important for the interpretation of older scientific texts. These are listed in Tables 1.2-11 – 1.2-16, but their use is not encouraged. Table 1.2-8 Non-SI units accepted for use with the International System

1.2.6.1 Units Used with the SI In 1996 the CIPM agreed upon a categorization of the units used with the SI into three groups: units accepted for use with the SI, units accepted for use with the SI whose values are obtained experimentally, and other units currently accepted for use with the SI to satisfy the needs of special interests. The three groups are listed in Tables 1.2-8 – 1.2-10. Table 1.2-9 lists three non-SI units accepted for use with the SI, whose values expressed in SI units must be obtained by experiment and are therefore not known exactly. Their values are given with their combined standard uncertainties, which apply to the last two digits, shown in parentheses. These units are in common use in certain specialized fields. Table 1.2-10 lists some other non-SI units which are currently accepted for use with the SI to satisfy the needs Table 1.2-9 Non-SI units

accepted for use with the International System, whose values in SI units are obtained experimentally

Name

Symbol

Value in SI units

minute hour day degree a minute of arc second of arc litre b tonne c

min h d

1 min = 60 s 1 h = 60 min = 3600 s 1 d = 24 h = 86 400 s 1◦ = (π/180) rad 1 = (1/ 60)◦ = (π/10 800) rad 1 = (1/ 60) = (π/648 000) rad 1 l = 1 dm3 = 10−3 m3 1 t = 103 kg

a b

c

◦  

l, L t

ISO 31 recommends that the degree be subdivided decimally rather than using the minute and second. Unfortunately, printers from all over the world seem not to be willing to admit that in some texts it would be very helpful to have distinguishable symbols for “the number 1” and “the letter l”. Giving up any further discussion, the 16th CGPM therefore decided in 1979 that the symbol L should also be adopted to indicate the unit litre in order to avoid the risk of confusion between “the number 1” and “the letter l”. This unit is also called the “metric ton” in some countries.

Unit

Definition

Symbol

Value in SI units

Electron volt a

b

eV

1 eV = 1.60217653(14) × 10−19 J

c

u

1 u = 1.66053886(28) × 10−27 kg

e

ua

1 ua = 1.49597870691(30) × 1011 m

Unified atomic mass Astronomical unit d a b c

d e

unit a

For the electron volt and the unified atomic mass unit, the values are quoted from the CODATA recommended values 2002 (see Chapt. 1.1). The electron volt is the kinetic energy acquired by an electron in passing through a potential difference of 1 V in vacuum. The unified atomic mass unit is equal to 1/12 of the mass of an unbound atom of the nuclide 12 C, at rest and in its ground state. In the field of biochemistry, the unified atomic mass unit is also called the dalton, symbol Da. The value given for the astronomical unit is quoted from the IERS Convention (1996). The astronomical unit is a unit of length approximately equal to the mean Earth–Sun distance. Its value is such that, when it is used to describe the motion of bodies in the solar system, the heliocentric gravitational constant is (0.01720209895)2 ua3 /d2 .

The International System of Units (SI), Physical Quantities, and Their Dimensions

Table 1.2-10 Other non-SI units currently accepted for use with the International System Unit

Value in SI units

are b hectare b Bar c

a ha bar

angstrom barn d

Å b

1 nautical mile = 1852 m 1 knot = 1 nautical mile per hour = (1852/3600) m/s 1 a = 1 dam2 = 102 m2 1 ha = 1 hm2 = 104 m2 1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa 1 Å = 0.1 nm = 10−10 m 1 b = 100 fm2 = 10−28 m2

nautical mile a knot

a

b c d

The nautical mile is a special unit employed for marine and aerial navigation to express distance. The conventional value given above was adopted by the First International Extraordinary Hydrographic Conference, Monaco, 1929, under the name “international nautical mile”. As yet there is no internationally agreed symbol. This unit was originally chosen because one nautical mile on the surface of the Earth subtends approximately one minute of arc at the center. The units are and hectare and their symbols were adopted by the CIPM in 1879 and are used to express areas of land. The bar and its symbol were included in Resolution 7 of the 9th CGPM (1948). The barn is a special unit employed in nuclear physics to express effective cross sections.

Table 1.2-11 deals with the relationship between CGS units and SI units, and lists those CGS units that were assigned special names. In the field of mechanics, the CGS system of units was built upon three quantities and their corresponding base units: the centimeter, the gram, and the second. In the field of electricity and magnetism, units were expressed in terms of these three base units. Because this can be done in different ways, this led to the establishment of several different systems, for example the CGS electrostatic system, the CGS electromagnetic system, and the CGS Gaussian system. In those three systems, the system of quantities used

Table 1.2-11 Derived CGS units with special names Unit

Symbol

Value in SI units

erg a dyne a poise a stokes gauss b oersted b maxwell b stilb a phot gal c

erg dyn P St G Oe Mx sb ph Gal

1 erg = 10−7 J 1 dyn = 10−5 N 1 P = 1 dyn s/cm2 = 0.1 Pa s 1 St = 1 cm2 /s = 10−4 m2 /s 1 G ≡ 10−4 T 1 Oe ≡ (1000/4π) A/m 1 Mx ≡ 10−8 Wb 1 sb = 1 cd/cm2 = 104 cd/m2 1 ph = 104 lx 1 Gal = 1 cm/s2 = 10−2 m/s2

a b

c

This unit and its symbol were included in Resolution 7 of the 9th CGPM (1948). This unit is part of the “electromagnetic” three-dimensional CGS system and cannot strictly be compared with the corresponding unit of the International System, which has four dimensions if only mechanical and electrical quantities are considered. For this reason, this unit is linked to the SI unit using the mathematical symbol for “equivalent to” (≡) here. The gal is a special unit employed in geodesy and geophysics to express the acceleration due to gravity.

and the corresponding system of defining equations for the derived quantities differ from those used with SI units. Table 1.2-12 deals with the natural units, which are based directly on fundamental constants or combinations of fundamental constants. Like the CGS system, this system is based on mechanical quantities only. The numerical values in SI units are given here according to the 2002 CODATA adjustment. Table 1.2-13 presents numerical values in SI units for some of the most frequently used atomic units (a.u.), again based on the 2002 CODATA adjustment. Table 1.2-14 presents numerical values in SI units (based on the 2002 CODATA adjustment) for some X-ray-related quantities used in crystallography.

Unit

Symbol and definition

Value in SI units

Table 1.2-12 Natural units

n.u. of velocity: speed of light in vacuum n.u. of action: reduced Planck constant n.u. of mass: electron mass n.u. of energy

c

299 792 458 m/s

(n.u.)

~ = h/2π

n.u. of momentum

mec

n.u. of length n.u. of time

λC = ~/m e c ~/m e c2

1.05457168(18) × 10−34 J s 6.58211915(56) × 10−16 eV s 9.1093826(16) × 10−31 kg 8.1871047(14) × 10−14 J 0.510998918(44) MeV 2.73092419(47) × 10−22 kg m/s 0.510998918(44) MeV/c 386.1592678(26) × 10−15 m 1.2880886677(86) × 10−21 s

me m e c2

21

Part 1 2.6

Symbol

2.6 Units Outside the SI

22

Part 1

General Tables

Table 1.2-13 Atomic units (a.u.)

Part 1 2.6

Unit

Symbol and definition

Value in SI units

a.u. of charge: elementary charge

e

1.60217653(14) × 10−19 C

a.u. of mass: electron mass

me

9.1093826(16) × 10−31 kg

a.u. of action: reduced Planck constant

~ = h/2π

1.05457168(18) × 10−34 J s

a.u. of length, 1 bohr: Bohr radius

a0 = α/(4πR∞ )

0.5291772108(18) × 10−10 m

EH

4.35974417(75) × 10−18 J

~/E H

2.418884326505(16) × 10−17 s

a.u. of force

E H /a0

8.2387225(14) × 10−8 N

a.u. of velocity

αc = a0 E H /~

2.1876912633(73) × 106 m/s

a.u. of momentum

~/a0

1.99285166(34) × 10−24 kg m/s

a.u. of current

eE H /~

6.62361782(57) × 10−3 A

a.u. of charge density

e/a03

1.081202317(93) × 1012 C/m3

a.u. of electric potential

E H /e

27.2113845(23) V

a.u. of electric field

E H /(ea0 )

5.14220642(44) × 1011 V/m

a.u. of electric dipole moment

ea0

8.47835309(73) × 10−30 C m

a.u. of electric polarizability

1.648777274(16) × 10−41 C2 m2 /J

a.u. of magnetic field B

e2 a02 /E H ~/(ea02 )

a.u. of magnetic dipole moment (2µB )

2µB = ~e/m e

1.85480190(16) × 10−23 J/T

a.u. of magnetizability

e2 a02 /m e e2 /(a0 E H )

7.89103660(13) × 10−29 J/T2

a.u. of energy, 1 hartree: Hartree

energy a

a.u. of time

a.u. of permittivity a

2.35051742(20) × 105 T

Fixed by definition as: 107 /c2 = 1.112650056. . .10−10 F/m

The Hartree energy is defined as E H = e2 /(4πε0 a0 ) = 2R∞ hc = α2 m e c2 .

Table 1.2-14 Units of some special X-ray-related quantities Unit

Definition

Symbol

Value in SI units

Cu X unit

λ(CuKα1 )/1537.400

xu(CuKα1 )

1.00207710(29) × 10−13 m

Mo X unit

λ(MoKα1 )/707.831

xu(MoKα1 )

1.00209966(53) × 10−13 m

λ(WKα1 )/0.2090100

Å∗

1.00001509(90) × 10−10 m

a

543.102122(20) × 10−12 m

√ d220 = a/ 8

d220

192.0155965(70) × 10−12 m

Vm (Si) = NA a3 /8

Vm (Si)

12.0588382(24) × 10−6 m3 /mol

angstrom star parameter a

Lattice of Si (in vacuum, at 22.5 ◦ C) (220) lattice spacing of Si (in vacuum, at 22.5 ◦ C) Molar volume of Si (in vacuum, at 22.5 ◦ C) a

This is the lattice parameter (unit cell edge length) of an ideal single crystal of naturally occurring silicon free from impurities and imperfections, and is deduced from measurements on extremely pure, nearly perfect single crystals of Si by correcting for the effects of impurities.

Table 1.2-15 lists some other units which are common in older texts. For current texts, it should be noted that if these units are used, the advantages of the SI are lost. The relation of these units to SI units should be specified in every document in which they are used.

For some selected quantities, there exists an international agreement that the numerical values of these quantities measured in SI units are fixed at the values given in Table 1.2-16.

The International System of Units (SI), Physical Quantities, and Their Dimensions

2.6 Units Outside the SI

23

Table 1.2-15 Examples of other non-SI units Symbol

Value in SI units

curie a röntgen b rad c,d rem d,e X unit f gamma d jansky fermi d metric carat g torr standard atmosphere calorie micron j

Ci R rad rem

1 Ci = 3.7 × 1010 Bq 1 R = 2.58 × 10−4 C/kg 1 rad = 1 cGy = 10−2 Gy 1 rem = 1 cSv = 10−2 Sv 1 X unit ∼ = 1.002 × 10−4 nm 1 γ = 1 nT = 10−9 T 1 Jy = 10−26 W/(m2 Hz) 1 fermi = 1 fm = 10−15 m 1 metric carat = 200 mg = 2 × 10−4 kg 1 Torr = (101 325/760) Pa 1 atm = 101 325 Pa

a b c e f d g h i

j

γ Jy

Torr atm h cal µ

Symbol mass a

12 C

Relative atomic of Molar mass constant Molar mass of 12 C Conventional value of the Josephson constant b Conventional value of the von Klitzing constant c Standard atmosphere Standard acceleration of free fall d

b c d

1 µ = 1 µm = 10−6 m

The curie is a special unit employed in nuclear physics to express the activity of radionuclides. The röntgen is a special unit employed to express exposure to X-ray or γ radiation. The rad is a special unit employed to express absorbed dose of ionizing radiation. When there is a risk of confusion with the symbol for the radian, rd may be used as the symbol for 10−2 Gy. The rem is a special unit used in radioprotection to express dose equivalent. The X unit was employed to express wavelengths of X-rays. Its relationship to SI units is an approximate one. Note that this non-SI unit is exactly equivalent to an SI unit with an appropriate submultiple prefix. The metric carat was adopted by the 4th CGPM in 1907 for commercial dealings in diamonds, pearls, and precious stones. Resolution 4 of the 10th CGPM, 1954. The designation “standard atmosphere” for a reference pressure of 101 325 Pa is still acceptable. Several “calories” have been in use: • the 15 ◦ C calorie: 1 cal15 = 4.1855 J (value adopted by the CIPM in 1950); • the IT (International Table) calorie: 1 calIT = 4.1868 J (5th International Conference on the Properties of Steam, London, 1956); • the thermochemical calorie: 1 calth = 4.184 J. The micron and its symbol, adopted by the CIPM in 1879 and repeated in Resolution 7 of the 9th CGPM (1948), were abolished by the 13th CGPM (1967–1968).

Quantity

a

i

Numerical value

Unit

Ar Mu M(12 C) K J-90

12 1 × 10−3 12 × 10−3 483 597.9

kg/mol kg/mol GHz/V

RK-90

25 812.807

Ω

gn

101 325 9.80665

Pa m/s2

(12 C)

The relative atomic mass Ar (X) of a particle X with mass m(X) is defined by Ar (X) = m(X)/m u , where m u = m(12 C)/12 = Mu /NA = 1 u is the atomic mass constant, Mu is the molar mass constant, NA is the Avogadro number, and u is the (unified) atomic mass unit. Thus the mass of a particle X is m(X) = Ar (X) u and the molar mass of X is M(X) = Ar (X)Mu . This is the value adopted internationally for realizing representations of the volt using the Josephson effect. This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect. The value given was adopted by the 3rd General Conference on Weights and Measures (CGPM), 1903, and was the conventional value used to calculate the now obsolete unit kilogram force.

Table 1.2-16 Internationally adopted numerical values for selected quantities

Part 1 2.6

Unit

24

Part 1

General Tables

1.2.7 Some Energy Equivalents

Part 1 2.7

In science and technology, energy is measured in many different units. Different units are used depending on the field of application, but owing to the different possible forms of the energy concerned, it is possible also to express the energy in terms of other quantities. All forms of the energy, however, are quantitatively related to one another and are therefore considered as being equivalent. Some of the most important equivalence relations are E = eU = mc2 = hc/λ = hν = kT .

These equations tell us that a given energy E, which is usually measured either in units of joule (J) or units of the Hartree energy (E H = 1 hartree), can also be specified by giving a voltage U, a mass m, a wavelength λ, a frequency ν, or a temperature T . These equations contain, in addition to those variables, only well-known fundamental constants. Table 1.2-17 gives the values of the energy equivalents of the joule and the hartree and for the SI units corresponding to the five quantities U, m, λ, ν, and T . The equivalents have been calculated on the basis of the 2002 CODATA adjustment of the values of the constants.

Table 1.2-17 Energy equivalents, expressed in the units joule (J), hartree (E H ), volt (V), kilogram (kg), (unified) atomic mass unit

(u), reciprocal meter (m−1 ), hertz (Hz), and kelvin (K)

Unit Energy Joule 1J

(1 J) = 1 J

1 EH

(1 E H ) = 4.35974417(75) × 10−18 J (1 eV) = 1.60217653(14) × 10−19 J (1 kg) c2 = 8.987551787 × 1016 J (1 u) c2 = 1.49241790(26) × 10−10 J (1 m−1 ) hc = 1.98644561(34) × 10−25 J (1 Hz) h = 6.6260693(11) × 10−34 J (1 K) k = 1.3806505(24) × 10−23 J

1 eV 1 kg 1u 1 m−1 1 Hz 1K

Hartree

Volt

Kilogram

(1 J) = 2.29371257(39) × 1017 E H (1 E H ) = 1 E H

(1 J) = 6.24150947(53) × 1018 eV (1 E H ) = 27.2113845(23) eV (1 eV) = 1 eV

(1 J)/c2 = 1.112650056 × 10−17 kg (1 E H )/c2 = 4.85086960(83) × 10−35 kg (1 eV)/c2 = 1.78266181(15) × 10−36 kg (1 kg) = 1 kg

(1 eV) = 3.67493245(31) × 10−2 E H (1 kg) c2 = 2.06148605(35) × 1034 E H (1 u) c2 = 3.423177686(23) × 107 E H (1 m−1 ) hc = 4.556335252760(30) × 10−8 E H (1 Hz) h = 1.519829846006(10) × 10−16 E H (1 K) k = 3.1668153(55) × 10−6 E H

(1 kg) c2 = 5.60958896(48) × 1035 eV (1 u) c2 = 931.494043(80) × 106 eV (1 m−1 ) hc = 1.23984191(11) × 10−6 eV (1 Hz) h = 4.13566743(35) × 10−15 eV (1 K) k = 8.617343(15) × 10−5 eV

(1 u) = 1.66053886(28) × 10−27 kg (1 m−1 ) h/c = 2.21021881(38) × 10−42 kg (1 Hz) h/c2 = 7.3724964(13) × 10−51 kg (1 K) k/c2 = 1.5361808(27) × 10−40 kg

Unit Energy Atomic mass unit 1J 1 EH 1 eV 1 kg 1u 1 m−1 1 Hz 1K

(1 J)/c2 = 6.7005361(11) × 109 u (1 E H )/c2 = 2.921262323(19) × 10−8 u (1 eV)/c2 = 1.073544171(92) × 10−9 u (1 kg) = 6.0221415(10) × 1026 u (1 u) = 1 u (1 m−1 ) h/c = 1.3310250506(89) × 10−15 u (1 Hz) h/c2 = 4.439821667(30) × 10−24 u (1 K) k/c2 = 9.251098(16) × 10−14 u

Reciprocal meter

Hertz

Kelvin

(1 J)/hc = 5.03411720(86) × 1024 m−1 (1 E H )/hc = 2.194746313705(15) × 107 m−1 (1 eV)/hc = 8.06554445(69) × 105 m−1 (1 kg) c/h = 4.52443891(77) × 1041 m−1 (1 u) c/h = 7.513006608(50) × 1014 m−1 (1 m−1 ) = 1 m−1

(1 J)/h = 1.50919037(26) × 1033 Hz (1 E H )/h = 6.579683920721(44) × 1015 Hz (1 eV)/h = 2.41798940(21) × 1014 Hz (1 kg) c2 /h = 1.35639266(23) × 1050 Hz (1 u) c2 /h = 2.252342718(15) × 1023 Hz (1 m−1 ) c = 299 792 458 Hz (1 Hz) = 1 Hz

(1 J)/k = 7.242963(13) × 1022 K (1 E H )/k = 3.1577465(55) × 105 K (1 eV)/k = 1.1604505(20) × 104 K (1 kg) c2 /k = 6.509650(11) × 1039 K (1 u) c2 /k = 1.0809527(19) × 1013 K (1 m−1 ) hc/k = 1.4387752(25) × 10−2 K (1 Hz) h/k = 4.7992374(84) × 10−11 K (1 K) = 1 K

(1 Hz)/c = 3.335640951 × 10−9 m−1 (1 K) k/hc = 69.50356(12) m−1

(1 K) k/h = 2.0836644(36) × 1010 Hz

The International System of Units (SI), Physical Quantities, and Their Dimensions

References

25

References 2.1

Bureau International des Poids et Mesures: Le système international d’unités, 7th edn. (Bureau International des Poids et Mesures, Sèvres 1998)

2.2

Organisation Intergouvernementale de la Convention du Mètre: The International System of Units (SI), Addenda and Corrigenda to the 7th Edition (Bureau International des Poids et Mesures, Sèvres 2000)

Part 1 2

26

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27

1.3. Rudiments of Crystallography

Rudiments of

The structure of a solid material is very important, because the physical properties are closely related to the structure. In most cases solids are crystalline: they may consist of one single crystal, or be polycrystalline, consisting of many tiny single crystals in different orientations. All periodic crystals have a perfect translational symmetry. This leads to selection rules, which are very useful for the understanding of the physical properties of solids. Therefore, most textbooks on solid-state physics begin with some chapters on symmetry and structure. Today we know that other solids, which have no translational symmetry, also exist. These are amorphous materials, which have little order (in most cases restricted to the short-range arrangement of the atoms), and aperiodic crystals, which show perfect long-range order, but no periodicity – at least in 3-D space. In this chapter of the book, the basic concepts of crystallography – how the space of a solid can be filled with atoms – are briefly discussed. Readers who want to inform themselves in more detail about crystallography are referred to the classic textbooks [3.1–5]. Many crystalline materials, especially minerals and gems, were described more than 2000 years ago. The regular form of crystals and the existence of facets, which have fixed angles between them, gave rise to

1.3.1

Crystalline Materials ........................... 1.3.1.1 Periodic Materials ................... 1.3.1.2 Aperiodic Materials..................

28 28 33

1.3.2 Disorder.............................................

38

1.3.3 Amorphous Materials ..........................

39

1.3.4 Methods for Investigating Crystallographic Structure....................

39

References ..................................................

41

local phenomena. The section is concluded by touching on the basics of diffraction methods, the most powerful tool kit used by experimentalists dealing with structure at the atomic level in the solid state.

a belief that crystals were formed by a regular repetition of tiny, identical building blocks. After the discovery of X-rays by Röntgen, Laue investigated crystals in 1912 using these X-rays and detected interference effects caused by the periodic array of atoms. One year later, Bragg determined the crystal structures of alkali halides by X-ray diffraction. Today we know that a crystal is a 3-D array of atoms or molecules, with various types of long-range order. A more modern definition is that all materials which show sharp diffraction peaks are crystalline. In this sense, aperiodic or quasicrystalline materials, as well as periodic materials, are crystals. A real crystal is never a perfect arrangement. Defects in the form of vacancies, dislocations, impurities, and other imperfections are often very important for the physical properties of a crystal. This aspect has been largely neglected in classical crystallography but is becoming more and more a topic of modern crystallographic investigations [3.6, 7]. As indicated in Table 1.3-1, condensed matter can be classified as either crystalline or amorphous. Both of these states and their formal subdivisions will be discussed in the following. The terms “matter”, “structure”, and “material” always refer to single-phase solids.

Part 1 3

Crystallography deals basically with the question “Where are the atoms in solids?” The purpose of this section is to introduce briefly the basics of modern crystallography. The focus is on the description of periodic solids, which represent the major proportion of condensed matter. A coherent introduction to the formalism required to do this is given, and the basic concepts and technical terms are briefly explained. Paying attention to recent developments in materials research, we treat aperiodic, disordered, and amorphous materials as well. Consequently, besides the conventional three-dimensional (3-D) descriptions, the higher-dimensional crystallographic approach is outlined, and so is the atomic pair distribution function used to describe

28

Part 1

General Tables

Table 1.3-1 Classification of solids

Periodic structures

Condensed matter (solids) Crystalline materials Aperiodic structures Modulated structures Composite structures Quasicrystals

Amorphous materials

1.3.1 Crystalline Materials 1.3.1.1 Periodic Materials Part 1 3.1

Lattice Concept A periodic crystal is described by two entities, the lattice and the basis. The (translational) lattice is a perfect geometrical array of points. All lattice points are equivalent and have identical surroundings. This lattice is defined by three fundamental translation vectors a, b, c. Starting from an arbitrarily chosen origin of the lattice, any other lattice point can be reached by a translation vector r that satisfies

r = ua + vb + wc , where u, v, and w are arbitrary integers. The lattice is an abstract mathematical construction; the description of the crystal is completed by attaching a set of atoms – the basis – to each lattice point. Therefore the crystal structure is formed by a lattice and a basis (see Fig. 1.3-1). The parallelepiped that is defined by the axes a, b, c is called a primitive cell if this cell has the small-

b

× a

Fig. 1.3-1 A periodic crystal can be described as a convolution of

a mathematical point lattice with a basis (set of atoms). Open circles, mathematical points; filled circles, atoms Table 1.3-2 Centering types for 3-D crystallographic unit cells

est volume out of all possible cells. It contains one lattice point per cell only (Fig. 1.3-2a). This cell is a type of unit cell which fills the space of the crystal completely under the application of the translation operations of the lattice, i. e. movements along the vectors r. Conventionally, the smallest cell with the highest symmetry is chosen. Crystal lattices can be transformed into themselves by translation along the fundamental vectors a, b, c, but also by other symmetry operations. It can be shown that only onefold (rotation angle ϕ = 2π/1), twofold (2π/2), threefold (2π/3), fourfold (2π/4), and sixfold (2π/6) rotation axes are permissible. Other rotational axes cannot exist in a lattice, because they would violate the translational symmetry. For example, it is not possible to fill the space completely with a fivefold (2π/5) array of regular pentagons. Additionally, mirror planes and centers of inversion may exist. The restriction to high-symmetry cells may also lead to what is known as centering. Figure 1.3-2b illustrates a 2-D case. The centering types in 3-D are listed in Table 1.3-2. Planes and Directions in Lattices If one peers through a 3-D lattice from various angles, an infinity of equidistant planes can be seen. The position and orientation of such a crystal plane are determined by three points. It is easy to describe a plane if all three points lie on crystal axes (i. e. the directions of unit cell vectors); in this case only the intercepts need to be used. It is common to use Miller indices to de-

Symbol

Description

Points per unit cell

P

No centering (primitive)

1

I

Body-centered (innenzentriert)

2

F

All-face-centered

4

S; A, B, C One-face-centered (seitenzentriert); 2 in specific cases (b, c), (a, c), and (a, b), respectively, in specific cases R

Hexagonal cell, rhombohedrally centered

3

Rudiments of Crystallography

a)

3.1 Crystalline Materials

29

b)

90◦ angles: a centered cell of symmetry 2mm is chosen. It contains two lattice points and is twice the area of the primitive cell z

2 (623) c 1

a

b

3 y

x

Fig. 1.3-3 Miller indices: the intercepts of the (623) plane with the coordinate axes

scribe lattice planes. These indices are determined as follows: 1. For the plane of interest, determine the intercepts x, y, z of the crystal axes a, b, c. 2. Express the intercepts in terms of the basic vectors a, b, c of the unit cell, i. e. as x/a, y/b, z/c (where a = |a|, . . . ). 3. Form the reciprocals a/x, b/y, c/z. 4. Reduce this set to the smallest integers h, k, l. The result is written (hkl). The distance from the origin to the plane (hkl) inside the unit cell is the interplanar spacing dhkl . Negative

intercepts, leading to negative Miller indices, are writ¯ Figure 1.3-3 shows a (623) plane and its ten as h. construction. A direction in a crystal is given as a set of three integers in square brackets [uvw]; u, v, and w correspond to the above definition of the translation vector r. A direction in a cubic crystal can be described also by Miller indices, as a plane can be defined by its normal. The indices of a direction are expressed as the smallest integers which have the same ratio as the components of a vector (expressed in terms of the axis vectors a, b, c) in that direction. Thus the sets of integers 1, 1, 1 and 3, 3, 3 represent the same direction in a crystal, but the indices of the direction are [111] and not [333]. To give another example, the x axis of an orthogonal x, y, z coordinate system has Miller indices [100]; the plane perpendicular to this direction has indices (100). For all crystals, except for the hexagonal system, the Miller indices are given in a three-digit system in the form (hkl). However, for the hexagonal system, it is common to use four digits (hkil). The four-digit hexagonal indices are based on a coordinate system containing four axes. Three axes lie in the basal plane of the hexagon, crossing at angles of 120◦ : a, b, and −(a + b). As the third vector in the basal plane can be expressed in terms of a and b, the index can be expressed in terms of h and k: i = −(h + k). The fourth axis is the c axis normal to the basal plane.

Part 1 3.1

Fig. 1.3-2a,b Possible primitive and centered cells in 2-D lattices. Open circles denote mathematical points. (a) In this lattice, the conventional cell is the bold square cell because of its highest symmetry, 4mm. (b) Here, convention prefers

30

Part 1

General Tables

Part 1 3.1

Crystal Morphology The regular facets of a crystal are planes of the type described above. Here, the lattice architecture of the crystal is visible macroscopically at the surface. Figure 1.3-4 shows some surfaces of a cubic crystal. If the crystal had the shape or morphology of a cube, this would be described by the set of facets {(100), (010), (001), (1¯ 00), (01¯ 0), (001¯ )}. An octahedron would be described by {(111), (1¯ 11), (11¯ 1), (111¯ ), (1¯ 1¯ 1¯ ), (11¯ 1¯ ), (1¯ 11¯ ), (1¯ 1¯ 1)}. The morphology of a crystalline material may be of technological interest (in relation to the bulk density, flow properties, etc.) and can be influenced in various ways, for example by additives during the crystallization process. The 32 Crystallographic Point Groups The symmetry of the space surrounding a lattice point can be described by the point group, which is a set of symmetry elements acting on the lattice. The crystallographic symbols for the symmetry elements of point groups compatible with a translational lattice are the rotation axes 1, 2, 3, 4, and 6, mirror planes m, and the center of inversion 1¯ . Figure 1.3-5 illustrates, as an example, the point group 2/m. The “2” denotes a twofold axis perpendicular (“/”) to a mirror plane “m”. Note that this combination of 2 and m implies, or generates automatically, an inversion center 1¯ . We have used the Hermann–Mauguin notation here; however, point groups of isolated molecules are more often denoted by the Schoenflies symbols. For a translation list, see Table 1.3-3. No crystal can have a higher point group symmetry than the point group of its lattice, called the holohedry. In accordance with the various rotational symmetries,

[111] (010) (111) (001)

[00-1] (100)

Fig. 1.3-4 Some crystal planes and directions in a cubic

crystal, and their Miller indices

2

–1

m

Fig. 1.3-5 The point group 2/m (C2h ). Any object in space

can be rotated by ϕ = 2π/2 around the twofold rotational axis 2 and reflected by the perpendicular mirror plane m, generating identical copies. The inversion center 1¯ is implied by the coupling of 2 and m

there are seven crystal systems (see Table 1.3-3), and the seven holohedries are 1¯ , 2/m, mmm, 4/mmm, 3¯ m, 6/mmm, and m 3¯ m. Other, less symmetric, point groups are also compatible with these lattices, leading to a total number of 32 crystallographic point groups (see Table 1.3-4). A lower symmetry than the holohedry can be introduced by a less symmetric basis in the unit cell. Since 3¯ m and 6/mmm are included in the same point lattice, they are sometimes subsumed into the hexagonal crystal family. So there are seven crystal systems but six crystal families. Note further that rhombohedral symmetry is a special case of centering (R-centering) of the trigonal crystal system and offers two equivalent possibilities for selecting the cell parameters: hexagonal or rhombohedral axes (see Table 1.3-4 again). It can be shown that in 3-D there are 14 different periodic ways of arranging identical points. These 14 3-D periodic point lattices are called the (translational) Bravais lattices and are shown in Fig. 1.3-6. Table 1.3-4 presents data related to some of the crystallographic terms used here. The 1-D and 2-D space groups can be classified analogously but are omitted here. The 230 Crystallographic Space Groups Owing to the 3-D translational periodicity, symmetry operations other than point group operations are possible in addition: these are glide planes and screw axes. A glide plane couples a mirror operation and a translational shift. The symbols for glide planes

3.1 Crystalline Materials

Rudiments of Crystallography

31

Table 1.3-3 The 32 crystallographic point groups: translation list from the Hermann–Mauguin to the Schoenflies notation

Hermann–Mauguin symbol

Schoenflies symbol

Crystal system

Hermann–Mauguin symbol

Schoenflies symbol

Triclinic

1 1¯

C1 Ci

Trigonal

3 3¯

C3 C3i

Monoclinic

2 m 2/m

C2 Cs C2h

32 3m 3¯ m

D3 C3v D3d

Orthorhombic

222 mm2 mmm

D2 C2v D2h

6 6¯ 6/m

C6 C3h C6h

4 4¯ 4/m 422 4mm 4¯ 2m 4/mmm

C4 S4 C4h D4 C4v D2d D4h

622 6mm 6¯ 2m 6/mmm 23 m 3¯ 432 4¯ 3m m 3¯ m

D6 C6v D3h D6h T Th O Td Oh

Tetragonal

are a, b, and c for translations along the lattice vectors a, b, and c, respectively, and n and d for some special lattice vector combinations. A screw axis is always parallel to a rotational axis. The symbols are 21 , 31 , 32 , 41 , 42 , 43 , 61 , 62 , 63 , 64 , and 65 , where, for example, 63 means a rotation through an angle ϕ = 2π/6 followed by a translation of 3/6 (= 1/2) of a full translational period along the sixfold axis. Thus the combination of 3-D translational and point symmetry operations leads to an infinite number of sets of symmetry operations. Mathematically, each of these sets forms a group, and they are called space groups. It can be shown that all possible periodic crystals can be described by only 230 space groups. These 230 space groups are described in tables, for example the International Tables for Crystallography [3.8]. In this formalism, a conventional space group symbol reflects the symmetry elements, arranged in the order of standardized blickrichtungen (symmetry directions). We shall confine ourselves here to explain one instructive example: P42 /mcm, space group number 132 [3.8]. The full space group symbol is P 42 /m 2/c 2/m. The mean-

Hexagonal

Cubic

aP

oP

mP

oI

oC

tP

tI

hP

cP

cI

cF

Fig. 1.3-6 The 14 Bravais lattices

Part 1 3.1

Crystal system

mC

oF

hR

32

Part 1

General Tables

Table 1.3-4 Crystal families, crystal systems, crystallographic point groups, conventional coordinate systems, and Bravais lattices

in three dimensions. Lattice point symmetries (holohedries) are given in bold Crystal family

Symbol

Triclinic (anorthic) monoclinic

Crystal system

Crystallographic point groups

No. of space

Conventional coordinate system

groups

Restrictions on cell parameters None

a

Triclinic

1, 1¯

2

m

Monoclinic

2, m, 2/m

13

Bravais lattice (Pearson symbol)

Parameters to be determined

Part 1 3.1

a, b, c, α, β, γ Setting with b unique: a, b, c, α = γ = 90◦ β

aP

Setting with c unique: α = β = 90◦ α = β = γ = 90◦

a, b, c, γ a, b, c

mP, mS (mC, mA, mI)

orthorhombic o

Orthorhombic

222, mm2, mmm

59

tetragonal

t

Tetragonal

68

a=b α = β = γ = 90◦

a, c

hexagonal

h

Trigonal

4, 4¯ , 4/m, 422, 4mm, 4¯ 2m, 4/mmm 3, 3¯ , 32, 3m, 3¯ m

mP, mS (mA, mB, mI) oP,oS, (oC, oA, oB) oI, oF tP, tI

18

a = b, α = β = 90◦ γ = 120◦ (hexagonal axes)

a, c

hP

7

a=b=c α = β = γ = 90◦ (rhombohedral axes)

a, α

hR

27

a = b, α = β = 90◦ γ = 120◦ a=b=c α = β = γ = 90◦

a, c

hP

a

cP, cI,cF

Hexagonal

cubic

c

Cubic

6, 6¯ , 6/m, 622, 6mm, 6¯ 2m, 6/mmm 23, m 3¯ , 432, 4¯ 3m, m3¯ m

36

ing of the symbols is the following: P denotes a primitive Bravais lattice. It belongs to the tetragonal crystal system indicated by 4. Along the first standard blickrichtung [001] there is a 42 screw axis with a perpendicular mirror plane m. Along [100] there is a twofold rotation axis, named 2, with a perpendicular glide plane c parallel to c. Third, along [110] there is a twofold rotation axis 2, with a perpendicular mirror plane m. Decoration of the Lattice with the Basis At this point we have to recall that in a real crystal structure we have not only the lattice, but also the basis. In [3.8], there are standardized sets of general and special positions (i. e. coordinates x, y, z) within the unit cell (Wyckoff positions). An atom placed in a general position is transformed into more than one atom by the action of all symmetry operators of the

respective space group. Special positions are located on special points which are mapped onto themselves by one or more symmetry operations – for example a position in a mirror plane or exactly on a rotational axis. Reference [3.8] also provides information about symmetry relations between individual space groups (group–subgroup relations). These are often useful for describing relationships between crystal structures and for describing phase transitions of materials. The use of the space group allows us to further reduce the basis to the asymmetric unit: this is the minimal set of atoms that needs to be given so that the whole crystal structure can be generated via the symmetry of the space group. This represents the main power of a crystallographically correct description of a material: just some 10 parameters are sufficient to describe an ensemble of some 1023 atoms.

Rudiments of Crystallography

Thus, a crystallographically periodic structure of a material is unambiguously characterized by

• • • •

the cell parameters; the space group; the coordinates of the atoms (and their chemical type) in the asymmetric unit; the occupation and thermal displacement factors of the atoms in the asymmetric unit.

• • • • •

the crystallographic structure; the Shubnikov group; the cell parameters of the magnetic unit cell; the coordinates of the atoms carrying magnetic moments (the asymmetric unit in the magnetic unit cell); the magnitude and direction of the magnetic moments on these atoms.

Structure Types It is useful to classify the crystal structures of materials by the assignment of structure types. The structure type is based on a representative crystal structure, the param-

eters of which describe the essential crystallographic features of other materials of the same type. As an example, we consider the structure of the spinel oxides AB 2 O4 . The generic structure type is MgAl2 O4 , cF56. The Pearson symbol, here cF56, denotes the cubic crystal family and a face-centered Bravais lattice with 56 atoms per unit cell (see Table 1.3-5 and also the last column in Table 1.3-4). Regarding the free parameters, for example a, the notation 8.174(1) in Table 1.3-5 means 8.174 ± 0.001. The chemical formula and the unit cell contents can easily be calculated from the site multiplicities (given by the Wyckoff positions) and the occupancies. So can the (crystallographic) density, using the appropriate atomic masses. There is a huge variety of other materials belonging to the same structure type as in this example. The only parameters that differ (slightly) are the numerical value of a, the types of atoms in the positions, the numerical value of the parameter x for Wyckoff position 32e, and the occupancies. Thus, for example, the crystal structure of the iron sulfide Fe3 S4 can be characterized in its essential features via the information that it belongs to the same structure type.

1.3.1.2 Aperiodic Materials In addition to the crystalline periodic state of matter, a class of materials exists that lacks 3-D translational symmetry and is called aperiodic. Aperiodic materials cannot be described by any of the 230 space groups mentioned above. Nevertheless, they show another type of long-range order and are therefore included in the term “crystal”. This notion of long-range order is the major feature that distinguishes crystals from amorphous materials. Three types of aperiodic order may

Table 1.3-5 Complete crystallographic parameter set for MgAl2 O4 , spinel structure type

Material Structure type Pearson symbol Space group a (Å)

MgAl2 O4 MgAl2 O4 , spinel cF56 Fd 3¯ m (No. 227) 8.174(1)

Atom

Wyckoff position

x

y

z

Occupancy

Mg Al O

8a 16d 32e

0 5/8 0.3863(2)

0 5/8 x

0 5/8 x

1.0 1.0 1.0

33

Part 1 3.1

For an example, the reader is referred to the crystallographic description of the spinel structure of MgAl2 O4 given below under the heading “Structure Types”. To complete the information on space group symmetries given here, periodic magnetic materials should also be mentioned. Magnetic materials contain magnetic moments carried by atoms in certain positions in the unit cell. If we take into account the magnetic moments in the description of the structure, the classification by space groups (the 230 “gray” groups, described above) has to be extended to 1651 the “black and white”, or Shubnikov, groups [3.9]. A magnetic periodic structure is then characterized by

3.1 Crystalline Materials

34

Part 1

General Tables

be distinguished, namely modulated structures, composite structures, and quasicrystals. All aperiodic solids exhibit an essentially discrete diffraction pattern and can be described as atomic structures obtained from a 3-D section of a n-dimensional (n-D) (n > 3) periodic structure.

Part 1 3.1

Modulated Structures In a modulated structure, periodic deviations of the atomic parameters from a reference or basic structure are present. The basic structure can be understood as a periodic structure as described above. Periodic deviations of one or several of the following atomic parameters are superimposed on this basic structure:

• • • •

atomic coordinates; occupancy factors; thermal displacement factors; orientations of magnetic moments.

Let the period of the basic structure be a and the modulation wavelength be λ; the ratio a/λ may be (1) a rational or (2) an irrational number (Fig. 1.3-7). In case (1), the structure is commensurately modulated; we observe a qa superstructure, where q = 1/λ. This superstructure is periodic. In case (2), the structure is incommensurately modulated. Of course, the experimental distinction between the two cases is limited by the finite experimental resolution. q may be a function of external variables such as temperature, pressure, or chemical composition, i. e. q = f(T, p, X), and may adopt a rational value to result in a commensurate “lock-in” structure. On the other hand, an incommensurate charge-density wave may exist; this can be moved through a basic crystal without changing the internal energy U of the crystal. When a 1-D basic structure and its modulation function are combined in a 2-D hyperspace R = Rparallel ⊕ a λ =1/q

Basic structure s(r)

Rperpendicular , periodicity on a 2-D lattice results. The real atoms are generated by the intersection of the 1-D physical (external, parallel) space Rparallel with the hyperatoms in the complementary 1-D internal space Rperpendicular . In the case of a modulated structure, the hyperatoms have the shape of the sinusoidal modulation function in Rperpendicular . Figure 1.3-8 illustrates this construction. We have to choose a basis (a1 , a2 ) in R where the slope of a1 with respect to Rparallel corresponds to the length of the modulation λ. It is clear that real atomic structures are always manifestations of matter in 3-D real, physical space. The cutting of the 2-D hyperspace to obtain real 1-D atoms illustrated in Fig. 1.3-8 may serve as an instructive basic example of the concept of higher-dimensional (n-D, n > 3) crystallography. The concept is also called a superspace description; it applies to all aperiodic structures and provides a convenient finite set of variables that can be used to compute the positions of all atoms in the real 3-D structure.

Rperpendicular

a2 a1

Rparallel, sm(r)

a

+ f(r) = sin(q r) = Modulated structure sm(r)

Fig. 1.3-7 A 1-D modulated structure sm (r) can be described as

a sum of a basic structure s(r) and a modulation function f(r) of its atomic coordinates. If a/λ is irrational, the structure is incommensurately modulated. Circles denote atoms

Fig. 1.3-8 2-D hyperspace description of the example of

Fig. 1.3-7. The basis of the hyperspace R = Rparallel ⊕ Rperpendicular is (a1 , a2 ); the slope of a1 with respect to Rparallel is proportional to λ. Atoms of the modulated structure sm (r) occur in the physical space Rparallel and are represented by circles

Rudiments of Crystallography

The modulation may occur in one, two, or three directions of the basic structure, yielding 1-D, 2-D, or 3-D modulated structures. If we introduce one additional dimension per modulation vector (the direction r that the modulation corresponding to λ runs along), these structures can be described as periodic in 4-D, 5-D, or 6-D superspace, respectively.

• • •

channel structures; columnar packings; layer packings.

These composite structures are also known as intergrowth or host–guest structures. Figure 1.3-9 illustrates an example of a host with channels along a, in which atoms of the substructure with a periodicity λa reside as a guest.

The higher-dimensional n-D formalism (n > 3) used to describe composite structures is essentially the same as that which applies to modulated structures. Quasicrystals Quasicrystals represent the third type of aperiodic materials. Quasiperiodicity may occur in one, two, or three dimensions of physical space and is associated with special irrational numbers such √ √ as the golden mean τ = (1 + 5)/2, and ξ = 2 + 3. The most remarkable feature of quasicrystals is the appearance of noncrystallographic point group symmetries in their diffraction patterns, such as 8/mmm, 10/mmm, 12/mmm, and 2/m 3¯ 5¯ . The golden mean is related to fivefold symmetry via the relation τ = 2 cos(π/5); τ can be considered as the “most irrational” number, since it is the irrational number that has the worst approximation by a truncated continued fraction, 1 τ = 1+ . 1 1+ 1 1+

1+

1 1+ 1+1 ...

This might be a reason for the stability of quasiperiodic systems where τ plays a role. A prominent 1-D example is the Fibonacci sequence, an aperiodic chain of short and long segments S and L with lengths S and L, where the relations L/S = τ and L + S = τL hold. A Fibonacci chain can be constructed by the simple substitution or inflation rule L → LS and S → L (Table 1.3-6, Fig. 1.3-10). Materials quasiperiodically modulated in 1-D along one direction may occur. Again, their structures are readily described using the superspace formalism as above. The Fibonacci sequence can be used to explain the idea of a periodic rational approximant. If the sequence . . .LSLLSLSLS. . . represents a quasicrystal, then the Table 1.3-6 Generation of the Fibonacci sequence using

the inflation rule L → LS and S → L. The ratio Fn+1 /Fn tends towards τ for n → ∞. Fn is a Fibonacci number; Fn+1 = Fn + Fn−1 . The sequence starts with F0 = 0, F1 = 1 λa c a b

Fig. 1.3-9 Host–guest channel structure. The guest atoms reside in channels parallel to a, with a periodicity λa

35

Sequence

n

Fn+1 /Fn

L LS LSL LSLLS LSLLSLSL ... . . . LSLLSLSLS . . .

1 2 3 4 5

1/1 = 1 2/1 = 2 3/2 = 1.5 5/3 = 1.66666. . . 8/5 = 1.6

∞

τ = 1.61803. . .

Part 1 3.1

Composite Structures Composite crystals are crystalline structures that consist of two or more periodic substructures, each one having its own 3-D periodicity to a first approximation. The symmetry of each of these subsystems is characterized by one of the 230 space groups. However, owing to their mutual interaction, the true structure consists of a collection of incommensurately modulated subsystems. All known composite structures to date have at least one lattice direction in common and consist of a maximum of three substructures. There are three main classes:

3.1 Crystalline Materials

36

Part 1

General Tables

a1 L

L

S L

S

S

L L

L

S

L L

S

a3

a4 L

S

L a5 L

S

a2 a6

L

Fig. 1.3-10 1-D Fibonacci sequence. Moving downwards

Part 1 3.1

corresponds to an inflation of the self-similar chains, and moving upwards corresponds to a deflation

periodic sequence . . .LSLSLSLSLS. . ., consisting only of the word LS, is its 2/1 approximant (Table 1.3-6). In real systems, such approximants often exist as largeunit-cell (periodic!) structures with atomic arrangements locally very similar to those in the corresponding quasicrystal. When described in terms of superspace, they would result via cutting with a rational slope, in the above example 2/1 = 2, instead of τ = 1.6180. . . . To date, all known 2-D quasiperiodic materials exhibit noncrystallographic diffraction symmetries of 8/mmm, 10/mmm, or 12/mmm. The structures of these materials are called octagonal, decagonal, and dodecagonal structures, respectively. Quasiperiodicity is present only in planes stacked along a perpendicular periodic direction. To index the lattice points in a plane, four basis vectors a1 , a2 , a3 , a4 are needed; a fifth one, a5 , describes the periodic direction. Thus a 5-D hypercrystal is appropriate for describing the solid periodically. In an analogous way to the 230 3-D space groups, the 5-D superspace groups (e.g. P105 /mmc) provide

• • •

the multiplicity and Wyckoff positions; the site symmetry; the coordinates of the hyperatoms.

Again, the quasiperiodic structure in 3-D can be obtained from an intersection with the external space. On the atomic scale, these quasicrystals consist of units of some 100 atoms, called clusters. These clusters, of point symmetry 8/mmm, 10/mmm, or 12/mmm

Fig. 1.3-11 Unit vectors a1 , . . . , a6 of an icosahedral lattice

(or less), are fused, may interpenetrate partially, and can be considered to decorate quasiperiodic tilings. In a diffraction experiment, their superposition leads to an overall noncrystallographic symmetry. There are a number of different tilings that show such noncrystallographic symmetries. Figure 1.3-12 depicts four of them, as examples of the octagonal, decagonal, and dodecagonal cases. Icosahedral quasicrystals are also known. In 3-D, the icosahedral diffraction symmetry 2/m 3¯ 5¯ can be observed for these quasicrystals. Their diffraction patterns can be indexed using six integers, leading to a 6-D superspace description (see Fig. 1.3-11). On the atomic scale in 3-D, in physical space, clusters of some 100 atoms are arranged on the nodes of 3-D icosahedral tilings; the clusters have an icosahedral point group symmetry or less, partially interpenetrate, and generate an overall symmetry 2/m 3¯ 5¯ . Many of their structures are still waiting to be determined completely. Figure 1.3-13 shows the two golden rhombohedra and the four Danzer tetrahedra that can be used to tile 3-D space icosahedrally.

Rudiments of Crystallography

a)

37

b)

Part 1 3.1

a2

a1

a3

a3

–(a1 + a2 + a3 + a4) a4

c)

3.1 Crystalline Materials

a2

a1

a4

d)

a4

a3 a2 a1

Fig. 1.3-12a–d Some 2-D quasiperiodic tilings; the corresponding four basis vectors a1 , . . . , a4 are shown. Linear
combinations of r = i u i ai reach all lattice points. (a) Penrose tiling with local symmetry 5mm and diffraction symmetry 10mm, (b) octagonal tiling with diffraction symmetry 8mm, (c) Gummelt tiling with diffraction symmetry 10mm, and (d) dodecagonal Stampfli-type tiling with diffraction symmetry 12mm

38

Part 1

General Tables

a)

Fig. 1.3-13 Icosahedral tilings. (a) The two golden rhombo-

hedra (bottom) can be used to form icosahedral objects (the rhombic triacontahedron with point symmetry m 3¯ 5¯ shown in gray). (b) Danzer’s {ABCK} tiling: three inflation steps for prototile A

Part 1 3.2 b)

1.3.2 Disorder In between the ideal crystalline and the purely amorphous states, most real crystals contain degrees of disorder. Two types of statistical disorder have to be distinguished: chemical disorder and displacive disorder (Fig. 1.3-14). Statistical disorder contributes to the entropy S of the solid and is manifested by diffuse scattering in diffraction experiments. It may occur in both periodic and aperiodic materials. Chemical Disorder Chemical disorder is observed, for example, in the case of solid solutions, say of B in A, or A1−x Bx for short. Here, an average crystal structure exists. On the crystallographic atomic positions, different atomic species (the chemical elements A and B) are distributed ran-

domly. Generally, the cell parameter a varies with x. For x = 0 or 1, the pure end member is present. A linear variation of a(x) is predicted by Vegard’s law. On the atomic scale, however, differences in the local structure, are present owing to the different contacts A–A, B–B, and A–B. These differences are usually represented by enlarged displacement factors, but can be investigated by analyzing the pair distribution function G(r). G(r) represents the probability of finding any atom at a distance r from any other atom relative to an average density. Chemical disorder can also occur on only one or a few of the crystallographically different atomic positions (e.g. A(X 1−x Yx )2 ). This type of disorder is often intrinsic to a material and may be temperature-dependent.

Rudiments of Crystallography

Displacive Disorder The displacive type of disorder can be introduced by the presence of voids or vacancies in the structure or may exist for other reasons. Vacancies can be an important feature of a material: for example, they may leading to ionic conductivity or influence the mechanical properties.

3.4 Methods for Investigating Crystallographic Structure

a)

39

b)

A B

Fig. 1.3-14 Schematic sketch of (a) chemical and (b) dis-

placive disorder

Part 1 3.4

1.3.3 Amorphous Materials The second large group of condensed matter is classified as the amorphous or glassy state. No long-range order is observed. The atoms are more or less statistically distributed in space, but a certain short-range order is present. This short-range order is reflected in the certain average coordination numbers or average coordination geometries. If there are strong (covalent) interactions between neighboring atoms, similar basic units may occur, which are in turn oriented randomly with respect to each other. The SiO4 tetrahedron in silicate glasses is a well-known example. In an X-ray diffraction experiment on an amorphous solid, only isotropic diffuse scattering is observed. From this information, the radial atomic pair distribution function (Fig. 1.3-15) can be obtained. This function G(r) can be interpreted as the probability of finding any atom at a distance r from any other atom relative to an average density.

G(r)

0

r

Fig. 1.3-15 Radial atomic pair distribution function G(r) of an amorphous material. Its shape can be deduced from diffuse scattering

1.3.4 Methods for Investigating Crystallographic Structure So far, we have been dealing with the formal description of solids. To conclude this chapter, the tool kit that an experimentalist needs to obtain structural information about a material in front of him/her will be briefly described. The major technique used to derive the atomic structure of solids is the diffraction method. To obtain the most comprehensive information about a solid, other techniques besides may be used to complement a model based on diffraction data. These tech-

niques include scanning electron microscopy (SEM), wavelength-dispersive analysis of X-rays (WDX), energy-dispersive analysis of X-rays (EDX), extended X-ray atomic fine-structure analysis (EXAFS), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), differential thermal analysis (DTA), and a number of other methods. For diffraction experiments, three types of radiation with a wavelength λ of the order of magnitude of

40

Part 1

General Tables

interatomic distances are used: X-rays, electrons, and neutrons. The shortest interatomic distances in solids are a few times 10−10 m. Therefore the non-SI unit the angstrom (1 Å = 10−10 m) is often used in crystallography. In the case of electrons and neutrons, their energies have to be converted to de Broglie wavelengths: λ = h/mv ,  λ(Å) = 0.28/ E(eV) .

θ

Part 1 3.4

Figure 1.3-16 compares the energies and wavelengths of the three types of radiation. From wave optics, it is known that radiation of wavelength λ is diffracted by a grid of spacing d. If we take a 3-D crystal lattice as such a grid, we expect diffraction maxima to occur at angles 2θ, given by the Bragg equation (Fig. 1.3-17) λ = 2dhkl sin θhkl .

d sin θ

Fig. 1.3-17 Geometrical derivation of the Bragg equation

For the aperiodic (n-D periodic crystal) case, dhkl has to be replaced by dh 1 h 2 ...h i ...h n . To give a simple 3-D example, for the determination of the cell parameter a in the cubic case, the Bragg equation can be rewritten in the form (Q/2π)2 = 4 sin2 θhkl /λ2 = (h 2 + k2 + l 2 )/a2 .

10

d

θ

λ(Å)

nλ = 2d sin θ. n can be set to 1 when it is included in a higher-order hkl

Thus the crystal lattice is determined by a set of θhkl . In the case of X-rays and neutrons, information about the atomic structure is contained in the set of diffraction 2 where F intensities Ihkl . Here we have Ihkl = Fhkl hkl are the structure factors. To reconstruct the matter distribution ρ(xyz) inside a unit cell of volume V , the crystallographic phase problem has to be solved. Once the phase factor φ for each hkl is known, the crystal structure is solved. ρ(xyz) = 1/V  |F| cos [2π(hx + ky + lz) − φ] . ×

5 X-ray

all h,k,l

1.0 0.5

Electron

Neutron

Non-Bragg diffraction intensities I(Q) and therefore a normalized structure function S(Q) can be obtained, for example, from an X-ray or neutron powder diffractogram. The sine Fourier transform of S(Q) yields a normalized radial atomic pair distribution function G(r): ∞ G(r) = (2/π) Q[S(Q) − 1] sin(Qr) dQ . 0

0.1

1

5 10 50 100 E/ keV (X-ray); 0.01eV (neutron); 100eV (electron)

Fig. 1.3-16 Wavelengths λ in Å and particle energies E

for X-ray photons (energies in keV), neutrons (energies in 0.01 eV), and electrons (energies in 100 eV)

For measurements at high Q, the 1-D function G(r) contains detailed information about the local structure. This function therefore resolves, for example, disorder or vacancy distributions in a material. The method can be applied to 3-D diffuse scattering distributions as well and thus can include angular information with respect to r.

Rudiments of Crystallography

Neutron Diffraction Neutrons, generated in a nuclear reactor, are useful for complementing X-ray diffraction information. They interact with the atomic nuclei, and with the magnetic moments of unpaired electrons if they are present in a structure. Hydrogen atoms, which are difficult to locate using X-rays (the contain one electron, if at all, near the proton), give a far better contrast in neutron diffraction experiments. The exact positions of atomic nuclei permit “X minus N” structure determinations, so that the location of valence electrons can be made observable. Furthermore, the magnetic structure of a material can be determined.

Electron Diffraction The third type of radiation which can be used for diffraction purposes is an electron beam; this is usually done in combination with TEM or HRTEM. Because electrons have only a short penetration distance – electrons, being charged particles, interact strongly with the material – electron diffraction is mainly used for thin crystallites, surfaces, and thin films. In the TEM mode, domains and other features on the nanometer scale are visible. Nevertheless, crystallographic parameters such as unit cell dimensions, and symmetry and space group information can be obtained from selected areas. In some cases, information about, for example, stacking faults or superstructures obtained from an electron diffraction experiment may lead to a revised, detailed crystal structure model that is “truer” than the model which was originally deduced from X-ray diffraction data. If only small crystals of a material are available, crystallographic models obtained from unit cell and symmetry information can be simulated and then adapted to fit HRTEM results. The descriptions above provide the equipment needed to understand the structure of solid matter on the atomic scale. The concepts of crystallography, the technical terms, and the language used in this framework have been presented. The complementarities of the various experimental methods used to extract coherent, comprehensive information from a sample of material have been outlined. The “rudiments” presented here, however, should be understood only as a first step into the fascinating field of the atomic structure of condensed matter.

References 3.1 3.2

3.3 3.4 3.5

L. V. Azaroff: Elements of X-Ray Crystallography (McGraw-Hill, New York 1968) J. Pickworth Glusker, K. N. Trueblood: Crystal Structure Analysis – A Primer (Oxford Univ. Press, Oxford 1985) E. R. Wölfel: Theorie und Praxis der Röntgenstrukturanalyse (Vieweg, Braunschweig 1987) W. Kleber, H.-J. Bautsch, J. Bohm: Einführung in die Kristallographie (Verlag Technik, Berlin 1998) C. Giacovazzo (Ed.): Fundamentals of Crystallography, IUCr Texts on Crystallography (Oxford Univ. Press., Oxford 1992)

3.6 3.7

3.8 3.9

C. Janot: Quasicrystals – A Primer (Oxford Univ. Press, Oxford 1992) S. J. L. Billinge, T. Egami: Underneath the Bragg Peaks: Structural Analysis of Complex Materials (Elsevier, Amsterdam 2003) T. Hahn (Ed.): International Tables for Crystallography, Vol. A (Kluwer, Dordrecht 1992) A. V. Shubnikov, N. V. Belov: Colored Symmetry (Pergamon Press, Oxford 1964)

41

Part 1 3

X-rays X-rays can be produced in the laboratory using a conventional X-ray tube. Depending on the anode material, wavelengths λ from 0.56 Å (Ag Kα) to 2.29 Å (Cr Kα) can be generated. Filtered or monochromatized radiation is usually used to collect diffraction data, from either single crystals or polycrystalline fine powders. A continuous X-ray spectrum, obtained from a tungsten anode, for example, is used to obtain Laue images to check the quality, orientation, and symmetry of single crystals. X-rays with a higher intensity, a tunable energy, a narrower distribution, and higher brilliance are provided by synchrotron radiation facilities. X-rays interact with the electrons in a structure and therefore provide information about the electron density distribution – mainly about the electrons near the atomic cores.

References

42

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43

Part 2

The Elemen Part 2 The Elements

1 The Elements Werner Martienssen, Frankfurt/Main, Germany

44

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45

This section provides tables of the physical and physicochemical properties of the elements. Emphasis is given to properties of the elements in the condensed state. The tables are structured according to the Periodic Table of the elements. Most of the tables deal with the properties of elements of one particular group (column) of the Periodic Table. Only the elements of the first period (hydrogen and helium), the lanthanides, and the actinides are arranged according to the periods (rows) of the Periodic Table. This synoptic representation is intended to provide an immediate overview of the trends in the data for chemically related elements.

2.1.1

Introduction ...................................... 2.1.1.1 How to Use This Section ...........

45 45

2.1.2 Description of Properties Tabulated ..... 2.1.2.1 Parts A of the Tables ................ 2.1.2.2 Parts B of the Tables ................ 2.1.2.3 Parts C of the Tables ................ 2.1.2.4 Parts D of the Tables ................

46 46 46 48 49

2.1.3 Sources ..............................................

49

2.1.4 Tables of the Elements in Different Orders..............................

49

2.1.5 Data .................................................. 54 2.1.5.1 Elements of the First Period...... 54 2.1.5.2 Elements of the Main Groups and Subgroup I to IV ................ 59 2.1.5.3 Elements of the Main Groups and Subgroup V to VIII ............. 98 2.1.5.4 Elements of the Lanthanides Period ................................... 142 2.1.5.5 Elements of the Actinides Period 151 References .................................................. 158

2.1.1 Introduction 2.1.1.1 How to Use This Section To find properties of a specific element or group of elements, start from one of Tables 2.1-1 – 2.1-5 and proceed in one of the following ways: 1. If you know the name of the element, refer to Table 2.1-1, where an alphabetical list of the elements is given, together with the numbers of the pages where the properties of these elements will be found. 2. If you know the chemical symbol of the element, refer to Table 2.1-2, where an alphabetical list of element symbols is given, together with the numbers of the pages where the properties of the corresponding elements will be found. 3. If you know the atomic number Z of the element, refer to Table 2.1-3, where a list of the elements in order of atomic number is given, together with the

numbers of the pages where the properties of these elements will be found. 4. If you know the group of the Periodic Table that contains the element of interest, refer to Table 2.1-4, which gives the numbers of the pages where the properties of the elements of each group will be found. 5. If you wish to look up the element in the Periodic Table, refer to Table 2.1-5, where the element symbol and the atomic number will be found. Then use Table 2.1-2 or Table 2.1-3 to find the numbers of the pages where the properties of the element of interest are tabulated. 6. Alternatively you can also find the name and the chemical symbol of the element you are looking for in the alphabetic index at the end of the volume. The index again will give you the first number of those pages on which

Part 2 1

The Elements 2.1. The Elements

46

Part 2

The Elements

Part 2 1.2

you can find the properties of the element described. The data-tables corresponding to the Periodes and Groups of the Periodic Table are subdivided in the following way: A. Atomic, ionic, and molecular properties. B. Materials data:

(a) Crystallographic properties. (b) Mechanical properties. (c) Thermal and thermodynamic properties. (d) Electronic, electromagnetic, and optical properties. C. Allotropic and high-pressure modifications. D. Ionic radii.

2.1.2 Description of Properties Tabulated 2.1.2.1 Parts A of the Tables The properties tabulated in parts A of the tables concern the atomic, ionic, and molecular properties of the elements:

• • •

• • • • • • • • •

The relative atomic mass, or atomic weight, A. The abundance in the lithosphere and in the sea. The atomic radius: the radius rcov for single covalent bonding (after Pauling), the radius rmet for metallic bonding with a coordination number of 12 (after Pauling), the radius rvdW for van der Waals bonding (after Bondi), and, for some elements, the radius ros of the outer-shell orbital are given. The completely and partially occupied electron shells in the atom. The symbol for the electronic ground state. The electronic configuration. The oxidation states. The electron affinity. The electronegativity X A (after Allred and Rochow). The first, second, third, and fourth ionization energies and the standard electrode potential E 0 . The internuclear distance in the molecule. The dissociation energy of the molecule.

2.1.2.2 Parts B of the Tables Parts B of the tables contain data on the macroscopic properties of the elements. Most of the data concern the condensed phases. If not indicated otherwise, the data in this section apply to the standard state of the element, that is, they are valid at standard temperature and pressure (STP, i. e. T = 298.15 K and p = 100 kPa = 1 bar). For those elements which are stable in the gas phase at STP, data are given for the macroscopic properties in the gas phase. The quantities describing the physical and physicochemical properties of materials can be divided into

two classes. The first class contains all those quantities which are not directly connected with external (generalized) forces, these quantities have well-defined values even in the absence of external forces. Some examples are the electronic ground-state configuration of the atom, the coordination number in the crystallized state and the surface tension in the liquid state. The second class contains those quantities which describe the response of the material to externally applied (generalized) forces F. Such a force might be a mechanical stress field, an electric or magnetic field, a field gradient, or a temperature gradient. The response of the material to the external force might be observed via a suitable observable O, such as a mechanical strain, an electric current density, a dielectric polarization, a magnetization, or a heat current density. Assuming homogeneous conditions, the dependence of the observable O on the force F can be used to define material-specific parameters χ, which are also called physical properties of the material. Some examples are the elastic moduli or compliance constants, the electrical conductivity, the dielectric constant, the magnetic susceptibility, and the thermal conductivity. In the linear-response regime, that is, under weak external forces F, these parameters χ are considered as being independent of the strength of the forces. The dependence of an observable O on a force F is then the simple proportionality O = χF .

(1.1)

For strong external fields, the dependence of the response on the strength of the forces can be expressed by a power expansion in the forces, which then – in addition to the linear parameters χ – defines nonlinear field-dependent materials properties χ (nl) (F ), where χ (nl) (F ) = χ + χ (1) F + . . . .

(1.2)

In general, the class of materials properties that describe the response to externally applied forces have tensor character. The rank of the property tensor χ de-

The Elements

Subdivisions B(a) of the Tables These parts deal with the crystallographic properties. Here you will find the crystal system and the Bravais lattice in which the element is stable in its standard state; the structure type in which the element crystallizes; the lattice constants a, b, c, α, β, γ (symmetry reduces the number of independent lattice constants); the space group; the Schoenflies symbol; the Strukturbericht type; the Pearson symbol; the number A of atoms per cell; the coordination number; and the shortest interatomic distance between atoms in the solid state and in the liquid state. Basic concepts of crystallography are explained in Chapt. 1.3. Subdivisions B(b) of the Tables These parts cover the mechanical properties. At the top of the table, you will find the density of the material in the solid state ( s ) and in the liquid state ( l ), and the molar volume Vmol in the solid state. Here, one mole is the amount of substance which contains as many elementary particles (atoms or molecules) as there are atoms in 0.012 kg of the carbon isotope with a relative atomic mass of 12. This number of particles is called Avogadro’s number and is approximately equal to

6.022 × 1023 . The next three rows present the viscosity η, the surface tension, and its temperature dependence, in the liquid state. The next properties are the coefficient of linear thermal expansion α and the sound velocity, both in the solid and in the liquid state. A number of quantities are tabulated for the presentation of the elastic properties. For isotropic materials, we list the volume compressibility κ = −(1/V )( dV/ dP), and in some cases also its reciprocal value, the bulk modulus (or compression modulus); the elastic modulus (or Young’s modulus) E; the shear modulus G; and the Poisson number (or Poisson’s ratio) µ. Hooke’s law, which expresses the linear relation between the strain ε and the stress σ in terms of Young’s modulus, reads σ = Eε. For monocrystalline materials, the components of the elastic compliance tensor s and the components of the elastic stiffness tensor c are given. The elastic compliance tensor s and the elastic stiffness tensor c are both defined by the generalized forms of Hooke’s law, σ = cε and ε = sσ. At the end of the list, the tensile strength, the Vickers hardness, and the Mohs hardness are given for some elements. Subdivisions B(c) of the Tables The thermal and thermodynamic properties are tabulated in these subdivisions of the tables. The properties tabulated are:

• • • • • • • • •

The thermal conductivity λ. The molar heat capacity at constant pressure, c p . The standard entropy S0 , that is, the molar entropy of the element at 298.15 K and 100 kPa. The enthalpy difference H298 − H0 , that is, the difference between the molar enthalpies of the element at 298.15 K and at 0 K. The melting temperature Tm . The molar enthalpy change ∆Hm and molar entropy change ∆Sm at the melting temperature. The relative volume change ∆Vm = (Vl − Vs )/Vl on melting. The boiling temperature Tb . The molar enthalpy change ∆Hb of boiling, and, for some elements, the molar enthalpy of sublimation.

In addition, the critical temperature Tc , the critical pressure pc , the critical density c , the triple-point temperature Ttr , and the triple-point pressure ptr are given for some elements. For the element helium, the table also contains data for the λ point, at which liquid helium passes from the normal-fluid phase helium I (above the λ point) to the superfluid phase helium II (below the λ point), for 4 He and 3 He.

47

Part 2 1.2

pends on the rank of the external force F and that of the observable O considered. In the case of Ohm’s law, j = σ E, in which the current density j and the electric field strength E are vectors, the conductivity tensor σ is of rank 2; in the case of the generalized Hooke’s law, ε = sσ, the strain tensor ε and the stress tensor σ both are of rank 2, so that the elastic compliance tensor s is of rank 4. A vector can be considered as a tensor of rank 1, and a scalar, correspondingly, as a tensor of rank 0. A second-rank tensor, such as the electrical conductivity σ, in general has nine components in threedimensional space; a tensor of rank n in general has 3n components in three-dimensional space. Symmetry, however, of both the underlying crystal lattice and the physical phenomenon (for example, action = reaction), may reduce the number of independent nonvanishing components in the tensor. The tensor components reflect the crystal symmetry by being invariant under those orthogonal transformations which are elements of the point group of the crystal. In cubic crystals, for example, physical properties described by tensors of rank 2 are characterized by only one nonvanishing tensor component. Therefore cubic crystals are isotropic with respect to their electrical conductivity, their heat conductivity, and their dielectric properties.

1.2 Description of Properties Tabulated

48

Part 2

The Elements

Part 2 1.2

Throughout Sect. 2.1, temperature is measured in units of kelvin (K), the unit of thermodynamic temperature. 1 K is defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. To convert data given in kelvin into degrees Celsius (◦ C), the following equation can be used: T(◦ C) = (T(K) − 273.15 K)(◦ C/K) . This can be expressed in words as follows: the Celsius scale is shifted towards higher temperatures by 273.15 K relative to the kelvin scale, such that the temperature 273.15 K becomes 0 ◦ C and the temperature 0 K becomes − 273.15 ◦ C. To convert data given in kelvin into degrees Fahrenheit (◦ F), the following equation can be used: T(◦ F) = (9/5)(T(K) − 273.15 K)(◦ F/K) + 32 ◦ F . This can be expressed approximately in words as follows: the Fahrenheit scale is shifted relative to the kelvin scale and also differs by a scaling so that its degrees are smaller than those of the kelvin scale by nearly a factor of 2. Subdivisions B(d) of the Tables These subdivisions of the tables present data on the electronic, electromagnetic, and optical properties of the elements. Data are given for the following:

• • • • • • • • • • • •

•

The electrical resistivity ρs in the solid state, and its temperature and pressure dependence. The electrical resistivity ρl in the liquid state, and the resistivity ratio ρl /ρs at the melting temperature. The critical temperature Tcr and critical field strength Hcr for superconductivity. The electronic band gap ∆E. The Hall coefficient R, together with the range of magnetic field strength B over which it was measured. The thermoelectric coefficient. The electronic work function. The thermal work function. The intrinsic charge carrier concentration. The electron and hole mobilities. The static dielectric constant ε of the element in the solid state, and in some cases also in the liquid state. The molar magnetic susceptibility χmol and the mass magnetic susceptibility χmass of the element in the solid state, and in some cases also in the liquid state. The susceptibilities are given in the definitions of both the SI system and the cgs system (see below). The refractive index n in the solid and liquid states.

The magnetic susceptibility is the parameter that describes the response of the material to an externally applied magnetic field H, as measured by the observable magnetization M, in the linear regime, via M = χH. Three different forms of the term “magnetization” are in use, depending on the specific application: first, the volume magnetization Mvol , equal to the magnetic dipole moment divided by the volume of the sample; second, the molar magnetization, or magnetization related to the number of particles, Mmol , equal to the magnetic dipole moment divided by the number of particles measures in moles; and third, the mass magnetization Mmass , equal to the magnetic dipole moment divided by the mass of the sample. Correspondingly, there are three different magnetic susceptibilities. The volume susceptibility χvol is a dimensionless number because in this case M and H are both measured in the same units, namely A/m in the SI system and gauss in the cgs system. The dimensionless character of χvol might be the reason why, in physics textbooks, mostly only this susceptibility is mentioned. The other two susceptibilities, the molar susceptibility χmol and the mass susceptibility χmass , are more useful for practical applications. In both the SI system and the cgs system, the molar susceptibility is measured in units of cm3 /mol, and the mass susceptibility is measured in units of cm3 /g. In this Handbook, data are given for the molar and mass susceptibilities. Although susceptibilities have the same dimensions in the SI and cgs systems, the numerical values in the cgs system are smaller than those in the SI system by a factor of 4π. This is due to the different definitions of the quantities dipole moment and magnetization in the two systems. The difference can be seen most clearly in the general relations between the magnetization M and the field strengths B and H in the two systems. In the SI system, this relation reads B = µ0 (H + M), whereas in the cgs system, it reads B = H + 4πM. Because of this difference, the magnetic-susceptibility data in Sect. 2.1.5 are given for both the SI and the cgs definitions.

2.1.2.3 Parts C of the Tables Parts C of the tables present crystallographic data for allotropic and high-pressure modifications of the elements. The left-hand columns contain data for allotropic modifications that are stable at a pressure of 100 kPa over the temperature ranges indicated, and the right-hand columns contain data for modifications stable at higher pressures as indicated. The modifications stable at 100 kPa are denoted by Greek letters

The Elements

2.1.2.4 Parts D of the Tables Parts D of the tables contain data on ionic radii determined from crystal structures. The first row lists the elements, and the second row lists the positive and negative ions for which data are given. The remaining rows give the ionic radii of these ions for the most common coordination numbers.

2.1.3 Sources Most of the data presented here have been taken from Landolt–Börnstein [1.1]. Additional data have been

taken from the D’Ans-Lax series [1.2] and the CRC Handbook of Chemistry and Physics [1.3].

2.1.4 Tables of the Elements in Different Orders Table 2.1-1 The elements ordered by their names Element

Symbol

Actinium Aluminium Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Bohrium Boron Bromine Cadmium Calcium Californium Carbon Cerium Cesium Chlorine Chromium Cobalt Copper Curium Darmstadtium Dubnium Dysprosium Einsteinium Erbium Europium

Ac Al Am Sb Ar As At Ba Bk Be Bi Bh B Br Cd Ca Cf C Ce Cs Cl Cr Co Cu Cm Ds Db Dy Es Er Eu

Atomic Number

Page

89 13 95 51 18 33 85 56 97 4 83 107 5 35 48 20 98 6 58 55 17 24 27 29 96 110 105 66 99 68 63

84 78 151 98 128 98 118 68 151 68 98 124 78 118 73 68 151 88 142 59 118 114 135 65 151 139 105 142 151 142 142

Element

Symbol

Gold Hafnium Hassium Helium Holmium Hydrogen Indium Iodine Iridium Iron Krypton Lanthanum Lawrencium Lead Lithium Lutetium Magnesium Manganese Meitnerium Mendelevium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen

Au Hf Hs He Ho H In I Ir Fe Kr La Lr Pb Li Lu Mg Mn Mt Md Hg Mo Nd Ne Np Ni Nb N No Os O

Atomic Number

Page

79 72 108 2 67 1 49 53 77 26 36 57 103 82 3 71 12 25 109 101 80 42 60 10 93 28 41 7 102 76 8

65 94 131 54 142 54 78 118 135 131 128 84 151 88 59 142 68 124 135 151 73 114 142 128 151 139 105 98 151 131 108

Element

Symbol

Praseodymium Promethium Protactinium Radium Radon Rhenium Rhodium Roentgenium Rubidium Ruthenium Rutherfordium Samarium Scandium Seaborgium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten Uranium

Pr Pm Pa Ra Rn Re Rh Rg Rb Ru Rf Sm Sc Sg Se Si Ag Na Sr S Ta Tc Te Tb Tl Th Tm Sn Ti W U

49

Part 2 1.4

in front of the chemical symbol of the element (normally starting with α for the modification stable over the lowest temperature range), and the high-pressure modifications are denoted by Roman numerals after the chemical symbol. In these parts of the tables, “RT” stands for “room temperature”, and “RTP” stands for “room temperature and standard pressure”, i. e. 100 kPa.

1.4 Tables of the Elements in Different Orders

Atomic Number

Page

59 61 91 88 86 75 45 111 37 44 104 62 21 106 34 14 47 11 38 16 73 43 52 65 81 90 69 50 22 74 92

142 142 151 68 128 124 135 59 131 94 142 84 114 108 88 65 59 68 108 105 124 108 142 78 151 142 88 94 114 151

50

Part 2

The Elements

Part 2 1.4

Table 2.1-1 The elements ordered by their names, cont. Element

Symbol

Fermium Fluorine Francium Gadolinium Gallium Germanium

Fm F Fr Gd Ga Ge

a

Atomic Number

Page

100 9 87 64 31 32

151 118 59 142 78 88

Element

Symbol

Palladium Phosphorus Platinum Plutonium Polonium Potassium

Pd P Pt Pu Po K

Atomic Number

Page

46 15 78 94 84 19

139 98 139 151 108 59

Atomic Number 64 32 1 2 80 72 67 108 53 49 77 19 36 57 3 103 71 101 12 25 42 109 7 11 41 60 10 28 102 93 8 76 15 91 82 46 61

Page

Element

Symbol

Vanadium Xenon Ytterbium Yttrium Zinc Zirconium

V Xe Yb Y Zn Zr

Element

Symbol Po Pr Pt Pu Ra Rb Re Rf Rg Rh Rn Ru S Sb Sc Se Sg Si Sm Sn Sr Ta Tb Tc Te Th Ti Tl Tm U V W Xe Y Yb Zn Zr

Atomic Number

Page

23 54 70 39 30 40

105 128 142 84 73 94

Atomic Number 84 59 78 94 88 37 75 104 111 45 86 44 16 51 21 34 106 14 62 50 38 73 65 43 52 90 22 81 69 92 23 74 54 39 70 30 40

Page

See Tungsten.

Table 2.1-2 The elements ordered by their chemical symbols Element Actinium Silver Aluminium Americium Argon Arsenic Astatine Gold Boron Barium Beryllium Bohrium Bismuth Berkelium Bromine Carbon Calcium Cadmium Cerium Californium Chlorine Curium Cobalt Chromium Cesium Copper Dubnium Darmstadtium Dysprosium Erbium Einsteinium Europium Fluorine Iron Fermium Francium Gallium

Symbol Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br C Ca Cd Ce Cf Cl Cm Co Cr Cs Cu Db Ds Dy Er Es Eu F Fe Fm Fr Ga

Atomic Number 89 47 13 95 18 33 85 79 5 56 4 107 83 97 35 6 20 48 58 98 17 96 27 24 55 29 105 110 66 68 99 63 9 26 100 87 31

Page 84 65 78 151 128 98 118 65 78 68 68 124 98 151 118 88 68 73 142 151 118 151 135 114 59 65 105 139 142 142 151 142 118 131 151 59 78

Element Gadolinium Germanium Hydrogen Helium Mercury Hafnium Holmium Hassium Iodine Indium Iridium Potassium Krypton Lanthanum Lithium Lawrencium Lutetium Mendelevium Magnesium Manganese Molybdenum Meitnerium Nitrogen Sodium Niobium Neodymium Neon Nickel Nobelium Neptunium Oxygen Osmium Phosphorus Protactinium Lead Palladium Promethium

Symbol Gd Ge H He Hg Hf Ho Hs I In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb Nd Ne Ni No Np O Os P Pa Pb Pd Pm

142 88 54 54 73 94 142 131 118 78 135 59 128 84 59 151 142 151 68 124 114 135 98 59 105 142 128 139 151 151 108 131 98 151 88 139 142

Polonium Praseodymium Platinum Plutonium Radium Rubidium Rhenium Rutherfordium Roentgenium Rhodium Radon Ruthenium Sulfur Antimony Scandium Selenium Seaborgium Silicon Samarium Tin Strontium Tantalum Terbium Technetium Tellurium Thorium Titanium Thallium Thulium Uranium Vanadium Tungsten Xenon Yttrium Ytterbium Zinc Zirconium

108 142 139 151 68 59 124 94 135 128 131 108 98 84 108 114 88 142 88 68 105 142 124 108 151 94 78 142 151 105 114 128 84 142 73 94

The Elements

1.4 Tables of the Elements in Different Orders

Element

Symbol

Atomic Number

Page

Element

Symbol

Atomic Number

Page

Element

Symbol

Atomic Number

Page

Hydrogen

H

1

54

Strontium

Sr

38

68

Rhenium

Re

75

124

Helium

He

2

54

Yttrium

Y

39

84

Osmium

Os

76

131

Lithium

Li

3

59

Zirconium

Zr

40

94

Iridium

Ir

77

135

Beryllium

Be

4

68

Niobium

Nb

41

105

Platinum

Pt

78

139 65

Boron

B

5

78

Molybdenum

Mo

42

114

Gold

Au

79

Carbon

C

6

88

Technetium

Tc

43

124

Mercury

Hg

80

73

Nitrogen

N

7

98

Ruthenium

Ru

44

131

Thallium

Tl

81

78

Oxygen

O

8

108

Rhodium

Rh

45

135

Lead

Pb

82

88

Fluorine

F

9

118

Palladium

Pd

46

139

Bismuth

Bi

83

98

Neon

Ne

10

128

Silver

Ag

47

65

Polonium

Po

84

108

Sodium

Na

11

59

Cadmium

Cd

48

73

Astatine

At

85

118

Magnesium

Mg

12

68

Indium

In

49

78

Radon

Rn

86

128

Aluminium

Al

13

78

Tin

Sn

50

88

Francium

Fr

87

59

Silicon

Si

14

88

Antimony

Sb

51

98

Radium

Ra

88

68

Phosphorus

P

15

98

Tellurium

Te

52

108

Actinium

Ac

89

84

Sulfur

S

16

108

Iodine

I

53

118

Thorium

Th

90

151

Chlorine

Cl

17

118

Xenon

Xe

54

128

Protactinium

Pa

91

151

Argon

Ar

18

128

Cesium

Cs

55

59

Uranium

U

92

151

Potassium

K

19

59

Barium

Ba

56

68

Neptunium

Np

93

151

Calcium

Ca

20

68

Lanthanum

La

57

84

Plutonium

Pu

94

151

Scandium

Sc

21

84

Cerium

Ce

58

142

Americium

Am

95

151

Titanium

Ti

22

94

Praseodymium

Pr

59

142

Curium

Cm

96

151

Vanadium

V

23

105

Neodymium

Nd

60

142

Berkelium

Bk

97

151

Chromium

Cr

24

114

Promethium

Pm

61

142

Californium

Cf

98

151

Manganese

Mn

25

124

Samarium

Sm

62

142

Einsteinium

Es

99

151 151

Iron

Fe

26

131

Europium

Eu

63

142

Fermium

Fm

100

Cobalt

Co

27

135

Gadolinium

Gd

64

142

Mendelevium

Md

101

151

Nickel

Ni

28

139

Terbium

Tb

65

142

Nobelium

No

102

151

Copper

Cu

29

65

Dysprosium

Dy

66

142

Lawrencium

Lr

103

151

Zinc

Zn

30

73

Holmium

Ho

67

142

Rutherfordium

Rf

104

94

Gallium

Ga

31

78

Erbium

Er

68

142

Dubnium

Db

105

105

Germanium

Ge

32

88

Thulium

Tm

69

142

Seaborgium

Sg

106

114

Arsenic

As

33

98

Ytterbium

Yb

70

142

Bohrium

Bh

107

124

Selenium

Se

34

108

Lutetium

Lu

71

142

Hassium

Hs

108

131

Bromine

Br

35

118

Hafnium

Hf

72

94

Meitnerium

Mt

109

135

Krypton

Kr

36

128

Tantalum

Ta

73

105

Darmstadtium

Ds

110

139

Rubidium

Rb

37

59

Tungsten

W

74

114

Roentgenium

Rg

111

Part 2 1.4

Table 2.1-3 The elements ordered by their atomic numbers

51

52

Part 2

The Elements

Part 2 1.4

Table 2.1-4 The elements ordered according to the Periodic Table Page Elements of the first period 1 Hydrogen

1 Deuterium

54 1 Tritium

2 Helium-4

2 Helium-3

19 Potassium

37 Rubidium

55 Cesium

79 Gold

111 Roentgenium

20 Calcium

38 Strontium

Elements of Group IA 3 Lithium

11 Sodium

59 87 Francium

Elements of Group IB 29 Copper

47 Silver

65

Elements of Group IIA 4 Beryllium

12 Magnesium

68 56 Barium

88 Radium

Elements of Group IIB 30 Zinc

48 Cadmium

73 80 Mercury

Elements of Group IIIA 5 Boron

13 Aluminium

78 31 Gallium

49 Indium

57 Lanthanum

89 Actinium

32 Germanium

50 Tin

72 Hafnium

104 Rutherfordium

33 Arsenic

51 Antimony

73 Tantalum

105 Dubnium

81 Thallium

Elements of Group IIIB 21 Scandium

39 Yttrium

84

Elements of Group IVA 6 Carbon

14 Silicon

88 82 Lead

Elements of Group IVB 22 Titanium

40 Zirconium

94

Elements of Group VA 7 Nitrogen

15 Phosphorus

98 83 Bismuth

Elements of Group VB 23 Vanadium

41 Niobium

105

Elements of Group VIA 8 Oxygen

16 Sulfur

108 34 Selenium

52 Tellurium

84 Polonium

74 Tungsten

106 Seaborgium

35 Bromine

53 Iodine

75 Rhenium

107 Bohrium

36 Krypton

54 Xenon

76 Osmium

108 Hassium

77 Iridium

109 Meitnerium

46 Palladium

78 Platinum

110 Darmstadtium

58 Cerium

59 Praseodymium

60 Neodymium

61 Promethium

62 Samarium

63 Europium

64 Gadolinium

65 Terbium

66 Dysprosium

67 Holmium

68 Erbium

69 Thulium

70 Ytterbium

71 Lutetium

90 Thorium

91 Protactinium

92 Uranium

93 Neptunium

94 Plutonium

95 Americium

96 Curium

97 Berkelium

98 Californium

99 Einsteinium

100 Fermium

101 Mendelevium

102 Nobelium

103 Lawrencium

Elements of Group VIB 24 Chromium

42 Molybdenum

114

Elements of Group VIIA 9 Fluorine

17 Chlorine

118 85 Astatine

Elements of Group VIIB 25 Manganese

43 Technetium

124

Elements of Group VIIIA 10 Neon

18 Argon

128 86 Radon

Elements of Group VIII(1) 26 Iron

44 Ruthenium

131

Elements of Group VIII(2) 27 Cobalt

45 Rhodium

135

Elements of Group VIII(3) 28 Nickel

139

Lanthanides

142

Actinides

151

The Elements

1.4 Tables of the Elements in Different Orders

Part 2 1.4

Table 2.1-5 Periodic Table of the elements

Periodic Table of the Elements IUPAC Notation CAS Notation Atomic Number Element Symbol

18 VIIIA

2

He

Unstable Nuclei

Main Groups 1 IA

1

2 IIA

13 IIIA

14 IVA

15 VA

16 VIA

17 VIIA

2

H

3

4

Li

11

19

37

55

87

12

Na

38

Rb

56

Cs

88

Fr

13

Mg

20

K

5

Be

31

Ca

49

Sr

14

Al

32

Ga

50

In

81

Ba

6

B

82

Tl

7

C

15

Si

51

Sn

83

Pb

84

Bi

35

Se

52

Sb

17

S

34

As

9

O

16

P

33

Ge

8

N

53

Te

85

Po

10

F

18 VIIIA

Shells

He

K

Ne

K–L

Ar

K–L–M

Kr

–L–M–N

Xe

–M–N–O

Rn

–N–O–P

18

Cl

36

Br

54

I

86

At

–O–P–Q

Ra

Subgroups 3 IIIB

21

39

57

89

4 IVB

22

Sc

40

Y

72

La

5 VB

23

Ti

41

Zr

73

Hf

104

Ac

V Nb Ta

105

Rf

Db

6 VIB

24

Cr

42

Mo

74

W

106

Sg

7 VIIB

8 VIII (1)

25

26

Mn

43

75

44

Tc

76

Re

107

27

Fe

45

Ru

Co Rh

77

Os

108

Bh

9 VIII (2)

Ir

109

Hs

Mt

10 VIII (3)

28

46

Ni Pd

78

Pt

110

Ds

11 IB

29

47

79

30

Cu

48

Ag

80

Au

111

12 IIB

Shells

Zn

–L–M–N

Cd

–M–N–O

Hg

–N–O–P

112

Rg

–O–P–Q

Lanthanides (Shells –N–O–P) 58

59

90

91

Ce

Pr

60

Nd

61

Pm

62

Sm

63

Eu

64

65

66

67

68

69

70

71

96

97

98

99

100

101

102

103

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Actinides (Shells –O–P–Q)

Th

Pa

92

U

93

Np

94

Pu

95

Am

Cm

Bk

Cf

Es

Fm

Md

53

No

Lr

54

Part 2

The Elements

Part 2 1.5

2.1.5 Data 2.1.5.1 Elements of the First Period Table 2.1-6A Elements of the first period (hydrogen and helium). Atomic, ionic, and molecular properties Element name

Hydrogen

Special name Chemical symbol Atomic number Z

Hydrogen H 1

Helium Deuterium Tritium 2 H or D 3 H or T 1 1

Helium 4 Helium 3 4 He 3 He 2 2 Units Remarks

Characteristics

Radioactive

Half-life

12.32

Relative atomic mass A (atomic weight)

1.00794(7)

2.01408

Abundance in lithosphere

1400 × 10−6 1.4 × 10−4

Abundance in sea

110 × 10−3

Atomic radius rcov

30

3.01605

y 4.002602(2) 4.2 × 10−7

Mass ratio Mass ratio

Atomic radius rmet

140

Covalent radius

pm

Metallic radius, CN a = 12

pm

van der Waals radius

Atomic radius rvdW

140

Electron shells

K

K

K

K

K

Electronic ground state Electronic configuration

2S 1/2 1s1

2S 1/2 1s1

2S 1/2 1s1

1S 0 1s2

1S 0 1s2

Oxidation states

1−, 1+

Electron affinity

0.754

0.19

Electronegativity χA

2.20

3.20

1st ionization energy

13.59844

24.58741

eV

54.41778

eV

2nd ionization energy Standard electrode potential E 0

0.00000

140

pm

eV Allred and Rochow

V

Reaction 2H+ + 2e− = H2

Molecular form in gaseous state H2 Internuclear distance in molecule

74.166

pm

Dissociation energy

4.475

eV

a

Coordination number.

Extrapolated to T = 0 K

The Elements

1.5 Data

high-pressure modifications, see Table 2.1-6C) Element name

Hydrogen

Special name Chemical symbol Atomic number Z

Hydrogen H 1

Helium

State

H2 at 4.2 K

At 1.5 K

Crystal system, Bravais lattice

hex

hex

Structure type

Mg

Mg

Lattice constant a

377.1

357.7

Lattice constant c

615.6

584.2

Deuterium 2 H or D 1

Tritium 3 H or T 1

Helium 4 4 He 2

Helium 3 3 He 2 Units

Space group

P63 /mmc

P63 /mmc

Schoenflies symbol

4 D6h

4 D6h

Strukturbericht type

A3

AQ3

Pearson symbol

hP2

hP2

Number A of atoms per cell

2

2

Coordination number

12

12

Shortest interatomic distance, solid

357

pm

pm

Remarks

Part 2 1.5

Table 2.1-6B(a) Elements of the first period (hydrogen and helium). Crystallographic properties (for allotropic and

55

56

Part 2

The Elements

Part 2 1.5

Table 2.1-6B(b) Elements of the fist period (hydrogen and helium). Mechanical properties Element name

Hydrogen

Special name Chemical symbol Atomic number Z

Hydrogen H 1

Deuterium 2 H or D 1

State

H2

D2

Density , liquid Density , gas

Helium

0.162 0.0899 × 10−3 0.0032 a

Molar volume Vmol , gas 13.26 Viscosity η, gas

8.67

Sound velocity, gas

1237

Sound velocity, liquid

1340

Elastic modulus E

0.2

Elastic compliance s11

2930 (4.2 K)

1400 (4.2 K)

Elastic compliance s33

2000 (4.2 K)

995 (4.2 K)

Elastic compliance s44

9090 (4.2 K)

4350 (4.2 K)

Tritium 3 H or T 1

Helium 4 4 He 2

Helium 3 3 He 2 Remarks

g/cm3

Near Tm

0.1785 × 10−3

g/cm3

At 273 K b

32.07

cm3 /mol

0.260 0.0031 a

Units

969 (STP) 0.1

mPa s

At 293 K, 101 kPa

m/s

STP

m/s

At Tm , 12 MHz

GPa

Solid state, estimated

+226 × 103 (1.6 K)

+202 × 103 (0.4 K)

1/TPa

+46 × 103 (1.6 K)

+108 × 103 (0.4 K)

1/TPa

−107 × 103

−91.6 × 103 (0.4 K)

1/TPa

Elastic compliance s12

−1240 (4.2 K) −490 (4.2 K)

Elastic compliance s13

−166 (4.2 K)

−81 (4.2 K)

Elastic stiffness c11

0.042 (4.2 K)

0.82 (4.2 K)

Elastic stiffness c33

0.51 (4.2 K)

1.02 (4.2 K)

Elastic stiffness c44

0.11 (4.2 K)

0.23 (4.2 K)

+21.7 × 10−3 (1.6 K) +9.2 × 10−3 (0.4 K)

Elastic stiffness c12

0.18 (4.2 K)

0.29 (4.2 K)

+28.1 × 10−3 (1.6 K) +16.4 × 10−3 (0.4 K) GPa

Elastic stiffness c13

0.05 (4.2 K)

Solubility in water αW

0.0178 b

a b

At 25 K. 101.3 kPa H2 pressure.

(1.6 K)

+31.1 × 10−3 (1.6 K) +20.0 × 10−3 (0.4 K) GPa

0.0086

GPa

The Elements

1.5 Data

Element name

Hydrogen

Special name Chemical symbol Atomic number Z

Hydrogen H 1

State

H2 gas

He gas

Thermal conductivity λ

0.171

Molar heat capacity c p

14.418

Standard entropy

S0

Helium Deuterium Tritium 2 H or D 3 H or T 1 1

Helium 4 4 He 2

Helium 3 3 He 2 Units

Remarks

143.0 × 10−3

W/(m K)

At 300 K

20.786

J/(mol K)

At 298 K

130.680

126.152

J/(mol K)

At 298 K and 100 kPa

Enthalpy difference H298 − H0

8.4684

6.1965

kJ/mol

At 298 K

Melting temperature Tm

13.81

0.95 a

K

Enthalpy change ∆Hm Boiling temperature T b Enthalpy change ∆H b

18.65

20.65

23.65

25.05

0.12 20.30

0.021 4.215

kJ/mol 3.2

K

0.46

0.082

kJ/mol

Sublimation enthalpy

0.376

0.060

kJ/mol

Critical temperature Tc

33.2

38.55

5.23

K

Critical pressure pc

1.297

1.645

0.229

MPa

Critical density c

0.03102

69.3 × 10−3

g/cm3

Triple-point temperature Ttr

14.0

b

K

Triple-point pressure ptr

7.2

λ point a b

At 2.6 MPa. He does not have a triple point.

39.95

kPa 2.184

0.0027

K

At 0 K

Part 2 1.5

Table 2.1-6B(c) Elements of the first period (hydrogen and helium). Thermal and thermodynamic properties

57

58

Part 2

The Elements

Part 2 1.5

Table 2.1-6B(d) Elements of the first period (hydrogen and helium). Electronic, electromagnetic, and optical properties Element name

Hydrogen

Special name Chemical symbol Atomic number Z

Hydrogen H 1

Helium

State Characteristics Dielectric constant (ε − 1), gas Dielectric constant ε, liquid Dielectric constant ε, solid Molar magnetic susceptibility χmol , gas (SI system) Molar magnetic susceptibility χmol , gas (cgs system) Mass magnetic susceptibility χmass , liquid (SI system) Mass magnetic susceptibility χmass , liquid (cgs system) Mass magnetic susceptibility χmass , gas (SI system) Refractive index (n − 1), gas

H2 gas Light gas +264 × 10−6 1.225

He gas Noble gas +68 × 10−6 1.048 (3.15 K)

−50.1 × 10−6

−25.4 × 10−6

cm3 /mol At 295 K

−3.99 × 10−6

−2.02 × 10−6

cm3 /mol At 295 K

Refractive index n, liquid

Deuterium Tritium Helium 4 2 H or D 3 H or T 4 He 1 1 2

Helium 3 3 He 2 Units

Remarks

At 273 K At 20.30 K

−68.4 × 10−6

cm3 /mol At 20.3 K

−5.44 × 10−6

cm3 /mol At 20.3 K

−25 × 10−6

−5.9 × 10−6

132 × 10−6

36 × 10−6

1.112

1.026 (3.7 K)

cm3 /g

At 295 K At 273.15 K, 101 × 105 Pa, λ = 589.3 nm λ = 589.3 nm

Table 2.1-6C Elements of the first period (hydrogen and helium). Allotropic and high-pressure modifications Element

Hydrogen

Modification

α-H (H2 )

β-H (H2 )

α-He

Helium β-He

γ -He

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, fc Cu 533.4

cub, bc W 4110

< 1.25 K

< 13.81 K

hex, cp Mg 357.7 584.2 P63 /mmc 4 D6h A3 hP2 2 12 357 < 0.95 K

cub, fc Cu 4240

Fm3m Oh5 A1 cF4 4 12

hex, cp Mg 377.1 615.6 P63 /mmc 4 D6h A3 hP2 2 12

Fm3m Oh5 A1 cF4 4 12 300 1.6 K; 0.125 GPa

Im3m Oh9 A2 cI2 2 8 356 1.73 K; 0.03 GPa

Units

pm pm

pm

Element name

Lithium

Sodium

Potassium

Rubidium

Cesium

Francium

Chemical symbol Atomic number Z

Li 3

Na 11

K 19

Rb 37

Cs 55

Fr 87 Units

Characteristics

Remarks

Radioactive

Relative atomic mass A (atomic weight)

6.941(2)

22.989770(2)

39.0983(1)

85.4678(3)

132.90545(2)

Abundance in lithosphere

65 × 10−6

28 300 × 10−6

25 900 × 10−6

280 × 10−6

3.2 × 10−6

Abundance in sea

0.18 × 10−6

10 770 × 10−6

380 × 10−6

0.12 × 10−6

4 × 10−10

Atomic radius rcov

123

157

203

216

253

pm

Covalent radius

Atomic radius rmet

156

192

238

250

272

pm

Metallic radius, CN = 12

Atomic radius ros

158.6

171.3

216.2

228.7

251.8

pm

Outer-shell orbital radius

Atomic radius rvdW

180

230

280

244

262

pm

van der Waals radius

Electron shells

KL

KLM

–LMN

–MNO

–NOP

–OPQ

Electronic ground state

2S 1/2

2S 1/2

2S 1/2

2S 1/2

2S 1/2

2S 1/2

Electronic configuration

[He]2s1

[Ne]3s1

[Ar]4s1

[Kr]5s1

[Xe]6s1

[Rn]7s1

Oxidation states

1+

1+

1+

1+

1+

1+

Electron affinity

0.618

0.548

0.501

0.486

0.472

0.46

Electronegativity χA

0.97

1.01

0.91

0.89

0.86

(0.86)

1st ionization energy

5.39172

5.13908

4.34066

4.17713

3.89390

4.0727

2nd ionization energy

75.64018

47.2864

31.63

27.285

23.15745

3rd ionization energy

122.45429

71.6200

45.806

40

98.91

60.91

52.6

−2.71

−2.931

−2.98

Standard electrode potential E 0

−3.040

Mass ratio Mass ratio

244.7

eV Allred and Rochow eV eV eV eV

−2.92

V

Reaction type Li+ + e− = Li

The Elements 1.5 Data 59

Part 2 1.5

4th ionization energy

[223]

2.1.5.2 Elements of the Main Groups and Subgroup I to IV

Table 2.1-7A Elements of Group IA (CAS notation), or Group 1 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-7D for ionic radii)

60

Part 2

The Elements

Part 2 1.5

Table 2.1-7B(a) Elements of Group IA (CAS notation), or Group 1 (new IUPAC notation). Crystallographic properties

(see Table 2.1-7C for allotropic and high-pressure modifications) Element name

Lithium

Sodium

Potassium Rubidium

Cesium

Francium

Chemical symbol Atomic number Z

Li 3

Na 11

K 19

Cs 55

Fr 87

Modification

β-Li

β-Na

Crystal system, Bravais lattice

cub, bc

cub, bc

cub, bc

cub, bc

cub, bc

Structure type

W

W

W

W

W

Lattice constant a

350.93

420.96

532.1

570.3

614.1

Space group

Im3m

Im3m

Im3m

Im3m

Im3m

Rb 37

Units Remarks Cs -I

Schoenflies symbol

Oh9

Oh9

Oh9

Oh9

Oh9

Strukturbericht type

A2

A2

A2

A2

A2

Pearson symbol

cI2

cI2

cI2

cI2

cI2

Number A of atoms per cell

2

2

2

2

2

Coordination number

8

8

8

8

8

Shortest interatomic distance, solid

303

371

462

487

524

Shortest interatomic distance, liquid

497 (313 K)

pm

pm pm

Table 2.1-7B(b) Elements of Group IA (CAS notation), or Group 1 (new IUPAC notation). Mechanical properties Element name

Lithium

Sodium

Potassium

Rubidium

Cesium

Francium

Chemical symbol Atomic number Z

Li 3

Na 11

K 19

Rb 37

Cs 55

Fr 87

Density , solid

0.532

0.970

0.862

1.532

1.87

2.410

Density , liquid

0.508 (453 K)

0.927

0.827

1.470

1.847

Molar volume Vmol

13.00

23.68

45.36

55.79

70.96

Viscosity η, liquid

0.566 (473 K)

0.565 (416 K)

0.64

0.52

Surface tension, liquid

0.396

0.193

0.116

0.092

−0.05 × 10−3

−0.06 × 10−3

70.6 × 10−6

83 × 10−6

Units

Temperature coefficient 56 × 10−6

Sound velocity, liquid

2395 (371 K)

mPa s 0.060

N/m

−0.046 × 10−3

N/(m K)

90 × 10−6

97 × 10−6

1/K

At 298 K

1260

967

m/s

At Tm , At 12 MHz

Sound velocity, solid, transverse

2820

1620

1230

770

590

m/s

Sound velocity, solid, longitudinal

6030

3310

2600

1430

1090

m/s

Compressibility κ

8.93 × 10−5

13.4 × 10−5

23.7 × 10−5

33.0 × 10−5

0.75 × 10−5

1/MPa

Elastic modulus E

11.5

6.80

3.52

2.35

1.69

GPa

Shear modulus G

4.24

2.94

1.28

0.91

0.65

GPa

Poisson number µ

0.36

0.34

0.35

0.29

0.30

Elastic compliance s11

315

549

1339

1330

1190 (280 K)

1/TPa

Elastic compliance s44

104

233

526

625

690 (280 K)

1/TPa

Elastic compliance s12

−144

−250

−620

−600

−450 (280 K)

1/TPa

Elastic stiffness c11

13.4

7.59

3.69

2.96

1.60 (280 K)

GPa

Elastic stiffness c44

9.6

4.30

1.90

1.60

1.44 (280 K)

GPa

Elastic stiffness c12

11.3

6.33

3.18

2.44

0.99 (280 K)

GPa

Tensile strength

0.6 0.37

0.15

Mohs hardness

Volume compressibility

MPa The Elements

Vickers hardness

Near Tm

cm3 /mol

0.6

1.5 Data 61

Part 2 1.5

Coefficient of linear thermal expansion α

g/cm3 9.25

Remarks

g/cm3

62

Part 2 1.5

Part 2 The Elements

Table 2.1-7B(c) Elements of Group IA (CAS notation), or Group 1 (new IUPAC notation). Thermal and thermodynamic

properties Element name

Lithium

Sodium

Potassium

Rubidium

Cesium

Francium

Chemical symbol Atomic number Z

Li 3

Na 11

K 19

Rb 37

Cs 55

Fr 87 Units

Remarks

Thermal conductivity λ

84.7

141

102.4

58.2

35.9

W/(m K)

At 300 K

Molar heat capacity c p

24.77

28.24

29.58

31.062

32.18

J/(mol K)

At 298 K

Standard entropy S0

29.120

51.300

64.680

76.776

85.230

101.00

J/(mol K)

At 298 K and 100 kPa

Enthalpy difference H298 − H0

4.6320

6.4600

7.0880

7.4890

7.7110

10.000

kJ/mol

Melting temperature Tm

300

K

453.69

370.87

336.86

312.47

301.59

Enthalpy change ∆Hm

3.0000

2.5970

2.3208

2.1924

2.0960

kJ/mol

Entropy change ∆Sm

6.612

7.002

6.890

7.016

6.950

J/(mol K)

Relative volume change ∆Vm

0.0151

0.027

0.0291

0.0228

0.0263

1620

1156

1040

970

947

147.7

75.7

Boiling temperature Tb Enthalpy change ∆Hb

(Vl − Vs )/Vl at Tm 950 (estimated)

K

99.2

79.1

67.7

kJ/mol

Critical temperature Tc

2500

2280

2010

K

Critical pressure pc

25.3

16.1

11.3

MPa

Critical density c

0.210

0.190

0.410

g/cm3

Table 2.1-7B(d) Elements of Group IA (CAS notation), or Group 1 (new IUPAC notation). Electronic, electromagnetic, and optical properties Element name

Lithium

Sodium

Potassium

Rubidium

Cesium

Francium

Chemical symbol Atomic number Z

Li 3

Na 11

K 19

Rb 37

Cs 55

Fr 87

Characteristics

Very reactive metal 85.5 48.9 × 10−4 −2.1 × 10−9 240 at Tm 1.68 −1.70 × 10−10 14.37

Reactive metal 42 54.6 × 10−4 −38.3 × 10−9

Soft, reactive metal 61 67.3 × 10−4 −69.7 × 10−9 129.7 1.56 −4.2 × 10−10 12

Soft, reactive metal 116 63.7 × 10−4 −62.9 × 10−9 220 1.612 −5.92 × 10−10 −8.26

Alkali metal 188 50.3 × 10−4 0.5 × 10−9 367 1.66 −7.8 × 10−10 0.2

Alkali metal

2.28

2.75

2.30

2.05

1.94

V

2.15

2.13

1.87

V

Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio at Tm Hall coefficient Ra Thermoelectric coefficient Electronic work function

1.44 −2.1 × 10−10

Units

Remarks

nΩ m 1/K 1/hPa nΩ m

Solid, at 293 K Solid Solid Liquid ρl /ρs at Tm At 300 K

m3 /(A s) µV/K

Thermal work function

2.39

Molar magnetic susceptibility χmol , solid (SI) Molar magnetic susceptibility χmol , solid (cgs) Mass magnetic susceptibility χmass , solid (SI) Mass magnetic susceptibility χmass , liquid (SI) Refractive index n, solid Refractive index n, liquid

178 × 10−6

201 × 10−6

261 × 10−6

214 × 10−6

364 × 10−6

cm3 /mol

At 295 K

14.2 × 10−6

16 × 10−6

20.8 × 10−6

17 × 10−6

29 × 10−6

cm3 /mol

At 295 K

25.6 × 10−6

8.8 × 10−6

6.7 × 10−6

2.49 × 10−6

2.8 × 10−6

cm3 /g

At 295 K

2.6 × 10−6

cm3 /g

0.024 (134 nm)

λ = 589.3 nm λ = 589.3 nm

B = 1–3 T The Elements 1.5 Data 63

Part 2 1.5

a

4.22 0.0045

64

Part 2 1.5

Part 2

Element

Lithium

Modification

α-Li

β-Li

γ -Li

Sodium α-Na

β-Na

Cesium Cs-I

Cs-II

Cs-III

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex, cp Mg 311.1 509.3 P63 /mmc 4 D6h A3 hP2 2 6+6 310

cub, bc W 309.3

cub, fc Cu

cub, bc W 420.96

cub, bc W 614.1

cub, fc Cu 598.4

cub, fc Cu 580.0

pm

Im3m Oh9 A2 cI2 2 8 303

Fm3m Oh5 A1 cF4 4 12 310

hex, cp Mg 376.7 615.4 P63 /mmc 4 D6h A3 hP2 2 12 377

Im3m Oh9 A2 cI2 2 8 371

Im3m Oh9 A2 cI2 2 8 524

Fm3m Oh5 A1 cF4 4 12 457

Fm3m Oh5 A1 cF4 4 12 410

pm

< 72 K

RT

< 36 K

RT

RTP

> 2.37 GPa

> 4.22 GPa

Units

Table 2.1-7D Elements of Group IA (CAS notation), or Group 1 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Lithium

Sodium

Potassium

Rubidium

Cesium

Francium

Ion

Li+

Na+

K+

Rb+

Cs+

Fr+

59 76 92

99 102 118 124

137 138 151

152 161

167 174

139

164

166 172

181 188

Coordination number 4 6 8 9 10 12

180

Units pm pm pm pm pm pm

The Elements

Table 2.1-7C Elements of Group IA (CAS notation), or Group 1 (new IUPAC notation). Allotropic and high-pressure modifications

The Elements

1.5 Data

Element name

Copper

Silver

Gold

Chemical symbol Atomic number Z

Cu 29

Ag 47

Au 79

Relative atomic mass Ar (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Atomic radius rvdW Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

63.546(3)

107.8682(2)

196.96655(2)

70 × 10−6 5 × 10−10 117 128 140 –LMN 2S 1/2 [Ar]3d10 4s1 2+, 1+ 1.24 1.75 7.72638 20.29240 36.841 57.38 +0.521 +0.342 +0.153

2.0 × 10−6 4 × 10−11 134 144 170 –MNO 2S 1/2 [Kr]4d10 5s1 1+ 1.30 1.42 7.57624 21.49 34.83

3 × 10−9 4 × 10−12 134 144 170 –NOP 2S 1/2 [Xe]4f14 5d10 6s1 3+, 1+ 2.309 (1.42) 9.22567 20.5

+0.7996

+1.692

+1.498 +1.401

Units

Remarks

pm pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12 van der Waals radius

eV Allred and Rochow eV eV eV eV V V V V V

Reaction type Cu+ + e− = Cu Reaction type Cu2+ + 2e− = Cu Reaction type Cu2+ + e− = Cu+ Reaction type Au3+ + 3e− = Au Reaction type Au3+ + 2e− = Au+

Table 2.1-8B(a) Elements of Group IB (CAS notation), or Group 11 (new IUPAC notation). Crystallographic properties Element name

Copper

Silver

Gold

Chemical symbol Atomic number Z

Cu 29

Ag 47

Au 79

Crystal system, Bravais lattice Structure type Lattice constant a Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Shortest interatomic distance, liquid

cub, fc Cu 361.49 Fm3m Oh5 A1 cF4 4 12 255.6 257 (1363 K)

cub, fc Cu 408.61 Fm3m Oh5 A1 cF4 4 12 288

cub, fc Cu 407.84 Fm3m Oh5 A1 cF4 4 12 288

Units

Remarks

pm

At 298 K

pm pm

At 293 K

Part 2 1.5

Table 2.1-8A Elements of Group IB (CAS notation), or Group 11 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-8D for ionic radii)

65

66

Part 2

The Elements

Part 2 1.5

Table 2.1-8B(b) Elements of Group IB (CAS notation), or Group 11 (new IUPAC notation). Mechanical properties Element name

Copper

Silver

Gold

Chemical symbol Atomic number Z

Cu 29

Ag 47

Au 79

Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

8.960 8.000 7.09 3.36 1.300 −0.18 × 10−3 16.5 × 10−6

10.50 9.345 10.27 3.62 0.923 −0.13 × 10−3 19.2 × 10−6

19.30 17.300 10.19 5.38 1.128 −0.10 × 10−3 14.16 × 10−6

Units g/cm3 g/cm3 cm3 /mol mPa s N/m N/(m K) 1/K

2300 4760 0.702 × 10−5

1690 3640 0.95 × 10−5

1190 3280 0.563 × 10−5

m/s m/s 1/MPa

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s44 Elastic compliance s12 Elastic stiffness c11 Elastic stiffness c44 Elastic stiffness c12 Tensile strength Vickers hardness

128 46.8 0.34 15.0 13.3 −6.3 169 75.3 122 209 369

80.0 29.5 0.38 23.0 22.0 −9.8 122 45.5 92 125 251

78.0 26.0 0.42 23.4 23.8 −10.8 191 42.2 162 110 216

GPa GPa 1/TPa 1/TPa 1/TPa GPa GPa GPa MPa

Remarks

At Tm

At 298 K

Volume compressibility

At 293 K At 293 K

Table 2.1-8B(c) Elements of Group IB (CAS notation), or Group 11 (new IUPAC notation). Thermal and thermodynamic

properties Element name

Copper

Silver

Gold

Chemical symbol Atomic number Z

Cu 29

Ag 47

Au 79

Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change Boiling temperature Tb Enthalpy change ∆Hb

1401 24.443 33.150 5.0040 1357.77 13.263 9.768 +0.0415 2843 300.7

429 25.36 42.551 5.7446 1234.93 11.297 9.148 0.038 2436 250.6

317 25.42 47.488 6.0166 1337.33 12.552 9.386 0.051 3130 334.4

Units W/(m K) J/(mol K) J/(mol K) kJ/mol K kJ/mol J/(mol K)

Remarks At 300 K At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm K kJ/mol

The Elements

1.5 Data

Element name

Copper

Silver

Gold

Chemical symbol Atomic number Z

Cu 29

Ag 47

Au 79

Characteristics Electrical resistivity ρs Temerature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio Hall coefficient R

Metal 16.78 43.8 × 10−4 −1.86 × 10−9 21.5 2.07 −0.536 × 10−10

Noble metal 147 43 × 10−4 −3.38 × 10−9

−0.84 × 10−10

Noble metal 20.5 40.2 × 10−4 −2.93 × 10−9 312 2.28 −0.704 × 10−10

Thermoelectric coefficient Electronic work function Thermal work function Molar magnetic susceptibility chi mol , solid (SI) Molar magnetic susceptibility χmol , solid (cgs) Mass magnetic susceptibility χmass , solid (SI) Mass magnetic susceptibilityχmass , liquid (SI)

1.72 4.65 4.39 −68.6 × 10−6

1.42 4.26 4.31 −245 × 10−6

1.72 5.1 4.25 −352 × 10−6

µV/K V V cm3 /mol

At 295 K

−5.46 × 10−6

−19.5 × 10−6

−28 × 10−6

cm3 /mol

At 295 K

−1.081 × 10−6

−2.27 × 10−6

−1.78 × 10−6

cm3 /g

At 295 K

−1.2 × 10−6

−2.83 × 10−6

−2.16 × 10−6

cm3 /g

Units

Remarks

nΩ m 1/K 1/hPa nΩ m

At 293 K

m3 /(A s)

ρl /ρs at Tm B = 0.3–2.2 T, 298 K

Table 2.1-8D Elements of Group IB (CAS notation), or Group 11 (new IUPAC notation). Ionic radii (determined from

crystal structures) Element

Copper

Ion

Cu+

Coordination number 2 4 6 8

46 60 77

Silver Cu2+

57 73

Ag+

100 115 128

Gold Ag2+

79 94

Au+

137

Au3+

64 85

Units pm pm pm pm

Part 2 1.5

Table 2.1-8B(d) Elements of Group IB (CAS notation), or Group 11 (new IUPAC notation). Electronic, electromagnetic, and optical properties. There is no Table 2.1-8C, because no allotropic or high-pressure modifications are known

67

68

Part 2 1.5

Part 2 The Elements

Table 2.1-9A Elements of Group IIA (CAS notation), or Group 2 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-9D for ionic radii) Element name

Beryllium

Magnesium

Calcium

Strontium

Barium

Radium

Chemical symbol Atomic number Z

Be 4

Mg 12

Ca 20

Sr 38

Ba 56

Ra 88 Radioactive [226]

Characteristics Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Atomic radius rvdW Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

9.012182(3)

24.3050(6)

40.078(4)

87.62(1)

137.327(7)

6 × 10−6 6 × 10−13 89 112

20 900 × 10−6 1290 × 10−6 136 160 170 KLM 1S 0 [Ne]2s2 2+ Not stable 1.23 7.64624 15.03528 80.1437 109.2655 −2.372

26 300 × 10−6 412 × 10−6 174 197

150 × 10−6 8.0 × 10−6 191 215

430 × 10−6 2 × 10−9 198 224

–LMN 1S 0 [Ar]4s2 2+ 0.0246 1.04 6.11316 11.87172 50.9131 67.27 −2.868

–MNO 1S 0 [Kr]5ss2 2+ 0.048 0.99 5.69484 11.03013 42.89 57 −2.89

–NOP 1S 0 [Xe]6s2 2+ 0.15 0.97 5.21170 10.00390

KL 1S 0 [He]2s2 2+ Not stable 1.47 9.32263 18.21116 153.89661 217.71865 −1.847

−2.90

230

Units

Remarks

pm pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12 van der Waals radius

–OPQ 1S 0 [Rn]7s2 2+ eV (0.97) 5.27892 10.14716

Allred and Rochow eV eV eV eV V

Reaction type Be++ + 2e− = Be

The Elements

1.5 Data

(see Table 2.1-9C for allotropic and high-pressure modifications) Element name

Beryllium

Magnesium Calcium Strontium

Barium

Radium

Chemical symbol Atomic number Z

Be 4

Mg 12

Ba 56

Ra 88

Modification Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

α-Be hex Mg 228.57 358.39 P63 /mmc 4 D6h A3 hP2 2 12 222

Ca 20

Sr 38

α-Ca cub, fc Cu 558.84

α-Sr cub, fc Cu 608.4

cub, bc W 502.3

cub, bc W 514.8

Fm3m Oh5 A1 cF4 4 12 393

Fm3m Oh5 A1 cF4 4 12 430

Im3m Oh9 A2 cI2 2 8 434

Im3m Oh9 A2 cI2 2 8 446

Units Remarks hex Mg 320.93 521.07 P63 /mmc 4 D6h A3 hP2 2 6+6 319

pm pm

pm

Part 2 1.5

Table 2.1-9B(a) Elements of Group IIA (CAS notation), or Group 2 (new IUPAC notation). Crystallographic properties

69

70

Part 2 1.5

Part 2 The Elements

Table 2.1-9B(b) Elements of Group IIA (CAS notation), or Group 2 (new IUPAC notation). Mechanical properties Element name

Beryllium

Magnesium

Calcium

Strontium

Barium

Radium

Chemical symbol Atomic number Z

Be 4

Mg 12

Ca 20

Sr 38

Ba 56

Ra 88

Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension γ , liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

1.85 1.420 (1770 K) 4.88

3.50 3.325 38.21

5.000

0.303

26.1 × 10−6

23 × 10−6

0.276 −0.095 20.7 × 10−6

0.45

11.5 × 10−6

1.55 1.365 25.86 1.06 0.361 −0.068 × 103 22 × 10−6

2.60 2.375 34.50

1.1 (1770 K)

1.74 1.590 13.98 1.23 0.563 (954 K)

8330

3170

2210

1520

1160

m/s

12 720

5700

4180

2780

2080

m/s

0.765 × 10−5

2.88 × 10−5

5.73 × 10−5 a

7.97 × 10−5

10.0 × 10−5

1/MPa

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness Brinell hardness

286 133 0.12 3.45 2.87 6.16 −0.28 −0.05 292 349 163 24 6 228–352 1670 1060–1300

44.4 16.9 0.28 22.0 19.7 60.9 −7.8 −5.0 59.3 61.5 16.4 25.7 21.4 90

19.6 a 7.85 a 0.31 a 104

15.7 6.03 0.28 218

12.8 4.84 0.28 157

71 −42

135 −90

105 −61

22.8

10.94

12.6

14 16.0

7.41 7.69

9.5 8.0

130

140

42

a

At 348 K. b Estimated.

300–500

45.2

20.2 × 10−6

13.2 b

Units g/cm3 g/cm3 cm3 /mol mPa s N/m N/(m K) 1/K

Remarks

Volume compressibility

GPa GPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa GPa At 293 K

Table 2.1-9B(c) Elements of Group IIA (CAS notation), or Group 2 (new IUPAC notation). Thermal and thermodynamic properties Element name Chemical symbol Atomic number Z

Beryllium Be 4

Magnesium Mg 12

Calcium Ca 20

Strontium Sr 38

Barium Ba 56

Radium Ra 88

Thermal conductivity λ Molar heat capacity c p Standard entropy S0

200 16.44 9.500

171 24.895 32.671

200 25.940 41.588

35.3 26.4 55.694

18.4 28.09 62.500

18.6 69.000

Units W/(m K) J/(mol K) J/(mol K)

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb

1.9500

4.9957

5.7360

6.5680

6.9100

7.2000

kJ/mol

1560.0 7.8950 5.061

923.00 8.4768 9.184 0.042

1115.0 8.5395 7.659 0.047

1050.0 7.4310 7.077

1000.0 7.1190 7.119

969.00 7.7000 7.946

K kJ/mol J/(mol K)

1366 127.4

1773 153.6

1685 137.19

2741 291.58

Remarks At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm 2118 141.5

K kJ/mol

136.7

Table 2.1-9B(d) Elements of Group IIA (CAS notation), or Group 2 (new IUPAC notation). Electronic, electromagnetic, and optical properties Element name Chemical symbol Atomic number Z

Beryllium Be 4

Magnesium Mg 12

Calcium Ca 20

Strontium Sr 38

Barium Ba 56

Radium Ra 88

Characteristics Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio Hall coefficient R

Light metal 28 90.0 × 10−4 −1.6 × 10−9 27.4

Light metal 39.4 41.2 × 10−4 −4.7 × 10−9

Metal 31.6 41.7 × 10−4 15.2 × 10−9

Soft metal 303 38.2 × 10−4 5.56 × 10−9

Soft metal 500 64.9 × 10−4 −3.0 × 10−9

Metal

1.78 −0.83 × 10−10

Remarks

nΩ m 1/K 1/hPa nΩ m

At RT

m3 /(A s)

ρl /ρs at Tm At 300 K, B = 1T

−8.2

4.98 3.37 −113 × 10−6

3.97 3.46 165 × 10−6

2.87 2.76 503 × 10−6

2.74 2.35 1.16 × 10−3

2.56 2.29 259 × 10−6

V V cm3 /mol

At 295 K

−9.0 × 10−6

13.1 × 10−6

40.0 × 10−6

92.0 × 10−6

20.6 × 10−6

cm3 /mol

At 295 K

−13 × 10−6

6.8 × 10−6

14 × 10−6

13.2 × 10−6

1.9 × 10−6

cm3 /g

At 295 K λ = 589 nm

71

Part 2 1.5

0.37

µV/K

1.5 Data

−0.4

The Elements

Thermoelectric coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol , solid (SI) Molar magnetic susceptibility χmol , solid (cgs) Mass magnetic susceptibility χmass , solid (SI) Refractive index n, solid

2.4 × 10−10

Units

72

Part 2 1.5

Part 2

Element

Beryllium

Modification

α-Be

β-Be

Calcium α-Ca

γ -Ca

Strontium α-Sr

β-Sr

γ -Sr

Sr-II

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell

hex, cp Mg 228.57 358.39 P63 /mmc 4 D6h A3 hP2 2

cub, bc W 255.15

cub, fc Cu 558.84

cub, bc W 448.0

cub, fc Cu 608.4

cub, bc W 487

cub, bc W 443.7

Im3m Oh9 A2 cI2 2

Fm3m Oh5 A1 cF4 4

Im3m Oh9 A2 cI2 2

Fm3m Oh5 A1 cF4 4

hex, cp Mg 428 705 P63 /mmc 4 D6h A3 hP2 2

Im3m Oh9 A2 cI2 2

Im3m Oh9 A2 cI2 2

Coordination number Shortest interatomic distance, solid Range of stability

12 222

8 221

12 393

8 388

12 430

12

8 422

8

RT

> 1523 K

RT

> 1010 K

RT

> 486 K

> 878 K

> 3.5 GPa

Units

pm pm

pm

Table 2.1-9D Elements of Group IIA (CAS notation), or Group 2 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Beryllium

Magnesium

Calcium

Strontium

Barium

Radium

Ion

Be2+

Mg2+

Ca2+

Sr2+

Ba2+

Ra2+

27 45

57 72 89

Coordination number 4 6 8 10 12

100 112 123 134

118 126 136 144

135 142

148

161

170

Units pm pm pm pm pm

The Elements

Table 2.1-9C Elements of Group IIA (CAS notation), or Group 2 (new IUPAC notation). Allotropic and high-pressure modifications

The Elements

1.5 Data

properties (see Table 2.1-10D for ionic radii) Element name

Zinc

Cadmium

Mercury

Chemical symbol Atomic number Z

Zn 30

Cd 48

Hg 80

Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Atomic radius rvdW Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energ 4th ionization energy Standard electrode potential E 0

65.39(2)

112.411(8)

200.59(2)

80 × 10−6 4.9 × 10−9 125 134 140 –LMN 1S 0 [Ar]3d10 4s2 2+ Not stable 1.66 9.39405 17.96440 39.723 59.4

0.18 × 10−6 1 × 10−10 141 149 160 –MNO 1S 0 [Kr]4d10 5s2 2+ Not stable 1.46 8.99367 16.90832 37.48

0.5 × 10−6 3 × 10−11 144 162 150 –NOP 1S 0 [Xe]4f14 5d10 6s2 2+, 1+ Not stable (1.44) 10.43750 18.756 34.2 +0.7973

−0.7618

−0.403

Units

Remarks

pm pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12 van der Waals radius

eV Allred and Rochow eV eV eV eV V V

Reaction type Hg2+ + 2e− = 2Hg Reaction type Cu2+ + 2e− = Cu

Table 2.1-10B(a) Elements of Group IIB (CAS notation), or Group 12 (new IUPAC notation). Crystallographic properties (see Table 2.1-10 for allotropic and high-pressure modifications) Element name

Zinc

Cadmium

Mercury

Chemical symbol Atomic number Z

Zn 30

Cd 48

Hg 80

Modification Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Lattice angle α Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

hex Mg 266.44 494.94

hex Mg 297.88 561.67

P63 /mmc 4 D6h A3 hP2 2 6+6 266

P63 /mmc 4 D6h A3 hP2 2 6+6 297

α-Hg trig, R α-Hg 300.5 (225 K) 70.53 (225 K) R3m 5 D3d A 10 hR1 1 6+6 299 (at 234 K)

Units

Remarks

pm pm deg

At 298 K At 298 K

pm

At 293 K

Part 2 1.5

Table 2.1-10A Elements of Group IIB (CAS notation), or Group 12 (new IUPAC notation). Atomic, ionic, and molecular

73

74

Part 2

The Elements

Part 2 1.5

Table 2.1-10B(b) Elements of Group IIB (CAS notation), or Group 12 (new IUPAC notation). Mechanical properties Element name

Zinc

Cadmium

Mercury

Chemical symbol Atomic number Z

Zn 30

Cd 48

Hg 80

Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, liquid Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic compliance s14 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Elastic stiffness c14 Tensile strength Brinell hardness

7.14 6.570 9.17 2.95 0.816 0.25 × 10−3 25.0 × 10−6

8.65 8.02 13.00 2.29 0.564 0.39 × 10−3 29.8 × 10−6

2790 2290

2200a 1690

3890

2980

1.65 × 10−5 92.7 34.3 0.29 8.22 27.7 25.3 0.60 −7.0

2.14 × 10−5 62.3 24.5 0.30 12.4 34.6 53.1 −1.2 −9.1

165 61.8 39.6 31.1 50.0

114.1 49.9 19.0 41.0 40.3

20–40 280–330

71 180–230

a

At 594 K

13.53 (25 ◦ C) 14.81 1.55 0.476 −0.20 × 10−3 18.1 1451

Units g/cm3 g/cm3 cm3 /mol mPa s N/m N/(m K) 1/K

Remarks

m/s m/s

12 MHza

At Tm

At 298.15 K

m/s 3.77 × 10−5 25

1/MPa GPa GPa

154 (83 K) 45 (83 K) 151 (83 K) −119 (83 K) −21 (83 K) −100 (83 K) 36.0 (83 K) 50.5 (83 K) 12.9 (83 K) 28.9 (83 K) 30.3 (83 K) 4.7 (83 K)

1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa GPa MPa

Volume compressibility

293 K

The Elements

1.5 Data

Element name

Zinc

Cadmium

Mercury

Chemical symbol Atomic number Z

Zn 30

Cd 48

Hg 80

State Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change Boiling temperature Tb Enthalpy change ∆Hb Critical temperature Tc Critical pressure pc Critical density c

Solid 121 25.44 41.631 5.6570

Solid 96.8 25.98 51.800 6.2470

Liquid 8.34 27.983 75.900 9.3420

692.68 7.3220 10.571 0.0730 1180 115.3

594.22 6.1923 10.421 0.0474 1040 97.40

234.32 2.2953 9.796 0.037 629 59.2 1750 167 5.700

Units

Remarks

W/(m K) J/(mol K) J/(mol K) kJ/mol

At 300 K At 298 K At 298 K and 100 kPa

K kJ/mol J/(mol K) (Vl − Vs )/Vl at Tm K kJ/mol K MPa g/cm3

Part 2 1.5

Table 2.1-10B(c) Elements of Group IIB (CAS notation), or Group 12 (new IUPAC notation). Thermal and thermodynamic

properties

75

76

Part 2

The Elements

Part 2 1.5

Table 2.1-10B(d) Elements of Group IIB (CAS notation), or Group 12 (new IUPAC notation). Electronic, electromagnetic,

and optical properties Element name

Zinc

Cadmium

Mercury

Chemical symbol Atomic number Z

Zn 30

Cd 48

Hg 80

Characteristics Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R

Ductile metal 54.3 41.7 × 10−4 −6.3 × 10−9 326 2.1 0.88

Soft metal 68 46.2 × 10−4 −7.32 × 10−9 337 1.97 0.55

Noble metal

53

30

0.63 × 10−10

Thermoelectric coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol , solid (SI) Molar magnetic susceptibility χmol , solid (cgs) Molar magnetic susceptibility χmol , liquid (SI) Molar magnetic susceptibility χmol , liquid (cgs) Mass magnetic suscepti-, bility χmass , solid (SI) Mass magnetic susceptibility χmass , liquid (SI) Refractive index (n − 1), gas Refractive index n, solid

1.19 (λ = 550 nm)

958 (298 K) 3.74–4.94 4.15 K

Units

Remarks

nΩ m 1/K 1/hPa nΩ m

At 293 K

K

ρl /ρs at Tm α-Hg

412

Oe

α-Hg

0.589 × 10−10

−0.73 × 10−10

m3 /(A s)

B = 0.3–2.2 T 298 K

2.9 4.22 3.74 −115 × 10−6

2.8 4.04 3.92 −248 × 10−6

−3.4

µV/K V V cm3 /mol

At 295 K

−9.15 × 10−6

−19.7 × 10−6

cm3 /mol

At 295 K

cm3 /mol

At 295 K

cm3 /mol

At 295 K At 295 K

−303 × 10−6 (234 K) −24.1 × 10−6 (234 K) −421 × 10−6 −33.5 × 10−6

−1.38 × 10−6

−2.21 × 10−6

cm3 /g

−1.32 × 10−6

−1.83 × 10−6

cm3 /g +1882 × 10−6 (Hg2 vapor)

1.8 (578 nm)

The Elements

1.5 Data

modifications Element

Mercury

Modification

α-Hg

β-Hg

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Lattice angle α Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

trig, R α-Hg 300.5 (225 K)

tetr In 399.5 282.5

Units

70.53 (225 K) R3m 5 D3d A10 hR1 1 6+6 299 < 234.2 K

pm pm

14/mmm 17 D4h tI2 2 2+8 283 77 K, high pressure

pm

Table 2.1-10D Elements of Group IIB (CAS notation), or Group 12 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Zinc

Cadmium

Mercury

Ion

Zn2+

Cd2+

Hg+

Coordination number 2 4 6 8 12

60 74 90

78 95 110 131

119

Hg2+ 69 96 102 114

Units pm pm pm pm pm

Part 2 1.5

Table 2.1-10C Elements of Group IIB (CAS notation), or Group 12 (new IUPAC notation). Allotropic and high-pressure

77

78

Part 2 1.5

Part 2 The Elements

Table 2.1-11A Elements of Group IIIA (CAS notation), or Group 13 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-11D for ionic radii) Element name

Boron

Aluminium

Gallium

Indium

Thallium

Chemical symbol Atomic number Z

B 5

Al 13

Ga 31

In 49

Tl 81

Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet

10.811(7)

26.981538(2)

69.723(1)

114.818(3)

204.3833(2)

10 × 10−6 4.4 × 10−6 81 89

81 300 × 10−6 0.002 × 10−6 125 143

15 × 10−6 3 × 10−11 125 153

0.06 × 10−6 1 × 10−13 150 167

0.3 × 10−6 1 × 10−11 155 170

KL 2P 1/2 [He]2s2 2p1 3+ 0.277 2.01 8.29803 25.15484 37.93064 259.37521

205 KLM 2P 1/2 [Na]3s2 3p1 3+ 0.441 1.47 5.98577 18.82856 28.44765 119.992

190 –LMN 2P 1/2 [Ar]3d10 4s2 4p1 3+ 0.3 1.82 5.99930 20.5142 30.71 64

190 –MNO 2P 1/2 [Kr]4d10 5s2 5p1 3+ 0.3 1.49 5.78636 18.8698 28.03 54

200 –NOP 2P 1/2 [Xe]4f14 5d10 6s2 6p1 3+, 1+ 0.2 1.44 6.10829 20.428 29.83

Atomic radius rvdW Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

−0.336 −1.662

−0.560

−0.338

Units

Remarks

pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12 van der Waals radius

pm

eV Allred and Rochow eV eV eV eV V V

+1.252

V

Reaction type Tl+ + e− = Tl Reaction type Al3+ + 3e− = Al Reaction type Tl3+ + 2e− = Tl+

The Elements

1.5 Data

Element name

Boron

Aluminium

Gallium

Indium

Thallium

Chemical symbol Atomic number Z

B 5

Al 13

Ga 31

In 49

Tl 81

Modification Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

β-B trig, R β-B

α-Al cub, fc Cu 361.49

α-Ga orth, C α-Ga 451.92 765.86 452.58 Cmca 18 D2h A11 oC8 8 1+2+2+2 247

Units

R3m 5 D3d hR105 105 162–192

Fm3m Oh5 A1 cF4 4 12 286

tetr, I In 459.90

hex Mg 345.63

494.70 I4/mmm 17 D4h A6 tI2 2 4+8 325

552.63 P63 /mmc 4 D6h A3 hP2 2

pm pm pm

pm

Remarks

Part 2 1.5

Table 2.1-11B(a) Elements of Group IIIA (CAS notation), or Group 13 (new IUPAC notation). Crystallographic properties (see Table 2.1-11C for allotropic and high-pressure modifications)

79

80

Part 2 1.5

Part 2 The Elements

Table 2.1-11B(b) Elements of Group IIIA (CAS notation), or Group 13 (new IUPAC notation). Mechanical properties Element name

Boron

Aluminium

Gallium

Indium

Thallium

Chemical symbol Atomic number Z

B 5

Al 13

Ga 31

In 49

Tl 81

Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension γ , liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, liquid Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

2.46

2.70 2.39 10.00 1.38 0.860 −0.135 × 10−3 23.03 × 10−6

5.91 6.200 11.81 1.70 0.718

11.85 11.29 17.24

18.3 × 10−6

7.31 6.990 15.71 1.65 0.556 −0.09 × 10−3 33 × 10−6

4650 3130

2740 750

6360 0.539 × 10−5

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s22 Elastic compliance s33 Elastic compliance s44 Elastic compliance s55 Elastic compliance s66 Elastic compliance s12 Elastic compliance s13 Elastic compliance s23

178a

a

Estimated.

4.62

5 × 10−6

Remarks

0.447 −0.07 × 10−3 28 × 10−6

Units g/cm3 g/cm3 cm3 /mol mPa s N/m N/(m K) 1/K

2215 710

m/s m/s

At 12 MHz

480

3030

2460

1630

m/s

1.33 × 10−5

1.96 × 10−5

2.70 × 10−5

3.41 × 10−5

1/MPa

70.2 27.8 0.34 16.0

9.81 6.67 0.47 12.2 14.0 8.49 28.6 23.9 24.8 −4.4 −1.7 −2.4

10.6 3.68 0.45 148.8

7.89 2.67 0.45 104

GPa GPa

196.2 153.7

31.1 139

83.2 −46.0 −94.5

−83 −11.6

35.3

−5.8

1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa

At Tm At Tm At Tm

Volume compressibility

The Elements

1.5 Data

Element name

Boron

Aluminium

Gallium

Indium

Thallium

Chemical symbol Atomic number Z

B 5

Al 13

Ga 31

In 49

Tl 81

Elastic stiffness c11 Elastic stiffness c22 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c55 Elastic stiffness c66 Elastic stiffness c12 Elastic stiffness c13 Elastic stiffness c23 Elastic stiffness c14 Tensile strength Vickers hardness Brinell hardness Mohs hardness

467

108

45.1

41.9

473 198

28.3

44.6 6.51

54.9 7.20

241

62

100 90.2 135 35.0 41.8 40.3 37 33 31

12.0 40.0 41.0

36.6 29.9

15.1 16–24a 49 000

90–100 167

a

8.9 9

Units GPa GPa GPa GPa GPa GPa GPa GPa GPa GPa MPa

Remarks

At 293 K

0.9 9.3

1.5–2.5

Amorphous.

Table 2.1-11B(c) Elements of Group IIIA (CAS notation), or Group 13 (new IUPAC notation). Thermal and thermodynamic

properties Element name

Boron

Aluminium

Gallium

Indium

Thallium

Chemical symbol Atomic number Z

B 5

Al 13

Ga 31

In 49

Tl 81

State Thermal conductivity λ Thermal conductivity (liquid) λl Molar heat capacity c p Standard entropy S0

Crystalline 27.0

81.6

46.1

Units

Remarks

W/(m K) W/(m K)

At Tm

237 90

33.5

11.20 5.900

24.392 28.300

26.15 40.727

26.732 57.650

26.32 64.300

J/(mol K) J/(mol K)

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Volume change ∆Vm

1.2220

4.5400

5.5720

6.6100

6.832

kJ/mol

2348.00 50.200 21.380

933.47 10.7110 11.474 0.065

302.91 5.5898 18.454 −0.034

429.75 3.2830 7.639 0.025

577.00 4.1422 7.179 0.0323

K kJ/mol J/(mol K)

Boiling temperature Tb Enthalpy change ∆Hb

4138 480.5

2790 294.0

2478 258.7

2346 231.45

1746 164.1

K kJ/mol

At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm

Part 2 1.5

Table 2.1-11B(b) Elements of Group IIIA (CAS notation), or Group 13 (new IUPAC notation). Mechanical properties , cont.

81

82

Part 2 1.5

Part 2

Element name

Boron

Aluminium

Gallium

Indium

Thallium

Chemical symbol Atomic number Z

B 5

Al 13

Ga 31

In 49

Tl 81 Units

Remarks

Characteristics

Semiconductor

Light metal

Soft metal

Soft metal

Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio at Tm Superconducting critical temperature Tcr Superconducting critical field Hcr Electronic band gap ∆E Electronic work function Thermal work function Intrinsic charge carrier concentration Electron mobility Hole mobility Hall coefficient R

6500 × 109

25.0 46 × 10−4 −4.06 × 10−9 200 1.64 1.2

136 39.6 × 10−4 −2.47 × 10−9 258 1.9 1.09

80.0 49.0 × 10−4 −12.2 × 10−9 331 2.18 3.4

Soft metal, toxic 150 51.7 × 10−4 −3.4 × 10−9 740

nΩ m 1/K 1/hPa nΩ m

a

2.4

K

99

51

293

171

Oe

4.28 3.74

4.35 4.12

4.08 4.0

4.05 3.76

eV V V 1/cm3

Thermoelectric coefficient Dielectric constant ε, solid Molar magnetic susceptibility χmol , solid (SI) Molar magnetic susceptibility χmol , solid (cgs) Mass magnetic susceptibility χmass , solid (SI) Mass magnetic susceptibility χmass , liquid (SI) Refractive index n, solid a

At 300 K.

a

1.5 4.79 5.71 +5 × 1014

ρl /ρs at Tm

−0.24 × 10−10

0.240 × 10−10

cm2 /(V s) cm2 /(V s) m3 /(A s)

2.4

0.4

µV/K

1 55 −0.343 × 10−10

−0.63 × 10−10

−0.6

At 300 K

At 430 K

B=1.0–1.8 T 300 K

13 (0.5 MHz) −84.2 × 10−6

207 × 10−6

−271 × 10−6

−128 × 10−6

−628 × 10−6

cm3 /mol

At 295 K

−6.7 × 10−6

16.5 × 10−6

−21.6 × 10−6

−10.2 × 10−6

−50.0 × 10−6

cm3 /mol

At 295 K

+7.9 × 10−6

−3.9 × 10−6

−1.4 × 10−6

−3.13 × 10−6

cm3 /g

At 295 K

−1.72 × 10−6

cm3 /g

At Tm

3.2 (λ=1 µm)

The Elements

Table 2.1-11B(d) Elements of Group IIIA (CAS notation), or Group 13 (new IUPAC notation). Electronic, electromagnetic, and optical properties

Table 2.1-11C Elements of Group IIIA (CAS notation), or Group 13 (new IUPAC notation). Allotropic and high-pressure modifications Element

Aluminium

Modification

α-Al

β-Al

α-Ga

Gallium β-Ga

γ -Ga

α-Tl

Thallium β-Tl

γ -Tl

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, fc Cu 404.96

hex, cp Mg 269.3

orth, C α-Ga 451.92 765.86 452.58 Cmca 18 D2h A11 oC8 8 1+2+2+2 247

tetr In 280.8

orth γ -Ga 1059.3 1352.3 520.3 Cmcm 17 D2h

hex, cp Mg 345.63

cub, bc W 387.9

cub, fc Cu

A6 tI2 2 4+8 281

Im3m Oh9 A2 cI2 2 8 336

Fm3m Oh5 A1 cF4 4 12

RTP

> 1.2 GPa

> 503 K

High pressure

Units

Fm3m Oh5 A1 cF4 4 12 286 RTP

439.8 P63 /mmc 4 D6h A3 hP2 2 12

> 20.5 GPa

445.8 I4/mmm

oC40 40

552.63 P63 /mmc 4 D6h A3 hP2 2

260–308 220 K, > 3.0 GPa

RTP

pm pm pm

Table 2.1-11D Elements of Group IIIA (CAS notation), or Group 13 (new IUPAC notation). Ionic radii (determined from crystal structures) Aluminium

Gallium

Indium

Thallium

Ion

Al3+

Ga3+

In3+

Tl+

39 48 54

47

62

62

80

Coordination number 4 5 6 8 12

Tl3+ 75

150 159 170

89 98

Units pm pm pm pm pm

The Elements 1.5 Data 83

Part 2 1.5

Element

84

Part 2 1.5

Part 2

ionic radii) Element name

Scandium

Yttrium

Lanthanum

Actinium

Chemical symbol Atomic number Z

Sc 21

Y 39

La 57

Ac 89 Radioactive [227]

Characteristics Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

44.955910(8)

88.90585(2)

138.9055(2)

5 × 10−6 6 × 10−13 144 166 –LMN 2D 3/2 [Ar]3d1 4s2 3+ 0.188 1.20 6.56144 12.79967 24.75666 73.4894

28.1 × 10−6 3 × 10−12 162 178 –MNO 2D 3/2 [Kr]4d1 5s2 3+ 0.307 1.11 6.217 12.24 20.52 60.597

18.3 × 10−6 3 × 10−12 169 187 –NOP 2D 3/2 [Xe]5d1 6s2 3+ 0.5 1.08 5.5770 11.060 19.1773 49.95 −2.522

188 –OPQ 2D 3/2 [Rn]6d1 7s2 3+

Units

Remarks

pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12

eV (1.00) 5.17 12.1

Allred and Rochow eV eV eV eV V

Reaction type La3+ + 3e− = La

The Elements

Table 2.1-12A Elements of Group IIIB (CAS notation), or Group 3 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-12D for

The Elements

1.5 Data

Element name Chemical symbol Atomic number Z

Scandium Sc 21

Yttrium Y 39

Lanthanum La 57

Modification Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

α-Sc hex Mg 330.88 526.80 P63 /mmc 4 D6h A3 hP2 2 12 166

α-Y hex Mg 364.82 573.18 P63 /mmc 4 D6h A3 hP2 2 6+6

α-La hex α-La 377.40 1217.1 P63 /mmc 4 D6h A3 hP4 4 12 364

Actinium Ac 89 Units

Remarks

pm pm

pm

Table 2.1-12B(b) Elements of Group IIIB (CAS notation), or Group 3 (new IUPAC notation). Mechanical properties Element name Chemical symbol Atomic number Z

Scandium Sc 21

Yttrium Y 39

Lanthanum La 57

Actinium Ac 89

Density , solid Molar volume Vmol Surface tension, liquid Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

2.989 15.04 0.9 10.0 × 10−6

4.50 19.89 0.9 10.6 × 10−6

6.70 22.60 0.71 4.9 × 10−6

10.07

2420

1540

m/s

4280

2770

m/s

2.22 × 10−5

2.62 × 10−5

3.96 × 10−5

1/MPa

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness

75.2 29.7 0.28 12.5 10.6 36.1 −4.3 −2.2 99.3 107 27.7 39.7 29.4 256 350

66.3 25.5 0.27 15.4 14.4 41.1 −5.1 −2.7 77.9 76.9 24.3 29.2 20 250–380 40

39.2 14.9 0.28 51.7 b

a b

Estimated. For lanthanum in its metastable fcc phase at room temperature.

55.7 b −19.2 b 34.5 b 18.0 b 20.4 b

491

25a

Units g/cm3 cm3 /mol N/m 1/K

GPa GPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa MPa

Remarks

Volume compressibility

Part 2 1.5

Table 2.1-12B(a) Elements of Group IIIB (CAS notation), or Group 3 (new IUPAC notation). Crystallographic properties (see Table 2.1-12C for allotropic and high-pressure modifications)

85

86

Part 2

The Elements

Part 2 1.5

Table 2.1-12B(c) Elements of Group IIIB (CAS notation), or Group 3 (new IUPAC notation). Thermal and thermodynamic

properties Element name

Scandium

Yttrium

Lanthanum

Actinium

Chemical symbol Atomic number Z

Sc 21

Y 39

La 57

Ac 89

Thermal conductivity λ Molar heat capacity c p Standard entropy S0

15.8 25.52 34.644

17.2 26.53 44.788

13.5 27.11 56.902

27.2 62.000

Units W/(m K) J/(mol K) J/(mol K)

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb

5.2174

5.9835

6.6651

6.7000

kJ/mol

1814.00 14.0959 7.771

1795.15 11.3942 6.347

1193.00 6.1965 5.194 0.006

1323.00 12.000 9.070

K kJ/mol J/(mol K)

3730 413.7

3473 293

3104 314.2

3611 363.3

Remarks At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm K kJ/mol

Table 2.1-12B(d) Elements of Group IIIB (CAS notation), or Group 3 (new IUPAC notation). Electronic, electromagnetic, and optical properties Element name Chemical symbol Atomic number Z

Scandium Sc 21

Yttrium Y 39

Lanthanum La 57

Actinium Ac 89

Characteristics

Soft metal

Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R Thermoelectric coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol , solid (SI) Molar magnetic susceptibility χmol , solid (cgs) Mass magnetic susceptibility χmass , solid (SI)

505 28.2 × 10−4

Reactive metal 550 27.1 × 10−4

Very reactive metal 540 21.8 × 10−4 −1.7 × 10−9 1350 5.0

−0.67 × 10−10 −3.6 3.5 3.23 3710 × 10−6

−0.770 × 10−10 2.2 3.1 3.07 2359 × 10−6

−0.8 × 10−10

295 × 10−6 88 × 10−6

Units

Remarks

nΩ m 1/K 1/hPa nΩ m K

At RT

At 293 K, B = 0.5–1.0 T

3.5 3.3 +1205 × 10−6

m3 /(A s) µV/K V V cm3 /mol

188 × 10−6

+95.9 × 10−6

cm3 /mol

At 295 K

27.0 × 10−6

+11 × 10−6

cm3 /g

At 295 K

Table 2.1-12C Elements of Group IIIB (CAS notation), or Group 3 (new IUPAC notation). Allotropic and high-pressure

modifications Element Modification

Scandium α-Sc

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex, cp Mg 330.88 526.80 P63 /mmc 4 D6h A3 hP2 2 12

β-Sc

Yttrium α-Y

β-Y

Lanthanum α-La

β-La

γ -La

β
-La Units

RT

cub, fc Cu 530.45

cub, bc W 426.5

cub, fc Cu 517

Im3m Oh9 A2 cI2 2 8 356

hex α-La 377.40 1217.1 P63 /mmc 4 D6h A3 hP4 4 12 374

Fm3m Oh5 A1 cF4 4 12 375

Im3m Oh9 A2 cI2 2 8 369

Fm3m Oh5 A1 cF4 4 12

> 1752 K

RTP

> 613 K

> 1141 K

> 2.0 GPa

pm pm

pm

87

Part 2 1.5

> 1607 K

cub, bc W

1.5 Data

Im3m Oh9 A2 cI2 2 8

hex, cp Mg 364.82 573.18 P63 /mmc 4 D6h A3 hP2 2 6+6

The Elements

RT

cub, bc W

Part 2 1.5 Yttrium

Lanthanum

Actinium

Ion

Sc3+

Y3+

La3+

Ac3+ 112

Coordination number

The Elements

Scandium

Units

6

75

90

103

8

87

102

116

9

pm pm

108

pm

10

127

pm

12

136

pm

Table 2.1-13A Elements of Group IVA (CAS notation), or Group 14 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-13D for

ionic radii) Element name

Carbon

Silicon

Germanium

Tin

Lead

Chemical symbol Atomic number Z

C 6

Si 14

Ge 32

Sn 50

Pb 82

Relative atomic mass A (atomic weight)

12.0107(8)

28.0855(3)

72.61(2)

118.710(7)

207.2(1)

Abundance in lithosphere

320 × 10−6

277 200 × 10−6

7 × 10−6

40 × 10−6

16 × 10−6

Abundance in sea

28 × 10−6

2 × 10−6

5 × 10−11

1 × 10−11

3 × 10−11

Atomic radius rcov

77

117

122

140

154

pm

Covalent radius

Atomic radius rmet

91

132

137

220

175

pm

Metallic radius, CN = 12

Atomic radius rvdW

170

210

234

158

200

pm

van der Waals radius

Electron shells

KL

KLM

–LMN

–MNO

–NOP

Electronic ground state

3P 0

3P 0

Electronic configuration

3P 0 1s2 2s2 2p2

[Ne]3s2 3p2

[Ar]3d

Oxidation states

4+, 4−, 2+

4+

4+

4+, 2+

4+, 2+

Electron affinity

1.26

1.39

1.23

1.11

0.364

Electronegativity χA

2.50

1.74

2.02

1.72

1.55

1st ionization energy

11.26030

8.15169

7.900

7.34381

7.41666

eV

2nd ionization energy

24.38332

16.34585

15.93462

14.63225

15.0322

eV

3rd ionization energy

47.8878

33.49302

34.2241

30.50260

31.9373

eV

4th ionization energy

64.4939

45.14181

45.7131

40.73502

42.32

eV

5th ionization energy

392.087

166.767

93.5

72.28

68.8

eV

−0.137

−0.126

V

Reaction type Sn2+ + 2e− = Sn

V

Reaction type Sn4+ + 2e− = Sn2+

Units

Standard electrode potential E 0

3P 0 10

4s2 4p2

Remarks

Mass ratio Mass ratio

3P 0 10

[Kr]4d

+0.151

5s2 5p2

Part 2

Element

88

Table 2.1-12D Elements of Group IIIB (CAS notation), or Group 3 (new IUPAC notation). Ionic radii (determined from crystal structures)

[Xe]4f14 5d10 6s2 6p2 eV Allred and Rochow

Table 2.1-13B(a) Elements of Group IVA (CAS notation), or Group 14 (new IUPAC notation). Crystallographic properties (see Table 2.1-13C for allotropic

and high-pressure modifications) Element name

Carbon

Silicon

Germanium

Tin

Lead

Chemical symbol Atomic number Z

C 6

Si 14

Ge 32

Sn 50

Pb 82

Modification

Diamond

Graphite

Crystal system, Bravais lattice Structure type Lattice constant a

cub Diamond 356.71

hex C 246.12

Units

Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

Fd3m Oh7

8 4 154.45

670.90 P63 /mmc 4 D6v A9 hP4 4 3 142.10

cub, fc Diamond 543.102 (22.5 ◦ C)

cub, fc Diamond 565.9(1) RT

Fd3m Oh7 A4 cF8 8 4 235

Fd3m Oh7 A4 cF8 8 4 244

β-Sn,a white tin, Sn I tetr, I β-Sn 581.97 (300 K) 317.49 I41 /amd 19 D4h A5 tI4 4 302

335.45 Range of stability

RT, > 60 GPa

pm pm

Fm3m Oh5 A1 cF4 4 12 349

pm pm

Graphite, within layers Graphite, between layers

RTP

At ambient pressure Sn crystallizes in the diamond structure (gray tin, α-Sn) and below 17 ◦ C in the β-tin structure (white tin, β-Sn, Sn-I) at room temperature. If it is alloyed with In or Hg, the simple hexagonal γ -Sn structure is observed

The Elements 1.5 Data 89

Part 2 1.5

a

cub, fc Cu 495.02

Remarks

Part 2 1.5

Part 2

Carbon

Silicon

Germanium

Tin

Lead

Chemical symbol Atomic number Z

C 6

Si 14

Ge 32

Sn 50

Pb 82

Modification Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension γ , liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, liquid Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

Diamond 3.513

Graphite 2.266

3.42

5.3

Bulk modulus B0 Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s66 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c66 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness Mohs hardness

444 545

a

1.06 × 10−6

1.9 × 10−6

a

Units

Remarks

11.4 10.678 18.26 1.67 0.470 −0.26 × 10−3 29.1 × 10−6

g/cm3 g/cm3 cm3 /mol mPa s N/m N/(m K) 1/K

At 293 K

At Tm , 12 MHz At 298 K

2.33 2.525 12.06 2.0 0.735 −0.5 × 10−3 2.56 × 10−6

5.32 5.500 13.64 0.650 −0.20 × 10−3 5.57 × 10−6

β-Sn (white) 7.30 6.978 16.24 2.71 0.545 −0.075 × 10−3 21.2 × 10−6

5845

2420

2270 1650

1790 710

m/s m/s

11 220

3450

8433

4580

3300

2050

m/s

2.25 × 10−6

1.56 × 10−6

10.2 × 10−6

13.4 × 10−6

18.3 × 10−6

23.7 × 10−6

1/MPa

98.0 112 80.5

56.6 52.9 19.9 0.33 41.6 14.9 45.6 42.8 31.2 4.6 72.30 88.40 22.03 24.00 59.40 35.78

0.951 1.732 −0.0987 1079 578 124.5

0.98 27.5 250

7.73

74.9 79.9 29.6 0.34 9.73

12.7

14.9

−0.16 −0.33 1060 36.5 4

−2.15

−2.64

165.6

129

79.6

67.1

180 15

63.9

48.3

690 2350 10

At 298 K, parallel to layer planes. The corresponding value perpendicular to the layer planes is 2.9 × 10−6 /K

15.8 5.54 0.44 93.7 68.0 −43.0 48.8 14.8 41.4 700 39

GPa GPa GPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa GPa MPa

At 293 K

Volume compressibility At 295 K

At 300 K At 300 K At 300 K At 300 K At 300 K At 300 K

The Elements

Element name

90

Table 2.1-13B(b) Elements of Group IVA (CAS notation), or Group 14 (new IUPAC notation). Mechanical properties

Table 2.1-13B(c) Elements of Group IVA (CAS notation), or Group 14 (new IUPAC notation). Thermal and thermodynamic properties Element name

Carbon

Silicon

Germanium

Tin

Lead

Chemical symbol Atomic number Z

C 6

Si 14

Ge 32

Sn 50

Pb 82

Modification Thermal conductivity λ

Diamond 1000–2320

83.7

58.6

β-Sn (white) 66.6

35.2

Molar heat capacity c p Standard entropy S0

6.11 2.360

Graphite 5.7a 1960b 8.519 5.742

20.00 18.810

33.347 31.090

27.17 51.180

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb Transformation temperature

0.5188

1.0540

3.2170

4.6360

4765.30 117.3690 24.630

1687.00 50.208 29.762 −0.10 3505 383.3

b

1900–2100

Remarks

26.51 64.800

W/(m K) W/(m K) J/(mol K) J/(mol K)

At 300 K At 300 K At 298 K At 298 K and 100 kPa

6.3230

6.8700

kJ/mol

1211.0 36.9447 30.498 −0.054

505.08 7.01940 14.243 0.028

600.61 4.7739 7.948 0.032

K kJ/mol J/(mol K)

3107 331

2876 295.8

2019 177.58

K kJ/mol K

(Vl − Vs )/Vl at Tm

Transforms to graphite

Perpendicular to layer planes. Parallel to layer planes.

The Elements 1.5 Data 91

Part 2 1.5

a

3915 710.9

Units

Part 2 1.5 Silicon

Germanium

Tin

Lead

C 6

Si 14

Ge 32

Sn 50

Pb 82

Modification Characteristics

Diamond Very hard insulator 1011

Semicondor

β-Sn(white) Ductile metal

Soft metal

110 × 10−9 46.5 × 10−4 −9.2 × 10−9

192 × 10−9 42.8 × 10−4 −12.5 × 10−9

3.72

1.94 7.2

K

309

803

Oe

0.1 302.5 0.6642

0.041 × 10−10 0.1

0.09 × 10−10 −0.1

At 300 K

5.0 4.56 3800 1820 16.0

4.42 4.11

m3 /(A s) µV/K eV eV/K V V cm2 /(V s) cm2 /(V s)

Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R a Thermoelectric coefficient Electronic band gap ∆E Temperature dependence Electronic work function Thermal work function Electron mobility Hole mobility Dielectric constant ε, static, solid Dielectric constant ε, high-frequency, solid Molar magnetic susceptibility χmol , solid c (SI) Molar magnetic susceptibility χmol , solid c (cgs) Mass magnetic susceptibility χmass , solid (SI) Mass magnetic susceptibility χmass , liquid (SI) Refractive index n, solid Refractive index n, liquid a b c

Graphite Soft conductor

Hard semicondor

1.4 × 10−5

0.45

710 0.071

−487 × 10−10 11.06 5.4

−100

1800 1400 5.68

1.107 −2.3 × 10−4 4.95 4.1 1900 480 11.7b

5.9(1)

12.0

16

24

4.81 4.00

4.25 3.83

Units

Remarks

Ωm 1/K 1/hPa nΩ m

At 293 K

ρl /ρs at Tm

At 300 K At 300 K

−74.1 × 10−6

−75.4 × 10−6

−39.2 × 10−6

−146 × 10−6

−470 × 10−6

−289 × 10−6

cm3 /mol

At 295 K

−5.88 × 10−6

−6.0 × 10−6

−3.12 × 10−6

−11.6 × 10−6

−37.4 × 10−6

−23 × 10−6

cm3 /mol

At 295 K

−6.17 × 10−6

−6.3 × 10−6

−1.8 × 10−6

−1.328 × 10−6

−3.3 × 10−6

−1.39 × 10−6

cm3 /g

At 295 K

−4.4 × 10−6 2.4173

B = 1.0–1.6 T. At 11 K and 1 MHz. The values for Sn apply to gray Sn.

4.24

4.00 (25 µm)

1.0 1.7

cm3 /g 2.01

λ = 589 nm

The Elements

Carbon

Chemical symbol Atomic number Z

Part 2

Element name

92

Table 2.1-13B(d) Elements of Group IVA (CAS notation), or Group 14 (new IUPAC notation). Electronic, electromagnetic, and optical properties

Table 2.1-13C Elements of Group IVA (CAS notation), or Group 14 (new IUPAC notation). Allotropic and high-pressure modifications Element

Silicon

Modification

α-Si

β-Si

γ -Si

δ-Si

Germanium α-Ge

β-Ge

γ -Ge

δ-Ge

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, fc Diamond 543.06

cub

hex α-La 380 628 P63 /mmc 4 D6v A3 hP4 4

cub, fc Diamond 565.74

cub, bc γ -Si 692

Fd3m Oh7 A4 cF8 8 4 245

tetr β-Sn 488.4 269.2 I41 /amd 19 D4h A5 tI4 4 4+2 253

tetr

Fd3m Oh7 A4 cF8 8 4 235

tetr β-Sn 468.6 258.5 I41 /amd 19 D4h A5 tI4 4 4+2 243

tP12 12 4+2+2 249

cI16 16

RTP

> 9.5 GPa

> 16.0 GPa

a

RTP

> 12.0 GPa

b

> 12.0 GPa

Units

636 Im3m Oh9 cI16

593 698 P43 21 2 D48

pm pm

Im3m

Decompressed β-Si. b Decompressed β-Ge. a

Table 2.1-13C Elements of Group IVA (CAS notation), or Group 14 (new IUPAC notation). Allotropic and high-pressure modifications, cont. Element

Tin

Modification

α-Sn (gray tin)

β-Sn (white tin)

γ -Sn

Lead Pb I

Pb II

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, fc Diamond 648.92

tetr, I β-Sn 583.16 318.15 I41 /amd 19 D4h A5 tI4 4

tetr In 370 337

cub, fc Cu 495.02

hex, cp Mg 326.5 538.7 P63 /mmc 4 D6h A3 hP2 2

Units

> 10.3 GPa

93

Part 2 1.5

> 9 GPa

1.5 Data

302 RT

tI2 2

Fm3m Oh5 A1 cF4 4 12 349 RTP

The Elements

Fd3m Oh7 A4 c8 8 4 281 < 291 K

pm pm

94

Part 2 1.5

Part 2

Element

Carbon

Silicon

Germanium

Tin

Lead

Ion

C4+

Si4+

Ge2+

Ge4+

Sn4+

Pb2+

15 16

26 40

73

39 53

55 69 81

Coordination number 4 6 8 10 12

119 129 140 149

Pb4+ Units pm pm pm

65 78 94

pm

Table 2.1-14A Elements of Group IVB (CAS notation), or Group 4 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-14D for

ionic radii) Element name

Titanium

Zirconium

Hafnium

Rutherfordium

Chemical symbol Atomic number Z

Ti 22

Zr 40

Hf 72

Rf 104 Radioactive [261]

Characteristics Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0 a

47.867(1)

91.224(2)

178.49(2)

4400 × 10−6 1 × 10−9 132 147 –LMN 3F 2 [Ar]3d2 4s2 4+, 3+ 0.079 1.32 6.8282 13.5755 27.4917 43.2672 −1.630 −0.368 −0.04

220 × 10−6 3 × 10−11 145 160 –MNO 3F 2 [Kr]4d2 5s2 4+ 0.426 1.22 6.63390 13.13 22.99 34.34 −1.553a

4.5 × 10−6 7 × 10−12 144 156 –NOP 3F 2 [Xe]4f14 5d2 6s2 4+ near 0 (1.23) 6.82507 14.9 23.3 33.33

Reaction type ZrO2 + 4H+ + 4e− = Zr + 2H2 O.

Units

Remarks

pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12

–OPQ 3F 2

eV Allred and Rochow eV eV eV eV V V V

Reaction type Ti2+ + 2e− = Ti Reaction type Ti3+ + e− = Ti2+ Reaction type Ti4+ + e− = Ti3+

The Elements

Table 2.1-13D Elements of Group IVA (CAS notation), or Group 14 (new IUPAC notation). Ionic radii (determined from crystal structures)

The Elements

1.5 Data

Element name

Titanium

Zirconium

Hafnium

Rutherfordium

Chemical symbol Atomic number Z

Ti 22

Zr 40

Hf 72

Rf 104

Modification Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

α-Ti hex Mg 295.03 468.36 P63 /mmc 4 D6h A3 hP2 2 12 291

α-Zr hex Mg 323.17 514.76 P63 /mmc 4 D6h A3 hP2 2 6+6

α-Hf hex Mg 319.46 505.11 P63 /mmc 4 D6h A3 hP2 2 12 318

Units

Remarks

pm pm

pm

Table 2.1-14B(b) Elements of Group IVB (CAS notation), or Group 4 (new IUPAC notation). Mechanical properties Element name

Titanium

Zirconium

Hafnium

Rutherfordium

Chemical symbol Atomic number Z

Ti 22

Zr 40

Hf 72

Rf 104

Density , solid Density , liquid Molar volume Vmol Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

4.50 4.110 10.55 1.65 0.26 × 10−3 8.35 × 10−6

6.49 5.80 14.02 1.48 −0.2 × 10−3 5.78 × 10−6

13.10 12.00 13.41 1.63 −0.21 × 10−3 5.9 × 10−6

Units g/cm3 g/cm3 cm3 /mol N/m N/(m K) 1/K

2920 6260

1950 4360

2000 3671

m/s m/s

0.779 × 10−5 1.08 × 10−5

0.80 × 10−5

1/MPa

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness

102 37.3 0.35 9.69 6.86 21.5 −4.71 −1.82 160 181 46.5 90 66 235 2000–3500

138 53.0 0.29 7.16 6.13 18.0 −2.48 −1.57 181 197 55.7 77 66 400 1760

GPa GPa

68.0 24.8 0.37 10.1 8.0 30.1 −4.0 −2.4 144 166 33.4 74 67 150–450 903

1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa MPa

Remarks

Near Tm

Volume compressibility

Part 2 1.5

Table 2.1-14B(a) Elements of Group IVB (CAS notation), or Group 4 (new IUPAC notation). Crystallographic properties (see Table 2.1-14C for allotropic and high-pressure modifications)

95

96

Part 2

The Elements

Part 2 1.5

Table 2.1-14B(c) Elements of Group IVB (CAS notation), or Group 4 (new IUPAC notation). Thermal and thermodynamic

properties Element name

Titanium

Zirconium

Hafnium

Rutherfordium

Chemical symbol Atomic number Z

Ti 22

Zr 40

Hf 72

Rf 104

21 25.02 30.720

α-Zr 22.7 25.36 39.181

23.0 25.3 43.560

W/(m K) J/(mol K) J/(mol K)

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Volume change ∆Vm

4.8240

5.5663

5.8450

kJ/mol

1941.00 14.1460 7.288

2127.85 20.9978 9.868

2506.00 27.1960 10.852

K kJ/mol J/(mol K)

Boiling temperature Tb Enthalpy change ∆Hb

3631 410.0

Units Modification Thermal conductivity λ Molar heat capacity c p Standard entropy S0

Remarks

At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm 4203 561.3

4963 575.5

K kJ/mol

Table 2.1-14B(d) Elements of Group IVB (CAS notation), or Group 4 (new IUPAC notation). Electronic, electromagnetic,

and optical properties Element name

Titanium

Zirconium

Hafnium

Rutherfordium

Chemical symbol Atomic number Z

Ti 22

Zr 40

Hf 72

Rf 104

Hard, light metal 390 54.6 × 10−4 −1.118 × 10−9 0.39

α-Zr Resistant metal 410 44.0 × 10−4 0.33 × 10−9 0.55

100

47

−1.2 × 10−10

0.212 × 10−10

0.43 × 10−10

m3 /(A s)

4.31 4.16 1898 × 10−6

4.05 4.12 1508 × 10−6

3.9 3.53 892 × 10−6

V V cm3 /mol

At 295 K

151 × 10−6

120 × 10−6

71 × 10−6

cm3 /mol

At 295 K

40.1 × 10−6

16.8 × 10−6

5.3 × 10−6

cm3 /g

At 295 K

Modification Characteristics Electrical resistivity ρs Temperature coefficient Pressure coefficient Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R Electronic work function Thermal work function Molar magnetic susceptibility χmol , solid (SI) Molar magnetic susceptibility χmol , solid (cgs) Mass magnetic susceptibility χmass , solid (SI)

Metal 296 44 × 10−4 −0.87 × 10−9 0.35

Units

Remarks

nΩ m 1/K 1/hPa K

At 293 K

Oe At 300 K, B = 0.4–2.8 T

The Elements

1.5 Data

Element

Titanium

Modification

α-Ti

β-Ti

Zirconium α-Zr

β-Zr

Hafnium α-Hf

β-Hf

Hf-II

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex, cp Mg 295.03 468.36 P63 /mmc 4 D6h A3 hP2 2 12 291

cub, bc W 330.65

cub, bc W 360.9

hex

Im3m Oh9 A2 cI2 2 8 313

hex, cp Mg 319.46 505.11 P63 /mmc 4 D6h A3 hP2 2 12 318

cub, bc W 361.0

Im3m Oh9 A2 cI2 2 8 286

hex, cp Mg 323.17 514.76 P63 /mmc 4 D6h A3 hP2 2 6+6

Im3m O9h A2 cI2 2 8 313

RT

>1173 K

>1138 K

RTP

>2268 K

Units

RT

pm pm

>38.8 GPa

Table 2.1-14D Elements of Group IVB (CAS notation), or Group 4 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Titanium

Ion

Ti2+

Coordination number 4 6 8 9

86

Zirconium

Hafnium

Ti3+

Ti4+

Zr4+

Hf

67

42 61 74

59 72 84 89

58 71 83

4+

Units pm pm pm pm

Part 2 1.5

Table 2.1-14C Elements of Group IVB (CAS notation), or Group 4 (new IUPAC notation). Allotropic and high-pressure

modifications

97

98

Part 2 1.5

Part 2

Nitrogen

Phosphorus

Arsenic

Antimony

Bismuth

Chemical symbol Atomic number Z

N 7

P 15

As 33

Sb 51

Bi 83

Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet

14.00674(7)

30.973761(2)

74.92160(2)

121.760(1)

208.98038(2)

20 × 10−6

1200 × 10−6

5 × 10−6

0.2 × 10−6

0.2 × 10−6

150 × 10−6 70 92

0.06 × 10−6 110 128

3.7 × 10−9 121 139

2.4 × 10−10 141 159

2 × 10−11 146 182

Atomic radius rvdW Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy 5th ionization energy 6th ionization energy

155 KL 4S 3/2 [He]2s2 2p3 5+, 3+, 3− Not stable 3.07 14.53414 29.6013 47.44924 77.4735 97.8902 552.0718

190 KLM 4S 3/2 [Ne]3s2 3p3 5+, 3+, 3− 0.747 2.06 10.48669 19.7694 30.2027 51.4439 65.0251 220.421

200 –LMN 4S 3/2 [Ar]3d10 4s2 4p3 5+, 3+, 3− 0.81 2.20 9.8152 18.633 28.351 50.13 62.63 127.6

220 –MNO 4S 3/2 [Kr]4d10 5s2 5p3 5+, 3+, 3− 1.046 1.82 8.64 16.53051 25.3 44.2 56 108

240 –NOP 4S 3/2 [Xe]4f14 5d10 6s2 6p3 5+, 3+ 0.946 (1.67) 7.289 16.69 25.56 45.3 56.0 88.3

Units

Remarks

Mass ratio

pm pm pm

Mass ratio Covalent radius Metallic radius, CN = 12 van der Waals radius

eV Allred and Rochow eV eV eV eV eV eV

The Elements

Element name

2.1.5.3 Elements of the Main Groups and Subgroup V to VIII

Table 2.1-15A Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-15D

for ionic radii)

The Elements

1.5 Data

Element name

Nitrogen

Phosphorus

Arsenic

Antimony

Bismuth

Chemical symbol Atomic number Z

N 7

P 15

As 33

Sb 51

Bi 83

State Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle α Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

N2 , 4.2 K cub, sc α-N 565.9

P, black orth, C P, black 331.36 1047.8 43 763

Pa3 Th6

Cmca 18 D2h A11 oC8 8 2+1 222

Units

cP8 4×2

trig, R α-As 413.20

trig, R α-As 450.65

trig, R α-As 474.60

54.12 R3m 5 D3d A7 hR2 2 3 252

57.11 R3m 5 D3d A7 hR2 2 3 291

57.23 R3m 5 D3d A7 hR2 2 3 307

pm pm pm deg

pm

Remarks

Part 2 1.5

Table 2.1-15B(a) Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Crystallographic properties (see Table 2.1-15C for allotropic and high-pressure modifications)

99

100

Part 2 1.5

Part 2 The Elements

Table 2.1-15B(b) Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Mechanical properties Element name

Nitrogen

Phosphorus

Arsenic

Antimony

Bismuth

Chemical symbol Atomic number Z

N 7

P 15

As 33

Sb 51

Bi 83

State Density , solid Density , liquid Density , gas Molar volume Vmol Viscosity η, gas Viscosity η, liquid Surface tension γ , liquid Coefficient of linear thermal expansion α Sound velocity, gas Sound velocity, liquid Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

N2 gas

P, black 2.690

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic compliance s14

1.2 a,b

Units

a b

Solid. Estimated.

1.2506 × 10−3 13.65 18.9

5.72

6.68

9.80 10.05

12.95

18.20

21.44

4.7 × 10−6

1.50 0.384 8.5 × 10−6

1.65 0.376 13.4 × 10−6

g/cm3 g/cm3 g/cm3 cm3 /mol µPa s mPa s N/m 1/K

1800

1635 1140

m/s m/s m/s

3140

2298

m/s

2.6 × 10−5

2.86 × 10−5

1/MPa

54.4 20.6 0.25 16.1 29.9 38.9 −6.1 −6.2 −12.3

34.0 12.8 0.33 26.0 42.0 114 −7.9 −11.9 −21.2

GPa GPa

336.9 929 (70 K)

30.4 b

22

46.71 202.9 44.91 36.94 −88.2 1.80

1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa

Remarks

At 273 K At 323 K Near Tm

Volume compressibility

Table 2.1-15B(b) Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Mechanical properties, cont. Element name

Nitrogen

Phosphorus

Arsenic

Antimony

Bismuth

Chemical symbol Atomic number Z

N 7

P 15

As 33

Sb 51

Bi 83

State Elastic stiffness c11 Elastic stiffness c22 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c55 Elastic stiffness c66 Elastic stiffness c12 Elastic stiffness c13 Elastic stiffness c14 Brinell hardness Mohs hardness Solubility in water αW , 293 K

N2 gas

P, black 73.9 277 53.7 15.6 11.5 56.7

Units

53.7

123.6

101

63.4

59.1 22.6

44.9 39.5

37.9 11.5

19.7 62.3 −4.16

32.2 27.6 21.8

24.5 24.9 7.3 200

Remarks

GPa GPa GPa GPa GPa GPa GPa GPa GPa

3.5 αW = vol (gas)/vol (water)

The Elements 1.5 Data 101

Part 2 1.5

0.01557

102

Part 2

The Elements

Part 2 1.5

Table 2.1-15B(c) Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Thermal and thermodynamic

properties Element name

Nitrogen

Phosphorus

Arsenic

Antimony

Bismuth

Chemical symbol Atomic number Z

N 7

P 15

As 33

Sb 51

Bi 83

State Thermal conductivity λ Molar heat capacity c p Standard entropy S0

N2 gas 0.02598 14.560 191.611

P, white a 23.824 41.090

α-As 50.0 24.65 35.689

25.9 25.23 45.522

7.87 25.52 56.735

W/(m K) J/(mol K) J/(mol K)

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Volume change ∆Vm

8.6692

5.3600

5.1170

5.8702

6.4266

kJ/mol

63.1458 0.720

317.30 0.6590 2.077

1090.00 24.4429 22.425 0.10

903.78 19.8740 21.990 −0.008

544.55 11.2968 20.745 −0.33

K kJ/mol J/(mol K)

Boiling temperature Tb Enthalpy change ∆Hb Critical temperature Tc Critical pressure pc Critical density c Triple-point temperature Ttr Triple-point pressure ptr

77.35 5.577 126.25 3.40 0.311 63.14 12.5

1860 165.8

1837 174.1

K kJ/mol K MPa g/cm3 K kPa

Units

a

550 51.9

34.8 1089 36

Remarks

At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm

In Landolt–Börnstein, Group IV, Vol. 19A, Part 1 [1.4], the white form of phosphorus has been chosen as the reference phase for all phosphides because the more stable red form is difficult to characterize.

Table 2.1-15B(d) Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Electronic, electromagnetic, and optical properties Element name

Nitrogen

Phosphorus

Arsenic

Antimony

Bismuth

Chemical symbol Atomic number Z

N 7

P 15

As 33

Sb 51

Bi 83

State Characteristics Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistvity ρl Resistivity ratio Electronic band gap ∆E Temperature coefficient Electronic work function Thermal work function Electron mobility Hole mobility Hall coefficient R Thermoelectric coefficient Dielectric constant (ε − 1), gas Dielectric constant ε, liquid Dielectric constant ε, solid Molar magnetic susceptibility χmol , (SI) Molar magnetic susceptibility χmol , (cgs) Mass magnetic susceptibility χmass , (SI) Refractive index (n − 1), gas Refractive index n, liquid Refractive index n, solid

N2 gas Gas

P, black Semiconductor

0.57 8 × 10−4

Semiconductor 260 42 × 10−4

Semimetal 370 51.1 × 10−4 6.0 × 10−9 1135 0.61

Brittle metal 1068 45.4 × 10−4 15.2 × 10−9 1280 0.43

1.14 4.79 5.71

4.56 4.08

4.36 4.28

0.45 × 10−7

0.27 × 10−7 35

−6.33 × 10−7 −70

220 350

Units

Remarks

nΩ m 1/K 1/hPa nΩ m

Solid, at RT

eV eV/K V V cm2 /(V s) cm2 /(V s) m3 /(A s) µV/K

580 × 10−6 1.45

Liquid ρl /ρs at Tm At 300 K

B = 0.4–1.0 T At 293 K At 74.8 K

−151 × 10−6

a,b

11.2 (optical) −70.4 × 10−6 c

−1244 × 10−6

−3520 × 10−6

cm3 /mol

At 295 K

−12.0 × 10−6

a,b

−5.60 × 10−6

−99 × 10−6

−280.1 × 10−6

cm3 /mol

At 295 K

−10 × 10−6

−16.8 × 10−6

cm3 /g

At 295 K

−5.4 × 10−6

−3.9 × 10−6

c

297 × 10−6 1.929 (78 K)

589.3 nm 589.3 nm 3.35 (0.8 µm)

White P: molar magnetic susceptibility: −26.7 × 10−6 (cgs) and −335 × 10−6 (SI) cm3 /mol. b Red P: molar magnetic susceptibility: −20.8 × 10−6 (cgs) and −261 × 10−6 (SI) cm3 /mol. c Yellow As: molar magnetic susceptibility: −292 × 10−6 (SI) and −23.2 × 10−6 (cgs) cm3 /mol.

The Elements

a

1.5 Data 103

Part 2 1.5

Part 2 1.5

Part 2

Arsenic

Nitrogen

Modification

α-N

β-N

γ -N

α-As

ε-As

Antimony Sb-I

Sb-II

Sb-III

Sb-IV

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle α Lattice angle β Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, P α-N 565.9

hex La 404.6

tetr

trig, R α-As 450.65

hex, cp Mg 337.6

mon

662.9

510.1

orth α-Ga 362 1085 448

cub

395.7

trig, R As 413.20

Units

54.12

534.1

556 404 422

57.11 86.0

Pa3 Th6 cP8 4×2

< 20 K

P63 /mmc 4 D6v A9 hP4 4 3

> 35.6 K

P42 /mnm 12 D4h tP4 4

R3m 5 D3d A7 hR2 2 3 252

Cmca 18 D2h A11 oC8 8

> 721 K

20 K, > 3.3 GPa

R3m 5 D3d A7 hR2 2 3 291 RTP

Pm3m Oh1

P63 /mmc 4 D6h

cP1 1

A3 hP2 2 pm

> 5.0 GPa

> 7.5 GPa

14.0 GPa

Table 2.1-15C Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Allotropic and high-pressure modifications, cont. Element

Bismuth

Modification

α-Bi

β-Bi

γ -Bi

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle α Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

trig, R α-As 474.60

mon

mon

δ-Bi

ε-Bi

ζ-Bi Units

57.23 R3m 5 D3d A7 hR2 2 3 307 RTP

cub, bc W 3800

605 420 465 C2/m 3 C2h mC4 4

pm pm pm deg

Im3m Oh9 A2 cI2 2

mP3 3

pm > 0.28 GPa

> 3.0 GPa

> 4.3 GPa

> 6.5 GPa

> 9.0 GPa

pm pm pm deg deg

The Elements

Element

299.2

104

Table 2.1-15C Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Allotropic and high-pressure modifications

Table 2.1-15D Elements of Group VA (CAS notation), or Group 15 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Nitrogen

Ion

N3+

Coordination number 4 5 6 16 8

N5+

Phosphorus

Arsenic

P5+

As3+

17 13

38

58

Antimony As5+

Sb3+

34

76

46

76

Bismuth Sb5+

60

Bi3+

96 103 117

Bi5+

76

Units pm pm pm pm

Table 2.1-16A Elements of Group VB (CAS notation), or Group 5 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-16D for

ionic radii) Element name

Vanadium

Niobium

Tantalum

Dubnium

Chemical symbol Atomic number Z

V 23

Nb 41

Ta 73

Db 105

Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy 5th ionization energy Standard electrode potential E 0

50.9415(1)

92.90638(2)

180.9479(1)

[262]

150 × 10−6 2.5 × 10−9 122 135 –LMN 4F 3/2 [Ar]3d3 4s2 5+, 4+, 3+, 2+ 0.525 1.45 6.7463 14.66 29.311 46.709 65.282 −1.175 −0.255

20 × 10−6 1 × 10−11 134 147 –MNO 6D 1/2 [Kr]4d4 5s1 5+, 3+ 0.893 1.23 6.75885 14.32 25.04 38.3 50.55

2.1 × 10−6 2 × 10−12 134 147 –NOP 4F 3/2 [Xe]4f14 5d3 6s2 5+ 0.322 (1.33) 7.89

Units

Remarks

pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12

–OPQ

eV Allred and Rochow

Reaction type V2+ + 2e− = V Reaction type V3+ + e− = V2+

The Elements 1.5 Data 105

Part 2 1.5

eV eV eV eV eV V V

106

Part 2

The Elements

Part 2 1.5

Table 2.1-16B(a) Elements of Group VB (CAS notation), or Group 5 (new IUPAC notation). Crystallographic properties Element name

Vanadium

Niobium

Tantalum

Dubnium

Chemical symbol Atomic number Z

V 23

Nb 41

Ta 73

Db 105

Crystal system, Bravais lattice Structure type Lattice constant a Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

cub, bc W 302.38 Im3m Oh9 A2 cI2 2 8 263

cub, bc W 330.07 Im3m Oh9 A2 cI2 2 8 285

cub, bc W 330.31 Im3m Oh9 A2 cI2 2 8 285

Units

Remarks

pm

pm

Table 2.1-16B(b) Elements of Group VB (CAS notation), or Group 5 (new IUPAC notation). Mechanical properties Element name

Vanadium

Niobium

Tantalum

Dubnium

Chemical symbol Atomic number Z

V 23

Nb 41

Ta 73

Db 105

Density , solid Density , liquid Molar volume Vmol Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

5.80 5.55 8.34 1.95 0.3 × 10−3 8.3× 10−6

8.35 7.830 10.84 2.0 −0.24 × 10−3 7.34 × 10−6

16.60 15,00 10.87 2.15 −0.25 × 10−3 6.64 × 10−6

Units g/cm3 g/cm3 cm3 /mol N/m N/(m K) 1/K

2780

2100

2900

m/s

6000

4900

4100

m/s

0.63 × 10−5

0.56 × 10−5

0.465 × 10−5

1/MPa

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s44 Elastic compliance s12 Elastic stiffness c11 Elastic stiffness c44 Elastic stiffness c12 Vickers hardness

127 46.6 0.36 6.75 23.2 −2.31 230 43.1 120 630

104 59.5 0.38 6.56 35.2 −2.29 245 28.4 132 70–250 (HV 10)

185 64.7 0.35 6.89 12.1 −2.58 264 82.6 158 80–300 (HV 10)

GPa GPa

Remarks

300 K

Volume compressibility

1/TPa 1/TPa 1/TPa GPa GPa GPa At 293 K

The Elements

1.5 Data

Element name

Vanadium

Niobium

Tantalum

Dubnium

Chemical symbol Atomic number Z

V 23

Nb 41

Ta 73

Db 105

Thermal conductivity λ Molar heat capacity c p Standard entropy S0

30.7 24.90 30.890

59.0 24.69 36.270

60.7 25.30 41.472

Units W/(m K) J/(mol K) J/(mol K)

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb

4.5070 2183.00 21.5000 9.849

5.2200 2750.00 30.0000 10.909

5.6819 3290.00 36.5682 11.115

kJ/mol K kJ/mol J/(mol K)

3690 451.8

5017 683.2

5778 743.1

K kJ/mol

Remarks At 300 K At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm

Table 2.1-16B(d) Elements of Group VB (CAS notation), or Group 5 (new IUPAC notation). Electronic, electromagnetic, and optical properties. There is no Table 2.1-16C, because no allotropic or high-pressure modifictions are known Element name

Vanadium

Niobium

Tantalum

Dubnium

Chemical symbol Atomic number Z

V 23

Nb 41

Ta 73

Db 105

Electrical resistivity ρs Temperature coefficient Pressure coefficient Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R

248 39.0 × 10−4 −1.6 × 10−9 5.3

152 25.8 × 10−4 −1.37 × 10−9 9.13

125 38.2 × 10−4 −1.62 × 10−9 4.49

Units nΩ m 1/K 1/hPa K

1020

1980

830

Oe

0.82 × 10−10

0.88 × 10−10

1.01 × 10−10

m3 /(A s)

4.3 4.09 3581 × 10−6

4.3 3.99 2614 × 10−6

−5.0 4.3 4.25 1935 × 10−6

µV/K V V cm3 /mol

At 295 K

285 × 10−6

208 × 10−6

154 × 10−6

cm3 /mol

At 295 K

62.8 × 10−6

27.6 × 10−6

10.7 × 10−6

cm3 /g

At 295 K

Thermoelectric coefficient Electronic work function Thermal work function Molar magnetic susceptibility, solid χmol , (SI) Molar magnetic susceptibility, solid χmol , (cgs) Mass magnetic susceptibility, solid χmass , (SI)

Remarks At RT

At 273 K, B = 0.5–2.9 T

Part 2 1.5

Table 2.1-16B(c) Elements of Group VB (CAS notation), or Group 5 (new IUPAC notation). Thermal and thermodynamic

properties

107

Part 2 1.5 V2+

Coordination number 4 5 6 8

79

V3+

64

Niobium V4+

53 58 72

V5+ 36 46 54

Nb3+

Tantalum Nb4+

Nb5+

Ta3+

Ta4+

Ta5+

48 72 79

68

64 74

72

68

64

The Elements

Vanadium

Ion

Units pm pm pm pm

Table 2.1-17A Elements of Group VIA (CAS notation), or Group 16 (new IUPAP notation). Atomic, ionic and molecular properties (see Table 2.1-17D for

ionic radii) Element name

Oxygen

Sulfur

Selenium

Tellurium

Polonium

Chemical symbol Atomic number Z

O 8

S 16

Se 34

Te 52

Po 84 Radioactive [209]

Units Characteristics Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet

15.9994(3)

32.066(6)

78.96(3)

127.60(3)

464 000 × 10−6

520 × 10−6

0.09 × 10−6

2 × 10−9

880 000 × 10−6 66

905 × 10−6 104 127

2 × 10−10 117 140

137 160

146 176

pm pm

150 KL 3P 2 [He]2s2 2p4 2− 1.46

185 KLM 3P 2 [Ne]3s2 3p4 6+, 4+, 2+, 2− 2.08

200 –LMN 3P 2 [Ar]3d10 4s2 4p4 6+, 4+, 2+, 2− 2.02

220 –MNO 3P 2 [Kr]4d10 5s2 5p4 6+, 4+, 2+, 2− 1.97

–NOP 3P 2 [Xe]4f14 5d10 6s2 6p4 4+, 2+ 1.9

eV

−8.75

−5.51

Electronegativity χA

3.50

2.44

2.48

2.01

(1.76)

1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

13.61806 35.11730 54.9355 77.41353

10.36001 23.3379 34.79 47.222 −0.476

9.75238 21.19 30.8204 42.9450 −0.924

9.0096 18.6 27.96 37.41 −1.143

8.41671

Atomic radius rvdW Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity

eV

+0.568

Remarks

Mass ratio

+0.56

Part 2

Element

108

Table 2.1-16D Elements of Group VB (CAS notation), or Group 5 (new IUPAC notation). Ionic radii (determined from crystal structures)

eV eV eV eV V V V

Mass ratio Covalent radius Metallic radius, CN = 12 van der Waals radius

Reaction type O + e− = O− Reaction type O− + e− = O2− Allred and Rochow

Reaction type Te2− = Te + 2e− Reaction type Po3+ + 3e− = Po Reaction type Te4+ + 4e− = Te

The Elements

1.5 Data

Element name

Oxygen

Sulfur

Selenium

Tellurium

Polonium

Chemical symbol Atomic number Z

O 8

S 16

Se 34

Te 52

Po 84

State

α-O, T < 23 K mon, C α-O 540.3 342.9 508.6 132.53 C2/m 3 C2h

S8 , α-S

Gray Se, Se chains hex γ -Se 436.55

hex γ -Se 445.61

495.76

592.71

P31 21 D34 A8 hP3 3 2 237

P31 21 D34 A8 hP3 3 2+4 283

Units

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle γ Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

mC4 2×2

orth, F α-S 1046.4 1286.60 2448.60 Fddd 24 D2h A16 oF128 128 2 204

α-Po cub, sc α-Po 336.6

Pm3m Oh1 Ah cP1 1 6 337

pm pm pm deg

pm

Remarks

Part 2 1.5

Table 2.1-17B(a) Elements of Group VIA (CAS notation), or Group 16 (new IUPAC notation). Crystallographic properties (see Table 2.1-17C for allotropic and high-pressure modifications)

109

110

Part 2

The Elements

Part 2 1.5

Table 2.1-17B(b) Elements of Group VIA (CAS notation), or Group 16 (new IUPAC notation). Mechanical properties Element name

Oxygen

Sulfur

Selenium

Tellurium

Polonium

Chemical symbol Atomic number Z

O 8

S 16

Se 34

Te 52

Po 84

State Density , solid Density , liquid Density , gas Molar volume Vmol Viscosity η, gas Viscosity η, liquid Surface tension, liquid Coefficient of linear thermal expansion α Sound velocity, gas Sound velocity, liquid Compressibility κ

O2 gas

α-S 2.037 1.819

Gray Se 4.79 3.990

6.24 5.797

9.40

15.49

16.48

20.45

22.4

11.5 0.061 74.33 × 10−6

1260 0.106 36.9 × 10−6

0.186 16.75 × 10−6

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s22 Elastic compliance s33 Elastic compliance s44 Elastic compliance s55 Elastic compliance s66 Elastic compliance s12 Elastic compliance s13 Elastic compliance s23 Elastic stiffness c11 Elastic stiffness c22 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c55 Elastic stiffness c66 Elastic stiffness c12 Elastic stiffness c13 Elastic stiffness c23 Tensile strength Brinell hardness Mohs hardness Solubility in water αW a

Estimated.

b

1.429 × 10−3 8.00 19.5

23 × 10−6

336.95 (70 K) 1079 (70 K)

1280 b

13.0 × 10−5

11.6 × 10−5

4.8 × 10−5

17.8 a

58.0 6.46 0.45

47.1 16.7 0.23

74.6 111 75.4 121 234 229 −13.1 −7.1 −45.8 14.22 12.68 18.30 8.27 4.28 4.37 2.99 3.14 7.95

3640 b

−570 b

2.60 b

0.275 b

2.06 b

10.8–12.25 250

Units

Remarks

g/cm3 g/cm3 g/cm3 cm3 /mol µPa s mPa s N/m 1/K

At 293 K

m/s m/s 1/MPa 26 a

At Tm At Tm

Volume compressibilty

GPa GPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa GPa GPa GPa GPa MPa

2.0 c

0.0310

γ -Oxygen, T = 54.4 K.

At 293 K and 1013 hPa c

αW = vol (gas)/vol (water).

The Elements

1.5 Data

properties Element name

Oxygen

Sulfur

Selenium

Tellurium

Polonium

Chemical symbol Atomic number Z

O 8

S 16

Se 34

Te 52

Po 84

State Thermal conductivity λ Molar heat capacity c p Standard entropy S0

O2 gas 0.0245 14.690 205.147

α-S 0.269 22.70 32.070

α-Se 2.48 25.04 41.966

α-Te 1.7 25.73 49.221

α-Po 20

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm

8.6800

4.4120

5.5145

54.361 0.444

388.36 1.7210 4.431 0.515

Boiling temperature Tb Enthalpy change ∆Hb Critical temperature Tc Critical pressure pc Critical density c Triple-point temperature Ttr Triple-point pressure ptr

90.18 6.2 154.58 5.4 0.419 54.4 1.52

882 9.62

Units

Remarks

62.000

W/(m K) J/(mol K) J/(mol K)

At STP At 298 K At 298 K and 100 kPa

6.0800

6.700

kJ/mol

494 6.6944 13.551 +0.168

722.66 17.3760 24.045 0.05

527.00 10.000 18.975

K kJ/mol J/(mol K)

958 90 1863 38

1261 104.6

1335 100.8

(Vl − Vs )/Vl at Tm K kJ/mol K MPa g/cm3 K hPa

Part 2 1.5

Table 2.1-17B(c) Elements of Group VIA (CAS notation), or Group 16 (new IUPAC notation). Thermal and thermodynamic

111

Part 2 1.5 Sulfur

Selenium

Tellurium

Polonium

Chemical symbol Atomic number Z

O 8

S 16

Se 34

Te 52

Po 84

State Characteristics Electrical resistivity ρs Electrical resistivity ρl Resistivity ratio at Tm Hall coefficient R Thermoelectric coefficient Electronic band gap ∆E Temperature coefficient Electronic work function Thermal work function Electron mobility Hole mobility Dielectric constant (ε − 1), gas Dielectric constant ε, liquid Dielectric constant ε, solid

O2 gas

Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmass (SI) Mass magnetic susceptibility χmass , liquid (SI) Refractive index (n − 1), gas Refractive index n, liquid Refractive index n, solid

43 341 × 10−6

a c

Liquid O2 , 90 K, At 280 K.

96 748 cm3 /mol;

Gray Se Semiconductor 100 20 1.0

Solid insulator

3.6 −6.8 × 10−4

1.79 −9 × 10−4 5.9 4.72

Semiconductor 1 –50 6.0 µΩ m 0.048–0.091 0.24 × 10−10 400 0.33 4.95 4.73 1100 560

Units

Remarks

MΩ m MΩ m

At RT

m3 /(A s) µV/K eV eV/K V V cm2 /(V s) cm2 /(V s)

At 298 K

Volatile metal

525 × 10−6 1.505

At 373 K At 81 K

3449 × 10−6 1.34 × 10−6

a

b c

−195 × 10−6

8.5 (λ = 3.3 cm) −314 × 10−6

5.0 c 2.2 ⊥ c −478 × 10−6

cm3 /mol

At 295 K

−15.5 × 10−6

−25 × 10−6

−38 × 10−6

cm3 /mol

At 295 K

−6.09 × 10−6

−4.0 × 10−6

−3.9 × 10−6

cm3 /g

At 295 K

−0.6 × 10−6

cm3 /g

270.6 × 10−6 1.221 (92 K) 4.0 solid O2 , 54 K,

128 177 cm3 /mol.

b

λ = 589.3 nm λ = 589.3 nm λ = 589.3 nm

Liquid O2 , 90 K, 7699 cm3 /mol; solid O2 , 54 K, 10 200 cm3 /mol.

Further remarks Liquid O3 has a molar magnetic susceptibility of 84.2 × 10−6 cm3 /mol (SI) and 6.7 × 10−6 cm3 /mol (cgs). The values given for the molar magnetic susceptibility χmol of sulfur apply to rhombic sulfur. The corresponding values for monoclinic sulfur are − 187 × 10−6 cm3 /mol (SI) and − 14.9 × 10−6 cm3 /mol (cgs).

The Elements

Oxygen

Part 2

Element name

112

Table 2.1-17B(d) Elements of Group VIA (CAS notation), or Group 16 (new IUPAC notation). Electronic, electromagnetic, and optical properties

The Elements

1.5 Data

modifications Element

Oxygen

Modification

α-O

β-O

γ -O

γ -Se

Selenium α-Se

β-Se

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle α Lattice angle γ Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability Characteristics

mon, C α-O 540.3 342.9 508.6

trig, R α-As 421.0

cub, P γ -O 683

hex γ -Se 436.55

mon

mon

905.4 908.3 233.6

1501.8 1471.3 887.9

90.82 P21 /m 2 C2h

93.6 P21 /b 5 C2h

2 233–235 RT Red, Se8 rings;

mP32 32 2 233–236 RT Red, Se8 rings

Units

495.76 46.27

132.53 C2/m 3 C2h

R3m 5 D3d A7 hR2 2

mC4 2×2

< 23 K

Pm3m Oh3 A15 cP16 16

> 23.9 K

P31 21 D34 A8 hP3 3 2 237 RT Gray, Se chains

> 43.6 K

pm pm pm deg deg

Table 2.1-17C Elements of Group VIA, or Group 16. Allotropic and high-pressure modifications, cont. Element

Tellurium

Modification

α-Te

β-Te

γ -Te

Polonium α-Po

β-Po

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Lattice angle α Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex γ -Se 445.61 592.71

trig, R α-As 469

trig, R α-Hg 300.2

cub, P α-Po 336.6

trig, R α-Hg 337.3

53.30 R3m 5 D3d A7 hR2 2

103.3 R3m 5 D3d A10 hR1 1

> 2 GPa

> 7.0 GPa

Pm3m Oh1 Ah cP1 1 6 337 RTP

98.08 R3m 5 D3d A10 hR1 1 6 337 > 327 K

Units

P31 21 D34 A8 hP3 3 2+4 283 RTP

pm pm deg

Table 2.1-17D Elements of Group VIA (CAS notation), or Group 16 (new IUPAC notation). Ionic radii (determined from

crystal structures) Element

Oxygen

Sulfur

Ion

O2−

S2−2

Coordination number 2 4 6 8

Selenium S4+

S6+

Se2−

Se4+

Tellurium Se6+

Te2−

Te4+

Polonium Te6+

Po4+

121 140 142

184

37

12 29

198

50

28 42

221

66 97

43 56

97

Units pm pm pm pm

Part 2 1.5

Table 2.1-17C Elements of Group VIA (CAS notation), or Group 16 (new IUPAC notation). Allotropic and high-pressure

113

114

Part 2 1.5

Part 2

ionic radii) Element name

Chromium

Molybdenum

Tungsten

Seaborgium

Chemical symbol Atomic number Z

Cr 24

Mo 42

W 74

Sg 106

Characteristics Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

Units

Remarks

pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12

Radioactive 51.9961(6)

95.94(1)

183.84(1)

200 × 10−6 3 × 10−10 118 129 –LMN 7S 3 [Ar]3d5 4s1 6+, 3+, 2+

2.3 × 10−6 0.01 × 10−6 130 140 –MNO 7S 3 [Kr]4d5 5s1 6+, 5+, 4+, 3+, 2+, 1+, 2− 0.748 1.30 7.09243 16.16 27.13 46.4

1 × 10−6 1 × 10−10 130 141 –NOP 5D 0 [Xe]4f14 5d4 6s2 6+, 5+, 4+, 3+, 2+, 1−, 2− 0.815 (1.40) 7.98

0.666 1.56 6.76664 16.4857 30.96 49.16 −0.913 −0.744 −0.407

−0.2

–OPQ

eV Allred and Rochow eV eV eV eV V V V

Reaction type Cr2+ + 2e− = Cr Reaction type Cr3+ + 3e− = Cr Reaction type Cr3+ + e− = Cr2+

The Elements

Table 2.1-18A Elements of Group VIB (CAS notation), or Group 6 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-18D for

The Elements

1.5 Data

Element name

Chromium

Molybdenum

Tungsten

Seaborgium

Chemical symbol Atomic number Z

Cr 24

Mo 42

W 74

Sg 106

Crystal system, Bravais lattice Structure type Lattice constant a Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

cub, bc W 288.47 Im3m Oh9 A2 cI2 2 8 249

cub, bc W 314.70 Im3m Oh9 A2 cI2 2 8 272

cub, bc W 316.51 Im3m Oh9 A2 cI2 2 8 273

Units

Remarks

pm

pm

Table 2.1-18B(b) Elements of Group VIB (CAS notation), or Group 6 (new IUPAC notation). Mechanical properties Element name

Chromium

Molybdenum

Tungsten

Seaborgium

Chemical symbol Atomic number Z

Cr 24

Mo 42

W 74

Sg 106

Density , solid Density , liquid Molar volume Vmol Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

7.19 6.460 7.23 1.6

10.220

6.2 × 10−6

9.39 2.25 −0.3 × 10−3 5.35 × 10−6

19.30 17.60 9.53 2.31 −0.29 × 10−3 4.31 × 10−6

Units g/cm3 g/cm3 cm3 /mol N/m N/(m K) 1/K

3980

3350

2870

m/s

6850

6250

5180

m/s

0.78 × 10−5

0.338 × 10−5

0.28 × 10−5

1/MPa

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s44 Elastic compliance s12 Elastic stiffness c11 Elastic stiffness c44 Elastic stiffness c12 Tensile strength

145 330 407 71.6 123 152 0.31 0.31 0.28 3.05 2.63 2.45 9.98 9.20 6.24 −0.49 −0.68 −0.69 348 465 523 100.0 109 160 67 163 203 Strongly dependent on microstructure

Vickers hardness

1060

160–400 (HV 10)

360–600 (HV 30)

GPa GPa 1/TPa 1/TPa 1/TPa GPa GPa GPa

Remarks

300 K

Volume compressibility

Part 2 1.5

Table 2.1-18B(a) Elements of Group VIB (CAS notation), or Group 6 (new IUPAC notation). Crystallographic properties (see Table 2.1-18C for allotropic and high-pressure modifications)

115

116

Part 2

The Elements

Part 2 1.5

Table 2.1-18B(c) Elements of Group VIB (CAS notation), or Group 6 (new IUPAC notation). Thermal and thermodynamic

properties Element name

Chromium

Molybdenum

Tungsten

Seaborgium

Chemical symbol Atomic number Z

Cr 24

Mo 42

W 74

Sg 106

Thermal conductivity λ Molar heat capacity c p Standard entropy S0

93.7 23.44 23.543

142 23.932 28.560

164 24.27 32.618

Units W/(m K) J/(mol K) J/(mol K)

Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy chnage ∆Hb Critical temperature Tc Critical pressure pc Critical density c

4.0500 2180.00 21.0040 9.635

4.5890 2893 37.4798 12.942

4.9700 3693 52.3137 14.158

kJ/mol K kJ/mol J/(mol K)

Remarks At 293 K At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm 2952 344.3

4952 582.2 11 000 540 2.630

5828 806.8

K kJ/mol K MPa g/cm3

Table 2.1-18B(d) Elements of Group VIB (CAS notation), or Group 6 (new IUPAC notation). Electronic, electromagnetic, and optical properties Element name

Chromium

Molybdenum

Tungsten

Seaborgium

Chemical symbol Atomic number Z

Cr 24

Mo 42

W 74

Sg 106

Electrical resistivity ρs Temperature coefficient Pressure coefficient Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R

127 30.1 × 10−4 −17.3 × 10−9

52 43.3 × 10−4 −1.29 × 10−9 0.92

54.9 51 × 10−4 −1.333 × 10−9 0.005

Thermoelectric coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmass (SI)

98

Units nΩ m 1/K 1/hPa K

Remarks At 293 K

Oe

3.63 × 10−10

1.26 × 10−10

0.856 × 10−10

m3 /(A s)

4.5 4.6 2099 × 10−6

5.9 4.39 4.26 905 × 10−6

1.5 4.54 4.50 666 × 10−6

µV/K eV V cm3 /mol

At 295 K

167 × 10−6

72 × 10−6

53 × 10−6

cm3 /mol

At 295 K

44 × 10−6

12 × 10−6

4.0 × 10−6

cm3 /g

At 295 K

B = 0.5–2.0 T, T = 293 K

The Elements

1.5 Data

modifications Element

Chromium

Modification

α-Cr

α
-Cr

Crystal system, Bravais lattice Structure type Lattice constant a Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, bc W 288.47 Im3m Oh9 A2 cI2 2 8 249 RTP

cub, bc W 288.2 Im3m Oh9 A2 cI2 2 8

Units

pm

High pressure

Table 2.1-18D Elements of Group VIB (CAS notation), or Group 6 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Chromium

Ion

Cr2+

Coordination number 4 5 6 73 7

Cr3+

62

Molybdenum Cr4+

Cr6+

41

26

55

44

Mo3+

69

Mo4+

65

Tungsten Mo5+

Mo6+

46

41

61

59 73

W4+

66

W5+

W6+

62

42 51 60

Units pm pm pm pm

Part 2 1.5

Table 2.1-18C Elements of Group VIB (CAS notation), or Group 6 (new IUPAC notation). Allotropic and high-pressure

117

118

Part 2 1.5

Part 2

Element name

Fluorine

Chlorine

Bromine

Iodine

Astatine

Chemical symbol Atomic number Z

F 9

Cl 17

Br 35

I 53

At 85 Radioactive [210]

Units Characterization Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rvdW

18.9984032(5)

35.4527(9)

79.904(1)

126.90447(3)

800 × 10−6

480 × 10−6

2.5 × 10−6

0.3 × 10−6

1.3 × 10−6 64 150–160

18 800 × 10−6 99 175

67 × 10−6 114 200

0.06 × 10−6 133 210

145

Electron shells Electronic ground state Electronic configuration Oxidation states

KL 2P 3/2 [He]2s2 2p5

–LMN 2P 3/2 [Ar]3d10 4s2 4p5

–MNO 2P 3/2 [Kr]4d10 5s2 5p5

–NOP 2P 3/2 [Xe]4f14 5d10 6s2 6p5

Electron affinity

3.40

KLM 2P 3/2 [Ne]3s2 3p5 1+, 3+, 5+, 7+, 1−, 3−, 5−, 7− 3.61

3.36

3.06

2.8

Electronegativity χA

4.10

2.83

2.74

2.21

(1.90)

1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0 Molecular form in gaseous state Internuclear distance in molecule Dissociation energy

17.42282 34.97082 62.7084 87.1398 +2.866

12.96764 23.814 39.61 53.4652 +1.358

11.81381 21.8 36 47.3 +1.066

10.45126 19.1313 33

F2

Cl2

Br2

I2

+0.536

198.8 2.475

Remarks

Mass ratio

pm pm

eV

eV eV eV eV V

Mass ratio Covalent radius van der Waals radius

Reaction type F + e− = F− Allred and Rochow

Reaction type 2Cl− = Cl2 + 2e−

pm 1.5417

eV

Extrapolated to T = 0 K

The Elements

Table 2.1-19A Elements of Group VIIA (CAS notation), or Group 17 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-19D for

ionic radii)

The Elements

1.5 Data

(see Table 2.1-19C for allotropic and high-pressure modifications) Element name

Fluorine

Chlorine

Bromine

Iodine

Astatine

Chemical symbol Atomic number Z

F 9

Cl 17

Br 35

I 53

At 85

State Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle β Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

F2 , < 45.6 K mon, C

Cl2 , 113 K orth, C

Br2 , 123 K orth, C

550 328 728 102.17 C2/m 3 C2h C34 mC6 6 1 149

624 448 826

668 449 874

I2 orth, C Ga 726.8 479.7 979.7

Cmca 18 D2h A11 oC8 2×4 1 198.0

Cmca 18 D2h A11 oC8 2×4 1 227

Cmca 18 D2h A11 oC8 2×4 1 269

Units

pm pm pm deg

pm

Remarks

Part 2 1.5

Table 2.1-19B(a) Elements of Group VIIA (CAS notation), or Group 17 (new IUPAC notation). Crystallographic properties

119

120

Part 2

The Elements

Part 2 1.5

Table 2.1-19B(b) Elements of Group VIIA (CAS notation), or Group 17 (new IUPAC notation). Mechanical properties Element name

Fluorine

Chlorine

Bromine

Iodine

Astatine

Chemical symbol Atomic number Z

F 9

Cl 17

Br 35

I 53

At 85

State Density , solid Density , liquid Density , gas Molar volume Vmol Viscosity η, gas Viscosity η, liquid Surface tension, liquid Sound velocity, gas Elastic compliance s11 Elastic compliance s22 Elastic compliance s33 Elastic compliance s44 Elastic compliance s55 Elastic compliance s66 Elastic compliance s12 Elastic compliance s13 Elastic compliance s23 Elastic stiffness c11 Elastic stiffness c22 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c55 Elastic stiffness c66 Elastic stiffness c12 Elastic stiffness c13 Elastic stiffness c23

F2 , gas

Cl2 , gas

Br2 , crystalline

I2 , crystalline 4.92

Units

Remarks

g/cm3

3.119 (293 K) 1.696 × 10−3 18.05 209.3 × 102

336 (375 K)

3.17 × 10−3 17.46

19.73

25.74

0.916 (299 K) 0.0441 (286 K)

2.27 0.0557

206 328 103 132 303 67.7 170 −97 −173 49 11.5 13.5 25.0 3.30 14.8 5.88 4.50 13.5 0.93

g/cm3 cm3 /mol µPa s mPa s N/m m/s 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa GPa GPa GPa GPa

At 273 K, 1 bar

STP

Table 2.1-19B(c) Elements of Group VIIA (CAS notation), or Group 17 (new IUPAC notation). Thermal and thermodynamic properties Element name

Fluorine

Chlorine

Bromine

Iodine

Astatine

Chemical symbol Atomic number Z

F 9

Cl 17

Br 35

I 53

At 85

State Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Enthalpy change ∆Hm Entropy change ∆Sm Volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb Critical temperature Tc Critical pressure pc Critical density c Triple-point temperature Ttr Triple-point pressure ptr Solubility in watera

F2 , gas 2.43 × 10−2 15.66 202.789 8.8250 53.48

Cl2 , gas 9.3 × 10−3 16.974 223.079 9.1810 172.18 6.41

Br2 , liquid

I2 , crystalline 0.4 27.21 116.139 13.1963 386.75 15.5172 40.122

At2 , crystalline 1.7

84.95

239.1 20.40 417 7.98 0.573 162 1.39 4.610

332.3 29.56

m3

gas/m3

265.90 10.8

54.000 13.4000 575 23.8 40.0

Remarks

W/(m K) J/(mol K) J / (mol K) kJ/mol K kJ/mol J/(mol K)

STP At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm

144.3 5.22 0.630 55 0.221

458.4 41.96 819

91

K kJ/mol K MPa g/cm3 K kPa At 273 K and 101 kPa

water.

The Elements 1.5 Data 121

Part 2 1.5

a

37.84 152.210

Units

122

Part 2 1.5

Part 2

Element name

Fluorine

Chlorine

Bromine

Iodine

Astatine

Chemical symbol Atomic number Z

F 9

Cl 17

Br 35

I 53

At 85

State Characteristics

F2 , gas Yellow gas, very reactive

Cl2 , gas Yellow-green gas

Br2 , liquid Liquid halogen

I2 , crystalline Solid semiconductor 2.8

1.517(83.2 K)

2.15 (213 K)

Units

Electronic work function Dielectric constant ε, liquid Molar magnetic susceptibility χmol , gas (SI) Molar magnetic susceptibility χmol , gas (cgs) Molar magnetic susceptibility χmol , liquid (SI) Molar magnetic susceptibility χmol , liquid (cgs) Molar magnetic susceptibility χmol , solid (SI) Molar magnetic susceptibility χmol , solid (cgs) Mass magnetic susceptibility χmass , solid (SI) Refractive index (n − 1), gas a

206 × 10−6

Refractive index n, liquid a a

λ = 589 nm.

b

At 92 K,

cm3 /mol

−73.5 × 10−6

cm3 /mol

−508 × 10−6

−709

cm3 /mol

−40.4 × 10−6

−56.4 × 10−6

cm3 /mol

−11.1 × 10−6

773 × 10−6 1.367 b

= 1.330 g/cm3 .

eV

−924

−7.2 × 10−6

Remarks

−1131 × 10−6

cm3 /mol

−90 × 10−6

cm3 /mol

−4.40 × 10−6

cm3 /g At 273 K and 101 kPa

1.659

The Elements

Table 2.1-19B(d) Elements of Group VIIA (CAS notation), or Group 17 (new IUPAC notation). Electronic, electromagnetic, and optical properties

The Elements

1.5 Data

Element

Fluorine

Modification

α-F (F2 )

β-F

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle γ Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

mon, C

cub, P γ -O 667

Units

550 328 728 102.17 C2/m 3 C2h C34 mC6 6 1 149 < 45.6 K

pm pm pm deg

Pm3m Oh3 A15 cP16 16 pm > 45.6 K

Table 2.1-19D Elements of Group VIIA (CAS notation), or Group 17 (new IUPAC notation). Ionic radii (determined from

crystal structures) Element

Fluorine

Chlorine

Ion

F−

Cl−

Coordination number 3 3 6

F7+

Cl5+

Bromine Cl7+

Br−

12 8

181

Br7+

I−

31 8

133

Iodine Br5+

196

I5+

I7+

44 25 39

220

95

42 53

Units pm pm pm

Part 2 1.5

Table 2.1-19C Elements of Group VIIA (CAS notation), or Group 17 (new IUPAC notation). Allotropic and high-pressure

modifications

123

124

Part 2 1.5

Part 2

Element name

Manganese

Technetium

Rhenium

Bohrium

Chemical symbol Atomic number Z

Mn 25

Tc 43

Re 75

Bh 107

54.938049(9)

Radioactive [98]

Characteristics Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

1000 × 10−6 2 × 10−10 118 137 –LMN 6S 5/2 [Ar]3d5 4s2 7+, 6+, 4+ 3+, 2+ Not stable 1.60 7.43402 15.63999 33.668 51.2 −1.185

Units

Remarks

pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12

186.207(1) 1 × 10−9

127 137 –MNO 6S 5/2 [Kr]4d5 5s2 7+ 0.55 1.36 7.28 15.26 29.54

128 137 –NOP 6S 5/2 [Xe]4f14 5d5 6s2 7+, 6+, 4+, 2+, 1− 0.15 (1.46) 7.88

–OPQ

eV eV eV eV eV V

Reaction type Tc + e− = Tc− Allred and Rochow

Reaction type Mn2+ + 2e− = Mn

The Elements

Table 2.1-20A Elements of Group VIIB (CAS notation), or Group 7 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-20D for

ionic radii)

The Elements

1.5 Data

(see Table 2.1-20C for allotropic and high-pressure modifications) Element name

Manganese

Technetium

Rhenium

Bohrium

Chemical symbol Atomic number Z

Mn 25

Tc 43

Re 75

Bh 107

State Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

α-Mn cub, bc α-Mn 892.19

Units

Im3m Td3 A12 cI58 58 226–293

hex Mg 273.8 439.4 P63 /mmc 4 D6h A3 hP2 2 12 274

hex Mg 276.08 445.80 P63 /mmc 4 D6h A3 hP2 2 12

Remarks

pm pm

pm

Table 2.1-20B(b) Elements of Group VIIB (CAS notation), or Group 7 (new IUPAC notation). Mechanical properties Element name

Manganese

Technetium

Rhenium

Bohrium

Chemical symbol Atomic number Z

Mn 25

Tc 43

Re 75

Bh 107

Density , solid Density , liquid Molar volume Vmol Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

7.470 6.430 7.38 1.10 0 23 × 10−6

11.50

8.06 × 10−6

21.00 18.80 8.86 2.65 −0.34 × 10−3 6.63 × 10−6

Units g/cm3 g/cm3 cm3 /mol N/m N/(m K) 1/K

3280 50.6 5560 3270 0.716 × 10−5 3.22 × 10−5

2930 5360 0.264 × 10−5

m/s m/s 1/MPa

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness

196 79.4 0.24

520 180 0.26 2.11 1.70 6.21 −0.80 −0.40 616 683 161 273 206 1.16 2.45–8.00

GPa GPa

9.81

8.6

407 162 0.26 3.2 2.9 5.7 −1.1 −0.9 433 470 177 199 199 0.40–0.74 1.510

1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa GPa

Remarks

Volume compressibility At 293 K

Part 2 1.5

Table 2.1-20B(a) Elements of Group VIIB (CAS notation), or Group 7 (new IUPAC notation). Crystallographic properties

125

126

Part 2

The Elements

Part 2 1.5

Table 2.1-20B(c) Elements of Group VIIB (CAS notation), or Group 7 (new IUPAC notation). Thermal and thermodynamic

properties Element name

Manganese

Technetium

Rhenium

Bohrium

Chemical symbol Atomic number Z

Mn 25

Tc 43

Re 75

Bh 107

State Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Transition Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb Critical temperature Tc Critical pressure pc Critical density c

α-Mn 29.7 26.28 32.220 4.9957

185 32.985

1519.00 δ–liquid 12.9089 8.498 0.017

2430.01 α–liquid 33.2912 13.700

2335 226.7

4538 592.9

Units

Remarks

71.2 25.31 36.482 5.3330

W/(m K) J/(mol K) J/(mol K) kJ/mol

At 298 K At 298 K and 100 kPa

3458.00 α–liquid 34.0750 9.854

K kJ/mol J/(mol K) (Vl − Vs )/Vl at Tm

5869 714.8 2090 14.5 0.320

K kJ/mol K MPa g/cm3

Table 2.1-20B(d) Elements of Group VIIB (CAS notation), or Group 7 (new IUPAC notation). Electronic, electromagnetic, and optical properties Element name

Manganese

Technetium

Rhenium

Bohrium

Chemical symbol Atomic number Z

Mn 25

Tc 43

Re 75

Bh 107

Characteristics Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio at Tm Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R

Brittle metal 1380 5.0 × 10−4 −3.54 × 10−9 400 0.61

Metal 1510

Metal 172 44.8 × 10−4

Electronic work function Thermal work function Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmass (SI)

Units

Remarks

nΩ m 1/K 1/hPa nΩ m

At RT

1.70

K

198

Oe

0.84 × 10−10

3.15 × 10−10

m3 /(A s)

4.08 3.91 6421 × 10−6

1445 × 10−6

About 5.0 4.96 842 × 10−6

V V cm3 /mol

At 295 K

511 × 10−6

115 × 10−6

67 × 10−6

cm3 /mol

At 295 K

121 × 10−6

31 × 10−6

4.56 × 10−6

cm3 /g

At 295 K

At 297 K, B = 0.5–5.0 T

The Elements

1.5 Data

Element

Manganese

Modification

α-Mn

β-Mn

γ -Mn

δ-Mn

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, bc α-Mn 892.19

cub, P β-Mn 631.52

cub, fc Cu 386.24

cub, bc W 308.06

Im3m Td3 A12 cI58 58

P41 32 O A13 cP20 20

226–293 RTP

> 1000 K

Fm3m Oh5 A1 cF4 4 12 273 > 1368 K

Im3m Oh9 A2 cI2 2 8 267 > 1408 K

Units

pm pm

pm

Table 2.1-20D Elements of Group VIIB (CAS notation), or Group 7 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Manganese

Ion

Mn2+

Coordination number 4 6 8

Mn3+

Mn4+

Mn5+

Mn6+

Mn7+

Technetium

Rhenium

Tc4+

Re4+

Re5+

Re6+

Re7+ Units

66 83 96

58

39 53

33

26

25

38 65

63

58

55

pm pm pm

Part 2 1.5

Table 2.1-20C Elements of Group VIIB (CAS notation), or Group 7 (new IUPAC notation). Allotropic and high-pressure

modifications

127

Part 2 1.5 Argon

Krypton

Xenon

Radon

Ne 10

Ar 18

Kr 36

Xe 54

Rn 86

Characteristics Relative atomic mass A (atomic weight) Atomic radius rcov Atomic radius rmet

20.1797(6)

39.948(1)

83.80(1)

131.29(2)

Radioactive [222]

(69) 154

(97) 188

110 202

130 216

240

Atomic radius rvdW Electron shells Electronic ground state Electronic configuration Electron affinity

160 KL 1S 0 [He]2s2 2p6 Not stable

188 KLM 1S 0 [Ne]3s2 3p6 Not stable

200 –LMN 1S 0 [Ar]3d10 4s2 4p6 Not stable

220 –MNO 1S 0 [Kr]4d10 5s2 5p6 Not stable

240 –NOP 1S 0 [Xe]4f14 5d10 6s2 6p6 Not stable

Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy

5.10 21.56454 40.96328 63.45 97.12

3.30 15.75962 27.62967 40.74 59.81

3.10 13.99961 24.35985 36.950 52.5

2.40 12.12987 21.20979 32.1230

(2.06) 10.74850

Units

Remarks

pm pm

Covalent radius Metallic radius, CN = 12 van der Waals radius

pm

eV

Reaction type He + e− = He− Allred and Rochow

eV eV eV eV

Table 2.1-21B(a) Elements of Group VIIIA (CAS notation), or Group 18 (new IUPAC notation). Crystallographic properties (see Table 2.1-21C for allotropic and high-pressure modifications) Element name

Neon

Argon

Krypton

Xenon

Radon

Chemical symbol Atomic number Z

Ne 10

Ar 18

Kr 36

Xe 54

Rn 86

State Crystal system, Bravais lattice Structure type Lattice constant a Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

At 4.2 K cub, fc Cu 446.22 Fm3m Oh5 A1 cF4 4 12 320

At 4.2 K cub, fc Cu 531.2 Fm3m Oh5 A1 cF4 4 12 383

At 4.2 K cub, fc Cu 564.59 Fm3m Oh5 A1 cF4 4 12 405

At 4.2 K cub, fc Cu 613.2 Fm3m Oh5 A1 cF4 4 12 441

Units

pm

pm

Remarks

The Elements

Neon

Chemical symbol Atomic number Z

Part 2

Element name

128

Table 2.1-21A Elements of Group VIIIA (CAS notation), or Group 18 (new IUPAC notation). Atomic, ionic, and molecular properties

Table 2.1-21B(b) Elements of Group VIIIA (CAS notation), or Group 18 (new IUPAC notation). Mechanical properties Element name

Neon

Argon

Krypton

Xenon

Radon

Chemical symbol Atomic number Z

Ne 10

Ar 18

Kr 36

Xe 54

Rn 86

Characterics Density , solid Density , gas Molar volume Vmol Viscosity η, gas Sound velocity, gas Sound velocity, liquid Elastic modulus E

Noble gas

Noble gas 1.736 (40 K)

Noble gas

Noble gas

Noble gas

0.8994 × 10−3

3.7493 × 10−3

5.8971 × 10−3

9.73 × 10−3

13.97 29.8 461

37.09 21.2 168

50.5

1.0

21 308 855 (85 K) 1.6

29.68 23.4 213

Elastic compliance s11 Elastic compliance s44 Elastic compliance s12 Elastic stiffness c11 Elastic stiffness c44 Elastic stiffness c12 Solubility in water αW

1020 (4.7 K) 1000 (4.7 K) −370 (4.7 K) 1.69 (4.7 K) 1.00 (4.7 K) 0.97 (4.7 K) 0.010

593 (80 K) 1073 (80 K) −205 (80 K) 2.77 (80 K) 0.98 (80 K) 1.37 (80 K) 0.0340

Units

1.8 618 (115 K) 744 (115 K) −226 (115 K) 2.85 (115 K) 1.35 (115 K) 1.60 (115 K) 0.059

690 (160.5 K) 708 (160.5 K) −271 (160.5 K) 2.93 (160.5 K) 1.41 (160.5 K) 1.89 (160.5 K) 0.108

g/cm3 g/cm3 cm3 /mol µPa s m/s m/s GPa

Remarks

At 273 K At 293 K At STP Low temperature, estimated values

1/TPa 1/TPa 1/TPa GPa GPa GPa At 293 K, αW = vol(gas)/vol(water)

Table 2.1-21B(c) Elements of Group VIIIA (CAS notation), or Group 18 (new IUPAC notation). Thermal and thermodynamic properties Krypton Kr 36

Xenon Xe 54

Radon Rn 86

State Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Transition Enthalpy change ∆Hm Boiling temperature Tb Enthalpy change ∆Hb Critical temperature Tc Critical pressure pc Critical density c Triple-point temperature Ttr Triple-point pressure ptr

Ne gas 49.3 × 10−3 20.786 146.328 6.1965 24.563 α–liquid 27.0 27.10 0.324 44.0 2.75 0.4835 24.5 43.3

Ar gas 18.0 × 10−3 20.87 154.842 6.1965 83.8 α–liquid 1.21 87.30 6.3 150.75 4.86 0.307 83.85 68.75

Kr gas 9.49 × 10−3 20.786 164.085 6.1965 115.765

Xe gas 5.1 × 10−3 20.744 169.575 6.1970 161.391 α–liquid 3.10 165.03 12.65 289.74 5.840 1.105 161.25 81.6

Rn gas 3.64 × 10−3 20.786 176.234 6.1970 202 α–liquid 2.7 211 18.1

1.64 119.80 9.05 209.4 5.50 0.9085 115.95 73.19

Units

Remarks

W/(m K) J/(mol K) J/(mol K) kJ/mol K

At 298.15 K At 298.15 K and 100 kPa At 298.15 K

kJ/mol K kJ/mol K MPa g/cm3 K kPa

129

Part 2 1.5

Argon Ar 18

1.5 Data

Neon Ne 10

The Elements

Element name Chemical symbol Atomic number Z

130

Part 2 1.5

Part 2

Element name

Neon

Argon

Krypton

Xenon

Radon

Chemical symbol Atomic number Z

Ne 10

Ar 18

Kr 36

Xe 54

Rn 86

State Dielectric constant ε − 1, gas Dielectric constant ε, liquid Molar magnetic susceptibility χmol , gas (SI) Molar magnetic susceptibility χmol , gas (cgs) Mass magnetic susceptibility χmass , gas (SI) Refractive index (n − 1), gas Refractive index n, liquid

Ne gas 130 × 10−6

Ar gas 545 × 10−6 1.516 (89 K) −243 × 10−6 −19.3 × 10−6 −6.16 × 10−6 281 × 10−6 1.233 (84 K)

Kr gas 7 × 10−6

Xe gas 1238 × 10−6

Rn gas

−364 × 10−6 −29.0 × 10−6 −4.32 × 10−6

−572 × 10−6 −45.5 × 10−6 −4.20 × 10−6 706 × 10−6

Units

−87.5 × 10−6 −6.96 × 10−6 −4.2 × 10−6 7.25 × 10−6

Table 2.1-21C Elements of Group VIIIA (CAS notation), or Group 18 (new IUPAC notation). Allotropic and high-pressure

modifications. There is no Table 2.1-21D, because no data on ionic radii are available Element

Argon

Modification

α-Ar

β-Ar

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, fc Cu 531.2

hex, cp Mg 376.0 614.1 P63 /mmc 4 D6h A3 hP2 2 12

Units

Fm3m Oh5 A1 cF4 4 12 383 < 83.8 K

pm pm

pm > 83.8 K

Remarks At STP

cm3 /mol cm3 /mol cm3 /g

At 295 K At 295 K At 293 K λ = 589.3 nm λ = 589.3 nm

The Elements

Table 2.1-21B(d) Elements of Group VIIIA (CAS notation), or Group 18 (new IUPAC notation). Electronic, electromagnetic, and optical properties

Table 2.1-22A Elements of Group VIII(1) (CAS notation), or Group 8 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-22D

for ionic radii) Element name

Iron

Ruthenium

Osmium

Hassium

Chemical symbol Atomic number Z

Fe 26

Ru 44

Os 76

Hs 108

55.845(2)

101.07(2)

190.23(3)

Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy 5th ionization energy Standard electrode potential E 0

50 000 × 10−6 2 × 10−9 116 126 –LMN 5D 4 [Ar]3d6 4s2 3+, 2+ 0.151 1.64 7.9024 16.1878 30.652 54.8 75.0 −0.447 −0.037 +0.771

125 132.5 –MNO 5F 5 [Kr]4d7 5s1 8+, 6+, 4+, 3+, 2+ 1.05 1.42 7.36050 16.76 28.47

126 134 –NOP 5D 4 [Xe]4f14 5d6 6s2 8+, 6+, 4+, 3+, 2+ 1.1 (1.52) 8.7

Units

Remarks

pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12

–OPQ

eV eV eV eV eV eV V V V

Reaction type Fe + e− = Fe− Allred and Rochow

Reaction type Fe2+ + 2e− = Fe Reaction type Fe3+ + 3e− = Fe Reaction type Fe3+ + e− = Fe2+

The Elements 1.5 Data 131

Part 2 1.5

Quantity Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states

132

Part 2

The Elements

Part 2 1.5

Table 2.1-22B(a) Elements of Group VIII(1) (CAS notation), or Group 8 (new IUPAC notation). Crystallographic

properties (see Table 2.1-22C for allotropic and high-pressure modifications) Element name Chemical symbol Atomic number Z

Iron Fe 26

Modification Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

α-Fe cub, bc W 286.65

Ruthenium Ru 44

Osmium Os 76

Hassium Hs 108 Units

Im3m Oh9 A2 cI2 2 8 248

hex Mg 270.53 428.14 P63 /mmc 4 D6h A3 hP2 2 6+6 265

hex Mg 273.48 439.13 P63 /mmc 4 D6h A3 hP2 2 6+6 267

Remarks

pm pm

pm

Table 2.1-22B(b) Elements of Group VIII(1) (CAS notation), or Group 8 (new IUPAC notation). Mechanical properties Element name Chemical symbol Atomic number Z

Iron Fe 26

Ruthenium Ru 44

Osmium Os 76

Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness

7.86 7.020 7.09 5.53 1.65

12.20 10.90 8.14

22.4 20.100 8.43

2.25 −0.31 × 10−3 9.1 × 10−6

2.5 −0.33 × 10−3 6.1 × 10−6

3740 6530 0.331 × 10−5 432 173 0.25 2.09 1.82 5.53 −0.58 −0.41 563 624 181 188 168 540 2 – 5 × 103

3340 5480 0.261 × 10−5 559 223 0.25

a

12.3 × 10−6 3220 5920 0.56 × 10−5 211 80.4 0.29 7.67 8.57 −2.83 230 117 135 193–206 a 608 a

Strongly dependent on microstructure

Hassium Hs 108 Units g/cm3 g/cm3 cm3 /mol mPa s N/m N/(m K) 1/K m/s m/s 1/MPa GPa GPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa MPa

800

Remarks

Volume compressibility

The Elements

1.5 Data

namic properties Element name

Iron

Ruthenium

Osmium

Hassium

Chemical symbol Atomic number Z

Fe 26

Ru 44

Os 76

Hs 108

Modification Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Transition Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb

α-Fe 80.2 25.10 27.280 4.4890 1811.0 δ–liquid 13.8060 7.623 0.034 3139 349.6

117 24.06 28.614 4.6024 2607.0 α–liquid 38.5890 14.802

87.6 24.7 32.635

4423 595.5

5285 746

3306.0 δ–liquid 57.8550 17.500

Units

Remarks

W/(m K) J/(mol K) J/(mol K) kJ/mol K

At 298.2 K At 298.15 K and 100 kPa At 298.15 K

kJ/mol J/(mol K) (Vl − Vs )/Vl at Tm K kJ/mol

Table 2.1-22B(d) Elements of Group VIII(1) (CAS notation), or Group 8 (new IUPAC notation). Electronic, electromagnetic, and optical properties Element name

Iron

Ruthenium

Osmium

Hassium

Chemical symbol Atomic number Z

Fe 26

Ru 44

Os 76

Hs 108

Characteristics Electrical resistivity ρs Temperature coefficient Pressure coefficient Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R

Soft metal 89 65.1 × 10−4 −2.34 × 10−9

Brittle metal 81 42 × 10−4

8 × 10−10

Metal 76 45.8 × 10−4 −2.48 × 10−9 0.49 66 2.2 × 10−10

Thermoelectric coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmass (SI)

−51.34 4.70 4.50 Ferromagnetic Ferromagnetic Ferromagnetic

4.71 4.73 490 39 5.37 × 10−6

0.66 65

4.83 138 11 0.65 × 10−6

Units

Remarks

nΩ m 1/K 1/hPa K Oe m3 /(A s)

At RT

µV/K V V cm3 /mol cm3 /mol cm3 /g

At 300 K, B = 4–5 T

At 295 K At 295 K At 295 K

Part 2 1.5

Table 2.1-22B(c) Elements of Group VIII(1) (CAS notation), or Group 8 (new IUPAC notation). Thermal and thermody-

133

134

Part 2

The Elements

Part 2 1.5

Table 2.1-22C Elements of Group VIII(1) (CAS notation), or Group 8 (new IUPAC notation). Allotropic and high-pressure

modifications Element

Iron

Modification

α-Fe

γ -Fe

δ-Fe

ε-Fe

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, bc W 286.65

cub, fc Cu 364.67

cub, bc W 291.35

Im3m Oh9 A2 cI2 2 8 248 RTP

Fm3m Oh5 A1 cF4 4 12 258 > 1183 K

Im3m Oh9 A2 cI2 2 8 254 > 1663 K

hex, cp Mg 248.5 399.0 P63 /mmc 4 D6h A3 hP2 2 6+6 241 > 13.0 GPa

Units

pm pm

pm

Table 2.1-22D Elements of Group VIII(1) (CAS notation), or Group 8 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Iron

Ion

Fe2+

Fe3+

Ruthenium

4

63

49

6

61

55

8

92

78

Ru3+

Ru4+

Osmium Ru5+

Ru7+

Ru8+

38

36

Os4+

Os5+

Os6+

Os8+

Coordination number

Units 68

62

57

39 63

58

55

pm pm pm

Table 2.1-23A Elements of Group VIII(2) (CAS notation), or Group 9 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-23D

for ionic radii) Element name

Cobalt

Rhodium

Iridium

Meitnerium

Chemical symbol Atomic number Z

Co 27

Rh 45

Ir 77

Mt 109

Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

58.933200(9)

102.90550(2)

192.217(3)

40 × 10−6 5 × 10−11 116 125 –LMN 4F 9/2 [Ar]3d7 4s2 3+, 2+ 0.662 1.75 7.8810 17.083 33.50 51.3 −0.28

0.001 × 10−6

1 × 10−9

125 134.5 –MNO 4F 9/2 [Kr]4d8 5s1 4+, 3+, 2+ 1.14 1.35 7.45890 18.08 31.06

127 136 –NOP 4F 9/2 [Xe]4f14 5d7 6s2 6+, 4+, 3+, 2+ 1.57 (1.44) 9.1

+1.156

Remarks

pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12

–OPQ

eV eV eV eV eV V V

Reaction type Co + e− = Co− Allred and Rochow

Reaction type Co2+ + 2e− = Co Reaction type Ir3+ + 3e− = Ir

The Elements 1.5 Data 135

Part 2 1.5

+0.6

Units

136

Part 2

The Elements

Part 2 1.5

Table 2.1-23B(a) Elements of Group VIII(2) (CAS notation), or Group 9 (new IUPAC notation). Crystallographic

properties (see Table 2.1-23C for allotropic and high-pressure modifications) Element name Chemical symbol Atomic number Z

Cobalt Co 27

Rhodium Rh 45

Modifaction Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

ε-Co hex, cp Mg 250.71 406.94 P63 /mmc 4 D6h A3 hP2 2 6+6 250

Iridium Ir 77

Meitnerium Mt 109 Units

cub, fc Cu 280.32

cub, fc Cu 383.91

Fm3m Oh5 A1 cF4 4 12 269

Fm3m Oh5 A1 cF4 4 12 271

Remarks

pm pm

pm

Table 2.1-23B(b) Elements of Group VIII(2) (CAS notation), or Group 9 (new IUPAC notation). Mechanical properties Element name Chemical symbol Atomic number Z

Cobalt Co 27

Modification Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Coefficient of linear thermal expansion α Surface tension, liquid Temperature coefficient Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

ε-Co 8.90 7.670 6.62 4.8 13.36 × 10−6

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness

Rhodium Rh 45

Iridium Ir 77

Meitnerium Mt 109 Units

12.40 10.800 8.29

22.50 20.000 8.57

8.40 × 10−6

6.8 × 10−6

g/cm3 g/cm3 cm3 /mol mPa s 1/K

1.520 −0.92 × 10−3 3000 5730 0.525 × 10−5

1.97 −0.3 × 10−3 3470 6190 0.350 × 10−5

2.250 −0.31 × 10−3 3050 5380 0.258 × 10−5

N/m N/(m K) m/s m/s 1/MPa

204 77.3 0.32 5.11 3.69 14.1 −2.37 −0.94 295 335 71.0 159 111 255 1043

379 149 0.27 3.46

528 209 0.26 2.28

GPa GPa

5.43 −1.10

3.90 −0.67

413

580

184 194

256 242

951 1246

623 × 103 1760

1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa MPa

Remarks

Near Tm

Volume compressibility

The Elements

1.5 Data

Element name

Cobalt

Rhodium

Iridium

Meitnerium

Chemical symbol Atomic number Z

Co 27

Rh 45

Ir 77

Mt 109

Modification Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Transition Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb

ε-Co 100 24.811 30.040 4.7655 1768.0 α–liquid 16.200 9.163

Units

3184 376.6

150 24.98 31.556 2237.0 α–liquid 26.5935 11.888 0.12 3970 493.3

147 24.98 35.505 5.2677 2719.0 α–liquid 41.124 15.125

Remarks

W/(m K) J/(mol K) J/(mol K) kJ/mol K kJ/mol J/(mol K) 1 K kJ/mol

4701 604.1

At 298 K At 298 K and 100 kPa

(Vl − Vs )/Vl at Tm

Table 2.1-23B(d) Elements of Group VIII(2) (CAS notation), or Group 9 (new IUPAC notation). Electronic, electromagnetic, and optical properties Element name

Cobalt

Rhodium

Iridium

Meitnerium

Chemical symbol Atomic number Z

Co 27

Rh 45

Ir 77

Mt 109

Modification Characteristics Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio at Tm Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R

α-Co Hard metal 56 6.04 × 10−3 −0.904 × 10−9 1020 1.05

360 × 10−12

50.5 × 10−12

Thermoelectronic coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmass (SI)

17.5 4.97 4.37 Ferromagnetic

1.0 4.98 4.68 1282 × 10−6

Metal 43.0 4.62 × 10−3 −1.62 × 10−9

Brittle metal 47 4.11 × 10−3 −1.37 × 10−9

Units

Remarks

nΩ m 1/K 1/hPa nΩ m

At RT

0.14

K

77 31.8 × 10−12

5.03 314 × 10−6

Oe m3 /(A s) At 300 K, B = 4.5–5.0 T µV/K V V cm3 /mol At 295 K

Ferromagnetic 102 × 10−6

25 × 10−6

cm3 /mol At 295 K

Ferromagnetic 13.6 × 10−6

1.67 × 10−6

cm3 /g

1.2

At 295 K

Part 2 1.5

Table 2.1-23B(c) Elements of Group VIII(2) (CAS notation), or Group 9 (new IUPAC notation). Thermal and thermody-

namic properties

137

138

Part 2

The Elements

Part 2 1.5

Table 2.1-23C Elements of Group VIII(2) (CAS notation), or Group 9 (new IUPAC notation). Allotropic and high-pressure

modifications Element

Cobalt

Modification

ε-Co

α-Co

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex, cp Mg 250.71 406.94 P63 /mmc 4 D6h A3 hP2 2 6+6 250 RTP

cub, fc Cu 354.45

Units

pm pm

Fm3m Oh5 A1 cF4 4 12 251 > 661 K

pm

Table 2.1-23D Elements of Group VIII(2) (CAS notation), or Group 9 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Cobalt

Ion

Co2+

Coordination number 4 6 8

56 65 90

Rhodium Co3+

55

Rh3+

67

Iridium Rh4+

60

Rh5+

55

Ir3+

68

Ir4+

63

Ir5+

57

Units pm pm pm

Table 2.1-24A Elements of Group VIII(3) (CAS notation) or Group 10 (new IUPAC notation). Atomic, ionic, and molecular properties (see Table 2.1-24D

for ionic radii) Element name

Nickel

Palladium

Platinum

Chemical symbol Atomic number Z

Ni 28

Pd 46

Pt 78

Relative atomic mass A (atomic weight) Abundance in lithosphere Abundance in sea Atomic radius rcov Atomic radius rmet Atomic radius rvdW Electron shells Electronic ground state Electronic configuration Oxidation states Electron affinity Electronegativity χA 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

58.6934(2)

106.42(1)

195.078(2)

100 × 10−6 1.7 × 10−9 115 125 160 –LMN 3F 4 [Ar]3d8 4s2 3+, 2+ 1.16 1.75 7.6398 18.16884 35.19 54.9 −0.257

0.01 × 10−6

5 × 10−9

128 138 160 –MNO 1S 0 [Kr]4d10 4+, 2+ 0.562 1.35 8.3369 19.43 32.93

130 137 170–180 –NOP 3D 3 [Xe]4f14 5d9 6s1 4+, 2+ 2.13 (1.44) 9.0 18.563

+0.951

+1.118

Uun 110 Units

Remarks

pm pm pm

Mass ratio Mass ratio Covalent radius Metallic radius, CN = 12 van der Waals radius

–OPQ

eV eV eV eV eV V

Reaction type Ni + e− = Ni− Allred and Rochow

Reaction type Ni2+ + 2e− = Ni

Table 2.1-24B(a) Elements of Group VIII(3) (CAS notation) or Group 10 (new IUPAC notation). Crystallographic properties Platinum

Pd 46

Pt 78

Crystal system, Bravais lattice Structure type Lattice constant a Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

cub, fc Cu 352.41 Fm3m Oh5 A1 cF4 4 12 249

cub, fc Cu 389.01 Fm3m Oh5 A1 cF4 4 12 274

cub, fc Cu 392.33 Fm3m Oh5 A1 cF4 4 12 277

Uun 110 Units

Remarks

pm

pm

139

Part 2 1.5

Palladium

Ni 28

1.5 Data

Nickel

Chemical symbol Atomic number Z

The Elements

Element name

140

Part 2

The Elements

Part 2 1.5

Table 2.1-24B(b) Elements of Group VIII(3) (CAS notation), or Group 10 (new IUPAC notation). Mechanical properties Element name

Nickel

Palladium

Platinum

Chemical symbol Atomic number Z

Ni 28

Pd 46

Pt 78

Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Compressibility κ

8.90 7.910 6.59 5.0 1.725 −0.98 × 10−3 13.3 × 10−6

12.00 10.700 8.85

21.40 19.700 9.10

1.50 −0.22 × 10−3 11.2 × 10−6

1.866 −0.17 × 10−3 9.0 × 10−6

Units g/cm3 g/cm3 cm3 /mol mPa s N/m N/(m K) 1/K

3080 5810 0.513 × 10−5

1900 4540 0.505 × 10−5

1690 4080 0.351 × 10−5

m/s m/s 1/MPa

Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s44 Elastic compliance s12 Elastic stiffness c11 Elastic stiffness c44 Elastic stiffness c12 Tensile strength Vickers hardness

220 78.5 0.31 7.67 8.23 −2.93 247 122 153 317 640

121 43.5 0.39 13.7 14.1 −6.0 221 70.8 171

170 60.9 0.39 7.35 13.1 −3.08 347 76.5 251 134 560

GPa GPa

461

Uun 110

1/TPa 1/TPa 1/TPa GPa GPa GPa MPa

Remarks

Volume compressibility

At 293 K At 293 K

Table 2.1-24B(c) Elements of Group VIII(3) (CAS notation), or Group 10 (new IUPAC notation). Thermal and

thermodynamic properties Element name

Nickel

Palladium

Platinum

Chemical symbol Atomic number Z

Ni 28

Pd 46

Pt 78

Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Transition Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb

83 26.07 29.796 4.7870 1728.30 α–liquid 17.4798 10.114

71.8 25.98 37.823 5.4685 1828.0 α–liquid 16.736 9.155

71.6 25.85 41.631 5.7237 2041.50 α–liquid 22.1750 10.862

3157 369.24

3237 357.6

4100 509.8

Uun 110 Units W/(m K) J/(mol K) J/(mol K) kJ/mol K

Remarks At 298 K At 298 K and 100 kPa

kJ/mol J/(mol K) (Vl − Vs )/Vl at Tm K kJ/mol

The Elements

1.5 Data

magnetic, and optical properties. There is no Table 2.1-24C, because no allotropic or high-pressure modifications are known Element name

Nickel

Palladium

Platinum

Chemical symbol Atomic number Z

Ni 28

Pd 46

Pt 78

Characteristics Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Resistivity ratio at Tm Hall coefficient R

Ductile metal 59.0 69.2 × 10−4 1.82 × 10−9 850 1.3 −60 × 10−12

Ductile metal 101 37.7 × 10−4 −2.1 × 10−9

Ductile metal 98.1 39.6 × 10−4 −1.88 × 10−9

−86 × 10−12

Thermoelectronic coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmass (SI)

−18 5.15 4.60 Ferromagnetic Ferromagnetic Ferromagnetic

−9.54 5.12 4.99 6786 × 10−6 540 × 10−6 67.0 × 10−6

Uun 110 Units

Remarks

nΩ m 1/K 1/hPa nΩ m

At RT

−24.4 × 10−12

m3 /(A s)

At 298 K, B = 0.3–4.6 T

−3.50 5.65 5.30 2425 × 10−6 193 × 10−6 13.0 × 10−6

µV/K V V cm3 /mol cm3 /mol cm3 /g

At 295 K At 295 K At 295 K

Table 2.1-24D Elements of Group VIII(3) (CAS notation), or Group 10 (new IUPAC notation). Ionic radii (determined from crystal structures) Element

Nickel

Ion

Ni2+

Coordination number 4 6

49 69

Palladium Ni3+

Pd2+

56

64 86

Platinum Pd3+

76

Pd4+

Pt2+

62

60 80

Pt4+

63

Units pm pm

Part 2 1.5

Table 2.1-24B(d) Elements of Group VIII(3) (CAS notation), or Group 10 (new IUPAC notation). Electronic, electro-

141

Part 2 1.5 Neodymium

Promethium

Samarium

Europium

Gadolinium

Pr 59

Nd 60

Pm 61

Sm 62

Eu 63

Gd 64

Radioactive [145]

150.36(3)

151.964(1)

157.25(3)

165 181 –NOP 6H 5/2 [Xe]4f5 6s2 3+ (1.07) 5.55 10.90 22.3 41.1

6.5 × 10−6 5 × 10−14 162 180 –NOP 7F 0 [Xe]4f6 6s2 3+, 2+ (1.07) 5.6437 11.07 23.4 41.4

1.1 × 10−6 1 × 10−14 185 200 –NOP 8S 7/2 [Xe]4f7 6s2 3+, 2+ (1.01) 5.6704 11.241 24.92 42.7

6.4 × 10−6 7 × 10−13 161 179 –NOP 9D 2 [Xe]4f7 5d1 6s2 3+ 1.11 6.1500 12.09 20.63 44.0

Units Characteristics Relative atomic mass A (atomic weight) Abundance in lithosphere a Abundance in sea a Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electronegativity χA b 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy a

Mass ratio.

b

140.116(1)

140.90765(2)

144.24(3)

41.6 × 10−6 1 × 10−12 165 182 –NOP 3H 4 [Xe]4f1 5d1 6s2 4+, 3+ (1.08) 5.5387 10.85 20.198 36.758

5.5 × 10−6 6 × 10−13 165 183 –NOP 4I 9/2 [Xe]4f3 6s2 4+, 3+ (1.07) 5.464 10.55 21.624 38.98

23.9 × 10−6 3 × 10−12 164 182 –NOP 5I 4 [Xe]4f4 6s2 3+ (1.07) 5.5250 10.73 22.1 40.4

pm pm

eV eV eV eV

According to Allred and Rochow.

Element name

Terbium

Dysprosium

Holmium

Erbium

Thulium

Ytterbium

Lutetium

Chemical symbol Atomic number Z

Tb 65

Dy 66

Ho 67

Er 68

Tm 69

Yb 70

Lu 71

Relative atomic mass A (atomic weight) Abundance in lithosphere a Abundance in sea a Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electronegativity χA b 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy

158.92534(2)

162.50(3)

164.93032(2)

167.26(3)

168.93421(2)

173.04(3)

174.967(1)

1 × 10−6 1 × 10−13 159 176 –NOP 6H 15/2 [Xe]4f6 6s2 4+, 3+ (1.10) 5.8639 11.52 21.91 39.79

4.5 × 10−6 9 × 10−13 159 175 –NOP 5I 8 [Xe]4f10 6s2 3+ (1.10) 5.9389 11.67 22.8 41.4

1.2 × 10−6 2 × 10−13 158 174 –NOP 4I 15/2 [Xe]4f11 6s2 3+ (1.10) 6.0216 11.80 22.84 42.5

2.5 × 10−6 8 × 10−13 157 173 –NOP 3H 6 [Xe]4f12 6s2 3+ (1.11) 6.1078 11.93 22.74 42.7

0.2 × 10−6 2 × 10−13 156 172 –NOP 2F 7/2 [Xe]4f13 6s2 3+, 2+ (1.11) 6.18431 12.05 23.68 42.7

2.7 × 10−6 8 × 10−13 174 194 –NOP 1S 0 [Xe]4f14 6s2 3+, 2+ (1.06) 6.25416 12.1761 25.05 43.56

0.8 × 10−6 2 × 10−13 156 172 –NOP 2D 3/2 [Xe]4f14 5d1 6s2 3+ (1.14) 5.42585 13.9 20.9594 45.25

Units

a

Mass ratio.

b

According to Allred and Rochow.

pm pm

eV eV eV eV

The Elements

Praseodymium

Ce 58

Part 2

Cerium

Chemical symbol Atomic number Z

2.1.5.4 Elements of the Lanthanides Period

Element name

142

Table 2.1-25A Lanthanides. Atomic, ionic, and molecular properties (see Table 2.1-25D for ionic radii)

Table 2.1-25B(a) Lanthanides. Crystallographic properties (see Table 2.1-25C for allotropic and high-pressure modifications) Element name

Cerium

Praseodymium

Neodymium

Promethium

Samarium

Europium

Gadolinium

Chemical symbol Atomic number Z

Ce 58

Pr 59

Nd 60

Pm 61

Sm 62

Eu 63

Gd 64 Units

Modification Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

cub, fc Cu 516.10 Fm3m Oh5 A1 cF4 4 12 364

hex α-La 367.21 1183.26 P63 /mmc 4 D6h A3 hP4 4 12

hex α-La 365.82 1179.66 P63 /mmc 4 D6h A3 hP4 4 12 364

α-Sm hex Se 362.90 2620.7

hex α-La 365 1165 P63 /mmc 4 D6h A3 hP4 4 12 362

cub, bc W 458.27 Im3m Oh9 A2 cI2 2 397

hex Mg 363.36 578.10 P63 /mmc 4 D6h A3 hP2 2 12 360

Element name

Terbium

Dysprosium

Holmium

Erbium

Thulium

Ytterbium

Lutetium

Chemical symbol Atomic number Z

Tb 65

Dy 66

Ho 67

Er 68

Tm 69

Yb 70

Lu 71

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

hex Mg 360.55 569.66 P63 /mmc 4 D6h A3 hP2 2 12 357

hex Mg 359.15 565.01 P63 /mmc 4 D6h A3 hP2 2 12 355

hex Mg 357.78 561.78 P63 /mmc 4 D6h A3 hP2 2 12 353

hex Mg 355.92 558.50 P63 /mmc 4 D6h A3 hP2 2 12 351

hex Mg 353.75 555.40 P63 /mmc 4 D6h A3 hP2 2 12 349

cub, fc Cu 548.48

hex Mg 350.52 554.94 P63 /mmc 4 D6h A3 hP2 2 12 347

pm pm

pm

Units

pm

The Elements 1.5 Data 143

Part 2 1.5

Fm3m Oh5 A1 cF4 4 12 388

pm pm

144

Part 2 1.5

Part 2 The Elements

Table 2.1-25B(b) Lanthanides. Mechanical properties Element name

Cerium a

Praseodymium

Neodymium

Promethium

Samarium

Europium

Gadolinium

Chemical symbol Atomic number Z

Ce 58

Pr 59

Nd 60

Pm 61

Sm 62

Eu 63

Gd 64

Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension, liquid Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Volume compressibility κ Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness

6.78

6.77 6.609 20.80 0.431 0.7 6.79 × 10−6

7.00

6.48

7.54

5.26

7.89

20.59

20.1

20.00

28.29

19.90

0.688 9.6 × 10−6

0.65 11 × 10−6

0.6 10.4 × 10−6

0.450 32 × 10−6

0.816 9.4 × 10−6

1410 2660 3.15 × 10−5 35.2 13.2 0.31 26.6 19.3 73.6 −11.3 −3.8 49.4 57.4 13.6 23.0 14.3 169 400

1440 2720 2.94 × 10−5 37.9 14.3 0.31 23.7 18.5 66.5 −9.5 −3.9 54.8 60.9 15.0 24.6 16.6 169 348

2.9 × 10−5 46 18 0.28

1290 2700 3.27 × 10−5 53.9 12.7 0.35

a

17.00 0.72 6.3 × 10−6 1230 3060 5.06 × 10−5 44.1 12.1 0.25 62.8 57.8 −22.3 26.0 17.3 14.3 117 275

The data for the elastic behavior of cerium concern γ -cerium.

170

157 412

8.13 × 10−5 18.2 7.8 0.17

167

1680 2950 2.47 × 10−5 56.3 22.4 0.26 18.0 16.1 48.1 −5.7 −3.6 67.8 71.2 20.8 25.6 20.7 122 510–638

Units g/cm3 g/cm3 cm3 /mol mPa s N/m 1/K m/s m/s 1/MPa GPa GPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa MPa

Table 2.1-25B(b) Lanthanides. Mechanical properties, cont. Terbium

Dysprosium

Holmium

Erbium

Thulium

Ytterbium

Lutetium

Chemical symbol Atomic number Z

Tb 65

Dy 66

Ho 67

Er 68

Tm 69

Yb 70

Lu 71

Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension, liquid Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Volume compressibility κ Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s33 Elastic compliance s44 Elastic compliance s12 Elastic compliance s13 Elastic stiffness c11 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c12 Elastic stiffness c13 Tensile strength Vickers hardness

8.27

8.54

8.80

9.05

9.33

9.840

19.31

19.00

18.75

18.44

18.12

0.65 7.0 × 10−6

0.650 10.0 × 10−6

0.650 11.2 × 10−6

0.620 9.2 × 10−6

0.62 13.3 × 10−6

6.98 6.292 24.84 0.424 0.85 25.0 × 10−6

1060 2920 2.40 × 10−5 57.5 22.8 0.26 17.4 15.6 46.0 −5.2 −3.6 69.2 74.4 21.8 25.0 21.8 About 122 863

1720 2960 2.50 × 10−5 63.1 25.5 0.24 16.0 14.5 41.2 −4.6 −3.2 74.0 78.6 24.3 25.5 21.8

1740 3040 2.42 × 10−5 67.1 26.7 0.26 15.3 14.0 38.6 −4.3 −2.9 76.5 79.6 25.9 25.6 21.0 About 132 481

1810 3080 2.34 × 10−5 73.3 29.6 0.24 14.1 13.2 36.4 −4.2 −2.6 84.1 84.7 27.4 29.4 22.6 139 589

544

2.42 × 10−5 74.0 30.4 0.27

1000 1820 7.24 × 10−5 18.4 7.16 0.28 89.2 56.4 −31.9 18.6 17.7 10.4

About 140 520

72.5 206

17.78

8.12 × 10−6

2.33 × 10−5 68.4 27.1 0.27 14.3 14.8 37.3 −4.2 −3.5 86.2 80.9 26.8 32.0 28.0 139 1160

Units g/cm3 g/cm3 cm3 /mol mPa s N/m 1/K m/s m/s 1/MPa GPa GPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa MPa

The Elements 1.5 Data 145

Part 2 1.5

Element name

146

Part 2 1.5

Part 2 The Elements

Table 2.1-25B(c) Lanthanides. Thermal and thermodynamic properties Element name

Cerium

Praseodymium

Neodymium

Promethium Samarium

Europium

Gadolinium

Chemical symbol Atomic number Z

Ce 58

Pr 59

Nd 60

Pm 61

Sm 62

Eu 63

Gd 64

Thermal conductivity λ Molar heat capacity c p Standard entropy S0

11.4 26.4 69.454

12.5 27.20 73.931

16.5 27.45 71.086

17.9

13.3 29.54 69.496

13.9 27.6 80.793

10.6 37.02 68.089

Enthalpy difference H298 − H0 Melting temperature Tm Transition Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm

7.2802 1072.0 δ–liquid 5.4601 5.093 0.011

7.4182 1204.0 β–liquid 6.8869 5.720 0.02

7.1337 1289.0 β–liquid 7.1421 5.541 0.09

7.3000 1315.0 β–liquid 7.7000 5.856

7.5730 1345.0 γ –liquid 8.6190 6.408 0.036

8.0040 1095.0 α–liquid 9.2132 8.414 0.048

9.0876 1586.15 β–liquid 9.6680 6.095 0.02

Boiling temperature Tb Enthalpy change ∆Hb

3699 414.2

3785 296.8

3341 273.0

3785

2064 166.4

1870 144.7

3569 359.4

72.00

Units Remarks W/(m K) J/(mol K) At 298.2 K J/(mol K) At 298.15 K and 100 kPa kJ/mol At 298.15 K K kJ/mol J/(mol K) (Vl − Vs )/Vl at Tm K kJ/mol

Table 2.1-25B(c) Lanthanides. Thermal and thermodynamic properties, cont. Element name

Terbium

Dysprosium

Holmium

Erbium

Thulium

Ytterbium

Lutetium

Chemical symbol Atomic number Z

Tb 65

Dy 66

Ho 67

Er 68

Tm 69

Yb 70

Lu 71

Thermal conductivity λ Molar heat capacity c p Standard entropy S0

11.1 28.91 73.8

10.7 28.16 74.956

16.2 27.15 75.019

14 28.12 73.178

16.8 27.03 74.015

38.5 26.74 59.831

16.4 26.86 50.961

Enthalpy difference H298 − H0 Melting temperature Tm Transition Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm

9.4266 1632 β–liquid 10.1504 6.220 0.031

8.8659 1685.15 β–liquid 11.3505 6.736 0.45

7.9956 1745.0 β–liquid 11.7570 6.738 0.074

7.3923 1802.0 α–liquid 19.9033 11.045 0.09

7.3973 1818.0 α–liquid 16.8406 9.263 0.069

6.7111 1097 γ –liquid 7.6567 6.980 0.051

6.3890 1936.0 α–liquid 18.6481 9.632 0.036

Boiling temperature Tb Enthalpy change ∆Hb

3496 330.9

2835 230

2968 242.50

3136 261.4

2220 190.7

1467 128.83

3668 355.9

Units Remarks W/(m K) J/(mol K) At 298.2 K J/(mol K) At 298.15 K and 100 kPa kJ/mol At 298.15 K K kJ/mol J/(mol K) (Vl − Vs )/Vl at Tm K kJ/mol

Table 2.1-25B(d) Lanthanides. Electronic, electromagnetic, and optical properties Element name

Cerium

Praseodymium

Neodymium

Promethium

Samarium

Europium

Gadolinium

Chemical symbol Atomic number Z

Ce 58

Pr 59

Nd 60

Pm 61

Sm 62

Eu 63

Gd 64

Characteristics

Metal

Metal

500 28 × 10−4

914 14.8 × 10−4 −3.57 × 10−9

Soft metal very reactive 890 81.3 × 10−4

Soft metal

730 9.7 × 10−4 −45.2 × 10−9

Reactive metal 610 21.3 × 10−4 −1.5 × 10−9 1550 0.971 × 10−10

Metal

Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Hall coefficient R Thermoelectric coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmass (SI)

Ductile reactive metal 650 17.1 × 10−4 −0.4 × 10−9 1130 0.709 × 10−10

2.7 69.5 × 10−3

3.2 3.3 74.5 × 10−3

2.7 3.2 16.1 × 10−3

2.5 2.54 388 × 10−3

2.5 × 10−3

5.53 × 10−3

5.93 × 10−3

1.28 × 10−3

217 × 10−6

474 × 10−6

490 × 10−6

106 × 10−6

1.92 × 10−10 4.39 2.88 2.6 31.4 × 10−3

Units

Remarks

At RT

3.1 3.07 2.324

nΩ m 1/K 1/hPa nΩ m m3 /(A s) µV/K V V cm3 /mol

30.9 × 10−3

185 × 10−3

cm3 /mol

At 295 K

2.81 × 10−3

14.9 × 10−3

cm3 /g

At 295 K

Units

Remarks

2440 −0.2 × 10−10

1260 17.6 × 10−4 −4.5 × 10−9 1950 0.95 × 10−10

Dysprosium

Holmium

Erbium

Thulium

Ytterbium

Lutetium

Tb 65

Dy 66

Ho 67

Er 68

Tm 69

Yb 70

Lu 71

Characteristics

Ductile metal 1130 11.9 × 10−4

Metal

Soft metal 814 17.1 × 10−4 −2.2 × 10−9 2210

Soft metal 810 20.1 × 10−4 −27 × 10−9 2260 −0.34 × 10−10

Ductile metal 670 19.5 × 10−4 −2.6 × 10−9

Ductile metal 250 13 × 10−4 9.7 × 10−9 1080 −0.53 × 10−10

Metal

3.09 916 × 10−3

3.12 603 × 10−3

3.12 329 × 10−3

a

72.9 × 10−3

48 × 10−3

8.00 × 10−3

5.49 × 10−3

3.33 × 10−3

Electrical resistivity ρs Temperature coefficient Pressure coefficient Electrical resistivity ρl Hall coefficient R Electronic work function Thermal work function Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmass (SI)

1930

3.4 2.136 a 170 × 10−3 15.3 × 10−3

3.09 1.232 a a

98 × 10−3

At RT

2.50 842 × 10−6

540 nΩ m 24 × 10−4 1/K −1.31 × 10−9 1/hPa nΩ m m3 /(A s) 3.3 V 3.14 V 2.30 × 10−3 cm3 /mol

26.2 × 10−3

67 × 10−6

183 × 10−6

cm3 /mol

At 295 K

1.90 × 10−3

4.9 × 10−6

13 × 10−6

cm3 /g

At 295 K

At 293 K, B < 1 T

At 295 K

The molar magnetic susceptibility is given for Tb and Dy for the α-phase [1.3].

147

Part 2 1.5

a

890 11.9 × 10−4 −2.3 × 10−9 2100

1.5 Data

Terbium

Chemical symbol Atomic number Z

At 295 K

The Elements

Element name

At 293 K, B < 1 T

148

Part 2

The Elements

Part 2 1.5

Table 2.1-25C Lanthanides. Allotropic and high-pressure modifications Element

Cerium

Modification

α-Ce

Praseodymium

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number

cub, fc hex Cu α-La 516.10 367.3 1180.2 Fm3m P63 /mmc 4 Oh5 D6h A1 A3 cF4 hP4 4 4 12 12

β-Ce

γ -Ce

α
-Ce

Ce-III

α-Pr

β-Pr

γ -Pr

cub, fc cub, fc Cu Cu 482

orth α-U

cub, bc W 413

cub, fc Cu 488

Fm3m Oh5 A1 cF4 4 12

Cmcm 17 D2h A20 oC4 4 2+2 +4 + 4

hex α-La 367.21 1183.26 P63 /mmc 4 D6h A3 hP4 4 12

Im3m Oh9 A2 cI2 2 8

Fm3m Oh5 A1 cF4 4 12

RTP

358 345 >1094 K >4.0 GPa

Units

Shortest interatomic distance, solid 364 Range of stability RTP

>263 K

Fm3m Oh5 A1 cF4 4 12

1.5 GPa 5.1 GPa

Element

Neodymium

Modification

α-Nd

β-Nd

γ -Nd

α-Pm

β-Pm

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex α-La 365.82 1179.66 P63 /mmc 4 D6h A3 hP4 4 12 364 RTP

cub, bc W 413

cub, fc Cu 480

cub, bc W

Im3m Oh9 A2 cI2 2 8 358 > 1135 K

Fm3m Oh5 A1 cF4 4 12 339 > 5.0 GPa

hex α-La 365 1165 P63 /mmc 4 D6h A3 hP4 4 12 362 RTP

Element

Samarium

Modification

α-Sm

β-Sm

γ -Sm

α-Gd

β-Gd

γ -Gd

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

trig α-Sm 362.90 2620.7 R3m 5 D3d A7 hR3 3 12 361 RTP

cub, bc W

hex α-La 361.8 1166 P63 /mmc 4 D6h A3 hP4 4 12 360 > 4.0 GPa

hex, cp Mg 363.36 578.10 P63 /mmc 4 D6h A3 hP2 2 12 360 RTP

cub, bc W 406

trig α-Sm 361 2603 R3m 5 D3d A7 hR3 3

pm pm

pm

Promethium

Units

pm pm Im3m Oh9 A2 cI2 2 8 pm > 1163 K

Gadolinium

Units

Im3m Oh9 A2 cI2 2 8 353 > 1190 K

Im3m Oh9 A2 cI2 2 8 351 > 1535 K

pm pm

pm > 3.0 GPa

The Elements

Element

Terbium

Modification

α-Tb

β-Tb

Tb-II

Dysprosium α-Dy

β-Dy

α
-Dy

γ -Dy

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex, cp Mg 360.55

cub, bc W

trig α-Sm 341

hex, cp Mg 359.15

cub, bc W

orth

trig α-Sm 343.6

2450 R3m 5 D3d A7 hR3 3

565.01 P63 /mmc 4 D6h A3 hP2 2 12 355 RTP

Units

569.66 P63 /mmc 4 D6h A3 hP2 2 12 357 RTP

Im3m Oh9 A2 cI2 2

>1589 K >6.0 GPa

Im3m Oh9 A2 cI2 2 8 345 >1243 K

Erbium

359.5 618.4 567.8 Cmcm 17 D2h

2483.0 R3m 5 D3d

oC4 4

hR3 3

7.5 GPa

pm pm pm

pm

Element

Holmium

Thulium

Modification

α-Ho

β-Ho

γ -Ho

α-Er

β-Er

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex, cp Mg 357.78 561.78 P63 /mmc 4 D6h A3 hP2 2 12 353 RTP

cub, bc W

trig α-Sm 334 2450 R3m 5 D3d A7 hR3 3

hex, cp Mg 355.92 558.50 P63 /mmc 4 D6h A3 hP2 2 12 351 RTP

cub, bc W

Element

Ytterbium

Modification

α-Yb

β-Yb

γ -Yb

α-Lu

β-Lu

Lu-II

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, fc Cu 548.48

cub, bc W 444

trig α-Sm

Im3m Oh9 A2 cI2 2 8 385 > 1005 K

hex, cp Mg 350.52 554.94 P63 /mmc 4 D6h A3 hP2 2 12 347 RTP

cub, bc W

Fm3m Oh5 A1 cF4 4 12 388 RTP

hex, cp Mg 387.99 638.59 P63 /mmc 4 D6h A3 hP2 2 6+6 388 < 270 K

α-Tm

β-Tm

Tm-II

cub, bc W

trig α-Sm

Units

Im3m Oh9 A2 cI2 2 8 343 High tem- > 4.0 perature GPa

hex, cp Mg 353.75 555.40 Im3m P63 /mmc 4 Oh9 D6h A2 A3 cI2 hP2 2 2 8 12 349 High tem- RTP perature

pm pm Im3m Oh9 A2 cI2 2 8

R3m 5 D3d hR3 3 pm

High tem- > 6.0 perature GPa

Lutetium Units

pm pm Im3m Oh9 A2 cI2 2 8 385 > 1005 K

R3m 5 D3d hR3 3 12 pm > 23 GPa

149

Part 2 1.5

Table 2.1-25C Lanthanides. Allotropic and high-pressure modifications, cont.

1.5 Data

150

Part 2

The Elements

Part 2 1.5

Table 2.1-25D Lanthanides. Ionic radii (determined from crystal structures) Element

Cerium

Ion

Ce3+

Coordination number 6 8 9 10 12

Praseodymium Ce4+

101 114

87 97

125 134

107 114

NeoPromedymium thium

Pr3+ Pr4+ Nd3+ 99 113

85 96

98 112 116

Samarium

Gadolinium

Pm3+

Sm2+ Sm3+ Eu2+

Eu3+

Gd3+

109

119 127

95 107

94 105

96 108

117 125 135

127

124

Element

Terbium

Dysprosium

Erbium

Thulium

Ion

Tb3+

Tb4+

Dy2+

Dy3+

Er3+

Tm2+

92

76

107

91

89

101 109

104

88

119

103

100

Coordination number 6 7 8 9

Europium

Ytterbium

Lutetium

Tm3+

Yb2+

Lu3+

88

102

99

114

Yb3+

86 99 104

97

Units pm pm pm pm pm

Units pm pm pm pm

Element name

Thorium

Protactinium

Uranium

Neptunium

Plutonium

Americium

Curium

Chemical symbol Atomic number Z

Th 90

Pa 91

U 92

Np 93

Pu 94

Am 95

Cu 96

Characteristics Relative atomic mass A (atomic weight) Abundance in lithosphere a Atomic radius rcov Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states

Radioactive 232.0381(1)

Radioactive 231.03588(2)

Radioactive 238.0289(1)

Radioactive [237]

Radioactive [244]

Radioactive [243]

Radioactive [247]

164 –OPQ 4K 11/2 [Rn]5f2 6d1 7s2 5+, 4+

Electronegativity χA b 1st ionization energy 2nd ionization energy 3rd ionization energy 4th ionization energy Standard electrode potential E 0

(1.11) 6.08 11.5 20.0 28.8 −1.899

4 × 10−6 142 154 –OPQ 5L 6 [Rn]5f3 6d1 7s2 6+, 5+, 4+, 3+ (1.22) 6.19405

150 –OPQ 6L 11/2 [Rn]5f4 6d1 7s2 6+, 5+, 4+, 3+ (1.22) 6.2657

164 –OPQ 7F 0 [Rn]5f6 7s2 6+, 5+, 4+, 3+ (1.22) 6.06

173 –OPQ 8S 7/2 [Rn]5f7 7s2 6+, 5+, 4+, 3+ (1.2) 5.993

Units

a

Mass ratio.

b

11.5 × 10−6 165 180 –OPQ 3F 2 [Rn]6d2 7s2 4+

c

(1.14) 5.89

According to Allred and Rochow.

c

pm 174 pm –OPQ 9D 2 [Rn]5f7 6d1 7s2 3+ (1.2) 6.02

2.1.5.5 Elements of the Actinides Period

Table 2.1-26A Actinides. Atomic, ionic, and molecular properties (see Table 2.1-26D for ionic radii)

eV eV eV eV V

Reaction type Th4+ + 4e− = Th

Element name

Berkelium

Californium

Einsteinium

Fermium

Mendelevium

Nobelium

Lawrencium

Chemical symbol Atomic number Z

Bk 97

Cf 98

Es 99

Fm 100

Md 101

No 102

Lr 103

Characteristics Relative atomic mass A (atomic weight) Atomic radius rmet Electron shells Electronic ground state Electronic configuration Oxidation states Electronegativity χA a 1st ionization energy

Radioactive [247]

Radioactive [251]

Radioactive [252]

Radioactive [257]

Radioactive [258]

Radioactive [259]

Radioactive [262]

170 –OPQ 6H 15/2 [Rn]5f9 7s2 4+, 3+ (1.2) 6.23

186 –OPQ 5I 8 [Rn]5f10 7s2 3+ (1.2) 6.30

186 –OPQ 5I 15/2 [Rn]5f11 7s2

–OPQ 3H 6 [Rn]5f12 7s2

–OPQ 2F 7/2 [Rn]5f13 7s2

–OPQ 1S 0 [Rn]5f14 7s2

–OPQ 2D 5/2 [Rn]5f14 6d1 7s2 3+

(1.2) 6.42

(1.2) 6.50

(1.2) 6.58

6.65

Units

The Elements

eV

According to Allred and Rochow.

1.5 Data 151

Part 2 1.5

a

pm

152

Part 2 1.5

Part 2 The Elements

Table 2.1-26B(a) Actinides. Crystallographic properties (see Table 2.1-26C for allotropic and high-pressure modifications) Element name

Thorium

Protactinium

Uranium

Neptunium

Plutonium

Americium

Curium

Chemical symbol Atomic number Z

Th 90

Pa 91

U 92

Np 93

Pu 94

Am 95

Cu 96 Units

Modification Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle γ Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid

cub, fc Cu 508.51

Fm3m Oh5 A1 cF4 4 12 360

324.2

α-U orth, C α-U 285.38 586.80 495.57

orth, P α-Np 666.3 472.3 488.7

I4/mmm 17 D4h A6 tI2 2 8+2 321

Cmcm 17 D2h A20 oC4 4 2+2+4+4 276

Pnma 16 D2h Ac oP8 8 8+6 259–335

tetr, I α-Pa 394.5

α-Pu mon, P α-Pu 618.3 482.2 1096.8 101.78 P21 /m 2 C2h mP16 16 257–278

hex α-La 346.8

hex α-La 349.6

1124.1

1133.1

P63 /mmc 4 D6h A3 hP4 4 6+6 347

P63 /mmc 4 D6h A3 hP4 4 6+6 349

Element name

Berkelium

Californium

Einsteinium

Fermium

Mendelevium

Nobelium

Lawrencium

Chemical symbol Atomic number Z

Bk 97

Cf 98

Es 99

Fm 100

Md 101

No 102

Lr 103

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell

hex α-La 341.6 1106.9 P63 /mmc 4 D6h A3 hP4 4

hex α-La

hex α-La

pm pm pm deg

pm

Units

pm pm P63 /mmc 4 D6h A3 hP4 4

P63 /mmc 4 D6h A3 hP4 4

Table 2.1-26B(b) Actinides. Mechanical properties Element name

Thorium

Protactinium

Uranium

Neptunium

Plutonium

Americium

Curium

Chemical symbol Atomic number Z

Th 90

Pa 91

U 92

Np 93

Pu 94

Am 95

Cu 96 Units

15.40 15.0

1.05 12.5 × 10−6 7.3 × 10−6 1630 2850 1.86 × 10−5 78.3 76 30.8 0.26 27.4

22.0

−10.9

77.0

45.5

50.9

1.53 −0.14 × 10−3 12.6 × 10−6 1940 3370 0.785 × 10−5 177 70.6 0.25 4.91 6.73 4.79 8.04 13.6 13.4 −1.19 0.08 −2.61 215 199 267 124 73.4 74.3 46 22 108 0.585 1960

20.40 11.71

27.5 × 10−6

55 × 10−6

68

92.7 45 0.18

0.525 2500–2800

13.60

13.510

g/cm3

17.78

18.3

cm3 /mol mPa s N/m N/(m K) 1/K m/s m/s 1/MPa GPa GPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa 1/TPa GPa GPa GPa GPa GPa GPa GPa GPa GPa GPa

1.5 Data

0.219 294–687

18.90 17.907 12.56

153

Part 2 1.5

11.70 10.35 19.80

α-Pu 19.80 16.623 12.3 7.4 0.55

The Elements

Modification Density , solid Density , liquid Molar volume Vmol Viscosity η, liquid Surface tension, liquid Temperature coefficient Coefficient of linear thermal expansion α Sound velocity, solid, transverse Sound velocity, solid, longitudinal Volume compressibility κ Elastic modulus E Shear modulus G Poisson number µ Elastic compliance s11 Elastic compliance s22 Elastic compliance s33 Elastic compliance s44 Elastic compliance s55 Elastic compliance s66 Elastic compliance s12 Elastic compliance s13 Elastic compliance s23 Elastic stiffness c11 Elastic stiffness c22 Elastic stiffness c33 Elastic stiffness c44 Elastic stiffness c55 Elastic stiffness c66 Elastic stiffness c12 Elastic stiffness c13 Elastic stiffness c23 Tensile strength Vickers hardness

154

Part 2 1.5

Part 2 The Elements

Table 2.1-26B(b) Actinides. Mechanical properties, cont. Element name

Berkelium

Californium

Einsteinium

Fermium

Mendelevium

Nobelium

Lawrencium

Chemical symbol Atomic number Z

Bk 97

Cf 98

Es 99

Fm 100

Md 101

No 102

Lr 103

Density , solid Molar volume Vmol

14.790 16.70

9.310 26.96

8.840 28.5

Units g/cm3 cm3 /mol

Table 2.1-26B(c) Actinides. Thermal and thermodynamic properties Element name

Thorium

Protactinium Uranium

Neptunium Plutonium

Americium Curium

Chemical symbol Atomic number Z

Th 90

Pa 91

U 92

Np 93

Pu 94

Am 95

Modification Thermal conductivity λ Molar heat capacity c p Standard entropy S0 Enthalpy difference H298 − H0 Melting temperature Tm Transition Enthalpy change ∆Hm Entropy change ∆Sm Relative volume change ∆Vm Boiling temperature Tb Enthalpy change ∆Hb

α-Th 77.0 27.32 51.800 6.3500 2022.99 β–liquid 13.8072 6.825 0.05 5061 514.1

α-Pa About 47 (27.61) 51.882 6.4392 1844.78 β–liquid 12.3412 6.690

α-U 22.0 27.66 50.200 6.3640 1408.0 γ –liquid 9.1420 6.493 0.022 4407 464.1

α-Np 6.3 29.62 50.459 6.6065 917.0 γ –liquid 3.1986 3.488

α-Pu 6.74 32.84 54.461 6.9023 913.0 ε–liquid 2.8240 3.093

About 10 25.9 55.396 6.4070 1449.0 γ –liquid 14.3930 9.933

423.4

3503 260.0

2880 238.5

Cu 96 Units

481

About 10 (27.70) 71.965 6.1337 1618.0 β–liquid 14.6440 9.051

Remarks

W/(m K) J/(mol K) At 298 K J/(mol K) At 298.15 K and 100 kPa kJ/mol K kJ/mol J/(mol K) (Vl − Vs )/Vl at Tm

395.7

Element name

Berkelium Californium

Einsteinium

Fermium

Mendelevium

Nobelium

Lawrencium

Chemical symbol Atomic number Z

Bk 97

Cf 98

Es 99

Fm 100

Md 101

No 102

Lr 103

Thermal conductivity λ Standard entropy S0 Melting temperature Tm Transition Enthalpy change ∆Hm Entropy change ∆Sm Enthalpy of boiling ∆Hb

About 10 (76.15) 1256

About 10 80.542 1213

About 10 89.471 1133.0 β–liquid 9.4056 8.302

87.236 1800 1.02 3.26

1100

1100

1900

K kJ/mol

Units Remarks W/(m K) J/(mol K) At 298.15 K and 100 kPa K kJ/mol J/(mol K) kJ/mol

Table 2.1-26B(d) Actinides. Electronic, electromagnetic, and optical properties Element name

Thorium

Protactinium

Uranium

Neptunium

Plutonium

Americium

Curium

Chemical symbol Atomic number Z

Th 90

Pa 91

U 92

Np 93

Pu 94

Am 95

Cu 96

Characteristics

Soft metal

Toxic metal

Reactive metal

147 27.5 × 10−4 −3.4 × 10−9 1.37

177

Metal, very toxic 1414

Metal

Electrical resistivity ρs Temperature coefficient Pressure coefficient Superconducting critical temperature Tcrit Superconducting critical field Hcrit Hall coefficient R a Thermoelectronic coefficient Electronic work function Thermal work function Molar magnetic susceptibility χmol (SI) Molar magnetic susceptibility χmol (cgs) Mass magnetic susceptibility χmol (SI)

Ductile metal 280 28.2 × 10−4

Metal, very reactive 860

162

Remarks

nΩ m 1/K 1/Pa K

At RT

Oe

−1.2 × 10−10

0.34 × 10−10 5.0

0.69 × 10−6

m3 /(A s) µV/K

3.67 3.42 1.22 × 10−3

4.8 3.48 × 10−3

3.47 3.47 5.14 × 10−3

7.23 × 10−3

6.60 × 10−3

V V cm3 /mol

97 × 10−6

277 × 10−6

409 × 10−6

575 × 10−6

525 × 10−6

cm3 /mol

7.2 × 10−6

21.6 × 10−6

31.7 × 10−6

50 × 10−6

cm3 /g

At 298 K, B = 0.3–0.7 T. Element name

Berkelium

Californium

Einsteinium

Fermium

Mendelevium

Nobelium

Lawrencium

Chemical symbol Atomic number Z

Bk 97

Cf 98

Es 99

Fm 100

Md 101

No 102

Lr 103

Characteristics

Metal

Metal

Metal

Metal

The Elements 1.5 Data 155

Part 2 1.5

a

680 33 × 10−4

Units

156

Part 2 1.5

Part 2

Element

Thorium

Protactinium

Uranium

Modification

α-Th

β-Th

α-Pa

β-Pa

α-U

β-U

γ -U

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

cub, fc Cu 508.51

cub, bc W 411

tetr, I In 394.5

cub, bc W

tetr

cub, bc W 352.4

Fm3m Oh5 A1 cF4 4 12 360 RTP

Im3m Oh9 A2 cI2 2 8 356 > 1673 K

324.2 I4/mmm 17 D4h A6 tI2 2 8+2 321 RTP

orth, C α-U 285.38 586.80 495.57 Cmcm 17 D2h A20 oC4 4 2+2+4+4 276 RTP

Units

Im3m Oh9 A2 cI2 2 2+2+4+4 > 1443 K

1075.9 565.4 P42 /mmm 14 C2h tP30 30 12 287–353 > 935 K

Im3m Oh9 A2 cI2 2 8 347 > 1045 K

Element

Neptunium

Modification

α-Np

β-Np

γ -Np

α-Pu

β-Pu

γ -Pu

δ-Pu

δ
-Pu

ε-Pu

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Lattice angle γ Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

orth, P α-Np 666.3 472.3 488.7

tetr

cub, bc W 352

mon, P

mon

orth 315.87 576.82 1016.2

cub, bc W 570.3

Pnma 16 D2h Ac oP8 8 8+6 260–336 RTP

P421 2 7 D4h Ad tP4 4 8+6 275–356 >553 K

928.4 1046.3 785.9 92.13 I2/m 3 C2h

tetr In 332.61

338.7

618.3 482.2 1096.8 101.78 P21 /m 2 C2h

cub, fc Cu 463.71

mP16 16

mI34 34

257–278 RTP

259–310 >395 K

oF8 8 4+2+4 303 >508 K

pm pm pm

pm

Plutonium

Units

489.6

Im3m Oh9 A2 cI2 2 8+6 305 >850 K

Fddd 24 D2h

446.30 Fm3m Oh5 A1 cF4 4 12 328 >592 K

I4/mmm 17 D4h A6 tI2 2 4+8 333 >726 K

Im3m Oh9 A2 cI2 2 8+6 315 >744 K

pm pm pm deg

pm

The Elements

Table 2.1-26C Actinides. Allotropic and high-pressure modifications

The Elements

Element

Americium

Modification

α-Am

β-Am

γ -Am

Curium α-Cm

β-Cm

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant b Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex α-La 346.8

cub, fc Cu 489.4

hex α-La 349.6

cub, fc Cu 438.1

1124.1 P63 /mmc 4 D6h A3 hP4 4 6+6 347 RTP

Fm3m Oh5 A1 cF4 4 12 346 > 878 K

orth α-U 306.3 596.8 516.9 Cmcm 17 D2h A20 oC4 4

1133.1 P63 /mmc 4 D6h A3 hP4 4 6+6 350 RTP

Fm3m Oh5 A1 cF4 4 12 310 > 1449 K

Units

> 15.0 GPa

Element

Berkelium

Californium

Modification

α-Bk

β-Bk

α-Cf

β-Cf

α-Es

β-Es

Crystal system, Bravais lattice Structure type Lattice constant a Lattice constant c Space group Schoenflies symbol Strukturbericht type Pearson symbol Number A of atoms per cell Coordination number Shortest interatomic distance, solid Range of stability

hex α-La 341.6 1106.9 P63 /mmc 4 D6h A3 hP4 4

cub, fc Cu 499.7

hex α-La

cub, fc Cu

hex α-La

cub, fc Cu

Fm3m Oh5 A1 cF4 4 12 353 > 1183 K

P63 /mmc 4 D6h A3 hP4 4

pm pm pm

pm

Einsteinium

Units

RTP

pm pm Fm3m Oh5 A1 cF4 4 12 406 > 1213 K

P63 /mmc 4 D6h A3 hP4 4

Fm3m Oh5 A1 cF4 4

RTP

> 1093 K

pm

Table 2.1-26D Actinides. Ionic radii (determined from crystal structures) Element

Thorium

Protactinium

Ion

Th4+

Pa3+

Coordination number 2 4 6 8 10 12

94 105 113 121

104

Pa4+

90

Uranium Pa5+

78

U3+

103

U4+

89 100 117

Neptunium U5+

76

U6+ 45 52 73 86

Np3+ Np4+ Np5+ Np6+

101

87

75

72

Units pm pm pm pm pm pm

157

Part 2 1.5

Table 2.1-26C Actinides. Allotropic and high-pressure modifications, cont.

1.5 Data

158

Part 2

The Elements

Part 2 1

Table 2.1-26D Actinides. Ionic radii (determined from crystal structures), cont. Element

Plutonium

Americium

Curium

Ion

Pu3+

Pu4+

Pu5+

Pu6+

Am3+

Am4+

Cm3+

Cm4+

Coordination number 6 8

100

86

74

71

98 109

85 95

97

85 95

Element

Berkelium

Ion

Bk3+

Bk4+

Cf

Coordination number 6 8

96

83 93

95

Units pm pm

Californium 3+

Cf 82 92

4+

Units pm pm

References 1.1

1.2

W. Martienssen (Ed.): Numerical Data and Functional Relationships in Science and Technology, Landolt–Börnstein, New Series III and IV (Springer, Berlin, Heidelberg 1970–2003) R. Blachnik (Ed.): Elemente, anorganische Verbindungen und Materialien, Minerale, D’Ans-Lax, Taschenbuch für Chemiker und Physiker, Vol. 3, 4th edn. (Springer, Berlin, Heidelberg 1998)

1.3

1.4

D. R. Lide (Ed.): CRC Handbook of Chemistry and Physics, 80th edn. (CRC Press, Boca Raton 1999) Lehrstuhl für Werkstoffchemie, T.H. Aachen: Thermodynamic Properties of Inorganic Materials, Landolt– Börnstein, New Series IV/19 (Springer, Berlin, Heidelberg 1999)

159

Part 3

Classes of M Part 3 Classes of Materials

1 Metals Frank Goodwin, Research Triangle Parc, USA Sivaraman Guruswamy, Salt Lake City, USA Karl U. Kainer, Geesthacht, Germany Catrin Kammer, Goslar, Germany Wolfram Knabl, Reutte, Austria Alfred Koethe, Dresden, Germany Gerhard Leichtfried, Reutte, Austria Günther Schlamp, Steinbach/Ts, Germany Roland Stickler, Vienna, Austria Hans Warlimont, Dresden, Germany 2 Ceramics Hans Warlimont, Dresden, Germany 3 Polymers Manfred D. Lechner, Osnabrück, Germany 4 Glasses Dieter Krause, Mainz, Germany

160

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161

hereas the fundamental properties of all metallic elements are covered systematically and comprehensively in Chapt. 2.1, this section chapter treats those metals that are applied as base and alloying elements of metallic materials. According to common usage, the section is subdivided into treatments of metallic materials based on a single elements (Mg, Al, Ti, Zr, Fe, Co, Ni, Cu, Pb), and treatments of groups of metals with common dominating features (refractory metals, noble metals). The term metal is used indiscriminately for pure metals and for multicomponent metallic materials, i. e., alloys. The properties of metallic materials depend sensitively not only on their chemical composition and on the electronic and crystal structure of the phases formed, but also to a large degree on their microstructure including the kind and distribution of lattice defects. The phase composition and microstructure of metallic materials are strongly dependent, in turn, on the thermal and mechanical treatments, which are applied under well-controlled conditions to achieve the desired properties. Accordingly, the production of metallic semifinished products and final parts on one hand, and the properties in the final state on the other hand, are usually intricately linked. This also applies to metallic materials treated in other chapters (Chapt. 4.2 on superconductors and Chapt. 4.3 on magnetic materials), as well as to the majority of other inorganic and organic materials. According to the complexity of the interrelations between fundamental (intrinsic) and microstructure-dependent (extrinsic) properties of metallic materials, this section provides a substantial amount of explanatory text. By the same token, the data given are mostly typical examples indicating characteristic ranges of properties achievable rather than providing complete listings. More comprehensive databases are indicated by way of reference.

3.1.1

Magnesium and Magnesium Alloys....... 3.1.1.1 Magnesium Alloys ................... 3.1.1.2 Melting and Casting Practices, Heat Treatment ....................... 3.1.1.3 Joining .................................. 3.1.1.4 Corrosion Behavior .................. 3.1.1.5 Recent Developments ..............

3.1.2 Aluminium and Aluminium Alloys ........ 3.1.2.1 Introduction ........................... 3.1.2.2 Production of Aluminium ......... 3.1.2.3 Properties of Pure Al ................ 3.1.2.4 Aluminium Alloy Phase Diagrams ............................... 3.1.2.5 Classification of Aluminium Alloys .................................... 3.1.2.6 Structure and Basic Mechanical Properties of Wrought WorkHardenable Aluminium Alloys ... 3.1.2.7 Structure and Basic Mechanical Properties of Wrought AgeHardenable Aluminium Alloys ... 3.1.2.8 Structure and Basic Mechanical Properties of Aluminium Casting Alloys .................................... 3.1.2.9 Technical Properties of Aluminium Alloys ................ 3.1.2.10 Thermal and Mechanical Treatment .............................. 3.1.2.11 Corrosion Behavior of Aluminium ......................... 3.1.3 Titanium and Titanium Alloys .............. 3.1.3.1 Commercially Pure Grades of Ti and Low-Alloy Ti Materials ....... 3.1.3.2 Ti-Based Alloys ....................... 3.1.3.3 Intermetallic Ti–Al Materials ..... 3.1.3.4 TiNi Shape-Memory Alloys ........ 3.1.4 Zirconium and Zirconium Alloys ........... 3.1.4.1 Technically-Pure and Low-Alloy Zirconium Materials ................. 3.1.4.2 Zirconium Alloys in Nuclear Applications ............ 3.1.4.3 Zirconium-Based Bulk Glassy Alloys ....................................

162 163 168 169 169 170 171 171 171 172 174 179

180

182

184 186 194 202 206 207 208 209 216 217 217 218 218

Part 3 1

Metals

3.1. Metals

162

Part 3

Classes of Materials

Part 3 1.1

3.1.5 Iron and Steels ................................... 3.1.5.1 Phase Relations and Phase Transformations ...................... 3.1.5.2 Carbon and Low-Alloy Steels .... 3.1.5.3 High-Strength Low-Alloy Steels 3.1.5.4 Stainless Steels ....................... 3.1.5.5 Heat-Resistant Steels............... 3.1.5.6 Tool Steels .............................. 3.1.5.7 Cast Irons ............................... 3.1.6 Cobalt and Cobalt Alloys ...................... 3.1.6.1 Co-Based Alloys ...................... 3.1.6.2 Co-Based Hard-Facing Alloys and Related Materials.............. 3.1.6.3 Co-Based Heat-Resistant Alloys, Superalloys............................. 3.1.6.4 Co-Based Corrosion-Resistant Alloys .................................... 3.1.6.5 Co-Based Surgical Implant Alloys............. 3.1.6.6 Cemented Carbides.................. 3.1.7 Nickel and Nickel Alloys....................... 3.1.7.1 Commercially Pure and Low-Alloy Nickels ............. 3.1.7.2 Highly Alloyed Ni-Based Materials.................. 3.1.7.3 Ni-Based Superalloys............... 3.1.7.4 Ni Plating ...............................

221 222 227 240 240 257 262 268 272 272 274 274 276 277 277 279 279 279 284 288

3.1.8 Copper and Copper Alloys .................... 296 3.1.8.1 Unalloyed Coppers................... 296 3.1.8.2 High Copper Alloys................... 297

3.1.8.3 Brasses .................................. 3.1.8.4 Bronzes.................................. 3.1.8.5 Copper–Nickel and Copper–Nickel– Zinc Alloys .............................. 3.1.9 Refractory Metals and Alloys ................ 3.1.9.1 Physical Properties .................. 3.1.9.2 Chemical Properties ................. 3.1.9.3 Recrystallization Behavior ........ 3.1.9.4 Mechanical Properties..............

298 298

300 303 306 308 311 314

3.1.10 Noble Metals and Noble Metal Alloys .... 3.1.10.1 Silver and Silver Alloys ............. 3.1.10.2 Gold and Gold Alloys ............... 3.1.10.3 Platinum Group Metals and Alloys .............................. 3.1.10.4 Rhodium, Iridium, Rhutenium, Osmium, and their Alloys .........

329 330 347

3.1.11 Lead and Lead Alloys .......................... 3.1.11.1 Pure Grades of Lead ................ 3.1.11.2 Pb–Sb Alloys........................... 3.1.11.3 Pb–Sn Alloys........................... 3.1.11.4 Pb–Ca Alloys ........................... 3.1.11.5 Pb–Bi Alloys ........................... 3.1.11.6 Pb–Ag Alloys........................... 3.1.11.7 Pb–Cu, Pb–Te, and Pb–Cu–Te Alloys ............... 3.1.11.8 Pb–As Alloys ........................... 3.1.11.9 Lead Cable Sheathing Alloys ..... 3.1.11.10 Other Lead Alloys ....................

407 407 411 414 416 419 420

363 386

421 421 421 421

References .................................................. 422

3.1.1 Magnesium and Magnesium Alloys Magnesium is the lightest structural metal with a density of 1.74 g cm−3 . It is produced by two basic processes. One is the electrolysis of fused anhydrous magnesium chloride (MgCl2 ) derived from magnesite, brine, or seawater, and recently from serpentine ores. The other one is the thermal reduction of magnesium oxide (MgO) by ferrosilicon derived from carbonate ores [1.1]. The use of primary Mg is shown in Fig. 3.1-1. Only one third is used for structural parts, mainly for castings, while the major amount of Mg is still used as an alloying element in Al alloys. Pure Mg is rarely used for structural applications due to its poor mechanical properties. Therefore, Al and Zn have been introduced as major alloying elements for high-pressure die casting alloys. The main reason

for using magnesium alloys is to lower the weigh load, predominantly in transportation industries. The weight reduction amounts to about 30% compared to Al alloys and to about 75% compared to steel. Magnesium has a hexagonal close-packed crystal structure (hcp). Therefore its deformation properties are poor. At room temperature slip occurs on the basal plane {0001} in the 112¯ 0 direction only. In addition to slip on basal planes the deformation by twinning is also possible, the twinning system is {101¯ 2}101¯ 1. Twin formation leads to different behavior of Mg alloys under tensile and compressive load. With increasing temperature above 200–225 ◦ C, prismatic slip planes are activated in addition. This is of main importance for the processing wrought magnesium alloys.

Metals

Desulphurisation of iron 12.7 %

Miscellaneous 4.7 %

Mg wrought materials 0.4 %

Alloying elements used in Mg alloys and their abbreviations applied in the designation of Mg materials are listed in Table 3.1-1. General data, maximum solubility data, and compounds formed in major binary magnesium alloy systems are given in Table 3.1-2 [1.4]. Since Al is one of the most important alloying elements, Fig. 3.1-2 [1.3] shows an example of an Al−Mg binary alloy system. The effect of alloying elements in Mg materials is given in Table 3.1-3 [1.3, 4].

3.1.1.1 Magnesium Alloys

Alloying of Al 43.3 %

Mg castings 33.5 %

Fig. 3.1-1 World consumption of Mg in 2001 (329 480 t)

[1.2]

The major alloying elements are manganese, aluminium, zinc, zirconium, silicon, thorium, and rare earth metals (E). At present E elements are the most promising candidates for magnesium alloys, with high temperature stability as well as improved corrosion behavior. E metals are forming stable intermetallic compounds at high temperature and therefore they decrease castability. Aluminium and zinc are introduced mainly to

Table 3.1-1 Alloying elements and abbreviations used for Mg materials [1.3]

A Al

C Cu

E Rare earth

K Zr

L Li

M Mn

Q Ag

S Si

W Y

Z Zn

Table 3.1-2 Solubility data and intermetallic phases in binary magnesium alloys [1.4] Solute element

Maximum solubility (wt%) (at%)

Adjacent intermetallic phase

Melting point of intermetallic phase (◦ C)

Type of equilibrium

Lithium Aluminium Silver Yttrium Zinc Neodymium Zirconium Manganese Thorium Cerium Indium Thallium Scandium Lead Thulium Terbium Tin Gallium Bismuth Calcium Samarium

5.5 12.7 15.0 12.5 6.2 ≈3 3.8 2.2 4.75 0.5 53.2 60.5 ≈ 24.5 41.9 31.8 24.0 14.5 8.4 8.9 1.35 ≈ 6.4

− Mg17 Al12 Mg3 Ag Mg24 Y5 MgZn Mg41 Nd5 Zr Mn Mg23 Th6 Mg12 Ge Mg3 In Mg5 Tl2 MgSc Mg2 Pb Mg24 Tm6 Mg24 Tb5 Mg2 Sn Mg5 Ga2 Mg3 Bi2 Mg2 Ca Mg6.2 Sm

− 402 492 620 347 560 1855 1245 772 611 484 413 − 538 645 − 770 456 821 714 −

Eutectic Eutectic Eutectic Eutectic Eutectic Eutectic Peritectic Peritectic Eutectic Eutectic Peritectic Eutectic Peritectic Eutectic Eutectic Eutectic Eutectic Eutectic Eutectic Eutectic Eutectic

17.0 11.8 3.8 3.75 2.4 ≈1 1.0 1.0 0.52 0.1 19.4 15.4 ≈ 15 7.75 6.3 4.6 3.35 3.1 1.1 0.82 ≈ 1.0

163

Part 3 1.1

Reduction of metals 1.2 %

Electrochemistry 4.2 %

1.1 Magnesium and Magnesium Alloys

Part 3

Classes of Materials

Part 3 1.1

T (°C) 0 700

10

20

30

40

50

660.452

60

Magnesium (wt %) 70 80 90 100

L

650

600 400 (Al)

450°C 18.6

452°C 458°C

λ

400

62.3 69

439°C 88.5

(Mg)

410°C

ε

(Al3Mg2)

164

300

γ

200 100

0

10 Al

20

30

40

50

60

70

80

90

100 Mg Magnesium (at %)

Fig. 3.1-2 Al−Mg phase equilibria [1.3]

increase castability. However, Al forms an intermetallic phase Mg17 Al12 which is brittle and limits ductility and, thus, the use of Al-containing alloys such as AZ91 above 120 ◦ C. Manganese has been introduced to increase ductility. It is replacing Zn in several cast alloys. Moreover, Mn is binding Fe in intermetallic phases. These can be separated before casting and therefore Mn can be used to purify the alloys. Silicon was also thought to increase high temperature stability by forming the intermetallic compound Mg2 Si. Due to the typical needle shape of this precipitate (so-called chinese script microstructure) it has only limited use because it acts like a notch, leading to crack formation at higher stress levels. Zirconium is not used in Al-containing alloys but it is added to other alloys acting as grain refiner. Wrought magnesium alloys are not used widely. The application of AZ31 is most common for forgings, extrusions, as well as for sheetmetal. There is an increasing demand for the use of wrought magnesium alloys, especially in the automotive industries, in the form of sheet

Table 3.1-3 General effects of alloying elements in magnesium materials [1.3–5]

Series Alloying elements

Melting and casting behavior

AZ

Al, Zn

QE

Ag, rare earths

Improve castability; tendency to microporosity; increase fluidity of the melt; refine weak grain Improve castability; reduce microporosity

AM

Al, Mn

AE

Al, rare earth

AS

Al, Si

WE

Y, rare earths

Mechanical and technological properties

Solid solution hardener; precipitation hardening at low temperatures (< 120 ◦ C); improve strength at ambient temperatures; tendency to brittleness and hot shortness unless Zr is refined Solid solution and precipitation hardening at ambient and elevated temperatures; improve elevated temperature tensile and creep properties in the presence of rare earth metals Improve castability; tendency to microporosity; Solid solution hardener; precipitation hardening control of Fe content by precipitating Fe–Mn at low temperatures (< 120 ◦ C); compound; refinement of precipitates increase creep resistivity Improve castability; Solid solution and precipitation hardening at reduce microporosity ambient and elevated temperatures; improve elevated temperature tensile and creep properties; increase creep resistivity Tendency to microporosity; decreased Solid solution hardener, precipitation hardening castability; formation of stable silicide at low temperatures (< 120 ◦ C); alloying elements; compatible with Al, Zn, improved creep properties and Ag; refine week grain Grain refining effect; Improve elevated temperature tensile and creep reduce microporosity properties; solid solution and precipitation hardening at ambient and elevated temperatures; improve elevated temperature tensile and creep properties

Metals

ties of the cast and wrought magnesium alloys are listed in Tables 3.1-6 and 3.1-7 [1.3, 4]. The system to denote Mg alloys is generally showing major alloying elements and their content in wt%. The first two letters are key letters and are used for the major alloying elements (Table 3.1-1). The two letters are followed by a number, which represents the nominal composition of the major alloying elements in wt%. The number indicates the content rounded to

Table 3.1-4 Nominal composition of selected cast Mg alloys [1.3, 4] ASTM

Nominal composition (wt%)

designation

Al

Zn

Mn

AZ63

6

3

0.3

AZ81

8

0.5

0.3

AZ91

9.5

0.5

0.3

AM50

5

0.3

AM20

2

0.5

AS41

4

0.3

1

AS21

2

0.4

1

Si

Cu

Zr

ZK51

4.5

0.7

ZK61

6

0.7

ZE41

4.2

ZC63

6

EZ33

2.7

0.5

HK31

RE (MM)

0.7

1.3

0.7

3.2

RE (Nd)

2.2

Y

Ag

3 0.7

HZ32

Th

3.2

0.7

3.2

QE22

0.7

2.5

QH21

0.7

1

2.5

WE54

0.5

3.25

5.1

WE43

0.5

3.25

4

1

2.5

Table 3.1-5 Nominal composition of selected wrought Mg alloys [1.3, 4] ASTM designation

Nominal composition (wt%) Al Zn Mn

M1 3

1

0.3 (0.20 min.)

AZ61

6.5

1

0.3 (0.15 min.)

AZ80

8.5

0.5

0.2 (0.12 min.)

ZM 21

2

1

ZMC711

6.5

0.75

ZK61

Cu

Li

1.2

1.25

0.15 (min.) 6

14 0.8

HK31

0.7

HM21 HZ11

Th

1.5

AZ31

LA141

Zr

0.8 0.6

2 0.6

0.8

3.2

165

Part 3 1.1

material. Therefore, a number of processes, which are introduced for the processing of aluminium and steel are under research to find out the economic boundary conditions for the processing of magnesium alloys. Beside the investigations on processing routes, there is ongoing research on alloy development since AZ31 does not meet the given aims in most requirements. The compositions of selected cast and wrought magnesium alloys are given in Tables 3.1-4 and 3.1-5. The mechanical proper-

1.1 Magnesium and Magnesium Alloys

166

Part 3

Classes of Materials

Part 3 1.1

Table 3.1-6 Typical tensile properties and characteristics of selected cast Mg alloys [1.3–5] ASTM

Condition

designation

Tensile properties 0.2%proof stress (MPa)

Tensile strength (MPa)

Characteristics Elongation to fracture (%)

AZ63

As-sand cast T6

75 110

180 230

4 3

Good room-temperature strength and ductility

AZ81

As-sand cast T4

80 80

140 220

3 5

Tough, leak-tight casting with 0.0015 Be, used for pressure die casting

AZ91

As-sand cast T4 T6 As-chill cast T4 T6

95 80 120 100 80 120

135 230 200 170 215 215

2 4 3 2 5 2

General-purpose alloy used for sand and die casting

AM50

As-die cast

125

200

7

High-pressure die casting

AM20

As-die cast

105

135

10

AS41

As-die cast

135

225

4.5

Good creep properties up to 150 ◦ C

AS21

As-die cast

110

170

4

Good creep properties up to 150 ◦ C

ZK51

T5

140

253

5

Sand casting, good room-temperature strength and ductility

ZK61

T5

175

275

5

As for ZK51

ZE41

T5

135

180

2

Sand casting, good room-temperature strength, improved castability

ZC 63

T6

145

240

5

Pressure-tight casting, good elevated temperature strength, weldable

EZ33

Sand cast T5 Chill cast T5

95 100

140 155

3 3

Good castability, pressure tight, weldable, creep resistant up to 250 ◦ C

HK31

Sand cast T6

90

185

4

Sand casting, good castability, weldable, creep resistant up to 350 ◦ C

HZ32

Sand or chill cast T5

90

185

4

As for HK31

QE22

Sand or chill cast T6

185

240

2

Pressure tight and weldable, high proof stress up to 250 ◦ C

QH21

As-sand cast T6

185

240

2

Pressure tight, weldable, good creep resistance and stress-proof to 300 ◦ C

WE54

T6

200

285

4

High strength at room and elevated temperatures, good corrosion resistance

WE43

T6

190

250

7

Weldable

the nearest digit for the range of that element. For variation within this range suffix letters A, B, C, etc., are used to indicate the stage of development of the alloy, and X is used for alloys which are still experimental. For example, AZ91D indicates that the two

Good ductility and impact strength

major alloying elements are 9 wt% Al and 1 wt% Zn. The letter D signifies that it is the fourth stage in development. The designations of the tempers are identical to those used for Al alloys and are given in Table 3.1-8 [1.3].

Metals

1.1 Magnesium and Magnesium Alloys

Table 3.1-8) ASTM

Condition

designation

Tensile properties 0.2% proof stress (MPa)

Tensile strength (MPa)

Characteristics Elongation to fracture (%)

M1

Sheet, plate F Extrusion F Forgings F

70 130 105

200 230 200

4 4 4

Low to medium strength alloy, weldable, corrosion-resistant

AZ31

Sheet, plate O H24 Extrusion F Forging F

120 160 130 105

240 250 230 200

11 6 4 4

AZ61

Extrusion F Forging F

105 160

260 275

7 7

High-strength alloy, weldable

AZ80

Forging T6

200

290

6

High-strength alloy

ZM 21

Sheet, plate O H24 Extrusions Forgings

120 165 155 125

240 250 235 200

11 6 8 9

ZMC711

Extrusions T6

300

325

3

LA141

Sheet, plate T7

95

115

10

ZK61

Extrusion F T5 Forging T5

210 240 160

185 305 275

6 4 7

High strength alloy

HK31

Sheet, plate H24 Extrusion T5

170 180

230 255

4 4

High-creep resistance to 350 ◦ C, weldable

HM21

Sheet, plate T8 T81 Forging T5

135 180 175

215 255 225

6 4 3

High-creep resistance to 350 ◦ C, weldable after short time exposure to 425 ◦ C

HZ11

Extrusion F

120

215

7

Creep resistance to 350 ◦ C, weldable

Medium-strength alloy weldable, good formability

Medium-strength alloy, good formability, good damping capacity High-strength alloy Ultra-light weight (S.G. 1.35)

Part 3 1.1

Table 3.1-7 Typical tensile properties and characteristics of selected wrought Mg alloys [1.3–5]. (For temper designations see

167

168

Part 3

Classes of Materials

Part 3 1.1

Table 3.1-8 Temper designations [1.3] General Designations As fabricated. Annealed, recrystallized (Wrought products only). Strain-hardened. Thermally treated to produce stable tempers other than F, O, or H. Solution heat-treated (unstable temper). Subdivisions of H Subdivisions of T H1, Plus one or more digits Strained only T2 Annealed (Cast products only) H2, Plus one or more digits Strain-hardened T3 Solution heat-treated and then partially annealed. and cold-worked H3, Plus one or more digits Solution heat-treated Strain-hardened and then T4 stabilized. T5 Artificially aged only T6 Solution heat-treated and artificially aged T7 Solution heat-treated and stabilized T8 Solution heat-treated, cold-worked and artificially aged T9 Solution heat-treated, artificially aged, and cold-worked T10 Artificially aged and cold-worked F O H T W

3.1.1.2 Melting and Casting Practices, Heat Treatment Due to the relatively low melting temperature of Mg, casting is the preferred processing route of Mg materials. The addition of Al and Zn are known to improve castability. All processing operations such as melting, alloying, refining, and the cleaning of melts can be carried out in plain carbon steel crucibles. The use of protective gases or fluxes is a recommended practice during melting. Fluxes consist of salts such as KCl, MgCl2 , BaCl2 , and CaCl2 [1.6]. Gases are used in different combinations, also forming a stable film during melting. Combinations of argon and/or nitrogen with additions of SF6 or SO2 are in use. The application of vacuum during melting cannot be recommended due to the high vapor pressure of liquid Mg at low pressure. During melting, a control of impurities is also necessary. The elements Fe, Ni, Co, and Cu are critical due to their effect of decreasing the corrosion resistance. The Fe content can be controlled by adding Mn, forming intermetallic compounds which are settling at the bottom of the melting crucible. But in general the amount of these critical elements has to be controlled during the primary production of Mg itself. Fortunately Cu is not part of any feedstock material used for primary

production. Therefore only master alloys or alloying elements for producing the diverse alloys have to be controlled for Co and also for Fe, which is a major impurity in a number of master alloys and alloying elements. Any casting process can be used to manufacture parts from Mg alloys. But in view of the low liquidus temperatures, the broad melting ranges, and the excellent fluidity of Mg casting alloys, high-pressure die casting (HPDC) is used most frequently at present. Mainly alloys from the AZ or AM series are used in HPDC but alloys from the AS or AE series are also useable when cast with cold chamber HPDC machines. Alloys from the QE or WE series are not suitable for HPDC but for sand casting or permanent mold casting. The mechanical properties of the Mg alloys can be improved by heat treatment. Mainly T4, T5, and T6 heat treatments are in use. A T4 treatment means dissolution of precipitates. In general, a T4 treatment is followed by an artificial aging (T6). Stress relieving can also be applied to the cast alloys. Major variables which affect the heat-treatments are section size and heating time, annealing time and temperature, and the protective atmosphere. Welded parts made of Mg alloys can be stress relieved. In general, the heat treatments can be applied to castings with the exception of HPDCs. It is not rec-

Metals

3.1.1.3 Joining Brazing and soldering are not praticable due to corrosion problems and the formation of brittle phases. Similar problems occur during welding processes such as metal inert gas welding, laser welding, or even electron beam welding. As with brazing or soldering, the formation of brittle phases leads to failures, drastically decreasing the reliability of welded joints. Riveting and mechanical joining using screws are well introduced. Especially when the joint is supported with adhesives for sealing and for adding additional forces for bonding, riveting and screwing can still be viewed as state of the art in the joining of Mg alloys. Mg alloys are seldom used as rivets or screws due to their limited mechanical properties. But it was proven that Al alloys (5052, 5056, or 6061) for rivets and surface coated steel for screws can be used to fasten Mg alloys due to similarity in corrosion

potentials. Moreover, the use of inert washers or layers to minimize contact between different materials is recommended [1.3, 7]. Due to the increasing demand for Mg wrought materials, especially in sheet form, new joining processes are under investigation. These processes are friction stir welding or clinching, often combined with the use of adhesives. While a certain degree of ductility (A > 12%) is necessary in clinching processes, friction stir welding appears to be independent of that requirement. Experiments have shown that even cast magnesium alloys can be joined using this process.

3.1.1.4 Corrosion Behavior In general only poor corrosion behavior is attributed to Mg and its alloys. This is mainly true when Mg is in contact with other metals and alloys in accordance with the electrochemical potential series of metals. Therefore, special care has to be taken to avoid conductive contact between Mg alloys and other metals with different electrochemical potentials. When joining Mg parts with other materials, insulating washers, surface-coated screws or nonconducting films and surface coatings can be applied. When investigating a Mg

Table 3.1-9 Heat treatments applied to magnesium alloys [1.3] Alloy Cast Alloy

Heat Treatment F

T4

T5

T6

AM100A

×

×

×

AZ63A

×

×

×

AZ81A

×

AZ91C

×

AZ92A

×

EZ33A

× × ×

EQ21A

×

QE22A

×

WE43A

×

WE54A

× ×

ZC63A ×

ZE41A

×

ZE63A ZK51A

× ×

ZK61A

×

Wrought Alloys ×

AZ80A ZC71A ZK60A

×

× ×

×

169

Part 3 1.1

ommended to heat-treat HPDCs materials because of the entrapment of gases during casting. The absorption of gases can be avoided by applying vacuum during casting. In this case all heat treatments can be applied as well. Table 3.1-9 shows Mg alloys with their respective useful heat treatments.

1.1 Magnesium and Magnesium Alloys

170

Part 3

Classes of Materials

Part 3 1.1

alloy by itself the material shows similar behavior as plain cabon steels, even in different environments. The main reason for an increase in corrosion rate could be found in the presence of impurities such as Fe, Ni, Co, and Cu. In order to improve the stand-alone corrosion properties these impurities have to be controlled regarding their content. While Co will normally not pose a problem since it is not part of any material used for the primary production of Mg, the content of the other elements needs to be controlled from the beginning in the production of primary Mg. According to the influence of Fe, Ni, and Cu, limits have been defined for high purity alloys which are mainly used today in the production of Mg parts (Fe/Mn < 0.0232, Cu < 0.04 wt%, Ni < 0.005 wt% for AZ91 hp). But it should be mentioned that these limits depend on the contents of other alloying elements as well as the casting processes applied [1.3, 8]. Figure 3.1-3 shows the influence of alloying elements on the rate of corrosion [1.7].

3.1.1.5 Recent Developments Squeeze casting and semi-solid metal processing (SSMP) are recent developments in casting technology by which high quality castings can be produced. Almost all Mg alloys can be subjected to SSMP if they have a broad melting interval [1.3]. First trials using AZ91 led also to the development of different processes which are making use of processing in the semi-solid state. Recently Thixomolding® was introduced, a technique similar to processing techniques for polymers. Thixomolding is in use mainly for the production of housings for handheld devices such as laptops or cameras. It is under research to investigate the capability of this technology for processing alloys which are showing limited castability mainly in HPDC. Another process using the semi-solid behavior of some magnesium alloys is thixocasting which is still a topic of research, not of production. The New RheoCast process (NRC) which is well introduced in Al industries can, also, be applied to casting semi-solid materials based on Mg. Beyond monolithic alloys the investigation of Mg matrix composites is still in progress. They can be processed using either the ingot metallurgy

20

15

Corrosion rate (mg/cm2 × d) Fe, Ni, Co Cu

Ag

10

Ca Zn

5

Cd Pb, Sn, Al 1

2

3

4 5 Constituent (mass %)

Fig. 3.1-3 Influence of alloying elements on the corrosion rate of Mg [1.7]

route or the powder metallurgy route. There are promising candidates that may be introduced to applications but the production routes are quite expensive and, moreover, the corrosion behavior is not well known. Apart from cast or powder metallurgical products, the use of wrought Mg materials is thought to increase in the future. To support the demands stemming mainly from the automotive industry the total production route is under investigation right now. This means that the developments of new wrought magnesium alloys as well as the development of suitable deformation processes in combination with appropriate joining techniques are underway. These studies are accompanied by developing modeling and simulation tools to ensure high quality and accurate prediction of properties and lifetime behavior of magnesium-based materials. Controlling corrosion is the most pressing problem under research at the moment. Since Mg alloys are about to be widely used in several applications, the corrosion problem, i. e., mainly contact corrosion in combination with other metals and alloys is receiving more and more attention. Therefore, the influence of alloying elements, mainly in combination with each other, is investigated intensively. Aside from alloying, different kinds of surface protection such as surface layers and coatings are under investigation. While castings are normally showing sufficient volume to withstand corrosion attack, this is not the case for magnesium sheet materials even for a long time.

Metals

1.2 Aluminium and Aluminium Alloys

3.1.2.1 Introduction Aluminium alloys are the second most widely used metallic materials after steels. Comprehensive treatments and data of Al-based materials are given in [1.9, 10]. Their most important properties are: low density (2.7 g/cm−3 ); alloying can result in significant further density reductions in Al-Li alloys; the low density can lead to significant energy savings, especially in applications in transportation; good mechanical properties offering optimum tensile strength ranging from 60 to 530 MPa; good workability permitting most varied shapes to be produced; good castability with a variety of casting techniques: sand, mould, diecasting; good machinability; ease of joining using all commonly applied techniques; comparatively high corrosion resistance thanks to the spontaneous formation of a strongly-adherent passivating surface film in air; different surface treatments are applicable; high electrical and thermal conductivity, especially of unalloyed aluminium; good optical properties depending on the degree of purity; non-magnetic; low absorption cross section for thermal neutrons; non-combustible, not causing sparking; no health risk is associated with the use of aluminium and its alloys; excellent recycling properties.

3.1.2.2 Production of Aluminium

2Al3+ + 6 e− → 2Al, and oxygen ions react with the carbon of the cathode to form CO2 (consumption of the cathode). A primary aluminium smelter requires on average 13 to 14 kW h per kg of Al. The main power used is hydro-electric (52.5% in 2001 [1.13]). In recent decades

To off-gas scrubbing

Anode ⫹ CO2

CO Crust Anode

Molten electrolyte (bath) Liquid aluminium Floor (cathode)

– Cathode

Steel shell

The production of aluminium is based on the electrolysis of molten alumina Al2 O3 using the Hall–Herault process. Alumina is extracted in the Bayer process form the bauxite ore which contains 20 to 30 wt% Al. In 2002 the main producers of the ore are Australia (28%), Guinea (20%), Brazil (14%), Jamaica (7%), India (4%), and Guyana (3%) [1.9]. After milling, the ore is first broken down using an Al-containing NaOH solution which is seeded to precipitate aluminium hydroxide Al(OH)3 . This is dehydrated at about 1100 ◦ C according to 2Al(OH)3 → Al2 O3 + 3H2 O. An electrolytic reduction is carried out in a cell as shown in Fig. 3.1-4. Cryolithe Na3 AlF6 is used as an additive to decrease the high melting point of pure Al2 O3 (about 2050 ◦ C) since the two compounds form a eutectic near 10 wt% of Al2 O3 in Na3 AlF6 , Fig. 3.1-5 [1.11, 12]. The electrolysis is carried out in a cell lined with carbon, which serves as the cathode. Carbon anodes are suspended from above the cell into the electrolyte. Two main reactions occur:

Fig. 3.1-4 Schematic representation of an electrolytic cell

for Al winning [1.9] T (°C) 1020

1000 L 980

β-Na3AlF6 + L

960

940 0

α-Na 3AlF6 +L

962.5 °C

β-Na 3AlF6 + α-Na 3 AlF6 5

10

15

20

25 mol %Al2O3

Fig. 3.1-5 Phase diagram of cryolithe Na3 AlF6 -alumina Al2 O3 [1.9]

Part 3 1.2

3.1.2 Aluminium and Aluminium Alloys

171

172

Part 3

Classes of Materials

Part 3 1.2

secondary production, i. e., recycling of scrap and waste material, has reached 30% of the total production, with high regional variations. Up to 95% less energy is needed to produce Al via secondary production.

3.1.2.3 Properties of Pure Al Aluminium can be classified as “unalloyed,” “pure,” or “refined,” depending on its degree of purity. The Al from conventional electrolysis is 99.5 to 99.9 wt% pure. Higher purity is produced by “triple-layer refining electrolysis” that can reach ≥ 99.99 wt% purity. The latter grade is used, for example, in the electronics sector. Physical Properties The physical properties of pure Al are given in Chapt. 2.1,Table 2.1-11. The temperature dependence of its density is shown in Fig. 3.1-6. The contraction of 6.5% upon solidification corresponds to an increase in density from 2.37 g cm−3 in the liquid state to 2.55 g cm−3 in the solid state. The temperature depen-

2.8

Density (g/cm3) 1

2.6

Mechanical Properties The ultimate tensile strength of pure aluminium increases markedly with increasing amounts of alloying or impurity additions, as shown in Fig. 3.1-10. Unalloyed aluminium is soft (tensile strength 10–30 MPa, Table 3.1-11) and, like all fcc metals, shows a low rate of work hardening.

2.4 2 2.2 2.0 1.8 1.6

0

500

1000

1500

2000

2500 T (°C)

Fig. 3.1-6 Density of solid and liquid aluminium as a func-

tion of temperature [1.9]

dence of the coefficient of thermal expansion is given in Table 3.1-10. The specific heat in the solid state increases with temperature from 720 kJ at −100 ◦ C, to 900 at 20 ◦ C, and 1110 at 500 ◦ C. At its melting point Al has a specific heat of 1220 (solid) and 1040 (liquid). In the liquid state the specific heat rises further, e.g., to 1060 kJ at 800 ◦ C. Aluminium has a high reflectivity for light, heat, and for electromagnetic radiation. The Youngs’s modulus E of aluminium materials is usually taken to be 70 GPa; it varies between 60 and 78 GPa depending on alloy composition. The shear modulus G varies between 22 and 28 GPa, the value for refined aluminium is 25.0 GPa. Poisson’s ratio ν varies between 0.32 and 0.40 (0.35 for refined aluminium). Unalloyed aluminium has an electrical conductivity of 34 to 38 m Ω−1 mm−2 . Due to this relatively high conductivity, a large fraction of unalloyed Al and Al−Mg−Si alloys are used for electrical conductors. The temperature dependence of the electrical conductivity depends on alloying additions, impurities, and microstructure (Figs. 3.1-7 – 3.1-9). Superconductivity occurs at Tc = 1.2 K in refined grades of aluminium (≥ 99.99 wt% Al). The electrical conductivity of highpurity aluminium is still high at 4.2 K.

Chemical Properties Aluminium, as a relatively reactive element, is a very strong base, as shown by its position in the electrochemical series and its low standard potential (VH = −1.66 V). Therefore, it is not possible to obtain the element from aqueous solutions by electrolysis. Similarly, it is not possible to obtain aluminium by a carbother-

Table 3.1-10 Coefficient of thermal expansion of Al 99.99 as a function of temperature [1.9] Temperature range (◦ C)

Average linear coefficient of thermal expansion (10−6 /K−1 )

(−200) − 20 (−200) − 20 20–100 20–200 20–400 20–600

18.0 21.0 23.6 24.5 26.4 28.5

1.2 Aluminium and Aluminium Alloys

Metals

Fig. 3.1-7 Electrical conductivity of as-cast binary alloys

Electrical conductivity χ (m/ Ω mm2) Sb

Cd

35

based on high-purity aluminium as a function of the alloying element concentration [1.14, 15] Sn

Bi

Co Si

Zn Fe

Ni

Cu

30 Zr

Ti

25

Electrical conductivity χ (m/ Ω mm2) 36.2

Mg

1 35.8

2

V

35.4 3

20

35.0 0 Cr

15

10

0

0.8 1.2 Alloying element content (mass%)

0.4

20

100 60 80 Degree of cold work %

40

Mn

Li

Fig. 3.1-9 Electrical conductivity of unalloyed Al (0.21 wt% Fe; 0.11 wt% Si) as a function of the degree of cold work and the degree of supersaturation and/or intermediate annealing temperature [1.14]; (1) intermediate annealing temperature 350 ◦ C; (2) intermediate annealing temperature 500 ◦ C; (3) as extruded

Electrical conductivity χ (m/ Ω mm2)

Tensile strength Rm (N/mm2)

40

Mg

Cu

35 Fe

Zn 30

80

Mn B

Cu

Cr, Ti

Si

25 Si Mg

20

60

15 40

Mn 10

0 0

2

4

6 8 10 12 14 Alloying element content (mass %)

Fig. 3.1-8 Electrical conductivity of as-cast binary alu-

minium alloys (containing larger amounts of the alloying additions) as a function of concentration of the alloying element [1.14, 15]

0.1

0.2

0.3

0.4

0.5 0.6 0.7 0.8 0.9 Alloying additions (mass %)

Fig. 3.1-10 Effect of small additions of alloying elements

or impurities on the ultimate tensile strength of aluminium of high-purity (99.98 wt% Al, soft condition, 5 h, 360 ◦ C) [1.14]

Part 3 1.2

40

173

174

Part 3

Classes of Materials

Part 3 1.2

Table 3.1-11 Typical mechanical properties of refined aluminium (Al 99.98) [1.9] Condition

Proof stress Rp0.2 (MPa)

Ultimate tensile strength Rm (MPa)

Elongation at fracture A10 (%)

Brinell hardness number HB

Soft Hard

10–25 69–98

39–49 88–118

30–45 1–3

15 25

mic reaction. In chemical compounds, aluminium is positively charged and trivalent (Al3+ ). It reacts readily with hydrochloric acid and caustic soda, but less readily with sulfuric acid; dilute sulfuric acid does not attack aluminium. It is not attacked by cold nitric acid at any concentration, and hardly so when heated. The reaction with sodium hydroxide is given by: 2Al + 2NaOH + 3H2 O → 2Na[Al(OH)4 ] + 3H2 . Aluminium-based materials are non-flammable. Even turnings and chippings do not ignite. Extremely fine aluminium particles can undergo spontaneous combustion and thus cause explosions. The heat of formation of the aluminium oxide Al2 O3 is about 1590 kJ mol−1 , making aluminium a very effective deoxidiser for the steel industry and in metalothermic metal reduction processes (aluminothermy; e.g., 3V2 O5 + 10Al → 6V + 5Al2 O3 and aluminothermic welding, “thermit process” 3Fe3 O4 + 8Al → 9Fe + 4Al2 O3 ). Important aluminium compounds include aluminium oxide Al2 O3 , which is commonly called alumina (in powder form) or corundum (in coarse crystalline structure), and aluminium hydroxide Al(OH)3 (“hydrated alumina,” usually extracted from bauxite in the Bayer process).

3.1.2.4 Aluminium Alloy Phase Diagrams The properties of aluminium strongly depend on the concentration of alloying additions and impurities. Even the low residual contents of Fe and Si in unalloyed aluminium (Al99 to Al99.9) have a marked effect. The main alloying elements of Al materials are Cu, Si, Mg, and Zn while Mn, Fe, Cr, and Ti are frequently present in small quantities, either as impurities or additives. Ni, Co, Ag, Li, Sn, Pb, and Bi are added to produce special alloys. Be, B, Na, Sr, and Sb may be added as important trace elements. All of these elements affect the structure and thus the properties of an alloy. The compositions of the more important aluminium materials are discussed below, using the relevant phase diagram. All alloying components are completely soluble in liquid aluminium if the temperature is sufficiently high. However, these elements have only limited solubility in solid solution. Continuous solid solubil-

ity does not occur in any of the alloy systems of Al. Aluminium-rich solid solutions are often formed and are referred to as α-phase, αAl -phase, or α-Al solid solution. Most of the phases occurring in equilibrium with α-Al are hard. They consist of elements or intermetallic compounds such as Al2 Cu, Al8 Mg5 , Al6 Mn, Al3 Fe, and AlLi. Binary Al-Based Systems Aluminium–Copper. Al–Cu forms a simple eutec-

tic system in the range from 0 to 53 wt% Cu, as shown in Fig. 3.1-11. The α-Al solid solution and the intermetallic compound Al2 Cu (θ phase) are in equilibrium. At intermediate temperatures, metastable transition phases may form and precipitate from the supersaturated solid solution. These metastable phases may be characterised according to their crystal structure, the nature of the phase boundary they form, and their size:

•

From room temperature up to ≈ 150 ◦ C the coherent Cu-rich Guinier-Preston zones I (GP I phase) form; they are only one to two {001} layers thick and have a highly strained, coherent phase boundary with the α-Al matrix phase. T (°C) 800 S

700

500

S + Al2Cu

S + Al

600 Al

400

53.5 % 591 °C

547 °C 33.2 %

5.7 %

Al2Cu

Al + Al2Cu

300 200 53.2 % 53.9 %

0

10

20

Fig. 3.1-11 Al−Al2 Cu

tem [1.16]

30

60 50 40 Copper content (mass %)

section of the Al−Cu sys-

1.2 Aluminium and Aluminium Alloys

Metals

• •

At ≈ 80 to ≈ 200 ◦ C the GP II phase, also called θ  phase, forms; it has a superlattice structure of the Al fcc lattice and has a coherent interface also, but the particle size grows larger than that of GP I. Above ≈ 150 ◦ C the θ  phase forms; it is only partially coherent. Above ≈ 300 ◦ C the incoherent, stable θ-phase Al2 Cu is formed (over-ageing).

These phase transformations are decisive for the precipitation-hardening behavior of Al–Cu-based technical Al alloys. Aluminium–Silicon. Al–Si forms a simple eutectic system (Fig. 3.1-12). At room temperature the solubility of Si in Al is negligible. Thanks to the good casting properties of the Al−Si eutectic, this alloy system is the basis of a major part of the Al-based casting alloys. However, when slowly cooled (e.g., in sand casting), a degenerate form of eutectic, microstructure may occur. Instead of the desired fine eutectic array, the alloy develops a structure that is characterised by larger, plate-like primary Si crystals, leading to very brittle behavior. This degenerate behavior can be suppressed by the addition of small amounts of Na, Sb, or Sr to the melt at about 720 to 780 ◦ C. This “modification” causes a lowering of the eutectic temperature and a shift in concentration of the

1500

eutectic point, as indicated in Fig. 3.1-12; the extent of the shift is dependent on the rate of solidification. Aluminium–Iron. Figure 3.1-13 shows the Al-rich part of this system. The solubility of Fe in Al is very low. In the range shown Al3 Fe is formed by a peritectic reaction at 1160 ◦ C. The eutectic between the Al phase and Al3 Fe crystallises in a degenerate manner to form brittle needles of Al3 Fe. The formation of Al3 Fe needles is also occurring in Al−Fe−Si alloys such as commercially (available) pure aluminium (Fig. 3.1-14). T (°C) 900 S 800

700

1430 °C

1400

S + Al 655 °C

0.04 % 1.8% 600 Al+ Al3 Fe 500

400 0

Temperature (°C)

S + Al3 Fe

1

2

3

4

5

6

7 8 9 10 Iron content (mass %)

Fig. 3.1-13 Al−Fe system up to 10 wt% Fe

1300 S 1200 1100 1000 900 660 °C

800

S + Si

S + Al

700

577 °C

600

1.65 %

12.5 %

500

Al + Si 400

0

10

20

30

40

50 60 70 80 90 100 Silicon content mass percent

Fig. 3.1-12 Al−Si system; the dotted line shows the extent

to which alloys can be supercooled

3 µm

Fig. 3.1-14 Al3 Fe needles formed after annealing commer-

cially pure aluminium sheet (Al99.5) for 65 h at 590 ◦ C, 800X [1.17]

Part 3 1.2

•

175

176

Part 3

Classes of Materials

Part 3 1.2

Table 3.1-12 Solubility of some elements in aluminium solid solutions [1.16, 18] Element

Temperature of eutectic (E) or peritectic (P) eqilibrium ◦ C

Phase in equilibrium with Al solid solution

Cu Fe Li Mg Mn Si Zn

547 (E) 655 (E) 602 (E) 450 (E) 657 (E) 577 (E) 275 Eutectoid equilibrium

Al2 Cu AL3 Fe AlLi Al8 Mg5 Al6 Mn Si Zn

TE or TP (wt%)

5.7 ∼ 0.04 4.7 17.4 1.82 1.65 31.6

Aluminium–Lithium. The Al-rich part of this system is

shown in Fig. 3.1-15. The Al(Li) solid solution and the η (Al3 Li) phase are in equilibrium. Al–Li-based alloys are used for their low density. Aluminium–Magnesium. This system is shown in Fig. 3.1-16. The solid phases are the α-Al solid solution and the β-Al8 Mg5 intermetallic compound. The high solubility of Mg in Al can be put to practical use for solid solution hardening. The β phase precipitates preferentially at grain boundaries, forming a continuous network at the grain boundaries of the Al-rich α solid solution, e.g., after slow cooling from temperatures above 400 ◦ C, especially in alloys containing more than 3 wt% Mg. Precipitates of the β phase are less noble 697 °C 19.8 %

T (°C) 700

Solubility (wt%) 400 ◦ C 300 ◦ C

500 ◦ C

4.4 0.005 2.8 ∼ 12.0 0.36 0.8

1.6 < 0.001 2.0 12.2 0.17 0.3

200 ◦ C

0.6

0.2

1.5 6.6 0.02 0.07

1.0 3.5 0.01 14.5

electrochemically than the α phase and are thus subject to preferential attack by corrosive media. Accordingly the disadvantage of Al−Mg alloys is their potentially high susceptibility to intergranular corrosion. Aluminium–Manganese. The Al-rich part of this sys-

tem includes the intermetallic phases Al4 Mn (above 710 ◦ C) and Al6 Mn (Fig. 3.1-17). The α-Al solid solution and the Al6 Mn phase form a eutectic (Fig. 3.1-17). The solubility of Mn in Al at room temperature is negligibly small. In hypereutectic Al−Mn alloys, preT (°C) 700

L 600

L 602 °C

600 Al

4.7 %

8%

L + Al

16.8 % 500

36% Al

500

Al + η

17.4 %

η

450˚C

y 34 %

400 β

400

Al+β

(Al8Mg5)

300 300

200

200 0

5

10

15 20 Lithium content (mass %)

Fig. 3.1-15 Al−Li system for up to 20 wt% Li [1.18]

0

10

30 40 20 Magnesium content (mass %)

Fig. 3.1-16 Al−Al8 Mg5 section of Al−Mg system

1.2 Aluminium and Aluminium Alloys

Metals

Part 3 1.2

T (°C)

T (°C)

800

S S + Al4Mn 4.1%

Al + S 700

1700 S

S + Al6Mn

1.9 % 1.8 %

Al

710˚C

AlTi Al3Ti

1500

657˚C

1460 °C

600 1340 °C

1300 Al + Al6Mn

β -Ti

γ

500 1100 400

0

1

2

3

4

5 6 7 8 9 10 Manganese content (mass %)

900

700

500

882 °C

665 °C 0.15%

α -Ti

Al Al + Al3Ti

300 0

10

20

30

40

50 60 70 80 90 100 Titatnium content (mass %)

Fig. 3.1-18 Al−Ti system

ture) than Al exist in this system: Al3 Ti (1340 ◦ C) and AlTi (1460 ◦ C) (Fig. 3.1-18). The structure of Al-rich Al–Ti alloys consists of Al3 Ti and an Al-rich solid solution.

2 µm

Fig. 3.1-17 (a) Al−Mn equilibrium system up to 10 wt% Mn. (b) Microstructure of an as-cast Al-1 wt% Mn

alloy (TEM micrograph, 7000X) [1.17]

cipitation of primary, bar-shaped Al2 Mn crystals occurs in the eutectic structure. These have a marked embrittling effect. Therefore, the maximum Mn content is limited to 2 wt% in commercial Al–Mn alloys. Aluminium–Titanium. Intermetallic phases with a sig-

nificantly higher melting point (dissociation tempera-

177

Aluminium–Zinc. Zn is highly soluble in Al. The eutectic point occurs at Zn-rich concentration (Fig. 3.1-19). The liquidus and solidus temperatures depend markedly on temperature.

Ternary Al-Based Systems Most technical Al alloys contain more than two components because of the presence of impuritiy and alloying elements. Aluminium–Iron–Silicon. Figure 3.1-20 shows the

Al-rich corner as a section for 0.5 wt% Fe. This concentration range is of particular interest for commercially pure, unalloyed Al. Apart from the solid solution and the AlFe and Si phases there are two ternary phases, i. e., α-Al12 Fe3 Si and β-Al9 Fe2 Si2 . The exact

Classes of Materials

T (°C)

L

700

600

L L + Al

L + Al + Al3Fe

Al + Al12Fe3Si + L

L+ZnAl

61.3%

98.2 %

71% 49 % 69.5% +ZnAl

300

Zn + ZnAl

i

1.25 % i2

382°C ZnAl 82.8 %

610 °C

+A l9 F e2 S

351°C

Al + L 0.75 %

Al + Al9Fe2Si2 + L 1.9%

573 °C

Al

400

600

70 %

α + ZnAl

3 Fe

72 %

Al

0.65 %

L+Zn 94.5 %

Al 12 F e3 S

500

Al

Part 3 1.2

T(°C) 700

Al +

Part 3

Al +

178

275°C

31.6%

78 %

99.4 %

500 Al + Al9Fe2Si2 + Si

200 Al + Zn

100 0

20

40

60

80 100 Zinc content (mass %)

Fig. 3.1-19 Al−Zn system

400

0

1

2 3 Silicon content (mass %)

Fig. 3.1-20 Section through the Al−Fe−Si phase diagram

at 0.5 wt% Fe [1.11]

compositions are subject to discussion and there are corresponding differences in the description of the solidification and precipitation processes. At the level of Fe and Si contents found in commercially pure aluminium (Al + Si ≤ 1 wt%), α-Al12 Fe3 Si will form as a result of the transformation of the α-solid solution and AlFe with decreasing temperature, as shown in Fig. 3.1-14. If the temperature further decreases, precipitation of β-Al9 Fe2 Si2 and even Si will occur. Due to the low rate of diffusion at low temperatures it is possible that all four phases coexist with the Al-rich solid solution phase. The solid solution becomes supersaturated in Fe and Si at the cooling rates used in industrial practice. Moreover, non-equilibrium ternary phases form, often locally at the grain boundaries of the as-cast microstructure. Fe and Si are in solution inside the grains. For a given cooling rate, the maximum Fe solubility decreases with increasing Si content of the alloy, whereas the Si solubility is independent of Fe content [1.19–21]. Thermodynamically, such nonequilibrium microstructures are very stable. The primary

non-equilibrium ternary phases only decompose to the secondary equilibrium phases Al3 Fe and Si at about 600 ◦ C [1.22]. Aluminium–Magnesium–Silicon. Figures 3.1-21a and 3.1-21b show the Al-rich corner as a quasi-binary section Al−Mg2 Si (Mg/Si ratio 1:0.58). It divides the system into the two simple ternary eutectic systems shown. The fine-grained microstructure of Al−Mg−Si alloys consists of α-Al(Mg,Si) and numerous intermetallic compounds, such as Mg2 Si (forming a characteristic particle shape called “Chinese script”), Al6 Mn, and Al3 Fe. Mg2 Si has an important effect on properties. Its solid solubility in the aluminium matrix is temperaturedependent and, thus, leads to hardening effects, which are exploited in technical alloys. A coarse network of intermetallic phases impairs forming behavior, but annealing before further processing produces finelydispersed precipitates. These improve workability but are, also, effective in retarding recrystallization.

Metals

L L +α

585 °C 1.85 %

600

500 α

Aluminium–Copper–Magnesium. In addition to the two binary phases, Al8 Mg5 (β) and Al2 Cu (θ), there are two ternary phases, Al2 CuMg (S) and Al6 Mg4 Cu (T), in equilibrium with the Al-rich solid solution. The microstructure of castings shows various ternary eutectics which, in addition to Al2 Cu, also contain Mg2 Si, resulting from Si as an impurity, and AlCuMg [1.9]. Aluminium–Copper–Lithium. In addition to binary

phases between all three elements, three ternary phases, Al7 Cu4 Li, Al2 CuLi, and Al5 Li3 Cu, occur in equilibrium with the Al-rich solid solution in the aluminium-rich corner of this system.

400

300 α + M2Si 200

100

0 Al

700

0.5

1.0

1.5

2.0 2.5 3.0 Mg2Si content (mass %)

T (°C) L

650 Al + L 600 550 Al

Al + Mg2Si + L

Al + Mg2Si + L

3.1.2.5 Classification of Aluminium Alloys

Al + Si Al + Si + Mg2Si

500

450

400

Al + Mg2Si

Quasi-binary 350 0

2

4

Aluminium–Zinc–Magnesium. The Al-rich corner consists of two binary phases, Al8 Mg5 and MgZn2 , and a ternary phase T with a nominal composition Al2 Mg2 Zn3 having a wide range of homogeneity. The Al−MgZn2 and Al−T sections may be regarded as quasi-binary systems with eutectic temperatures at 475 and 489 ◦ C, respectively. The Al−Al8 Mg5 −T range constitutes a ternary eutectic, TE = 450 ◦ C. In the Al−T−Zn range there is a four-phase reaction in which the T phase transforms to Mg2 Zn. At high Zn contents, Mg2 Zn11 transforms to MgZn2 in another four-phase reaction at 365 ◦ C. MgZn2 subsequently solidifies eutectically at 343 ◦ C together with Al and Zn. There is evidence of eutectic solidification in the as-cast structure of these alloys. If ternary Al−Zn−Mg alloys are solution-treated at temperatures above 450 ◦ C they, consist of a homogeneous α phase solid solution which is supersaturated with respect to one phase at least, corresponding to its composition [1.9].

6

10 12 8 Mg2Si content (mass %)

Fig. 3.1-21a,b Al−Mg−Si system (a) Quasi-binary section Al−Mg2 Si; (b) Section at a constant Si content of 1 wt% [1.11]

Technical aluminium alloys are subdivided first into the two main groups of cast and wrought alloys (Fig. 3.1-22). Typically, the alloying content of casting alloys is 10 to 12 wt%. This is significantly higher than the value for wrought alloys, most of which contain only a total of 1 to 2 wt% alloying elements; their content may be as high as 6 or even 8 wt% in individual cases. Aluminium alloys are further subdivided, depending on whether or not an alloy can be hardened by the addition of alloying elements, as is the case with

• •

Precipitation-hardenable alloys which can be strengthened by aging and Non-precipitation-hardenable alloys which can be strengthened by work-hardening only.

179

Part 3 1.2

T(°C) 700

1.2 Aluminium and Aluminium Alloys

180

Part 3

Classes of Materials

Part 3 1.2

Casting alloys

Wrought alloys Fe

Al Fe Si Al Mg

Si

Si

Al Si Al Mg

Al Si

Workhardenable alloys

Al Mn Mn

Mg Al

Al Si Cu Al Si Mg

Zn

Al Mg Mn Al

Al Mg Si Al Cu

Cu

Mg

Al Zn Mg

Al Zn Al Mg Si

Zn

Cu

Al Cu (Si, Mn) Al Cu Mg Al Zn Mg

Li

Agehardenable alloys

Al Zn Mg Cu Al Cu (mg) Li

Fig. 3.1-22 Schematic array of cast and wrought aluminium alloys. The numbers are given according to Euro-

pean standardization. In the case of wrought alloys the numbers are the same as those used in North-American standardization

The addition of further alloying elements will always cause hardening, but not all elements have the same hardening effect. Hardening will also depend on whether the solute atoms are present in solid solution or as particles. Alloy hardening can be divided into

• •

Solid-solution hardening (as with non-precipitation hardening, work-hardenable alloys) and Hardening due to elements that are initially in solid solution and are precipitating as second phases (as is the case with age-hardenable alloys).

It should be noted that age-hardenable alloys can be strengthened by the use of a suitable heat treatment whereas the same heat treatment of alloys which are not age-hardenable leads to a loss in strength.

3.1.2.6 Structure and Basic Mechanical Properties of Wrought Work-Hardenable Aluminium Alloys Al–Fe–Si and Unalloyed Aluminium (1xxx) Al−Fe−Si contains about 0.6 wt% Fe and 0.8 wt% Si that has been added deliberately. The properties of

Al−Fe−Si alloys, and of unalloyed aluminium, are strongly influenced by the elements which are in solid solution and the binary and higher phases that form. Increasing amounts of alloying additions lead to a marked increase in strength but there is a decrease in electrical conductivity since transition elements have a high effective scattering power for electrons. Wrought Al–Mn (3xxx) Manganese additions increase the strength of unalloyed aluminium (Fig. 3.1-23). The chemical resistance is not impaired. These alloys have very good forming properties, when the Mn content is below the maximum solubility of Mn in the Al-rich α-phase, i. e., practically below 1.5 wt%. At higher Mn content, brittle Al6 Mn crystals form and impair workability. If Al−Mn alloys are rapidly solidified as in continuous casting, considerable supersaturation of Mn occurs. Fe reduces the solubility for Mn and promotes its precipitation in the form of multicomponent phases. Fe is often added to counteract supersaturation and for an increase of the tensile strength (Fig. 3.1-24). Depending on the amount of precipitation, Mn can inhibit recrystallization.

Metals

Elongation to fracture A (%) 50

Fig. 3.1-23 Effect of manganese additions on the strength

of aluminium; alloys based on 99.5 wt% Al, quenched from 565 ◦ C, sheet samples, 1.6 mm thick [1.23]

100 80 60

400 A

40

30 Rm

20 0

Tensile strength Rm and 0.2 % proof stress Rp0.2 (MPa)

40 Rm

300

Rp0.2 0

0.2

0.4

0.6 0.8 1.0 Manganese content (mass %)

20 200

Tensile strength Rm 0.2% proof stress Rp0.2 (MPa) 120

Elongation to fracture A (%) Brinell hardness HB 100

Rm

R p0.2

34

100

0 HB 80

32 40 0.4 % Si 0.2 % Si

60

2

4

6 8 Magnesium content (mass %)

Elongation to fracture A (%)

30 30

40

45 R p0.2

A10

20

0 0.01

35

0.15

0.3

25 0.5 0.7 Iron content (mass %)

Fig. 3.1-24 Effect of iron and silicon on the strength of an Al−Mn alloy containing 1.2 wt% Mn; soft condition, sheet sample [1.24]

Wrought Al–Si (4xxx) Aside from 1 to 12.5 wt% Si, wrought Al−Si alloys contain other elements such as Mg, Fe, Mn or Cu. Wrought Al–Mg and Al–Mg–Mn (5xxx) The two non-age-hardening alloy systems Al−Mg and Al−Mg−Mn cover the entire compositional range from 0.5 to 5.5 wt% Mg, 0 to 1.1 wt% Mg, and 0 to 0.35 wt% Cr. Alloys with more than 5.6 wt% Mg are of no significance as wrought alloys. In Al−Mg alloys both tensile strength and 0.2% proof stress increase with increasing Mg content,

20 Mn in % 0 0.1 0.5 0.9

10

0

2

4

6 8 Magnesium content (mass %)

Fig. 3.1-25 Effect of Mn content on the mechanical prop-

erties of Al−Mg alloys [1.23]

whereas elongation shows a steady decrease up to about 3 wt% Mg, beyond which it increases again slightly. Embrittlement does not occur at low temperatures. The solubility of Mg in the Al-rich solid solution decreases rapidly with decreasing temperature. Thus most Al−Mg alloys are effectively supersaturated at room temperature. This is of practical significance in alloys containing more than 3 wt% Mg, where precipitation of the β-Al8 Mg5 can occur, especially after prior

181

Part 3 1.2

Tensile strength Rm and 0.2% proof stress Rp0.2 (MPa)

1.2 Aluminium and Aluminium Alloys

182

Part 3

Classes of Materials

Part 3 1.2

cold working. This is not associated with any beneficial increases in strength but leads to deterioration in the corrosion resistance by intergranular corrosion (Fig. 3.1-16). It is necessary to avoid the formation of continuous networks of β particles at the grain boundaries. Individual β particles can be obtained by a globulization treatment (200–250 ◦ C), followed by slow cooling. Another means to increase strength is the addition of Mn. Al−Mn−Mg alloys show an additional increase in tensile strength, which is significantly higher than for binary Al–Mn alloys (Fig. 3.1-26). The alloys show good toughness and can be used at low temperatures. If the Mn content exceeds 0.6 wt%, the recrystallization temperature can be increased to such an extent that recrystallization does not occur during extrusion. With extruded sections, there is an increase in tensile strength and proof stress in the longitudinal direction termed “press effect.”

3.1.2.7 Structure and Basic Mechanical Properties of Wrought Age-Hardenable Aluminium Alloys Wrought Al–Cu–Mg and Al–Cu–Si–Mn (2xxx) Alloys The 2xxx series alloys usually contain 3.5 to 5.5 wt% Cu and additions of Mg, Si and Mn and residual Fe. They show a significant increase in tensile strength by aging (310 to 440 MPa). Natural (room temperature) or artificial aging (at elevated temperature) may be preferable, depending on the alloy composition (Fig. 3.1-26). Additions of up to 1.5 wt% Mg increase both tensile strength and proof stress. At these Mg contents, the Al-rich solid solution is in equilibrium with the ternary Al2 CuMg phase which, together with the θ phase (Al2 Cu), is responsible for hardening. Mn additions increase the strength (Fig. 3.1-27) and can also cause a press effect. For achieving good ductility, the Mn content is limited to ≈ 1 wt%. Wrought Al–Mg–Si (6xxx) Al−Mg−Si alloys are the most widely used wrought age-hardenable alloys. Hardening is attributable to the formation of the Mg2 Si phase. The compositional range of interest is 0.30 to 1.5 wt% Mg, 0.20 to 1.6 wt% Si, up to 1.0 wt% Mn, and up to 0.35 wt% Cr. This is equivalent to about 0.40 to 1.6 vol% Mg2 Si and varying amounts of free Si and/or Mg. Some alloys are close to the pseudo-binary section Al−Mg2 Si, in others there is a significant excess of Si. This affects the maximum

Elongation to fracture A (%) 50

Tensile strength Rm 0.2 % p roof stress Rp0.2 (MPa) 500 A 400

40

1 2 3

300

30

4

20

200

4

3 1

100

0

Rm 4

2 10

3

2

1

R p0.2 0

1

2

3

4

Tensile strength Rm 0.2 % proof stress Rp0.2 (MPa) 500

5 6 7 Copper content (%)

0

Elongation to fracture A (%) Rm

400

300

30 R p0.2 20

200 A2" 100

0 0

10

0 1 2 Manganese content (mass %)

Fig. 3.1-26a,b Behavior of wrought Al−Cu-alloys (a) Effect of copper on the strength of binary Al−Cu alloys; base material 99.95 wt% Al, 1.6 mm thick sheet [1.23]. (1) Soft annealed; (2) Solution annealed and quenched; (3) Naturally aged; (4) Artificially aged. (b) Effect of Mn on the strength of an Al−Cu−Mg alloy with approx. 4 wt% Cu and 0.5 wt% Mg; naturally aged [1.23]

1.2 Aluminium and Aluminium Alloys

Metals

Part 3 1.2

Tensile strength R m (MPa) 400

Tensile strength Rm (MPa) 320

b

240

300

a

c 160

b

a

a 200

80

0

c 0

0.2

0.4

0.6

1.0 0.8 1.4 1.2 Manganese content (mass %)

100

Fig. 3.1-27 Effect of Mg2 Si on tensile strength [1.9] (1) stoichiometric composition, (2) 0.3 wt% excess Mg, (3) 0.3 wt% excess Si. The solid line refers to alloys that were quenched + immediate ageing at 160 ◦ C, the dotted line represents data for alloys that were quenched + intermediate ageing for 24 h at 20 ◦ C + ageing at 160 ◦ C

0

0

1

2

3

4

5 6 7 Zinc content (mass %)

Fig. 3.1-28 Effect of Zn and Mg on the strength and aging

attainable strength values because of the resulting variations in the amount of Mg2 Si, as shown in Fig. 3.1-28 for the quenched and artificially aged condition. Additions of 0.2 to 1.0 wt% Mn lead to an increase in the notch impact toughness of Al−Mg−Si alloys (Fig. 3.1-29), and affect the recrystallization behavior. Additions of Cr cause similar effects. Wrought Al–Zn–Mg- and Al–Zn–Mg–Cu Alloys (7xxx) Additions of Zn to Al lead to an insignificant increase in strength. Combined additions of Zn and Mg cause age hardening and thus an increase in strength (Fig. 3.1-28). The sum of the Zn and Mg contents is limited to about 6–7% because of the risk of stress corrosion cracking at higher levels in Cu-free Al−Zn−Mg alloys; this results in medium strength. Zr, Mn, and Cr are added to reduce the tendency to recrystallize. If suitably heattreated, such alloys have adequate corrosion resistance. It is important that cooling after solution treatment is not too rapid and that the proper precipitation treatment, usually step ageing, should be used. The alloys are of interest for welded structures because of their low quench Fig. 3.1-29 Effect of Mn and Fe on the notch impact toughness of AlMgSi1 alloy 1 wt% Si and 0.75 wt% Mg; artificially aged, flat bars, 60 × 10mm 2 [1.24]

effect of Al–Zn–Mg alloys [1.24] (1) Solution treatment at 450 ◦ C and quenching. (2) Solution treatment at 450 ◦ C and quenching plus natural aging for 3 months. (3) Ageing effect i. e., the increase in strength attributable to natural ageing; difference between (1) and (2) Notch impact toughness (J / cm2) 24 0.1 % Fe

22 0.3 % Fe

20 18 16 14 12 10

0

0.2

0.4

183

1.0 0.8 0.6 Manganese content (mass %)

184

Part 3

Classes of Materials

Part 3 1.2

Tensile strength R m (MPa) 600 Rm R p0.2 500 A5

Elongation to fracture A (%)

150

30

200

20

100

10 0

1

2

25

40

300

0

3

Elongation to fracture A (%) 30 1

3 % Mg 1 % Mg

400

Tensile strength R m (MPa) 200

4

5 6 7 8 Zinc content (mass %)

Rm 2

100

20

50

15

0 0

1

A5

10

Fig. 3.1-30 Effect of zinc on the tensile properties of Al–

Zn–Mg–Cu alloys; solution treated at 460 ◦ C, quenched, aged for 12 h at 135 ◦ C, 1.5 wt% Cu [1.23]

sensitivity. The low-strength heat-affected zone formed during welding is restored to full hardness without the need for renewed solution treatment. Al−Zn−Mg alloys usually contain 0.1 to 0.2 wt% Zr and some Ti in order to improve their weldability and resistance to stress corrosion cracking. Cu additions are avoided, despite their favourable effect on stress corrosion cracking, because they increase susceptibility to weld cracking. Al–Zn–Mg–Cu Alloys The addition of 0.5 to 2.0 wt% Cu strengthens Al−Zn−Mg alloys. Cu also reduces the tendency for stress corrosion cracking so that the upper limit for (Zn + Mg) can be increased to 9 wt%, provided additions of Cr are also made. The Zn/Mg ratio should preferably lie between 2 and 3. Al−Zn−Mg−Cu alloys can be aged both naturally and artificially. They attain the highest strength levels of all aluminium alloys. The actual hardening mechanism is attributable to Mg and Zn. Cu increases the rate of aging and acts as a nucleus for the hardening phases. Figure 3.1-30 shows some properties as a function of the Zn content at constant Cu content and two different Mg contents.

3.1.2.8 Structure and Basic Mechanical Properties of Aluminium Casting Alloys Al–Si Casting Alloys Due to the Al−Si eutectic (Fig. 3.1-12), these alloys, containing 5 to ≤ 20 wt% Si, have good casting

5 2

0

2

4

6

8

14 16 10 12 Silicon content (mass %)

0

Fig. 3.1-31 Effect of Si on the strength and ductility of Al−Si casting alloys; modified and unmodified sand castings. [1.9] (1) modified; (2) unmodified

properties. The tensile strength increases with the Si content (Fig. 3.1-31). Apart from Si other elements may be added, e.g., for the modification of the eutectic. Cu is present in residual amounts and impairs chemical resistance if levels exceed 0.05 wt%. Additions of about 1 wt% Cu yield an increase in solid solution hardening and thus reduce the tendency for smearing during machining. Residual Fe reduces sticking tendency, but leads to the formation of β-AlFeSi needles which reduce strength and ductility. Therefore the Fe content must be limited. An addition of Mn has a favorable effect on the sticking tendency. Mn leads to the formation of a quaternary phase; but it poses no problem because of its globular shape. “Piston alloys” have hypereutectic compositions of up to 25 wt% Si. During solidification, primary Si crystals are formed which increase wear strength and reduce thermal expansion. Al–Si–Mg Casting Alloys These alloys contain about 5 wt%, 7 wt%, or 10 wt% Si and between 0.3 and 0.5 wt% Mg. The optimum amount of Mg decreases with increasing Si content. Mg causes high strength and a moderate ductility depending on the

1.2 Aluminium and Aluminium Alloys

Metals

Elongation to fracture A (%) Brinell hardness HB 110 HB 100 R

temper (Fig. 3.1-32). The alloys can be age hardened both naturally and artificially. Fe leads to a reduction in sticking tendency, but also to a drastic reduction in ductility.

m

280

90 Rp0.2

80

240

70 60

200

5 4

160

Al–Mg Casting Alloys These alloys contain 3–12 wt% Mg. Strength increases with increasing Mg content (Fig. 3.1-33). Above about 7 wt% Mg, the alloy has to be heat-treated to homogenise the structure and thus obtain good tensile properties. With Mg contents of up to 5 wt%, Si additions of up to 1 wt% are possible, and these lead mainly to improvements in the casting properties. The addition of Si causes hardening due to the formation of Mg2 Si.

3 2 A3

120 0

1 0

0.2

0.6 0.4 Magnesium content (mass %)

Fig. 3.1-32 Effect of Mg on the mechanical properties of

G-AlSi10Mg casting alloy (with 9.5 wt% Si, 0.45 wt% Fe and 0.3 wt% Mn), sand cast and artificially aged [1.25–27] Tensile strength R m 0.2% proof stress Rp0.2 (MPa) 35

Elongation to fracture A (%) Brinell hardness HB 120

Al–Zn–Mg Casting Alloys They contain 4 to 7 wt% Zn and 0.3 to 0.7 wt% Mg. They can be naturally or artificially age hardened in the as-cast condition, without the need for prior solution treatment. Mg has a significant effect on the mechanical properties in the aged condition (Fig. 3.1-34). If the Mg content is limited, Al−Zn−Mg casting alloys can exhibit particularly good elongation to fracture. Tensile strength R m 0.2 % proof stress Rp0.2 (MPa) 35

Elongation to fracture A (%) Brinell hardness HB 120

30

100

30

100

25

80

25

80

60

20

15

15

10

10

20

HB

60

HB

Rm 15

Rm R p 0.2

10

10

A5

A5

5

0

0

2

4

15

Rp 0.2

6

8

10

12

14

16

Magnesium content (mass %)

5

5

0

0

5

0

2

4

6

8

10

12

14

16

0

Magnesium content (mass %)

Fig. 3.1-33a,b Effect of Mg on the mechanical properties of Al–Mg casting alloys, sand cast, untreated and homogenised [1.9]. (a) As-cast condition. (b) Homogenized

Part 3 1.2

Tensile strength R m 0.2% proof stress Rp0.2 (MPa) 320

185

Classes of Materials

Tensile strength Rm (MPa) 600

400

Rm R p0.2

300

240

200 5 % Zn 100

4 % Zn

AlCuMg2 AlZnMgCu0.5 AlZnMgCu1.5

500

AlZn4.5Mg1 AlCuMg1 AlMg4.5Mn

Elongation to fracture A (%)

8 0

0.5

1.0 1.5 2.0 Magnesium content (mass %)

0

Tensile strength Rm (MPa) 500

Fig. 3.1-34 Effect of Mg on the strength of cast Al–Zn–Mg

alloys; sand casting, artificially aged [1.9]

400

3.1.2.9 Technical Properties of Aluminium Alloys

300

The applications of aluminium and its alloys are depending on the properties. In most cases, mechanical properties are an important criterion for assessing the suitability of an Al alloy for a specific application. Other properties, such as electrical conductivity or corrosion resistance, may also be included in the assessment process. Mechanical Properties Hardness. The Brinell hardness number HB ranges from 15 for unalloyed Al in the soft temper to about 140 for an artificially aged Al−Zn−Mg−1.5 wt%Cu alloy. Tensile Strength. Figures 3.1-35 and 3.1-36 indicate

the typical levels of strength attainable with wrought and cast aluminium alloys, respectively. There will be a range of tensile strengths in specific alloying systems because of possible additional increases in strength due to hardening by cold work or precipitation. The different alloying elements cause differing degrees of strengthening.

200

100

0

G-AlMg10 G-AlSi9Mg G-AlSi7Mg

0

wrought aluminium alloys [1.9]

G-AlMg9

80

Fig. 3.1-35 Ranges of tensile strength for some important

G-AlSiCu3 G-AlSi10Mg

4 A5

Alloy

G-AlCu4Ti G-AlCu4TiMg

160

G-AlSi6Cu4 G-AlSi5Mg

Part 3 1.2

Tensile strength R m 0.2% proof stress Rp0.2 (MPa) 320

Al99.8 Al99.5 Al99 AlMn AlMg1 AlMgSi0.5 AlMg2Mn0.3 AlMgSi1 AlMg3

Part 3

G-AlMg3 G-AlMg5 G-AlMg3Si G-AlSi12

186

Alloy

Fig. 3.1-36 Ranges of tensile strength for some important

aluminium casting alloys [1.9] Strength at Elevated Temperatures. An example of the temperature and time dependence of the different mechanical properties is given in Fig. 3.1-37. With regard to the resistance to softening the materials can be classified as follows, depending on their temper:

• •

Wrought alloys in the soft temper and as-cast nonage-hardenable casting alloys are all practically thermally stable. For cold worked wrought alloys, partially annealed to obtain an intermediate temper, the increase in

Metals

Strength (MPa)

• 1

300 10 h 102 h 103 h 200

2

3

4h

0

103 h

7

10

10

8

4

5 6 200 300 400 Test or annealing temperature (°C)

100

0

4h

10 h

Fig. 3.1-37 Properties of 6061-T6 at elevated temperatures;

1.0 wt% Mg, 0.6 wt% Si, 0.3 wt% Cu, 0.25 wt% Cr, artificially aged [1.9]. (1) tensile strength Rm at 20 ◦ C, (2) stress rupture strength, (3) duration of exposure, (4) fatigue strength, (5) tensile strength at test temperature, (6) solution treated a) 400

75 °C

0.2 % proof stress Rp0.2 (MPa)

High Temperature Mechanical Properties in ShortTerm Tests. In materials that are not thermally stable,

there will be an effect due to irreversible changes in properties. Its magnitude depends on the temperature and duration of exposure, Figs. 3.1-40 and 3.1-41. Creep Behavior. Creep of Al alloys starts to play an

important role at temperatures above 100 to 150 ◦ C (Figs. 3.1-42 and 3.1-43). Material, amount of cold work

c) 30 20

250 °C

200 °C

10 300°C

100

d) 1200

Tensile strength Rm (MPa)

400 130°C 300 200

75 °C 100 °C

75, 100, 130 °C

Brinell hardness HB (MPa) 75 °C 100 °C

1000 800

200 °C

250°C

200 °C 160 °C

0

0

130 °C

250 °C

160°C

200 °C 600

300 °C

160 °C

300 °C

400

100

200 0.25 0.5 1 (h)

6 12 1

2

30

10 0 18 36 0 720 0

0

250 °C

160°C

200

b)

300 °C

100°C

130°C 300

Elongation to fracture A (%)

(d) Exposure time

0.25 0.5 1 (h)

6 12 1

2

30 (d)

10 0 18 0 36 0 72 0

100

•

3

N = 10 6

strength due to forming is diminished with increasing temperature and exposure time. Artificially aged alloys do not undergo any permanent changes on annealing up to approaching the ageing temperature. At higher temperatures, aging continues from the point where it was interrupted during the aging process (Figs. 3.1-38 and 3.1-39). Naturally aged alloys usually exhibit increased hardening when exposed to higher temperatures as a result of artificial ageing. At higher temperatures, the behavior is similar to that of artificially aged alloys.

Exposure time

Fig. 3.1-38a–d Effect of temporary exposure to elevated temperature on the mechanical properties of artificially aged AlSi1MgMn [6082] at 20 ◦ C [1.9]. (a) tensile strength; (b) 0.2% proofstress RP 0.2; (c) elongation to fracture A; (d) Brinell

hardness

187

Part 3 1.2

400

1.2 Aluminium and Aluminium Alloys

188

Part 3

Classes of Materials

Part 3 1.2

a)

b)

Brinell hardness HB 120 175 °C

100 80

250 °C

300 °C

60

40

40

20

100°C

150 °C

80

0

4 Time (h)

160 °C

200

250°C

250 °C

100

20

2

300 100 °C

200 °C

350 °C

0

Tensile strength Rm (MPa) 400

100

60

0

c)

Brinell hardness HB

120

1

30

90

180 Time (h)

0

1

30

90

360 Time (h)

180

Fig. 3.1-39a–c Effect of temporary exposure to elevated temperature on the hardness and tensile strength at 20 ◦ C of cast G-AlSi10Mg [43000, AlSi10Mg(a)] alloy, artificially aged [1.28]. (a) 0–4 h; (b) 1–180 d; (c) 1–360 d High-temperature tensile strength (MPa) 200

High-temperature tensile strength (MPa) 120 100 2

160

Rm

80 1

HB 60

120 40

R p0.2 80

20 G-AlMg5 G-AlMg5Si 10

100

200

20 1

Rm

15

A10 0

2 25

40

0

20

30

0 300 T (°C)

10 5 2

Fig. 3.1-40 High-temperature tensile strength of G-AlMg5

20

[51300] and G-AlMg5Si [51400] casting alloys, sand cast, after 30 min prior exposure to the test temperature [1.29]

and degree of age-hardening can affect creep behavior in various ways. With non-age-hardenable alloys, the effect of cold working is more pronounced at low temperatures, below about 150 ◦ C. At higher temperatures, the behavior rapidly approaches that of the softened material. Thus, more highly alloyed materials in the soft temper may exhibit better creep properties than cold worked alloys that are less highly alloyed. Artificially

30

1 A10 50

100

10 0

150

200

250

300

350 T(°C)

Fig. 3.1-41 High-temperature tensile strength of cast-

ing alloys [1.28]. (1) As-cast G-AlSi12 alloy [44300, AlSi12(Fe)]. (2) G-AlSi10Mg alloy [43000, AlSi10Mg(a)] after preheating for 8 days at the test temperature

Metals

AlMgSiF32 200

102 h 103 h 104 h 105 h

50

20 0

50

100

150

200

250

300 T(°C)

Fig. 3.1-42 Creep rupture behavior of 6082, AlSi1MgMn, T6 alloy, strain-hardened, min. tensile strength 320 MPa; extruded rods, 25 mm diameter [1.30, 31]

400

Creep rupture strength (MPa)

200 100 Rm 50 2

10 h

Fatigue. There is a marked effect of composition, heat treatment, and method of processing on fatigue strength. Solid solution hardening, cold work, and age hardening all lead to an increase in fatigue strength. For a given alloy composition, extruded sections usually have a higher fatigue strength than sheet or forgings. Fine grains are generally beneficial whereas coarse grains and coarse intermetallic phase particles can lead to a reduction in fatigue strength. Often there is an increase in fatigue strength with decreasing sample thickness, especially with bending stresses. Moreover, the effect of roughness or surface defects in thin specimens is usually less than that in thicker samples. With wrought aluminium alloys, there is a marked difference between age-hardenable alloys and non-age-hardenable alloys. It manifests itself in the shape of the S–N curve (Fig. 3.1-47), which is almost horizontal after about 106 cycles for non-age-hardenable alloys and after about 108 cycles for age-hardenable alloys. Fig-

3

10 h

20

4

10 h 10

Tensile strength Rm 0.2 % proof stress Rp0.2 (MPa)

5

0

100

200

10 h 300 T(°C)

Fig. 3.1-43 Creep rupture behavior of AlSi10MgCa

[43000] casting alloy, artificially aged, 100 h prior exposure to the test temperature [1.30, 31]

50

200

40

150

30

100

aged alloys should only be exposed for prolonged periods to temperatures that are significantly lower than the temperature of artificial ageing, otherwise over-ageing will lead to a complete loss of strength. Mechanical Properties at Low Temperatures. Based

on its fcc crystal structure, Al and its alloys show neither a rapid increase in yield stress nor a rapid de-

Elongation A (%)

250

50 0 – 200

20

Rm Rp0.2

– 100

10

0 20 T (°C)

0 – 200

–100

189

Part 3 1.2

crease in fracture toughness with decreasing temperature (Figs. 3.1-44 – 3.1-46). Tests carried out on Al−Mn, Al−Mg, Al−Mg−Si, Al−Cu−Mg, and Al−Zn−Mg wrought alloys at −268 ◦ C showed that the values of elongation to fracture at extremely low temperatures were even higher than at room temperature. In most cases, tensile strength and 0.2% proof stress increased weakly with decreasing temperature. Casting alloys behave similar to wrought alloys at low temperatures. The behavior will depend on composition, temper (especially size, shape and distribution of precipitates), and on the casting process used (Fig. 3.1-47).

Creep rupture strength (MPa) 400

100

1.2 Aluminium and Aluminium Alloys

0 20 T (°C)

Fig. 3.1-44a,b Mechanical properties of unalloyed aluminium AA 1100 (Al99) at low temperatures [1.9]. (a) Tensile strength Rm ; (b) Elongation A

190

Part 3

Classes of Materials

Part 3 1.2

a) Tensile strength Rm

c)

b)

0.2 % proof stress Rp0.2 (MPa)

Elongation A (%)

400

Reduction of area Z (%)

80

80

60

60

AlMg4.5Mnw28 AlMg4Mnw24 300 AlMg2.5w17 40

200

AlMg2.5w17 + AlMg4Mnw24

AlMg2.5w17

40 AlMg4Mnw24

20

AlMg4.5Mnw28

20

100 AlMg4.5Mnw28

0 –200

– 100

0 20 T(°C)

0 – 200

–100

0 20 T (°C)

0 – 200

– 100

0 20 T (°C)

Fig. 3.1-45a–c Mechanical properties at low temperatures for some Al−Mg and Al−Mg−Mn alloys in the soft temper [1.9]. (a) Tensile strength Rm and 0.2 proof stress Rp0.2 ; (b) Elongation A2 ; (c) reduction of area AlMg4Mn (≈ 5086, AlMg4), W24

∼O/H111; AlMg2.5 (≈ 5052, AlMg2.5), W17 ∼O/H111; AlMg4.5Mn (≈ 5083, AlMg4.5Mn), W28 ∼O/H111

a) Tensile strength R m

0.2% proof stress Rp0.2 (MPa) 400

Elongation A reduction of area Z (MPa)

b) 80

5052-0 5052-H32 5052-H34 5052-H38

300

60

200

40

100

20 A4 Z

Rm Rp0.2 0 –200

– 100

0 20 T (°C)

0 – 200

– 100

0 20 T (°C)

Fig. 3.1-46a,b Effect of cold working on the tensile properties of AlMg2.5 (5052) at low temperatures [1.9]. (a) Tensile strength and 0.2 proof stress; (b) Elongation and reduction of area

ure 3.1-48 illustratesthat the choice of 108 cycles as the ultimate number of stress cycles is regarded as adequate. Figure 3.1-49 shows fatigue curves for a number of casting alloys.

Technological Properties Abrasion Resistance. The wear resistance of Al al-

loys is low, especially in the absence of lubricants. There is no relation between hardness, strength and

Metals

Bending fatigue strength σbw (MPa) 180 1 2 160 3 140

300 Rm

120

250

4 100 5

80

200 Elongation to fracture A (%) 15

150

60

10 5

10 6

10 8 10 7 Number of stress cycles N

1

Fig. 3.1-49 Bending fatigue strength of two aluminium

2

100

10

50

5

A 10

0 –200

0 – 100

0 20 T(°C)

Fig. 3.1-47 Mechanical properties of artificially aged G-AlSi12 and G-AlSi10Mg casting alloys at low temperatures [1.28]. The solid line represents G-AlSi10Mg, artificially aged; the dotted line represents G-AlSi12, ascast 400

300 AlZnMgCu1.5F53 200 AlMg5W25 100 4 10

10 5

pressure die-casting alloys; flat samples with cast skin [1.9]. (1) Fracture; (2) Fracture, with evidence of defect; (3) No fracture; (4) GD-AlSi6Cu3; (not in EN); (5) GD-AlSi12 [≈ 44300, AlSi12(Fe)]

abrasion resistance. Under suitable conditions of lubrication, aluminium alloys can be safely used where they will encounter friction, as shown by their widespread use in the fabrication of pistons and sliding bearings. Wear can be drastically reduced by the suitable surface treatments. Sheet Formability. Typical values for deep-drawing in-

dices for commonly used sheet materials are shown in Fig. 3.1-50, whereas typical values of strain-hardening exponent n and degree of anisotropy r are given in Table 3.1-13. The r value is strongly dependent on the manufacturing process in particular, as is the case with all texture-dependent properties. In general, materials with high n and r values are deep-drawable.

Bending fatigue strength σbw (MPa)

10 6 10 7 10 8 Number of stress cycles N

Fig. 3.1-48 Typical S-Ncurves for reverse bending tests on an age-hardenable and a non-age-hardenable alloy [1.9], AlZnMgCu1.5 F53 (≈ 7075, AlZn5.5MgCu, T651) and AlMg5 (≈ 5019, AlMg5), W25

Table 3.1-13 Typical values of strain-hardening exponent n and degree of anisotropy r for some aluminium-base materials

based on data from various sources [1.9]; n.a. – not available Material, Alloy Al99.5 AlMn1 AlMg3 AlMg3 AlMg3 AlMg2Mn0.8 AlMg2Mn0.8 AlMg4.5Mn

1050A 3103 5754 5754 5754 5049 5049 5063

191

Part 3 1.2

Tensile strength R m (MPa) 350

1.2 Aluminium and Aluminium Alloys

Temper

n

r

O/H111 O/H111 O/H111 H14 H18 O/H111 H112 O/H111

0.25 0.15 0.20 0.16 0.12 0.20 0.20 0.15

0.62 n.a. 0.64 0.75 1.10 0.66 0.92 n.a.

192

Part 3

Classes of Materials

Part 3 1.2

Erichsen cupping index mm 12

Erichsen cupping index mm 12

Al99W8/Al99W7 Al99F10/Al99.5F9

10

AlMg1F13

10

AlMg1W10

8

8

AlMg3W19

Al99F14/Al99.5F15 6

AlMg2Mn0.8W19

6

Al99F12/Al99.5F11

4 12

AlMg3F24

4 12 AlMgSi1W 10

10 AlCuMg1W

8

8 AlMgSi1F21 6 4

6

AlCuMg1F40 AlMgSi1F28 0

AlMnW9 AlMnF14

0.5

1.0

2.0 1.5 Sheet thickness (mm)

AlMnF17 4

0.5

0

1.0

1.5 2.0 Sheet thickness (mm)

Fig. 3.1-50 Dependence of deep-drawing index on sheet thickness for different aluminium sheet alloys [1.9]

Machinability. There are difficulties to classify alu-

minium alloys according to their machinability. In general, soft wrought alloys perform worse than other materials regardless of the machining conditions because of chip shape. Harder wrought alloys perform somewhat better and special machining alloys and casting alloys perform best of all. In Si-containing alloys, including wrought alloys, there is a marked increase in tool wear with increasing Si content if the relatively hard Si is present in its elemental form.

Physical Properties The most important physical properties of pure Al are listed in Chapt. 2.1,Table 3.1-11 Characteristic ranges of property variations with the amount of impurities or alloying elements are compiled in Table 3.1-14. Coefficient of Thermal Expansion. Values of the av-

erage linear coefficient of thermal expansion for some Al-based materials at temperatures of practical significance are given in Table 3.1-15. Alloying leads to

Table 3.1-14 Examples for physical properties of aluminium alloys [1.9]a Designation EN EN former designation

Density (g cm−3 )

Freezing range b (◦ C)

Electrical conductivity (m
−1 mm−2 )

Thermal conductivity (W m−1 K−1 )

Coefficient of linear expansion (10−6 /K)

37.6 34–36 33–34 34–35 22–28 23–29 25–27 23–25 23–31 19–21 20–23 15–19 20–25

232 210–220 205–210 210–220 160–200 160–200 180–190 160–190 160–220 130–150 140–160 110–140 140–180

23.6 23.5 23.5 23.5 23.5 23.2 23.2 23.2 23.6 23.8 23.9 24.1 23.7

Wrought alloys 1098 1050A 1200 8011A 3103 3003 3105 3004 5005A 5052 5754 5019 5049

Al99.98 Al99.5 Al99 AlFeSi(A) AlMn1 AlMn1Cu AlMn0.5Mg0.5 AlMn1Mg1 AlMn1(C) AlMg2.5 AlMg3 AlMg5 AlMg2Mn0.8

Al99.98R Al99.5 Al99 AlFeSi AlMn AlMnCu AlMn0.5Mg0.5 AlMnlMg1 AlMg1 AlMg2.5 AlMg3 AlMg5 AlMg2Mn0.8

2.70 2.70 2.71 2.71 2.73 2.73 2.71 2.72 2.69 2.68 2.66 2.64 2.71

660 646–657 644–657 640–655 645–655 643–654 635–654 629–654 630–650 607–649 610–640 575–630 620–650

Metals

1.2 Aluminium and Aluminium Alloys

Designation EN EN former designation

Density (g cm−3 )

5454 5086 5083 6060 6181 6082 6012 2011 2007 2117 2017A 2024 2014 7020 7022 7075

AlMg2.7Mn AlMg4 AlMg4.5Mn0.7 AlMgSi AlSi1Mg0.8 AlSi1MgMn AlMgSiPb AlCu6BiPb AlCu4PbMgMn AlCu2.5Mg0.5 AlCu4MgSi(A) AlCu4Mg1 AlCu4SiMg AlZn4.5Mg1 AlZn5Mg3Cu AlZn5.5MgCu

AlMg2.7Mn AlMg4Mn AlMg4.5Mn AlMgSi0.5 AlMgSi0.8 AlMgSi1 AlMgSiPb AlCuBiPb AlCuMgPb AlCu2.5Mg0.5 AlCuMg1 AlCuMg2 AlCuSiMn AlZn4.5Mg1 AlZnMgCu0.5 AlZnMgCul.5

2.68 2.66 2.66 2.70 2.70 2.70 2.75 2.82 2.85 2.74 2.80 2.78 2.80 2.77 2.78 2.80

44100 47000 43000 43200 42000 51000 51300 51400 51200 46200 45000 21100 21000

AlSi12(b) AlSi12(Cu) AlSi10Mg(a) AlSi10Mg(Cu) AlSi7Mg AlMg3(b) AlMg5 AlMg5(Si) AlMg9 AlSi8Cu3 AlSi6Cu4 AlCu4Ti AlCu4MgTi

G-AlSi12 G-AlSil2(Cu) G-AlSil0Mg G-AlSil0Mg(Cu) G-AlSi7Mg G-AlMg3 G-AlMg5 G-AlMg5Si GD-AlMg9 G-AlSi8Cu3 G-AlSi6Cu4 G-AlCu4Ti G-AlCu4TiMg

2.65 2.65 2.65 2.65 2.70 2.70 2.60 2.60 2.60 2.75 2.75 2.75 2.75

a b

Freezing range b (◦ C) 602–646 585–641 574–638 585–650 585–650 585–650 585–650 535–640 507–650 554–650 512–650 505–640 507–638 600–650 485–640 480–640 Casting alloys 575–585 570–585 575–620 570–620 550–625 580–650 560–630 560–630 510–620 510–610 510–620 550–640 540–640

Electrical conductivity (m
−1 mm−2 )

Thermal conductivity (W m−1 K−1 )

Coefficient of linear expansion (10−6 /K)

19–21 17–19 16–19 28–34 24–32 24–32 24–32 22–26 18–22 21–25 18–28 18–21 20–29 19–23 19–23 19–23

130–150 120–140 110–140 200–220 170–220 170–220 170–220 160–180 130–160 150–180 130–200 130–150 140–200 130–160 130–160 130–160

23.6 23.8 24.2 23.4 23.4 23.4 23.4 23.1 23 23.8 23.0 22.9 22.8 23.1 23.6 23.4

17–27 16–23 17–26 16–20 21–32 16–24 15–22 16–21 11–15 14–18 15–18 16–20 16–20

120–190 110–160 120–180 110–140 150–220 110–170 100–160 110–150 80–110 100–130 110–130 110–140 110–140

20 20 20 20 22 23 23 23 24 22 22 23 23

The actual values will depend on the material composition within the permitted range; electrical and thermal conductivity will also depend on the material structure Where a eutectic structure is expected to form because of segregation, this will solidify at the lowest temperature given

Table 3.1-15 Linear coefficient of thermal expansion of some Al alloys for different ranges of temperature [1.9] Designation (according to EN 573.3 and EN 1706)

Average coefficient of linear expansion (10−6 K−1 ), for the range −50 to 20 ◦ C 20 to 100 ◦ C 20 to 200 ◦ C 20 to 300 ◦ C

1098 1050A 3003 3004 5005A 5019 5474 6060 2011 44100

21.8 21.7 21.5 21.5 21.8 22.5 21.9 21.8 21.4 –

Al99.98 Al99.5 AlMn1Cu AlMn1Mg1 AlMg1(C) AlMg5 AlMg3Mn AlMgSi0.5 AlCu6BiPb AlSi12(b)

23.6 23.5 23.2 23.2 23.6 24.1 23.7 23.4 23.1 20.0

24.5 24.4 24.1 24.1 24.5 25.1 24.6 24.5 24.0 21.0

25.5 25.4 25.2 25.1 25.5 26.1 25,6 25,6 25,0 22.0

Part 3 1.2

Table 3.1-14 Examples for physical properties of aluminium alloys [1.9]a , cont.

193

194

Part 3

Classes of Materials

Part 3 1.2

only small changes in the coefficient of thermal expansion (Tables 3.1-14 and 3.1-15). Si additions with 1.2% reduction in the coefficient of thermal expansion for each wt% Si have the greatest effect of the alloying elements commonly used. This effect is applied to the manufacture of piston alloys.

Tensile strength Rm 0.2 % proof stress Rp0.2 (MPa) 400

κ

Elongation A (%) Electrical conductivity κ (m/ Ω mm2) 34 33 Rm

300 Rp0.2

Specific Heat. The specific heat of aluminium in the

solid state increases continuously from 0 at 0 K to a maximum at the melting point. This is only the case with alloys when there are no solid state reactions. The effect of alloying elements in solution is not very marked.

31

200

30 29

100

10

A100

5

Elastic Properties. The Young’s modulus of Al and its

alloys is usually taken to be about 70 GPa. Values given in the literature for aluminium of all grades of purity and aluminium alloys range from about 60 GPa to 78 GPa. Unalloyed and low-alloyed materials are found in the lower part of the range. The age-hardenable alloys are in the middle to upper part. The Young’s modulus is dependent on texture, because the elastic anisotropy as expressed by the ratio of the elastic moduli for single crystals with [111] and [100] orientations is 1.17. Furthermore, there is a marked effect of cold working and test temperature (Fig. 3.1-51). Electrical Conductivity. The electrical conductivity is influenced largely by alloying or impurities and the Young’s modulus (GPa) 80

AlCuMg2 70

AlMg3

60 AlMg2Mn0.3

0

4

8

12

0 16 20 Ageing time (h)

Fig. 3.1-52 Changes in the mechanical properties and

electrical conductivity of electrical grade E-AlMgSi (≈ 6101) alloy wire during artificial ageing at 160 ◦ C; solution treated at 525 ◦ C, water quenched, naturally aged for 14 days, 95% cold-worked and then artificially aged [1.14]

structure. Elements present in solid solution lead to a greater reduction in electrical conductivity than precipitates (Figs. 3.1-7 and 3.1-8). By use of a suitable combination of heat treatment and cold working, it is possible to obtain microstructures with an adequate combination of tensile strength and electrical conductivity. This is shown in Fig. 3.1-52, using E-AlMgSi wire as an example.

Nuclear Properties. Thanks to its small absorption

50

cross section for thermal neutrons, aluminium is often used in reactor components requiring low neutron absorption.

40 30

0

0

Behavior in Magnetic Fields. Aluminium is weakly paramagnetic. The specific susceptibility of Al and its alloys is about 7.7 × 10−9 m3 kg−1 at room temperature.

AlCuMg1

Al

32

100

200

300

400

500

T (°C)

Fig. 3.1-51 Dependence of Young’s modulus E of different Al alloys on temperature; determined using 9 mm thick plate [1.32]

Optical Properties. The integral reflection is almost independent of the technical brightening process applied, but it depends on the purity of the metal. It is 84–85% for high-purity aluminium Al99.99 and 83–84% for unalloyed aluminium Al99.9. Higher amounts of diffuse reflection can be obtained by mechanical or chemical pre-treatment, such as sand blasting or strong pickling before brightening.

1.2 Aluminium and Aluminium Alloys

Metals

Thermal and mechanical treatments have a great influence on the properties of aluminium and its alloys. Moreover these treatments influence some physical properties, for example the electrical conductivity. Thus these treatments are used to obtain a material with an optimum of properties required. Work Hardening Strengthening by work hardening can be achieved by both cold- and warm working. Figures 3.1-53 – 3.1-56 illustrate the effect of cold working. During hot working, strengthening and softening processes occur simultaneously; with aluminium-based materials, this will be above about 150–200 ◦ C. Therefore hardness decreases with increasing hot-working temperature (Fig. 3.1-57). The formation of subgrains occurs in the microstructure; their size increases with increasing rolling temperature. Alloying atoms, such as Mg, impede growth or coarsening of the subgrains. Thermal Softening Figures 3.1-57a and 3.1-57b show typical softening curves for aluminium alloys in three characteristic stages: recovery, recrystallization, and grain-growth. In the case of the untreated continuously cast and rolled strip shown in Fig. 3.1-57a, recrystallization will occur at temperatures between about 260 and 290 ◦ C. In Fig. 3.1-57b, recrystallization starts after about half an hour and is complete after about an hour. The

300

Part 3 1.2

3.1.2.10 Thermal and Mechanical Treatment Tensile strength Rm 0.2 % proof stress Rp0.2 (MPa) Rm

250 1

200

2

150 100 Rp0.2

50 0

20

40

60 80 100 Degree of cold work ε (%)

40

60 80 100 Degree of cold work ε (%)

Elongation A (%) 40 2

30 1

20 10 0

0

20

Fig. 3.1-54 Typical mechanical properties of (1) continuously cast and rolled strip and (2) strip produced conventionally by hot-rolling and then cold-rolling cast billets of AlMn1 (3103) [1.34] Tensile strength Rm (MPa) 500

AlMg4.5Mn AlMg5

200

Tensile strength Rm 0.2% proof stress Rp0.2 (MPa)

Elongation A (%) 50

AlMg4.5

400

AlMg2.7Mn

AlMg3 AlMg2.5

AlMg2Mn0.8

300 AlMg1

160

120

200

Rp0.2

40

10

Al99.98

0 A10 20

40

AlMn0.5Mg0.5

100

80

0

AlMn

Al99.5

30 20

0

AlMnCu

40 Rm

0 80 100 60 Degree of cold work ε (%)

Fig. 3.1-53 Hardening of Al99.5 strip (0.15 wt% Si,

0.28 wt% Fe) after recrystallization annealing and subsequent cold-rolling [1.33]

0

20

40

60

80 100 0

195

20

40

60

80

100

Degree of cold work ε (%)

Fig. 3.1-55 Tensile strength of various wrought non-age-hardenable

aluminium alloys as a function of the degree of cold work [1.33]: AlMg4.5 – 5082; AlMg5 – 5019; AlMg3 – 5754; AlMg2.5 – 5052; AlMg1 – 5005; Al99.5 – 1050A; Al99.8 – 1080◦ ; AlMg4.5Mn – 5083; AlMg2.7Mn – 5454; AlMg2Mn0.8 – 5049; AlMn0.5Mg0.5 – 3105; AlMn – 3103; AlMnCu – 3003

196

Part 3

Classes of Materials

Part 3 1.2

120

Vickers hardness (VHN)

110

Grain size (µm) 500 30 % 50 %

5082

100

400

5052

90

300

80

Al99.99

70

200

3004

60 100

1100

50 40

AlRMg2

0 0

30

200

100

300 Rolling temperature (°C)

Fig. 3.1-56 Effect of rolling temperature on hardness;

20

100 60 80 Degree of cold work ε (%)

40

Fig. 3.1-58 Grain size after complete recrystallization of

specimens quenched after hot-rolling: Al99.0Cu – 1100; AlMn1Mg2 – 3004; AlMg2.5 – 5052; AlMg4.5 – 5082

Al99.99 and AlRMg2 as a function of degree of cold work (annealed at 350 to 415 ◦ C until complete recrystallization) [1.9]

softening curves depend not only on the alloy composition but also on the degree of prior cold working to a marked extent. Further factors are the content of alloying and impurity elements, annealing time, heating rate, the microstructure prior to deformation and prior thermomechanical treatment, which can also include the casting process used to produce the starting material.

The softening due to recovery or partial recrystallization is very important when producing semi-finished products of medium hardness (e.g., half hard). The relationship between the degree of cold work and grain size is apparent in Fig. 3.1-58. If the degree of cold work is below a critical value, no recrystallization will occur. This threshold depends on material and prior thermo-

a) 200

b) Tensile strength Rm (MPa)

Tensile strength Rm (MPa) 1

Elongation A (%)

5

6

170

2

160

4

200

40 Rm

140

3

50

30

110

20

80

10

120 50

0

A

80 200

240

280

320 360 400 Annealing temperature (°C)

0.1 0.2

0.5 1

2

50 100 5 10 20 Annealing temperature (°C)

Fig. 3.1-57a,b Typical softening curves for cold-rolled Al99.5 [1.35, 36]. (a) Recrystallization after different initial tempers to 90% cold work and subsequent annealing for 1 h at different temperatures: (1) Continuously cast and rolled strip, subsequently cold-worked without an intermediate annealing treatment; (2) as 1 but with an intermediate annealing treatment for 1 h at 580 ◦ C; (3) Strip conventionally produced using permanent mould casting and hot-rolling. (b) Continuously cast and rolled strip, cold-worked 90% and then annealed at 320 ◦ C for time shown: (4) Recovery; (5) Recrystallization; (6) Grain growth

Metals

3 1

Grain size (µm) 104

650 630 600 2 550 102 500 10 450 1 400 350 10–1 300 Annealing 10–2 temperature 10–3 (°C) 0 3 6 10 20 30 40 50 60 70 80 90 100 Reduction in thickness by rolling (%) 103

140 130 120 110 100 90 80 70 60 50 40 30 20 10 0

Vickers hardness HV1

AlMg5

AlMg3 AlMg1.5 Al99.5

0

100

200

300 400 500 Annealing temperature (°C)

Fig. 3.1-60 Effect of Al−Mg alloy composition on the

softening behavior; the material was 90% cold-worked and annealed for 1 h at temperature shown [1.36] Tensile strength Rm (MPa) 320 1 280 240

Fig. 3.1-59 Recrystallization diagram showing grain size of Al99.6

(1060) as a function of cold work and annealing for 2 h at the temperatures shown [1.9]: (1) Coarse grains in the region of critical degree of cold work (primary recrystallization); (2) Area of primary recrystallization with fine and medium-sized grains, (3) Coarse grains as a result of secondary recrystallization

This is dependent on the amount and distribution of these elements, i. e., whether they are present as precipitates or in supersaturated solid solution, and/or whether they form intermetallic phases. In Fig. 3.1-62 it is clearly apparent that solution treatment reduces the degree of supersaturation and that the range over which tensile strength and 0.2% proof stress decrease rapidly with temperature is thus shifted to significantly lower temperatures. Interactions between the various elements present can also affect recrystallization behavior.

3 200 2 160 3 120 80 200 240 280

320 360 400 440 480 520 560 Annealing temperature (°C)

Fig. 3.1-61 Comparison of softening curves for cast and

hot-rolled Al99.5 and AlMn1 strip; material cold-worked 90% and annealed for 1 h at the temperature shown [1.36]: (1) Cast and hot-rolled AlMn1 (3103) strip; (2) Cast and hot-rolled Al99.5 (1050A) strip; (3) Recrystallization range

Soft Annealing, Stabilization With cold-worked materials, soft annealing consists of recrystallization annealing. The duration of the treatment, degree of cold work, and intermediate annealing treatments need to be selected with grain size in mind. In age-hardenable alloys, soft annealing permits most of the supersaturated components to precipitate out in coarse form or coherent or partially coherent phases to transform to incoherent stable phases. Soft annealing of casting alloys involves annealing the as-cast structure at 350 to 450 ◦ C. With age-hardenable alloys, this is also possible using a solution treatment followed by furnace cooling

197

Part 3 1.2

mechanical treatment, and is about 2–15%. If the degree of cold work is near the critical value, coarse grains can form during recrystallization, as clearly shown in the three-dimensional diagram in Fig. 3.1-59. Other elements can affect the recrystallization temperature and the grain size after recrystallization. Mg does not have a marked effect (Fig. 3.1-60), while Mn, Fe, Cr, Ti, V, and Zr increase the recrystallization temperature (Fig. 3.1-61 delaying effect = plateau).

1.2 Aluminium and Aluminium Alloys

198

Part 3

Classes of Materials

Part 3 1.2

0.2% proof stress Rp0.2 (MPa)

Elongation A (%)

1 300

2 50

250 Rp0.2 200

40

150

30 3

100

20 A10

50 0

10 RT

200

250

300

350 400 450 500 Annealing temperature (°C)

Fig. 3.1-62 Softening curves for continuously cast and

rolled AlMn1 strip after annealing for 4 h at elevated temperatures [1.37,38]: (1) Untreated material, as-cast condition; (2) Homogenised at 540 ◦ C after cold working; (3) Coarse grains

or nonforced air cooling. Al−Mg alloys with more than 4 wt% Mg may have to be stabilized to produce a structure that is not susceptible to intergranular corrosion. Stress-Relieving The temperatures used for thermal stress relief are relatively low, i. e., at the lower end of the recovery range, or even lower, and between 200 and 300 ◦ C for nonage-hardenable alloy castings, otherwise there will be an unacceptably large loss of strength. Table 3.1-16 Conditions for aging treatments a

Homogenization This treatment is used for the elimination of residual casting stresses and segregation, for dissolution of eutectoid components at grain boundaries, or for producing a more uniform precipitation of supersaturated elements (e.g., Mn and Fe). Additionally, the elements which are responsible for hardening in age-hardenable alloys are taken into solid solution. A homogenization is carried out at temperatures which are composition-dependent and close to the solidus temperature of the alloy in question. Long exposure times are required, typically about 10–12 hr but possibly even longer, depending on the relevant diffusion coefficients and microstructure. Aging Age hardening treatments require the three steps of solution treatment, quenching, and aging (Fig. 3.1-63). The purpose of solution treatment is to produce a homogenous α-Al solid solution. The annealing temperature is determined by the relevant phase. It should be as high as possible in order to avoid excessively long annealing times, but lower than the solidus of α and the melting point of the lowest melting phase (Table 3.1-16). It should be noted that segregation effects tend to displace the effective phase boundaries to lower temperatures and incipient melting may occur. In addition, the effect of the selected solution treatment temperature on strength levels attained after aging will vary with alloy (Figs. 3.1-64 and 3.1-65). The annealing time depends Fig. 3.1-64 Effect of solution treatment temperature on the tensile strength of wrought aluminium alloys [1.9]: AlZnMgCu1.5 (≈ 7075, AlZn5.5MgCu), 24 h at 120 ◦ C; AlCuMg1 [≈ 2017A, AlCu4MgSi(A)], 5 days at room temperature; AlZn4.5Mg1 7020, (≈ AlZn4.5Mhg1), 1 month at room temperature; AlMgSi1 (≈ 6082, AlSi1MgMn), 16 h at 160 ◦ C I

Alloy

Annealing Temperature b (◦ C)

Quenching medium

Natural aging time (d)

Artificial aging Temperature (◦ C)

E-AlMgSi AlMgSi0.5 AlMgSi1 AlMg1SiCu AlCuBiPb AlCuMg1 AlCuMg2 AlZn4.5Mg

525–540 525–540 525–540 525–540 515–525 495–505 495–505 460–485

Water Air/water Water/air Water/air Water up to 65 ◦ C Water Water Air At least

5–8 5–8 5–8 5–8 5–8 5–8

155–190 155–190 155–190 155–190 165–185

a

90

d

180–195d I 90–100/ II 140–160c

Recommendations only; exact specification as per agreement with semi-finishing plant Metal temperature Stages I and II of step annealing d Usually only naturally aged b c

Time (h) 4–16 4–16 4–16 4–16 8–16 4d 16–24d I 8 –12/ II 16–24c

Metals

Renewed heat traeatment

Solution treatment Solute atoms taken into solid solution, with increase in vacancy concentration Quenching Reversion Natural ageing

Solid solution supersaturated in: 1. Solute atoms 2. Vacancies

Artificial ageing

Ageing at moderately elevated temperatures Coherent and partly coherent precipitations

Coherent precipitates; naturally aged condition

Temperature inrease

Borderline conditions between natural and artificial ageing

Temperature inrease

Partly coherent precipitates; artificial aged condition Artificial ageing for a longer period Partially coherent and incoherent precipitates Softening Artificial ageing for a longer period Stable incoherent equilibrium phases; stable condition

Fig. 3.1-63 Schematic of the age hardening process Tensile strength Rm (MPa) 600

AlZnMgCu1.5

320

Tensile strength Rm 0.2 % proof stress Rp0.2 (MPa) Brinell hardness HB

500 Rm

AlCuMg1

240

400 AlZn4.5Mg1

AlMgSi1

300 160 200 300

400

500 600 Solution treatment temperature (°C)

120 R p0.2

80

HB

A5

100 80

2 1

Fig. 3.1-65 Effect of solution treatment temperature on the mechanical properties of G-AlSi10Mg casting alloy after subsequent aging [≈ 43 000, AlSi10Mg(a)] [1.9] I

0 500

0 520 540 Solution treatment temperature(°C)

Elongation A (%)

199

Part 3 1.2

Starting condition e.g. stable cast strucure or other unknown starting condition

1.2 Aluminium and Aluminium Alloys

200

Part 3

Classes of Materials

Part 3 1.2

mainly on the initial condition of the semi-finished material, type of semi-finished product, and the wall thickness (Figs. 3.1-66 and 3.1-67). During quenching, it is important to pass through the temperature range around 200 ◦ C as quickly as pos120

Brinell hardness HB 10 mm 10 mm 50 mm

100

100 mm

80

60

1 2

0

4

12

8

20 16 Annealing time (h)

Fig. 3.1-66 Effect of annealing time on the hardness of arti-

ficially aged G-AlSi10Mg casting alloy for different casting techniques and specimen diameters [1.9]: (1) Sand cast; (2) Permanent mould cast Tensile strength Rm 0.2 % proof stress Rp0.2 (MPa) 450

Elongation A (%)

450 350

sible, in order to prevent premature precipitation of the elements in supersaturated solid solution. Some alloys require high cooling rates, such as those obtained by quenching in water. For others, especially with thinner sections, cooling in a forced draft of air or a mist spray suffices. In this case, quenching takes place immediately after hot working or even directly in the extrusion press. With most alloys it is important that the annealed material is rapidly transferred to the quenching bath as any delay (incipient cooling) can have a detrimental effect on strength and corrosion resistance. After the first two stages of the hardening process, the solid solution will be supersaturated in both vacancies and solute atoms. It will tend to attain equilibrium conditions by precipitation of the supersaturated solute atoms. As the process is both temperature- and time-dependent, precipitation is basically possible either by natural or artificial aging, i. e., at room or elevated temperature respectively. Aging at room temperature, or slightly elevated temperature, is accompanied by the formation of metastable Guinier–Preston zones (GP zones). These metastable phases increase the strength by differing amounts depending on their type, size, volume fraction, and distribution. With fully coherent precipitates, the crystal lattice is strongly strained locally, resulting in a marked increase in hardness and strength, while ductility and electrical conductivity decreases (Figs. 3.1-68 and 3.1-69). At higher aging temperatures of about 100 ◦ C to 200 ◦ C, metastable phases form that are partially coherent. The local coherency strain is less pronounced

300 300 250

20

200

15

150

10

Elongation A (%)

Tensile strength Rm 0.2 % proof stress Rp0.2 (MPa)

30

Rm 20

200

100 50 490

Rm Rp0.2

500

A5

1 2

A Rp0.2

5

10

100

0 520 530 540 510 Solution treatment temperature (°C)

Fig. 3.1-67 Dependence of mechanical properties of naturally aged G-AlCu4TiMg casting alloy on the maximum solution treatment temperature: (1) Step annealing; (2) Single step annealing

0

0

1– 3

0 1

3 6 9 Ageing time (day)

Fig. 3.1-68 Natural aging of AlMgSi1 alloy [1.39]

Metals

1.2 Aluminium and Aluminium Alloys

110 °C

150 °C

100

400

170 °C

90

180 °C

135 °C

300

150 °C

80 200 °C 70 60

180 °C

200

190 °C 230 °C

225 °C

260 °C

100 0

4

8

12

16 20 Ageing time (d)

205 °C

Elongation A (%) 30

205 °C

190 °C

260 °C

230 °C

180 °C

150 °C

135 °C

110°C

Fig. 3.1-69 Artificial aging of G-AlSi10Mg casting al-

loy [1.9]

20

because the stresses are partly reduced by the formation of interfacial dislocations. This would lead to a lower increase in strength in principle. However, since the particle size of the metastable phases formed in this range is often larger than that of the coherent phases which result from natural aging, there is a marked increase in strength (Figs. 3.1-70 and 3.1-71). Higher temperatures and longer aging times lead to the formation of incoherent equilibrium phases (e.g., Al2 Cu, Mg2 Si, and MgZn2 ) and there is a reduction in the hardening effect. This is called over-aging.

10

Effects of Plastic Deformation on Age-Hardening Behavior For wrought age-hardenable aluminium alloys, the combination of heat treatments with hot and/or cold working (thermo-mechanical treatment) is of great practical significance. It can be a method to obtain a better combination of mechanical properties, such as moderate ductility and higher strength. The effects of thermomechanical treatments can be attributed to the fact that all processes occurring during heat treatment are influenced by the concentration of defects introduced during working. It is not necessary to carry out both steps simultaneously; the heat treatment can be carried out after forming [1.40]. As far as precipitation is concerned, lattice defects facilitate diffusion and at the same time act as nucleation sites. Thus, by deforming a material by a certain amount prior to aging and thereby obtaining the desired defect concentration, one can influence the size, quantity and distribution of the precipitates that form subsequently. It is important, however, that the

0

0

10 – 2

10 – 1

10 0

10 1

10 2

10 3 10 4 Ageing time (h)

Fig. 3.1-70 Artificial aging curves for AlCuSiMn alloy [1.9]

final ageing treatment is carried out at a temperature below the recrystallization temperature, as the lattice defect concentration that is generated is fully effective only then. Controlled hot working, often in combination with additional heat treatments, is another form of thermomechanical treatment and is used to improve fracture toughness, creep strength and fatigue strength. One tries to obtain a suitable recrystallized grain size and an optimum distribution of lattice defects and precipitates. Such treatments are very often used with high strength Al−Zn−Mg−Cu alloys. They usually consist of a series of solution treatments with controlled cooling and hot-rolling under well defined conditions. Cold working carried out between the various stages of a step-aging treatment is also referred to as thermomechanical treatment. Examples are shown in Fig. 3.1-72 and Fig. 3.1-73. Simultaneous Softening and Precipitation One of the factors that influence the softening of an alloy is the possible supersaturation by alloying of impurity elements. Supersaturation can be achieved deliberately, e.g., by solution treatment and subsequent quenching, or, as is often the case, it may be the result of rapid cool-

Part 3 1.2

0.2 % proof stress Rp0.2 (MPa)

Brinell hardness HB 110

201

Part 3

Classes of Materials

Part 3 1.2

Brinell hardness HB

Elongation A (%)

Tensile strength 400

150

350 130

200

C

0°

C

C

12

5°

15

0°

C

16

5°

B 5%

0°

300

50 % 20 %

110

14

250

17

350

A

C

300 0.2% proof stress Rp0.2 (MPa)

90

2% 1%

Rm

C

70

20

A 15

150

125 °

C

150

160

100

10

140 °

°C

C

°C

10

2

10 3 10 4 Ageing time (min)

Fig. 3.1-72 Effect of cold work on the natural aging of

AlCuMg1 (2017A) [1.9]; A – Rolled; B – Stretched; C – Without cold work Change in 0.2 % proof stress Rp0.2 (MPa) 150 AlZnMgCu0.5

175 °C

Rp0.2 50

10

1

°C 125

°C

140

150

160

°C

200

°C

150 °C

250

175

202

0

1 (h)

2

4

8

1

3 6 9 (d) Ageing time

5 100

Fig. 3.1-71 Artificial aging curves for AlMgSi1 alloy after solution treatment at 520 ◦ C and water quenching 50

ing, e.g., of castings. If such a supersaturated material is cold-worked and then aged, it reveals markedly different softening behavior because solute atom clusters or precipitates are formed during recovery at lattice defects in the deformed or recovered structure which pin lattice defects and the formation of solute atom clusters or of precipitates during recrystallization at the recrystallization front, which pin down the recrystallization front. There is a slowing down of the softening process as a result of these pinning effects (Figs. 3.1-74a and 3.1-74b). The Stage III area in Fig. 3.1-74b is of particular interest, as by definition this is a thermomechanical treatment because the lattice defects introduced by working are fully effective during the formation of the precipitates. Dislocations, which are present in large quantities, act as nuclei for precipitation and this results in the formation of numerous finely-dispersed precipitates. These impair subsequent recrystallization at every stage – the

0 10 1

10 2

10 4 10 3 Ageing time (min)

Fig. 3.1-73 Changes in the 0.2% proof stress during natural aging of 0.5 mm diameter wire specimens AlZnMgCu0.5 (7022) alloys after different degrees of cold working. The alloys were first solution-treated at 490 ◦ C and then immediately subjected to cold working as indicated below [1.41]

formation of recrystallization nuclei, the moving of boundaries and the subsequent grain growth. These effects increase the thermal resistance and delay the loss of strength that occurs after prolonged exposure because of grain growth. The Figs. 3.1-77 to 3.1-79 show some examples of TTT-Diagrams for unalloyed aluminium and for alloys.

a) Temperature

1.2 Aluminium and Aluminium Alloys

203

AlFe0.25Si0.13 ε = 90 %

Part 3 1.2

Metals

T(°C) 450 1

400 I

350 2 300

Ti II

log v Grain-boundary migration velocity v

b) Temperature I

1

II

Ti 250 10 – 2

ti 10 – 1

10 0

10 1

Fig. 3.1-75 TTT diagram for Al-0.25 wt% Fe-0.13 wt% Si alloy Hunter-Engineering cast strip after 90% cold work [1.35]. (1) First signs of precipitation; (2) Recrystallization zone 600

T(°C) AlMn0.7 ε = 90 %

2

Ti

10 2 Time (min)

550 III 500

log t

1 Ageing time

Fig. 3.1-74a,b Effect of segregation and precipitation on

recrystallization (grain-boundary migration): (1) Start of recrystallization; (2) Start of precipitation. (a) Basic effects of solute atom clusters on the grain boundary migration velocity [1.42]. Region I, high temperatures: The grain boundary migration velocity is only weakly dependent on temperature because it is unaffected by the clustering (→ high velocity). Region II: Below Ti , the mobility of the boundaries is reduced because atom clusters have to be dragged along by the boundary, and the diffusion rate of these atoms determines the migration velocity of the boundary (→ low velocity). (b) Interrelationship between recrystallization and precipitation as TTT (time-temperature-transformation) diagram [1.43]. Region I: Recrystallization as a homogenous stable solid solution, unaffected by precipitation processes, i. e., at these temperatures there is no longer any supersaturation. Region II: Recrystallization in a supersaturated solid solution; the number of potential precipitation nuclei (dislocations) decreases. Result: Fewer but larger precipitations. Region III: Precipitation prior to recrystallization, or simultaneously (Ti ) the precipitates delay recrystallization significantly

450 400 2 350 300 10 – 1

10 0

10 1

10 2

10 4 10 3 Time (min)

Fig. 3.1-76 TTT diagram showing precipitation and recrystallization in 90% cold-rolled, high-purity AlMn0.7 alloy, strip produced by permanent mould casting, hot-rolling, and then cold-rolling [1.44]. (1) Start of precipitation; (2) Recrystallization zone T(°C) AlFe0.5Si0.15 ε = 80 %

500 450

1

Ti

2

400 350

Fig. 3.1-77 TTT diagram for Al-0.5 wt%Fe-0.15 wt% Si

alloy Harvey cast strip after 80% cold work [1.45] (1) Start of precipitation; (2) Recrystallization zone

300 10 – 2

ti 10 – 1

10 0

10 1

10 2 Time (min)

204

Part 3

Classes of Materials

Part 3 1.2

600

T(°C)

600 AlMn1Fe1 ε = 80 %

550 500

T(°C) AlMn1Fe1 ε= 40 %

550 500

2

2

450

450

400

400

350

350 1

300

300

250

250

10 0

10 1

10 2

10 3

10 4 Time (min)

10 0

1

10 1

10 2

10 3

10 4 Time (min)

Fig. 3.1-79a,b TTT diagrams for precipitation and recrystallization in commercially pure AlMn1Fe1 (0.16 wt% Si), Hunter-Engineering cast strip after varying degrees of cold-rolling [1.49]. (1) Start of precipitation; (2) Recrystallization zone. (a) 90%. (b) 40% Fig. 3.1-78 TTT diagram showing precipitation and reT(°C) crystallization in commercially pure AlMn0.8 alloy strip 600 AlMn0.8 + 0.4 %Fe + 0.15 %Si 1 (0.4 wt% Fe and 0.15 wt% Si) produced by strip casting and ε = 80% 85% cold-rolled [1.46–48]. (1) Start of precipitation; (2) 550 Recrystallization zone 500 2

Ti 450 400 350 300 10 – 2

ti 10 – 1

10 0

10 1

10 2 Time (min)

3.1.2.11 Corrosion Behavior of Aluminium From a thermodynamic point of view, aluminium would have to react with water to form hydrogen. However, Al and Al alloys have proven to be very corrosion-resistant in a wide range of practical applications. This corrosion resistance is attributable to the reaction of Al with oxygen or water vapor and the formation of a thin but compact natural oxide film when it is exposed to air, i. e. Al is passivated. In contrast to the oxide layers formed on many other materials, this oxide layer is strongly adherent and thus protects the underlying metal against further oxidation. This property explains the good re-

sistance of aluminium when exposed to the weather or a large number of organic and inorganic substances. The corrosion resistance can be increased further by various surface treatments. Aluminium and all standardized aluminium alloys are non-toxic. Aluminium products are easy to clean, can be sterilized and meet all hygienic and antitoxic requirements. Surface Layers Aluminium and Al alloys react with oxygen and water vapor in the air to produce a thin, compact surface oxide film which protects the underlying metal from further attack (Fig. 3.1-80). The surface layer contains mainly amorphous Al2 O3 in several layers. The so-called barrier layer has an extremely low conductivity for electrons and ions and thus acts as an insulator in any interfacial electrochemical reactions. It thus affords effective protection against corrosion. If mechanical damage of the protective layer occurs, or if the layer is removed by pickling, it re-forms immediately. Aluminium and Al alloys thus exhibit good corrosion resistance to chemicals, seawater, and the weather.

Metals

1 2 2

3

Weight gain (µm/cm2) 90

3 2

1

5 – 10 nm 1 – 2 nm

≤ 50 µm

5

5

80

4

Al

Fig. 3.1-80 Schematic representation of the structure of

the oxide film formed on unalloyed aluminium in dry air; the total thickness is typically 0.005 to 0.02 mm [1.50]. Al = Aluminium; 1 = Surface layer; 2 = Mixed oxides; 3 = Pores; 4 = Barrier layer; 5 = Heterogeneous components

The oxide film which forms on bare aluminium in dry air at room temperature grows to a thickness of a few µm in a few minutes. It then grows to about two or three times this thickness in a few days at a continuously decreasing rate, so-called self-protection. Higher temperatures, such as those during heat treatments, accelerate the rate of growth of the natural oxide layer and lead to the growth of thicker films (Fig. 3.1-81). In moist air, the oxide films grow rapidly at first but then more slowly, and they are markedly thicker than the films formed in dry air. The composition of the atmosphere has a significant effect on the behavior of the oxide layer. The aggressiveness of the atmosphere is particularly dependent on the amounts of sulfur dioxide, sulfur trioxide, dust, soot, and salts present. Rain water hitting the surface and running off flushes away these substances and thus reduces their influence. Tap water or natural waters cause growth of the outer layer on top of the barrier layer of the oxide. The growth will depend on the alloy composition, the nature of the water and temperature. In aggressive waters, especially those containing chlorides and heavy metals, pitting corrosion can occur if oxygen from the air or other oxidizing media are introduced into the water. Traces of Cu (from copper piping or fittings containing copper) are particularly aggressive. Copper ions enter the oxide layer on the aluminium surface via defects and precipitate out as metallic Cu. Copper then acts as a cathode in the resulting local galvanic element such that Al is dissolved anodically. Corrosion If Al is exposed to acids or bases these dissolve the oxide film. The pH value of the electrolyte strongly influences corrosion in aqueous media. The protective film on aluminium is practically insoluble in the pH range from 4.5

450 °C

70 60

500 °C 650 °C

50

550 °C

40 600 °C

30 20 10 400 °C

0

0

20

40

60

80

205

Part 3 1.2

3

1.2 Aluminium and Aluminium Alloys

100

120 140 160 Oxidation time (h)

Fig. 3.1-81 Growth of the oxide film on super-purity aluminium in dry oxygen during the first 160 h [1.22]

to 8.5, which explains why aluminium is usually only used in this range. Aluminium alloys have heterogeneous microstructural components such as intermetallic phases and resulting oxides in the surface and barrier layers. This explains why unalloyed aluminium and aluminium alloys have lower corrosion resistance than high-purity aluminium. Apart from the effects of alloying and impurities, there are some other factors affecting corrosion, for example, changes in microstructure by thermal or mechanical treatments and ensuing changes of the surface condition. Corrosion protection covers any measure aimed at modifying a corrosion system in order to mitigate corrosion damage. This can involve influencing the properties of the metal or the corrosive medium, or separating the metal from the medium by the use of protective layers. One can differentiate between active and passive measures. Passive measures, such as the use of organic polymer coatings (paints), will provide temporary protection, the level of which will depend on the nature, thickness, and quality of the layer. Active measures, such as the use of sacrificial magnesium or zinc anodes, offer long-term protection.

Part 3

Classes of Materials

Part 3 1.3

3.1.3 Titanium and Titanium Alloys Titanium and its alloys are used as technical materials mainly because of the low density ( = 4.5 g cm−3 ) of Ti at technically useful levels of mechanical properties, and the formation of a passivating, protective oxide layer in air, which leads to a pronounced stability in corrosive media and at elevated temperatures. Further useful properties to be noted are its paramagnetic behavior, low temperature ductility, low thermal conductivity (κ = 21 W m−1 K−1 ), low thermal expansion coefficient (λ = 8.9 × 10−6 K−1 ), and its biocompatibility which is essentially due to its passivating oxide layer. Five groups of materials based on Ti may be distinguished [1.51–53]: commercially pure (i. e., commercially available) Ti (cp-Ti), low-alloy Ti materials, Ti-base alloys, intermetallic Ti-Al materials, and highly alloyed functional materials: TiNi shape memory alloys, Nb–Ti superconducting materials (Sect. 4.2.1), and Ti-Fe-Mn materials for hydrogen storage. Titanium undergoes a structural phase transformation at 882 ◦ C. Like in steels, this transformation is crucial for the microstructural design and the mechanical properties of Ti-based alloys. The low temperature phase α-Ti has an almost close packed hexagonal (A3) structure that is somewhat compressed along the c axis. Its

2200

T(°C) 0

lattice parameters are c = 0.4679 nm and a = 0.2951 nm at room temperature. The high-temperature phase β-Ti has a body-centered cubic (A2) structure. The lattice parameter of β-Ti at room temperature can be obtained as a = 0.3269 nm by extrapolation from alloy solid solutions. The binary phase diagrams of Ti [1.54] indicate that several interstitial components such as O, N, C, and H form extended solid solutions with α-Ti. As an example Fig. 3.1-82 shows the Ti-rich part of the Ti–O phase diagram. The high local lattice strains caused by the interstitial atoms lead to pronounced solid solution strengthening which is exploited, in particular, to harden commercially pure Ti by O additions. On average, the interstitials lead to a pronounced elongation of both the a and c axes of the α-Ti lattice, as shown in Fig. 3.1-83. Figure 3.1-84 shows the influence of the concentration of residual impurity elements O, N, C, Fe, and Si on the increase of hardness HB. Commercially pure grades of Ti, cp-Ti, are produced via the reduction of TiCl4 by Mg (Kroll process). The product is Ti sponge. Table 3.1-17 gives typical concentration levels of the main impurity components and corresponding hardness values of the Ti sponge. Impu-

10

2000

20

wt % Oxygen 40

30

TinO2n–1

~1885 °C

1842 °C

L

1870 °C

1800 1670 °C

1400

(β Ti)

γ TiO

~1250 °C

(α Ti) 1200

β TiO 940 °C

1000 882 °C

800

α Ti1–2O

Ti3O2 α TiO

600 400

TiO2(rutile)

Higher Magneli phase

1600

βTi2O3

206

α Ti1–2O

(Ti3O)

0

10

Fig. 3.1-82 Ti−O phase diagram

20

Ti2O

30

40

50

60

70 at % Oxygen

Metals

1.3 Titanium and Titanium Alloys

Reduction process/ element Magnesium

Sodium electrolysis

120

C

N

O

H

0.006 0.008 0.008 0.008 0.009 0.003 0.013 0.018

0.003 0.005 0.005 0.005 0.004 0.002 0.004 0.004

0.045 0.05 0.06 0.07 0.07 0.01 0.03 0.04

0.002 0.002 0.002 0.002 0.01 0.003 0.004 0.004

Increase in hardnesss (HB) O

80 60

C

40

Fe

20 0

Si 0

0.05

0.1 0.15 0.2 0.25 Residual impurity content (wt %)

Fig. 3.1-84 Increase of hardness HB of Ti as a function of concentration of residual impurities O, N, C, Fe, and Si

rity levels resulting from earlier reduction processes by Na and electrolysis are also listed. The concentration of the residual content of the reducing elements Mg, Na, and their chlorides is lowered by the subsequent melting processes. High purity levels (5N) of Ti can be obtained by the iodide reduction process. These grades are used for electronic devices.

3.1.3.1 Commercially Pure Grades of Ti and Low-Alloy Ti Materials Materials designated as commercially pure grades of Ti are interstitial solid solutions of O, N, C, and H in Ti. Oxygen is the only element added deliberately for solid solution strengthening. The other interstitial solutes are impurities resulting from the production process as indicated. Table 3.1-18 shows the chemical compositions and mechanical properties of commercially pure grades of Ti. The temperature dependence of their mechanical properties is shown in Fig. 3.1-85. Low-alloy Ti materials containing Pd, Ru, and Ni + Mo, respectively, are providing increased corrosion resistance at

Mg

0.02 0.04 0.05 0.06 0.016 0.001 0.004 0.020

a) N

100

(wt%) Fe

Na

0.03 0.03 0.03 0.08

Cl

Maximum hardness (HB)

0.10 0.09 0.08 0.09 0.13 0.08 0.09 0.16

95 100 110 120 120 60 75 90

Part 3 1.3

Table 3.1-17 Chemical composition of titanium sponge [1.53]

a(A) Ti– C

2.955 2.954 2.953 2.952 2.951 2.950 0.0

b)

Ti – N Ti – O 0.2

0.4

0.6

0.8

1.0

1.2 1.4 1.6 Interstitial content (at %)

c(A)

4.705 Ti – C 4.700 4.695

Ti – N Ti – O

4.690 4.685 4.680

0

10

20

30 40 50 Interstitial content (at %)

Fig. 3.1-83a,b Lattice parameters a (a) and c (b) of α-Ti as a function of interstitial content

identical levels of mechanical properties as those of the corresponding cp-Ti grades. The compositions and mechanical properties of typical alloys are also shown in Table 3.1-18. All commercially pure and low-alloy Ti materials may be strengthened by cold work. The tensile strength Rm is about doubled by cold work, which amounts to 80 to 90% reduction in area, and the fracture strain A5 and the reduction in area are about halved.

207

208

Part 3

Classes of Materials

Part 3 1.3

Table 3.1-18 Chemical composition (maximum contents) and mechanical properties of commercially pure and low-alloy

grades of Ti O wt%

Tensile strength Rm (MPa)

Yield strength Rp0.2 (MPa)

Fracture strain A10 (%)

Standard grade a cp

Standard grade a low alloyed

0.12 0.18

290–410 390–540

> 180 > 250

> 30 > 22

Grade 1 Grade 2

0.25 0.35 0.25

460–590 540–740 > 480

> 320 > 390 > 345

> 18 > 16 > 18

Grade 3 Grade 4

Pd: grade 11 Pd: grade 7 Ru: grade 27 Ru: grade 26

a

Ni+Mo: grade 12

ASTM B265, ed. 2001; Nmax : 0.03 wt%; Cmax : 0.08 wt%; Hmax : 0.015 wt%

Tensile strength (N/ mm2) 800

Fracture strain (%) 80

a) Stress (MPa)

Stress (ksi)

550

Rupture 70

450

60

5 % creep 600

60

350

50

2 1

40

0.5

250

30 3.7065 3.7055 3.7035 3.7025

400

Values used for pressure vessel calculations

1

10

100

1000

b) 250

20

200

0

40

150 0.1

200

30

150

20

100 Tensile strength

10

50 0

0

100

200

300

400 T (°C)

Fig. 3.1-85 High-temperature tensile strength and fracture

strain of titanium, and values used for titanium pressure vessel calculations (105 h)

Most applications of cp-Ti and low-alloy Ti materials are based on their high corrosion resistance, such as components in chemical plants, heat exchangers, offshore technology, seawater desalination plants, Ni winning, electroplating plants, medical applications such as heart pacer casings, surgical implants including ear implants [1.55], and automotive applications. Applications of unalloyed Ti in architecture and jewellery are based on coloring the surface by oxide growth upon heat treatment in air. Unalloyed Ti grades are, also, applied at elevated temperature because of their favorable mechanical properties and oxidation resistance at high temperature. Figure 3.1-86 shows the creep date for grade 4 Ti.

0 0.1

1

10

100

0 1000

c) 80 10 60

8 6

40

4

20

2 0 0.1

1

10

0 100 1000 Test time (h)

Fig. 3.1-86a–c Creep behavior of commercially pure Ti

grade 4, mill annealed with a minimum yield stress of 480 MPa [1.56]. (a) 25 ◦ C; (b) 425 ◦ C; (c) 540 ◦ C

Metals

Alloying elements are added to Ti to improve its mechanical properties. Based on the phase transformation of pure Ti, alloying elements influence the phase equilibria and, thus, the transformations and the resulting microstructural states. The phase composition of the microstructure may be varied from pure α through (α + β) to pure β, depending on the alloy content [1.54]. The α phase is stabilized by O, N, C, and Al. The β phase range is expanded by H, V, Mo, Fe, Cr, Cu, Pd, and Si. High solubility in α and β is exhibited by Zr and Sn. The alloy variants are characterized by the phases present in the annealed state at room temperature, as shown in Table 3.1-19. Alloys consisting partially or fully of the β phase are more easily deformed because of the larger number of slip systems in the bcc structure of the β phase compared to those in the hcp α phase. The alloying elements provide, also, solid solution strengthening. A further increase in yield strength may be attained by quenching and aging of β-phase alloys which leads to the coherent precipitation of the α and ω phases. However, the strength increase is moderate (10–20%) compared to

that caused by precipitation hardening effects in Al and Cu-based alloys. Based on their high specific strength, Ti alloys are widely used in aerospace applications, furthermore for high-speed moving parts, corrosion resistant pressure vessels and pipes, and for sports gear. The high-temperature strength has been increased by alloying for elevated temperature applications, as shown in Table 3.1-20. The densely packed hcp structure of the α phase is more creep-resistant than the more open bcc structure of the β phase. Accordingly the creep strength of the α- and near-α-phase alloys is clearly higher than that of α + β-phase alloys, as shown in Fig. 3.1-87. Titanium alloys may be processed like stainless steel. This leads to a cost effective production of a wide range of semi-finished and finished products and parts. If the tendency to oxidation and welding above approximately 350 ◦ C and the low thermal conductivity are taken into account, parts can be manufactured from Ti alloys, quite similar to manufacturing from stainless steels. A wide variety of working, joining, and coating processes is well established.

Table 3.1-19 Chemical composition and mechanical properties of Ti-base alloys at room temperature (minimum values) Alloy composition a

Alloy type

Ti5Al2.5Sn

α

830

Ti6Al2Sn4Zr2MoSi

near α

900

Ti6Al5Zr0.5MoSi

near α

Ti5.8Al4Sn3.5Zr0.7Nb 0.5Mo0.2Si0.05C

near α

Ti6Al4V Ti4Al4Mo2Sn

Density  (g/cm3 )

Young’s modulus E (GPa)

Main property

780

4.48

110

High strength

830

4.54

114

High-temperature strength

3.7145

950

880

4.45

125

High-temperature strength

3.7155

1030

910

4.55

120

High-temperature strength

α+β

900

830

4.43

114

High strength

α+β

1100

960

4.60

114

High strength

3.7185

Ti6Al6V2Sn

α+β

1030

970

4.54

116

High strength

3.7175

Ti10V2Fe3Al

near β

1250

1100

4.65

103

High strength

Ti15V3Cr3Sn3Al

β

1000

965

4.76

103

High strength; cold formability

Ti3Al8V6Cr4Zr4Mo

β

1170

1100

4.82

103

High corrosion; resistance

Ti15Mo3Nb3AlSi

β

1030

965

4.94

96

High corrosion; resistance

a b

Tensile strength Rm (MPa)

Figure before chemical symbol denotes nominal wt% according to DIN 17851, ASTM B 265 ed. 2001

Yield strength Rp0.2 (MPa)

Standard grade b

209

Part 3 1.3

3.1.3.2 Ti-Based Alloys

1.3 Titanium and Titanium Alloys

210

Part 3

Classes of Materials

Part 3 1.3

Table 3.1-20 Upper temperature limit for Ti alloys developed for elevated-temperature applications Alloy

Alloy type

Year of introduction

Useful maximum ◦ C

Ti-6Al-4V (Ti-64) Ti-4Al-2Sn-4Mo-0.5Si (IMI-550) Ti-8Al-1Mo-1V (Ti-811) Ti-2Al-11Sn-5Zr-1Mo-0.2Si (IMI-679) Ti-6Al-2Sn-4Zr-6Mo (Ti-6246) Ti-6Al-2Sn-4Zr-2Mo (Ti-6242) Ti-3Al-6Sn-4Zr-0.5Mo-0.5Si (Hylite 65) Ti-6Al-5Zr-0.5Mo-0.25Si (IMI-685) Ti-5Al-5Sn-2Zr-2Mo-0.2Si (Ti5522S) Ti-6Al-2Sn-1.5Zr-1Mo-0.1Si-0.3Bi (Ti-11) Ti-6Al-2Sn-4Zr-2Mo-0.1Si (Ti-6242S) Ti-5Al-5Sn-2Zr-4Mo-0.1Si (Ti-5524S) Ti-5.5Al-3.5Sn-3Zr-0.3Mo-1Nb-0.3Si (IMI-829) Ti-5.5Al-4Sn-4Zr-0.3Mo-1Nb-0.5Si-0.06C (IMI-834) Ti-6Al-2.75Sn-4Zr-0.4Mo-0.45Si (Ti-1100) Ti-15Mo-3Al-2.75Nb-0.25Si (Beta-21S)

α+β α+β near-α near-α α+β near-α near-α near-α near-α or α + β near-α near-α near-α or α + β near-α near-α near-α β

1954 1956 1961 1961 1966 1967 1967 1969 1972 1972 1974 1976 1976 1984 1987 1988

300 400 425 450 450 450 520 520 520 540 520 500 580 590 590 590

500 Stress 700 for 0.1% 600 creep in 150 h 500 (MPa)

600

700

800

900

1000

1100 100 80

1400 β–Ti

Ti-8Al-1Mo-1V

60 Ti-6Al-2Sn-4Zr-2Mo

300

α–Ti

1200 α2 –Ti3Al

40

5Al-2.5Sn

γ–TiAl

1000

200

0 260

Ti1–xAl1+x Ti5Al11 Ti2Al5

1600

Ti-6Al-2Sn-4Zr-6Mo

400

100

T (°C)

Stress for 0.1 % creep in 150 h (ksi)

Approximate T (F°)

α–Ti

20

Ti-6Al-6V-2Sn Ti-6Al-4V

315

370

425

0 480 535 590 Approximate T(°C)

Fig. 3.1-87 Creep strength for α (Ti-5Al-2.5Sn), near-α (Ti-8Al-

1Mo-1V and Ti-6Al-2Sn-4Zr-2Mo), and α + β (Ti-6Al-4V and Ti6Al-2Sn-4Zr-6Mo) alloys

3.1.3.3 Intermetallic Ti–Al Materials The intermetallic compounds Ti3 Al and TiAl are studied for high-temperature materials developments. Extensive accounts [1.52, 57] are the sources of the data presented here. In Table 3.1-21 the property ranges of Ti3 Al- and TiAl-based alloys are compared to those of conventional Ti alloys and Ni-based superalloys.

Ti

10

30

50

70

r/h–TiAl2 TiAl3 90 Al (at. %)

Fig. 3.1-88 Ti−Al phase diagram

Various versions of the binary Ti–Al phase diagram are available [1.54] and are still under discussion because of conflicting results. The phase diagram shown in Fig. 3.1-88 incorporates recent results. Ti3 Al-Based Alloys Various Ti3 Al-based alloys have been developed with niobium as a major alloying element and further components for obtaining an optimised balance of strength, formability, toughness, and oxidation resistance. The alloys are two-phase or three-phase. Current Ti3 Albased alloys with engineering significance are listed in Table 3.1-23.

Metals

1.3 Titanium and Titanium Alloys

Property

Ti-based alloys

Ti3 Al-based intermetallic materials

TiAl-based intermetallic materials

Ni-based superalloys

Structure

A3/A2

D019 /A2/B2

L10 /D019

A1/L12

Density (g/cm3 )

4.5–4.6

Thermal conductivity (W/m K)

21

Young’s modulus at room temperature (GN/m2 )

4.1–4.7

3.7–3.9

7

22

7.9–9.1 11

95–115

100–145

160–180

195–220

Yield strength at room temperature (MN/m2 )

380–1150

700–990

400–650

250–1310

Tensile strength at room temperature (MN/m2 )

480–1200

800–1140

450–800

Temperature limit due to creep (◦ C)

600

760

1000

1090

Temperature limit due to oxidation (◦ C)

600

650

900

1090

Tensile strain to fracture at room temperature (%)

10–25

2–26

1 –4

Tensile strain to fracture at high temperature (%)

12–50

10–20

10–60

13–42

10–20

Fracture toughness KIc at room temperature (MN/m3/2 )

High

620–1620

3–50 8–125 25

Table 3.1-22 Crystal structure data Phase designation

Composition

Strukturbericht designation (prototype)

α-Ti(Al)

0–45 at.% Al

A3 (Mg)

β-Ti(Al)

0–47.5 at.% Al

A2 (W)

β1

B2 (CsCl)

α2 -Ti3 Al

22–39 at.% Al

DO19 (Ni3 Sn)

γ -TiAl

48–69.5 at.% Al

L10 (AuCu)

O

Ti2 AlNb

ω

Ti4 Al3 Nb

B82

Table 3.1-23 Major Ti3 Al-based alloys [1.50] Alloy composition (at.%)

Phases

Designation

Ti-24Al-11Nb

α2 + β

24-11

Ti-25Al-11Nb

α2 + β

25-11

Ti-25Al-8Nb-2Mo-2Ta

α2 + β

8-2-2

Ti-25Al-16Nb

α2 + β + O

25-16

Ti-25Al-17Nb

α2 + β + O

25-17

Ti-27Al-15Nb

α2 + β + O

27-15

Ti-27Al-15Nb-1Mo

α2 + β + O

27-15-1

Ti-22Al-17Nb-1Mo

α2 + β + O

22-17-1

Ti-25Al-17Nb-1Mo

α2 + β + O

25-17-1

Ti-25Al-10Nb-3V-1Mo

α2 + β + O

10-3-1

Ti-25Al-24Nb

O+β

25-24

Ti-22Al-27Nb

O+β

22-27

Ti-30Al-20Nb

O+ω

30-20 (1986)

SCS/6Ti-24Al-11Nb

α2 + β + SiC

SCS-6/24-11

Alloy 24-11 and alloy 10-3-1 have already been produced on a production mill scale.

Part 3 1.3

Table 3.1-21 Properties of alloys based on the titanium aluminides Ti3 Al and TiAl [1.50] and of conventional titanium alloys and nickel based superalloys

211

212

Part 3

Classes of Materials

Part 3 1.3

Mechanical Properties. The elastic properties of se-

lected alloys are presented in Table 3.1-24. Strength, ductility, and toughness of the Ti3 Al-based alloys are sensitive functions of both composition and microstructure which are controlled by prior processing. Characteristic data are shown in Table 3.1-25 for various alloys. Different property data for the same alloy composition indicate the effect of different prior thermomechanical treatments. The effect of microstructure on toughness is exemplified by Table 3.1-26. Particularly high strengths can be obtained in intermetallic Ti3 Albased matrix composites.

Table 3.1-26 Effect of microstructure variation on fracture toughness K Ic at room temperature for a Ti-25Al-10Nb3V-1Mo alloy Microstructure

K Ic [MPa m1/2 ]

Coarse globular

11

Fine globular

10

Coarse bimodal

11

Fine bimodal

14

Fine lamellar

8

Coarse lamellar

50

Table 3.1-24 Elastic moduli E, G, K , and Poisson’s ratio ν at various temperatures T for selected simple Ti3 Al-based

alloys Alloy (at.%)

T (◦ C)

E (GPa)

G (GPa)

ν

Ti-25.5Al Ti-25.5Al Ti-25Al-10Nb-3V-1Mo (coarse globular) Ti-25Al-10Nb-3V-1Mo (fine lamellar) Ti-25Al-10Nb-3V-1Mo (coarse lamellar) Ti-26.6Al-4.9Nb Ti-27.4Al-20.3Nb Ti-22Al-23Nb/Ultra-SCS Ti-22Al-23Nb/Ultra-SCS Ti-22Al-23Nb/Ultra-SCS

27 −270 23 23 23 26–883 25 25 649 760

144 151 72 120 159 134.47–0.0482T 128.8 201 ± 8 173 135 ± 8

56.2 59.0

0.283 0.280

53.56–0.0180T 48.8

0.257–0.00004T 0.32

K (GPa)

118.4

Table 3.1-25 Selected tensile data for yield stress Rp , fracture stress Rm , total elongation A, fracture toughness K Ic at room temperature, and creep time to rupture tr at 650 ◦ C and 380 MPa for various Ti3 Al-based alloys Alloy (at.%)

Rp (MPa)

Ti-25Al Ti-24Al-11Nb Ti-24Al-11Nb Ti-24Al-11Nb Ti-24Al-14Nb Ti-24Al-14Nb Ti-15Al-22.5Nb Ti-25Al-10Nb-3V-1Mo Ti-25Al-10Nb-3V-1Mo Ti-25Al-10Nb-3V-1Mo Ti-25Al-10Nb-3V-1Mo Ti-25Al-10Nb-3V-1Mo Ti-24.5Al-17Nb Ti-24.5Al-17Nb Ti-25Al-17Nb-1Mo Ti-22Al-23Nb Ti-22Al-27Nb Ti-22Al-20Nb-5V Ti-22Al-20Nb-5V

538 787 510 761 831 790 860 825 823 745 759 942 952 705 989 863 1000 900 1092

Rm (MPa) 538 824 967 977 963 1042 950 907 963 1097 1010 940 1133 1077 1161 1308

A (%) 0.3 0.7 2.0 4.8 2.1 3.3 6.7 2.2 0.8 1.1 2.6 2.7 5.8 10.0 3.4 5.6 5.0 18.8 8.8

K Ic (MPa m1/2 )

tr (h) 44.7

20.7

15.8 42.3 13.5

59.5 60.4 0.9 360

28.3

62

20.9

476

30.0

Metals

Ti3 Al-based alloys is higher than that of conventional Ti alloys with TiO2 formation, but lower than that of Al2 O3 -forming alloys. The rate controlling mechanisms are complex and change with atmosphere, temperature, and time. Oxidation is moderate with porous scales up to 800 ◦ C whereas spallation occurs at higher temperatures. The addition of Nb to the Ti3 Al-based alloys is beneficial to the oxidation resistance as well as nitrogen in the atmosphere [1.58]. Table 3.1-27 presents characteristic data for oxidation at 800 ◦ C. It should be noted that H is easily dissolved in Ti3 Al-based alloys, leading to embrittlement and stress corrosion cracking. Furthermore, the thermal stability of intermetallic Ti3 Al-based matrix composites – in particular SCS-6 SiC/Ti-25Al-10Nb-3V-1Mo – is affected by chemical reactions between the matrix and the strengthening phase. TiAl-Based Alloys Alloys based on γ -TiAl, also called gamma titanium aluminides, excel due to their high strength per unit density. These alloys contain the α2 -phase Ti3 Al as a second phase and are further alloyed with other elements for property optimization. The composition range is Ti-(45–48)Al-(0–2)(Cr, Mn, V)-(0–5)(Nb, Ta, W)-(0– 2)(Si, B, Fe, N) (at.%). Further components such as Hf,

Sn, C, and/or 0.8–7 vol.% TiB2 are added for dispersion strengthening [1.59]. Table 3.1-28 shows the standard microstructures and Table 3.1-29 lists the alloys of primary interest. Various jet engine and car engine components have been identified for application of TiAl-based alloys. It is particularly noteworthy that large sheets, which are suitable for superplastic forming and joining by diffusion bonding, can be produced from these intrinsically brittle intermetallic compound alloys. Physical Properties. Some thermal data for single crystalline and polycrystalline TiAl alloys are shown in Tables 3.1-30 and 3.1-31. Mechanical Properties. Elastic properties of TiAl-based

materials are compiled in Table 3.1-32. Strength, ductility, and toughness of the TiAl-based alloys are sensitive functions of both composition and microstructure which is controlled by prior processing [1.59]. Characteristic data are shown in Table 3.1-33 for various alloys. Different property data for the same alloy composition indicate the effect of different prior thermo-mechanical treatments. It is noted that TiAl-based alloys are prone to hydrogen/environmental embrittlement depending on the amount of α2 from Ti3 Al [1.60]. Creep and fatigue data are available [1.59, 61].

Table 3.1-27 Characteristic oxidation data for various Ti3 Al-based alloys at 800 ◦ C. Apparent parabolic rate constant kp

and apparent activation energy Q [1.58] Test duration (h)

kp (10−12 g2 cm−4 s−1 )

Q (kJ mol−1 )

Alloy (at.%)

Atmosphere

Ti-25Al

O2

9

Ti-25Al-11Nb

O2

4

2.0

330

Ti-24Al-15Nb

O2

6

2.2

329

Ti-24Al-15Nb

20% O2 + 80% N2

5

0.25

274

Ti-24Al-10Nb-3V-1Mo

20% O2 + 80% N2

15

Ti-25Al-10Nb-3V-1Mo

Air

24

19

1150 2.4

289

217 248

Table 3.1-28 Standard microstructures of TiAl-based alloys [1.59] Type

Phase distribution

Near-gamma (NG)

γ grains + α2 particles

Duplex (DP)

γ grains + α2 plates or particles

Nearly lamellar (NL)

Lamellar γ + γ grains

Fully lamellar (FL)

Lamellar γ + residual γ grains on grain boundaries

Modified NL (MNL)

Lamellar γ + fine γ grains

Modified FL (MFL)

Lamellar γ

213

Part 3 1.3

Chemical Properties. The oxidation resistance of the

1.3 Titanium and Titanium Alloys

214

Part 3

Classes of Materials

Part 3 1.3

Table 3.1-29 Important TiAl-based alloys with microstructures according to Table 3.1-28 [1.59] Composition (at.%)

Microstructure type

Designation

Ti-48Al-1V-0.3C-0.2O

DP

48-1-(0.3C)

Ti-48Al-1V-0.2C-0.14O

DP/NL

48-1-(0.2C)

Ti-48Al-2Cr-2Nb

DP, NL, DP/FL

48-2-2

Ti-47Al-1Cr-1V-2.6Nb

DP/FL

G1

Ti-45Al-1.6Mn

NL

Sumitomo

Ti-47.3Al-0.7V-1.5Fe-0.7B

–

IHI Alloy

Ti-47Al-2W-0.5Si

DP

ABB Alloy

Ti-47Al-2Mn-2Nb-0.8TiB2

NL + TiB2

47XD

Ti-45Al-2Mn-2Nb-0.8TiB2

MFL + TiB2

45XD

Ti-46.2Al-xCr-y(Ta,Nb)

NL

GE Alloy 204b

Ti-47Al-2Nb-2Cr-1Ta

DP

Ti-47Al-2Nb-2Cr-1Ta

Ti-46Al-4Nb-1W

NL

Alloy 7

Ti-46.5Al-2Cr-3Nb-0.2W

DP/MFL

Alloy K5

Ti-48Al-2Cr

NG, DP, FL

Ti-48Al-2Cr

Ti-47Al-1.5Nb-1Cr-1Mn-0.7Si-0.5B

MFL

γ -TAB

Ti-46.5Al-4(Cr, Nb, Ta, B)

MFL

γ -Met

Table 3.1-30 Temperature dependence of the thermal expansion coefficient α for single crystalline TiAl Alloy (at.%) Ti-56Al

T (◦ C)

α[100] (K−1 )

25–500

9.77 × 10−6 + 4.46 × 10−9 (T

α[001] (K−1 ) 9.26 × 10−6 + 3.76 × 10−9 (T + 273)

+ 273)

Table 3.1-31 Thermal expansion coefficient α, thermal conductivity λ and specific heat c p at various temperatures T for

polycrystalline TiAl alloys [1.62] Alloy (at.%)

T (◦ C)

α (K−1 )

λ (W K−1 m−1 )

c p (J g−1 K−1 )

Ti-50Al

27

11 × 10−6

11

0.4

Ti-50Al

850

13 × 10−6

19

0.5

Ti-48Al-2Cr

100

9.1 × 10−6

–

–

Ti-48Al-2Cr

700

11.8 × 10−6

–

–

Table 3.1-32 Young’s modulus E, shear modulus G, Poisson’s ratio ν and bulk modulus K for single-phase TiAl and a TiAl composite T (◦ C)

E (GPa)

G (GPa)

ν

25–935

173.59–0.0342T

70.39–0.0141T

0.234

Ti-50Al

25

185

75.7

110

Ti-50Al

−273

190

78.3

112

Ti-47Al-2V-7 vol.%TiB2

27

180

Ti-47Al-2V-7 vol.%TiB2

647

162

Alloy (at.%) Ti-49.4Al

K (GPa)

Metals

1.3 Titanium and Titanium Alloys

Alloy designation

Alloy condition, processing, microstructure

T [◦ C]

Rp (MPa)

Rm (MPa)

A (%)

K Ic (MPa m1/2 )

48-1-(0.3C)

Forging + HT

48-1-(0.2C)

Casting-duplex Forging + HT

48-2-2

Casting + HIP + HT

RT 760 RT RT 815 RT 760 RT 870 RT 700 RT 600 800 RT 800 RT 800 RT 760 RT 760 RT 760 RT 840 RT 870 RT 760 RT 870 RT 700 RT 700

392 320 490 480 360 331 310 480/454 330/350 510 421 480/330 383/– 324/290 465 370 – – 425 350 402 344 550–590 415 442 381 430 334 648 517 462/473 –/362 390 340 475 385

406 470 – 530 450 413 430 – – 597 581 548/383 507/– 492/378 566 540 520 424 520 460 482 458 670–720 510 575 549 515 403 717 692 579/557 –/485 405 395 – –

1.4 10.8 – 1.5 720 2.3 – 3.1/0.5 53/19 2.9 5.2 2.3/0.8 3.1/– 55/1.5 1.4 14 0.6 40 1.0 2.5 1.5 – 1.5 19 1.5 12.2 1.0 14.6 1.6 – 2.8/1.2 –/12.0 1.5 2.7 1.6 6.0

12.3 – 24.3 – – 20–30 – – – – – 12/30-36 16/ – –/40-70 – – – – 22 – 15–16 – 15–19 – 34.5 – – – – – 11/20-22 – – – – –

Extrusion + HT: DP/FL PM extrusion + HT G1

Forging + HT: DP/FL

Sumitomo

Reactive sintering

IHI Alloy

Casting

ABB Alloy

Casting + HT

47XD

Casting + HIP + HT

45XD

Casting + HIP + HT

GE Alloy 204b

Casting + HIP + HT

Ti-47Al-2Nb-2Cr-1Ta

Casting + HIP + HT

Alloy 7

Extrusion + HT

Alloy K5

Forging + HT: DP/MFL

Ti-48Al-2Cr

Casting + HIP + HT

γ -TAB

Casting + HIP + HT

Chemical Properties. The oxidation behavior of TiAl al-

loys is complex as both Al2 O3 and/or TiO2 are formed at parabolic rate constants ranging from 3 × 10−13 to 3 × 10−9 g2 cm−4 s−1 at 950 ◦ C, depending not only on alloy composition, atmosphere, and temperature, but also on alloy surface quality. The oxidation rate is higher in air than in pure oxygen. Alloying additions of Nb, W, Ta, or Si generally improve the oxidation resis-

tance. Additions of V and Mo promote Al2 O3 formation above 900 ◦ C, which is beneficial, but accelerates scale growth at lower temperatures, i. e., at possible service temperatures. Small additions of Cr reduce the oxidation resistance whereas larger amounts improve it. Small additions of P or Cl have been found to increase the oxidation resistance. Some characteristic data are shown in Table 3.1-34.

Part 3 1.3

Table 3.1-33 Selected tensile data for yield stress Rp , fracture stress Rm , total elongation A, toughness K Ic at room temperature (RT) or higher temperature T for the TiAl-based alloys of Table 3.1-29 with microstructures of Table 3.1-28 [1.59, 61]

215

216

Part 3

Classes of Materials

Part 3 1.3

Table 3.1-34 Characteristic oxidation data for some TiAl-based alloys of Table 3.1-29. Apparent parabolic rate constant kp at 800 ◦ C in air Alloy designation

Test duration (h)

kp (10−12 g2 cm−4 s−1 )

48-2-2 Alloy K5 Alloy 7 (5 at.% Nb)

500 1000 1000

2 0.5 0.1

Usually γ -TiAl-based alloys contain α2 -Ti3 Al as a second phase and are, therefore, subject to hydrogen uptake and hydrogen/environmental embrittlement depending on the amount of α2 -Ti3 Al.

Ms(K) 400

300

3.1.3.4 TiNi Shape-Memory Alloys The shape-memory effect is based on martensitic transformations of intermetallic phases with a high degree of reversibility [1.63]. The alloy TiNi is the most advanced and has widespread shape memory. The present state of development and applications is summarized in [1.63, 64]. The high-temperature TiNi phase, having a cubic B2 (CsCl type) structure, is transformed martensitically, i. e., by a combination of transformation shears, into a low-temperature phase with a monoclinic DO19 structure upon cooling or upon applying a stress and strain. The transformation can be associated with a macroscopic shape change. The transformation and the associated shape change are reversed on heating (shapememory effect) or on releasing the stress and strain isothermally (superelasticity). The range of transformation start temperatures Ms varies between −200 ◦ C and 110 ◦ C depending on the alloy composition, as shown in Fig. 3.1-89. Further reversible, diffusionless, but non-martensitic transformation phenomena occur in the TiNi high temperature phase on approaching the temperature range of martensitic transformation. Microscopically, these transformation phenomena are associated with phonon softening. Crystallographically, they are observable as localised rhombohedral distortions of the B2 structure. Furthermore, these localized displacements appear to be stabilized by annealing. Annealing treatments in the temperature range of 300 to 800 ◦ C are increasing the Ms temperature. Figure 3.1-90 shows a characteristic example. The shape-memory effect is a complex function of composition, martensite start temperature Ms , stress, strain, microstructure, texture, and aging treatment. It consists essentially of a reversible transformation strain and the associated macroscopic shape change. At low numbers of transformation cycles (e.g., up to 100), the

200

100

0

0.49

0.50

0.51 Ni content (at.%)

Fig. 3.1-89 Martensite start temperature Ms of the TiNi phase as a function of Ni content Ms (°C)

–80

–90

–100 300

400

500

600 700 800 Ageing temperature (°C)

Fig. 3.1-90 Effect of aging temperature on the Ms tem-

perature of an Ni47.3 Ti43.8 Nb8.9 alloy

reversible transformation strain decreases from a typical initial value 8% to about 6%; even after ≥ 100 000 transformation cycles it stays at a technically useful level of ∼ = 2%. A considerable number and variety of technical and medical applications of the shape-memory effect and of the closely related effect of superelasticity have been developed [1.65, 66].

Metals

1.4 Zirconium and Zirconium Alloys

Zirconium is used – similarly to titanium but less extensively so – as a special structural material of high corrosion resistance due to its highly stable protective oxide layer. This oxide layer forms in air at ambient temperature spontaneously and can be increased in thickness and stability by heat treatment in air. More extensive treatments are found in [1.51, 67]. Technically-pure and low-alloy Zr materials are especially used in applications requiring structural parts of high chemical stability. The processing is closely analogous to that of Ti. Another main application of Zr is in high-purity Zr alloys used as cladding and structural materials in nuclear applications due to the low thermal neutron capture cross section of Zr. A third group of Zr-based materials with application potential is due to the fact that some Zr-based alloys form the amorphous state easily upon cooling at a comparatively low rate. They are suitable for the production of bulk glassy alloys. At 1138 K, Zr undergoes a structural phase transformation from low-temperature, hexagonal close-packed α-Zr to high-temperature, body-centered cubic β-Zr. Alloying elements such as Nb stabilize the β phase. On slow cooling and annealing of the β phase, a metastable

ω phase can be obtained which forms by coherent precipitation.

3.1.4.1 Technically-Pure and Low-Alloy Zirconium Materials Only two zirconium materials are standardised: Zr 702 which is essentially technically-pure Zr and consists of the α phase only, and Zr 705 which contains 2 to 3 wt% Nb, has an α + β microstructure and a higher yield stress. Their composition ranges and mechanical properties are listed in Tables 3.1-35 and 3.1-36. Since Hf is usually contained in the Zr ore zircon (ZrSiO4 ) and is difficult to separate, the Zr materials are specified to contain Hf up to 4.5 wt%. The presence of Hf in Zr alloys up to this level of composition does not affect the mechanical and corrosion properties significantly. The Zr–Nb phase diagram (Fig. 3.1-91) indicates that α + β microstructures can be obtained at the 2–3 wt% Nb level. This leads to both substitutional solid solution strengthening and dual phase strengthening effects. Oxygen has a high interstitial solubility in α-Zr. Fig. 3.1-92 shows the Zr–O phase diagram. It is inter-

Table 3.1-35 Composition of technically-pure and low-alloy Zr materials Common designation ASTM/UNS designation

Zr 702 R 60702

Zr 705 R 60705

Alloying, elements (wt%) Zr+Hf, min

99.2

95.5

Hf, max

4.5

4.5

Fe+Cr, max

0.20

0.20

Nb

–

2.0–3.0

O, max

0.16

0.18

H, max

0.005

0.005

N, max

0.025

0.025

C, max

0.05

0.05

Table 3.1-36 Mechanical properties of technically-pure and low-alloy Zr materials Alloy

Property

Test temperature (◦ C) 20 95

150

260

370

Zr 702

Rp0.2 (MPa)

321

267

196

129

82

Rm (MPa)

468

364

304

201

157

A (%) Zr 705

28.9

31.5

42.5

49.0

Rp0.2 (MPa)

506

272

196

Rm (MPa)

615

389

326

A (%)

18.8

31.7

28.9

44.1

Part 3 1.4

3.1.4 Zirconium and Zirconium Alloys

217

218

Part 3

Classes of Materials

Part 3 1.4

Zr (wt. %) 80 90

T 10

3000 K 2600

20

30

40

50

60

70

2741 K

Nb–Zr L

2128 K 2013 K

2200

78.3

1800

(Nb, β–Zr)

1400

1261 K

1136 K

39.4

1000

883 (10) K

99.4

9.0

600 Nb

10

20

30

40

50

60

70

81.5

α–Zr

80

90 Zr (at. %)

Fig. 3.1-91 Zr−Nb phase diagram

esting to note that the O atoms undergo ordering on the interstitial lattice sites of the α-Zr solid solution above about 10 at.% O. These interstitially ordered phases are termed suboxides. The interstitial O content leads to a strong interstitial solid solution strengthening effect: about 0.01 wt% O increases the yield stress by about 150 MPa. Extensive data and references are available on the corrosion behavior of Zr in many types of media and under various conditions of exposure [1.67]. T 1

3200 K

3

5

7

10

15

O (wt %) 30

20

L+G

Zr–O

p =1 atm

2983 K

2800

γ– ZrO2–x

L 2243 K

2400

≈ 1798 K (α–Zr)

β –ZrO2–x

63.5 66.5

31.2

1600

≈ 1478 K 29.8 (α'–Zr)

1200 1136 K

≈ 1243 K

Zr

10

20

α– ZrO2–x

≈ 733 K (?)

(α ''–Zr)

66.7 66.7

29.1

(α2''–Zr)

800

Based on its low cross section for thermal neutrons and its high corrosion resistance in water, Zr is the preferred material for structural parts and cladding in pressurized and boiling water nuclear reactors. An extensive account of these materials and of their behavior under irradiation is given in [1.68]. Designations and composition ranges of the 4 standardized alloys are listed in Table 3.1-37. The addition of Sn gives rise to a strengthening contribution and increases corrosion resistance by reducing the deleterious effect of nitrogen. The metals Fe, Cr, and Ni, which are highly soluble in the β phase, have very low solubility in α-Zr (maximum solubility: Fe 120 ppm, Cr 200 ppm). This is the basis of a heat treatment involving a high-temperature solution annealing and a low-temperature precipitation treatment. The resulting precipitates are the Laves phases Zr2 (Ni, Fe) and Zr(Cr, Fe)2 . In their presence the corrosion resistance is increased by reducing forms of localized corrosion. A specified O content serves to adjust the yield stress due to interstitial solid solution strengthening. Hafnium is removed and its upper limit is specified in Zr alloys for nuclear applications because of its high cross section for thermal neutrons. The irradiation effects on the mechanical properties are significant. The interstitial atoms and vacancies resulting from irradiation-induced atomic displacements give rise to the formation of dislocation loops of interstitial and vacancy type. These dislocation loops act as obstacles to slip dislocations and lead to an increase in yield stress and decrease in elongation upon fracture as a function of dose, as shown in Fig. 3.1-93. The effect saturates at about 1024 nm−2 .

3.1.4.3 Zirconium-Based Bulk Glassy Alloys

19.5

2000 (β–Zr)

400

62

35 40 10.5

≈ 2338 K

2338 K

2128 K

3.1.4.2 Zirconium Alloys in Nuclear Applications

28.6 (α3''–Zr)

30

Fig. 3.1-92 Zr−O phase diagram

40

66.7

50

60

70 80 O (at. %)

Zirconium-based alloys were among the first non-noble metal-based alloys found to solidify in the amorphous state upon cooling from the melt at comparatively low rates R, such as 10 K s−1 [1.69,70]. The term bulk glassy alloys refers to the fact that this solidification behavior permits us to obtain bulky parts with an amorphous structure by conventional casting procedures, e.g., in rod form, up to 30 mm. Data are given in [1.71, 72]. The tendency to solidification in the amorphous state is due to a low rate of nucleation of the equilibrium phase(s) at a particular alloy composition. An empirical method to determine the ease of glass formation has proved to be an evaluation of the glass-transition tem-

Metals

1.4 Zirconium and Zirconium Alloys

Common designation ASTM/UNS designation

Zircaloy-2 R 60802

Zircaloy-4 R 60804

Alloying elements (wt%) 1.2–1.7 1.2–1.7 Sn 0.07–0.2 0.18–0.24 Fe 0.05–0.15 0.07–0.13 Cr Ni 0.03–0.08 – Nb – – O 0.010–0.014 (t.b.s.)a Impurity elements, maximum permissible content (wt ppm) Al 75 75 270 270 C 50 50 Cu 100 100 Hf Mn 50 50 Mo 50 50 Ni – 80 Si 120 120 Ti 50 50 100 100 W a

Zr–Nb R 60901

Zr–Nb R 60904

– – – – 2.4–2.8 0.09–0.13

– – – – 2.5–2.8 (t.b.s.)a

75 270 50 100 50 50 80 120 50 100

75 150 50 50 50 50 65 120 50 100

t.b.s. – to be specified

a) 0.2% YS and UTS (MPa) 600

perature Tg and the crystallization temperature Tx , which can be determined by thermal analysis of the amorphous alloy in question upon heating. For a great number of alloys which form the amorphous state upon cooling, it has been shown that the critical cooling rate Rc , i. e., lowest rate which is sufficient for complete glass formation, decreases strongly with two parameters:

UTS YS UTS

YS

400

200

1018 1020 1021 1022 1019 Integrated neutron flux (E>1MeV)(n cm–2)

b) Tensile elongation (%) 30 20 Annealed 10 0

Cold worked 1018 1019 1020 1021 1022 Integrated neutron flux (E>1MeV)(n cm–2)

Fig. 3.1-93 Irradiation effects on mechanical properties of a zircaloy [1.68]. YS – yield stress; UTS – ultimate tensile strength. Solid lines: irradiation in the annealed state. Dashed lines: irradiation in the 10% cold worked state

• •

The relative glass-transition temperature Trg = Tg /Tl/el , where Tl/el is the liquidus temperature, and The magnitude of the temperature range ∆Tx = Tx − Tg .

Figures 3.1-94 – 3.1-97 show characteristic data for Zr alloys which have been investigated in a wide range of compositions. It is impossible to date to derive from first principles which alloy compositions are prone to easy glass formation. It has been found empirically that multi-component alloys with components of significantly different ionic radii are suitable candidates in principle. Examples of Zr-based systems that show bulk glassy solidification behavior are listed in Table 3.1-38. Empirical findings have been subjected to a systematic treatment involving a mismatch entropy term Sσ and the enthalpy of mixing ∆H [1.73]. Such re-

Part 3 1.4

Table 3.1-37 Designations and compositions of the standardized Zr alloys for nuclear applications [1.68]

219

220

Part 3

Classes of Materials

Part 3 1.4

Ni

Ni 10

10

90 Tx (K)

80

20

30

Al (at.%) 40 50

60 Ni (at. %) 50

60

40

80

Al

10

20

30

40 50 60 Zr (at. %)

70

60

40

60

660 700 740

80

40

50

30

30 20

80

20

90

10

Zr

90

Ni (at. %) 50

70

60

70 20

860 840 820 780

790 750 620 520

70

50

30

70

90

Al (at. %)

∆ Tx(= Tx–Tg) (K)

80

20

70

30

90

Al

10 10

20

30

40 50 60 Zr (at. %)

70

80

90

Zr

Fig. 3.1-94 Dependence of crystallization temperature Tx

Fig. 3.1-96 Dependence of ∆Tx on composition in amor-

on composition in amorphous Zr−Al−Ni alloys [1.72]

phous Zr−Al−Ni alloys [1.72] Cu

Exothermic (arb. units) 40 K/min Tx

5

Zr55Al20Ni25

20

Tx (K)

740

4.23 kJ / mol Tg

Co (at. %) 10

Tx

Zr55Al15Ni30

730

15

Cu (at. %)

710

2.80 kJ / mol 15

Tg

700

10

Tx Zr55Al10Ni35

20

∆Hx = 2.44 kJ / mol

710

Tg Co 650

750

5

850

T (K)

Fig. 3.1-95 Dependence of ∆Tx on composition as de-

termined by differential thermal analysis of amorphous Zr−Al−Ni alloys [1.72] Table 3.1-38 Zr-based alloy systems exhibiting bulk glassy

behavior Alloy system

Reference

Zr–Al–TM Zr–Al–Ni–Cu–(Ti, Nb, Pd) Zr–Al–Co Zr–Ti–Ni–Cu–(Be) Zr–Cu–Ni–(Al, Ti, Ta)

[1.72] [1.72] [1.74] [1.75] [1.76]

5

10 15 Ni (at. %)

20

Ni

Fig. 3.1-97 Dependence of Tx on composition in amorphous Zr65 Al7.5 Cu2.5 (Co1−x−y Nix Cu y )25 alloys [1.72]

lations are based on systematic investigations of the effects of individual alloying elements on the characteristic properties Tg , Tx , and ∆Tx , as shown in Fig. 3.1-98 for a characteristic example. There are no tabulated data of the properties of Zrbased bulk glassy alloys available yet. A typical set of data is given in Table 3.1-39 [1.75].

Metals

1.5 Iron and Steels

E (GPa)

G (GPa)

ν

Elastic strain limit %

Rp0.2 (GPa)

HV

 g/cm3

Rp0.2 / (GPa cm3 g −1 )

Aae (%)

Abc (%)

K 1c (MN m1/2 )

90±1

33±1

0.354

2.0–2.2

1.9±0.05

590

5.9

0.32

∼1

1–20

20–40

a

Plastic strain to failure in tension b Plastic strain to failure in compression

Fig. 3.1-98 Variation of Tg , Tx , and ∆Tx with M content

Tg, Tx (K)

for melt-spun Zr65 Al10 Cu15 Ni10−x Mx (M = Fe, Co, Pd, Ag) amorphous alloys

Zr65Al10Cu15Ni10–xMx 750 Tx 700 Tg 650 0 ∆Tx(=Tx–Tg) (K)

5

10 M content x (at. %)

5

10 M content x (at. %)

100

M = Fe M = Co M = Pd M =Ag

50 0

3.1.5 Iron and Steels Iron is technically the most versatile and economically the most important base metal for a great variety of structural and magnetic materials, most of which are called steels. With increasing temperature, iron undergoes two structural phase transitions, α (bcc) ↔ γ (fcc) at 911 ◦ C and γ (fcc) ↔ δ (bcc) at 1392 ◦ C, and a magnetic phase transition, αferromagnetic ↔ αparamagnetic at 769 ◦ C, at ambient pressure. At elevated pressure levels, Fe forms a third structural phase ε (hcp). These phase

transitions, their variation upon alloying, and the concomitant phase transformations are the thermodynamic, structural and microstructural basis for the unique variety of iron-based alloys and of their properties [1.52, 77–80]. The wide variety of standards for steels which have developed from national standards and efforts of international standardization are compiled in [1.81]. In the present section we are using different standard designations as provided by the sources used. In the following sections, the SAE (Society of Automotive Engineers), AISI (American Iron and Steel Institute), and UNS (Unified Numbering System) designations are the dominating ones.

Part 3 1.5

Table 3.1-39 Properties of amorphous Zr41.2 Ti13.8 Cu12.5 Ni10 Be22.5

221

222

Part 3

Classes of Materials

Part 3 1.5

3.1.5.1 Phase Relations and Phase Transformations Iron–Carbon Alloys The most frequent alloying element of iron is carbon. The Fe−C phase diagram (Fig. 3.1-99) shows the important metastable phase equilibria involving the metastable carbide Fe3 C, called cementite, in dashed lines, whereas the stable equlibria with graphite C are shown in solid lines. The formation of Fe3 C predominates in most carbon and low-alloy steels because the activation energy of its nucleation is considerably lower than that of graphite. At higher carbon contents (2.5–4.0 wt% C) and in the presence of Si (1.0–3.0 wt% Si), graphite formation is favored. This is the basis of alloying and microstructure of gray cast iron (see Sect. 3.1.5.7). The Fe−C phase forms interstitial solid solutions of α- and γ -Fe. The solid solution phase of α-Fe is called ferrite, the solid solution phase based on γ -Fe is called austenite in the binary Fe−C system. These T (K)

1

2

terms for the solid solutions phases of α- and γ -Fe are applied to all other Fe-based alloy systems as well. Since phase transformations induced by cooling from the austenite phase field play a major role to induce particular microstructures and properties, some resulting microstructures have also been given particular terms and form the basis of the nomenclature in steels. Cooling of Fe−C alloys from the austenite phase field can lead to three different phase transformations below the eutectoid temperature of 1009 K (736 ◦ C). Their kinetics of formation depends on composition and cooling rate. The transformation products are:

•

Pearlite, a lamellar product of ferrite and cementite. It is formed by a discontinuous (pearlitic) transformation, i. e., both phases are formed side by side in the reaction front. The lamellar spacing decreases with decreasing temperature of formation. The maximum rate of formation occurs at about 500 ◦ C.

3

4

1700

7

C(wt %) Fe–C

Stable Metastable Curie temperature

1809 K 1766 K

1800

6

5

1900

2.43 δ 1665 K

L + (C)

Fe3C

1600 1525 K 1500

γ

9.06

1400

1426 K 1420 K 17.1 17.3

9.23

1300 1184 K

1200

1043 K

1100

1009 K

1000

α

3.12 3.43

1000 K

900 800

Fe

2

4

6

8

10

12

14

16

18

20

22

24

26 28 C(at. %)

Fig. 3.1-99 Fe−C phase diagram. Metastable equilibria involving cementite Fe3 C are shown in dashed lines, stable

equilibria with graphite C are shown in solid lines [1.82] (dotted lines – Curie temperature)

Metals

•

Bainite, a plate- or spearhead-shaped product consisting of a ferrite matrix in which carbide particles are dispersed. The bainitic transformation mechanism depends sensitively on alloy composition and the temperature of transformation, yielding essentially two microstructural variants. A somewhat coarser transformation product formed at about 450 ◦ C is called upper bainite and a finer transformation product formed at about 350 ◦ C is termed lower bainite. Martensite, a plate-shaped product formed by a diffusionless, athermal transformation. Thermodynamically it is a metastable ferrite, designated as α and supersatured in carbon. But by the displacive mechanism of the transformation, the distribution of the C atoms in the martensite lattice is anisotropic such that is has a body-centered tetragonal crystal structure and its c and a parameters vary with the C content accordingly (Fig. 3.1-100). The temperature below which martensite begins to form upon queching is termed martensite start temperature Ms and depends strongly on the C concentration (Fig. 3.1-101). Mf designates the temperature at which the transformation is complete. In order to promote the diffusionless martensitic transformation, the diffusion-dependent transformations to pearlite and bainite have to be suppressed by rapid cooling, usually termed quenching.

Since martensite formation is used as a main hardening mechanism in steels, the hardenability is a main concern of alloy design and consequence of alloy composition. The lower the rate of formation of the

Transformation temperature (°C) 600 Ms 400 Mf 200 0

•

• •

0.290 a 0.280 Fe

2

4

6

8 C (at.%)

Fig. 3.1-100 Lattice parameters of Fe−C martensite as

a function of composition [1.82]

1.2 1.6 C content (wt %)

diffusion-dependent transformations, the higher is the fraction of martensite formed upon cooling from the austenite range, i. e., the hardenability (see Sect. 3.1.5.2). The rates of pearlite and bainite formation are reduced by alloying with carbon and all substitutional alloying elements except by Co. But the decrease of Ms with increasing alloy content has, also, to be taken into account. Subsequent heat treatment of the phases formed is termed annealing with regard to ferrite and bainite, and tempering with regard to martensite. These heat treatments play a major role in optimizing the microstructure to obtain specific properties. Upon subsequent heat treatment the transformation products listed above undergo the following reactions:

c 0.300

0.8

site transformation temperatures. Ms – martensite start; Mf – martensite finish, i. e., austenite is transformed completely

a, c (nm) Fe–C

0.4

Fig. 3.1-101 Concentration dependence of the marten-

0.310 Martensite T = 298 K

0

223

Part 3 1.5

•

1.5 Iron and Steels

Pearlite is coarsened by the transition of the cementite lamellae into spherical particles, thus reducing the interfacial free energy per unit volume. The process is called spheroidization and consequently the resulting microstructural constituent is termed spheroidite. Bainite is coarsened as well both by recovery of the ferrite plates and by coarsening of the carbide particles. Martensite is essentially transformed into bcc ferrite by the precipitation of carbide particles during tempering. The tempering treatment usually leads to the precipitation of metastable carbides from the martensite phase. Different metastable carbides may be formed depending on alloy composition (including substitutional alloying elements), temperature, and time of annealing. A compilation of all metastable carbides occurring in Fe−C(−X) alloys is given in Table 3.1-40.

224

Part 3

Classes of Materials

Part 3 1.5

Table 3.1-40 Metastable and stable carbide phases occurring in the Fe−C(−X) alloy system [1.82] Phase

Structure

Fe4 C Fe3 C ε-Fe3 C Fe2−3 C Fe5 C2

cub orth hex hex mon

Fe7 C3 Fe20 C9

hex orth

Type Fe3 C

Mn5 C2 Th7 Fe3

Heat Treatments The heat treatments referred to above need to be specified rather succinctly such that they can be correlated with the ensuing microstructures and properties. Furthermore, the specifications of heat treatments require taking the cross section and form of the part to be heat treated into account (at least if the cross sections get larger than, say, 0.5 mm). The finite thermal conductivity and the heat capacity of the material will cause any temperature change applied to the surface to occur at a decreasing rate with increasing depth in the heat-treated part. Thus, not only the time and temperature of an isothermal treatment but also the rate of cooling or the rate of heating are common parameters to be specified. Beyond those referred to above, the following treatments are widely applied to steels: Austenitizing. Heating to and holding in the range of

the austenite phase is commonly the first stage of transformation heat treatments. The higher the austenitizing temperature, the more lattice defects such as dislocations and grain boundaries are annihilated. This lowers the rate of nucleation of subsequent phase transformations. Soft Annealing. This term is used for heat treatment

of hardenable steels containing ≥ 0.4 wt% C at temperatures closely below the eutectoid temperature for a duration of ≤ 100 h. It results in a microstructure of coarse grained, ductile ferrite, and coarsened cementite.

a (nm) 0.3878 0.50889 0.273 0.4767 1.1563 0.6882 0.9061

b (nm)

c (nm)

0.67433

0.452353 0.433 0.4354 0.5058

0.4573 β = 97.73◦ 1.5695

0.4540 0.7937

a fairly fine-grained austenite and ferrite structure in the hypo-eutectoid and in a fine-grained austenite with coagulated grain boundary cementite in the hyper-eutectoid compositions. Upon cooling, the austenite transforms into pearlite and this microstructural state has a favorable combination of strength, ductility, and machinability. Substitutional Iron-Based Alloys For the phase diagrams with substitutional alloying components shown in later sections, a major aspect pertaining to both the binary alloys shown and the steels alloyed with these components is whether the α or the γ phase of Fe is stabilized. i. e., which phase field is expanded or contracted upon alloying. Fe−Ni. Figure 3.1-102 shows the Fe−Ni phase equilibria indicating that Ni stabilizes the fcc γ phase. If Fe-rich alloys are quenched from the γ phase field they transform martensitically to bcc α martensite. The transformation temperatures are shown in Fig. 3.1-103. The Fe−Ni phase diagram is particularly relevant for the controlled thermal expansion and constant-modulus alloys as well as for the soft magnetic Fe−Ni based materials at higher Ni contents. These, in turn, derive their magnetic properties in part from the occurrence of the superlattice phase FeNi3 . Nickel is added to Fe−C alloys to increase the hardenability and to increase the yield strength of ferrite by solid solution hardening. Fe−Mn. Figure 3.1-104 shows the Fe−Mn phase equi-

Normalizing. This heat treatment is applied to obtain

a uniform, fine-grained microstructure. The first step consists of heating the metal rapidly to, and holding it at a temperature 30–50 K above the (α + γ)/γ phase boundary (also referred to as the Ac3 line) for hypoeutectoid steels, and heating rapidly to and holding at about 50 K above the eutectoid temperature (also referred to as Ac1 line). This step results in the formation of

libria indicating that Mn is stabilizing the fcc γ phase similar to Ni. It should be noted that quenching Ferich alloys from the γ -phase field leads to two different martensitic transformations which may result in a bcc structure (α martensite) or an hcp structure (ε martensite). The transformation temperatures are shown in Fig. 3.1-105. The martensitic transformation can also be induced by deformation. This property is exploited

Metals

1.5 Iron and Steels

20

30

40

50

60

70

80

90

1300 Fe– Ni 1195 K

1200

1043 K 1100 (γ – Fe, Ni) 1000 TC TC

900

790 K

800 ( α –Fe) 700

FeNi3

620 K 600

4.7

49

627 K

63

500 400 Fe

10

20

30

40

50

60

70

80

90

Ni (at. %)

Fig. 3.1-102 Fe−Ni phase diagram. TC – Curie temperature [1.82] T(K) 1400 1200

Ni (wt %) 10

20

30 (γ – Fe, Ni)

1185 K

T (K) 2000

Fe – Ni

10

20

50

60

70

Mn (wt %) 90 Fe– Mn

1519 K (δ – Mn)

(δ – Fe) 1667 K

1400 800

1200

1416 K 1352 K

(γ – Fe, γ – Mn)

1185 K

(β – Mn)

Af

(α – Fe)

1000 As

Martensite 400

Ms 20

983 K 800 (α – Mn)

(α – Fe)

Mf 10

80

1811 K

1600

200 Fe

40

1800

1000

600

30

600 30

40 Ni (at. %)

400 Fe

10

20

30

40

50

60

Fig. 3.1-103 Martensitic transformation temperatures of

Fe-rich Fe−Ni alloys. The reverse transformation is characterized by the As (austenite start) and Af (austenite finish) temperatures [1.82]

Fig. 3.1-104 Fe−Mn phase diagram [1.82]

70

80

90 Mn (at. %)

Part 3 1.5

Ni (wt %) 10

225

226

Part 3

Classes of Materials

Part 3 1.5

1200

T (K)

T (K) Fe – M n

1000

10

2400

20

30

40

50

60

70

Fe–Cr

α'→ γ

L

Af

2000

As

1800

Ms

600

ε→ γ

γ→α'

400

Af ε→ γ As

Mf

(Cr,α – Fe)

1789 K 1667 K

1600

(Cr Fe) (Cr, γ – Fe)

1400

1185 K

1200

200

1105 K

ε→α'

Ms

γ→ ε

Ms 0 Fe

1811 K

α'→ γ

γ→α'

4

8

12

16

20

Fe (wt %) 90

2136 K

2200

800

80

24

28 32 Mn (at. %)

Fig. 3.1-105 Martensitic transformation temperatures of

Fe-rich Fe−Mn alloys. The superscripts indicate the transforming phases [1.82]

in the design of wear-resistant steels (Hatfield steel: 12 wt% Mn, 1 wt% C). Manganese is contained in practically all commercial steels because it is used for deoxidation of the melt. Typical contents are 0.3–0.9 wt% Mn. Manganese increases the hardenability of steels and contributes moderately to the yield strength by solid solution hardening. Fe−Cr. The Fe−Cr phase diagram, Fig. 3.1-106, is the prototype of the case of an iron-based system with an α-phase stabilizing component. Chromium is the most important alloying element of corrosion resistant, ferritic stainless steels and ferritic heat-resistant steels. If α-Fe−Cr alloys are quenched from above 1105 K and subsequently annealed, they decompose according to a metastable miscibility gap shown in Fig. 3.1-107. This decomposition reaction can cause severe embrittlement which is called “475 ◦ C-embrittlement” in ferritic chromium steels. Embrittlement can also occur upon formation of the σ phase. In carbon steels, Cr is added to increase corrosion and oxidation resistance because it promotes the formation of stable passivating and protective oxide layers. Moreover, Cr is a strong carbide former which modifies and delays the formation of pearlite and bainite, thus increasing the hardenability. In heat-resistant steels Cr contributes to the high-temperature yield strength.

TC

1000

1043 K

σ

800 600 Cr

10

20

30

40

50

60

70

80

90 Fe (at. %)

Fig. 3.1-106 Fe−Cr phase diagram [1.82] T (K) 10

1100

20

30

40

50

60

70

80

Fe (wt %) 90 Cr– Fe

1000

TC = 950 K

(Cr,α – Fe)

900 Two solid phases 800 700

Cr

10

20

30

40

50

60

70

80

90 Fe (at. %)

Fig. 3.1-107 Metastable miscibility gap in the Fe−Cr alloy

system [1.82] Fe−Si. The phase diagram Fe−Si, Fig. 3.1-108, shows that Si is a strong ferrite former. The main application of binary Fe−Si alloys is in the form of steels with ≤ 3.5 wt% Si which have an optimum combination of high magnetic moment, low magnetostriction, and low magnetocrystalline anisotropy such that they are the ideal material for high induction and low magnetic power loss applications such as power transformers. Data are given in Sect. 4.3.2.3. In Fe−C steelmaking, Si is one of the principal deoxidizers. It may amount to 0.05–0.3 wt% Si in the steel depending on the deoxidizing treatment and the amount of other deoxidants used. At these levels of concentration Si contributes only moderately to the strength of ferrite and causes no significant loss of ductility.

Metals

5

10

20

30

40

50

60

70

80

Si (wt %) 90 Fe– Si

1900

1811 K

1800 1700

1687 K

1683 K

1667 K

1600 1500

1485 K

(γ –Fe)

1400

α2 (α –Fe) 1185 K

1100

1043 K

1000

α1

1480 K ( β – Fe Si2)

1333 K

1300 1200

1493 K

1485 K

1476 K (Fe2 Si)

1255 K

1238 K

1201 K

Fe5 Si3 70.5

1098 K

α – FeSi2

TC

(FeSi)

(Si)

1900 TC

800 700

Fe

10

20

30

40

50

60

70

80

90

Si Si (at. %)

Fig. 3.1-108 Fe−Si phase diagram [1.82]

3.1.5.2 Carbon and Low-Alloy Steels The largest group of steels produced both by number of variants and by volume is that of carbon and lowalloy steels. It is characterized by the fact that most of the phase relations and phase transformations may be referred to the binary Fe−C phase diagram or comparatively small deviations from it. These steels are treated extensively in [1.80]. Compositions and Properties of Carbon Steels According to the effect of carbon concentration on the phases formed and on their properties, Fig. 3.1-109 shows the variation of the effective average mechanical properties of as-rolled 25-mm bars of plain carbon steels as an approximate survey of the typical concentration dependence. Carbon steels are defined as containing up to 1 wt% C and a total of 2 wt% alloying elements. Apart from the deoxidizing alloying elements Mn and Si, two impurity elements are always present in carbon steels: phosphorous and sulfur. Phosphorus increases strength

and hardness significantly by solid solution hardening, but severely decreases ductility and toughness. Only in exceptional cases may P be added deliberately to increase machinability and corrosion resistance. Sulfur has essentially no effect on the strength properties since it is practically insoluble in ferrite. However, it decreases the ductility and fracture toughness. But S is added deliberately along with an increased Mn content to promote the formation of MnS. This compound is formed in small particles which are comparatively soft and serve as effective chip breakers in free-cutting steel grades, thus increasing machinability. On the basis of these effects of the most common alloying and impurity elements, carbon steel compositions are specified as listed in Table 3.1-41 and free-cutting carbon steel compositions are specified as listed in Table 3.1-42. A survey of the alloying elements used and of the ranges of composition applied in carbon and lowalloy steels may be gained from the SAE–AISI system of designations for carbon and alloy steels listed in Table 3.1-43. Extensive cross references to other standards may be found in [1.81].

227

Part 3 1.5

T (K) 1 2000

1.5 Iron and Steels

228

Part 3

Classes of Materials

Part 3 1.5

Table 3.1-41 Standard carbon steel compositions applicable to semi-finished products for forging, hot-rolled and cold-finished

bars, wire rods, and seamless tubing [1.80]. Selected grades Designation UN number

SAE-AISI number

G10050 G10100 G10200 G10300 G10400 G10500 G10600 G10700 G10800 G10900

1005 1010 1020 1030 1040 1050 1060 1070 1080 1090

a

Cast or heat chemical ranges and limits a (wt%) C Mn

Pmax

S max

0.06 max 0.08–0.13 0.18–0.23 0.28–0.34 0.37–0.44 0.48–0.55 0.55–0.65 0.65–0.75 0.75–0.88 0.85–0.98

0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040

0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050

0.35 max 0.30–0.60 0.30–0.60 0.60–0.90 0.60–0.90 0.60–0.90 0.60–0.90 0.60–0.90 0.60–0.90 0.60–0.90

When silicon ranges or limits are required for bar and semifinished products, the following ranges are commonly used: 0.10% max; 0.10 to 0.20%; 0.15 to 0.35%; 0.20 to 0.40%; or 0.30 to 0.60%. For rods the following ranges are commonly used: 0.10 max; 0.07–0.15%; 0.10–0.20%; 0.15–0.35%; 0.20–0.40%; and 0.30–0.60%. Steels listed in this table can be produced with additions of leaf or boron. Leaded steels typically contain 0.15–0.40% Pb and are identified by inserting the letter L in the desingnation (10L45); boron steels can be expected to contain 0.0005–0.003% B and are identified by inserting the letter B in the desingnation (10B46)

Brinell hardness (HB)

Impact Impact value (ft lbf) value (J) 70 50

340

Brinell hardness

50

Tensile 260 and yield strength180 (MPa) 1200

60

40

Charpy impact

100

30

40

20

30

10 1000

20 10

Tensile strength

800

Yield strength

600 400 200

0 0 100 Tensile and yield 60 strength (ksi) 20

0

Elong- 80 ation and re- 60 duction of area 40 (%)

Reduction of area

20 0

Elongation in 2 in. 0

0.2

0.4

0.6

0.8

1.0 1.2 1.4 Carbon content (%)

Fig. 3.1-109 Variations in average mechanical properties of as-

rolled 25-mm-diam. bars of plain carbon steels as a function of carbon content [1.80]

1.5 Iron and Steels

229

Table 3.1-42 Standard free-cutting (re-sulfurized) carbon steel compositions applicable to semi-finished products for forging,

Part 3 1.5

Metals

hot-rolled and cold-finished bars, and seamless tubing [1.80] Designation UN number

SAE-AISI number

G11080 G11100 G11170 G11180 G11370 G11390 G11400 G11410 G11440 G11460 G11510

1108 1110 1117 1118 1137 1139 1140 1141 1144 1146 1151

a

Cast or heat chemical ranges and limits a (wt%) C Mn

Pmax

S

0.08–0.13 0.08–0.13 0.14–0.20 0.14–0.20 0.32–0.39 0.35–0.43 0.37–0.44 0.37–0.45 0.40–0.48 0.42–0.49 0.48–0.55

0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040

0.08–0.13 0.08–0.13 0.08–0.13 0.08–0.13 0.08–0.13 0.13–0.20 0.08–0.13 0.08–0.13 0.24–0.33 0.08–0.13 0.08–0.13

0.85–0.98 0.30–0.60 1.00–1.30 1.30–1.60 1.35–1.65 1.35–1.65 0.70–1.00 1.35–1.65 1.35–1.65 0.70–1.00 0.70–1.00

When lead ranges or limits are required or when silicon or limits are required for bars or semifinished products, the values in Table 5 apply. For rods, the following ranges and limits for silicon are commonly used: up to SAE 1110 inclusive, 0.10% max; SAE 1117 and over, 0.10%, 0.10–0.20%, or 0.15–0.35%

Table 3.1-43 SAE–AISI system of designations for carbon and low-alloy steels [1.80] Numerals and digits

Type of steel and nominal alloy content (wt%)

Carbon steels 10xxa 11xx 12xx 15xx Manganese steels

Plain carbon (Mn 100 max) Resulfurized Resulfurized and rephosphorized Plain carbon (max Mn range: 1.00–1.65)

13xx Nickel steels

Mn 1.75

23xx 25xx Nickel–chromium steels 31xx 32xx 33xx 34xx Molybdenum steels

Ni 3.50 Ni 5.00 Ni 1.25; Cr 0.65 and 0.80 Ni 1.75; Cr 1.07 Ni 3.50; Cr 1.50 and 1.57 Ni 3.00; Cr 0.77

40xx Mo 0.20 and 0.25 44xx Mo 0.40 and 0.52 Chromium–molybdenum steels 41xx Cr 0.50, 0.80, and 0.95; Mo 0.12, 0.20, 0.25, and 0.30 Nickel–chromium–molybdenum steels 43xx 43BVxx 47xx 81xx 86xx

Ni 1.82; Cr 0.50 and 0.80; Mo 0.25 Ni 1.82; Cr 0.50; Mo 0.12 and 0.25; V 0.03 min Ni 1.05; Cr 0.45; Mo 0.20 and 0.35 Ni 0.30; Cr 0.40; Mo 0.12 Ni 0.55; Cr 0.50; Mo 0.20

230

Part 3

Part 3 1.5

Table 3.1-43 SAE–AISI system of designations for carbon and low-alloy steels [1.80] , cont.

Classes of Materials

Numerals and digits

Type of steel and nominal alloy content (wt%)

87xx 88xx 93xx 94xx 97xx 98xx Nickel–molybdenum steels

Ni 0.55; Cr 0.50; Mo 0.25 Ni 0.55; Cr 0.50; Mo 0.35 Ni 3.25; Cr 1.20; Mo 0.12 Ni 0.45; Cr 0.40; Mo 0.12 Ni 0.55; Cr 0.20; Mo 0.20 Ni 1.00; Cr 0.80; Mo 0.25

46xx 48xx Chromium steels

Ni 0.85 and 1.82; Mo 0.20 and 0.25 Ni 3.50; Mo 0.25

50xx 51xx 50xxx 51xxx 52xxx Chromium–vanadium steels

Cr 0.27, 0.40, 0.50, and 0.65 Cr 0.80, 0.87, 0.92, 0.95, 1.00, and 1.05 Cr 0.50; C 1.00 min Cr 1.02; C 1.00 min Cr 1.45; C 1.00 min

61xx Cr 0.60, 0.80, and 0.95; V 0.10 and 0.15 min Tungsten–chromium steels 72xx Silicon–manganese steels

W 1.75; Cr 0.75

92xx Boron steels

Si 1.40 and 2.00; Mn 0.65, 0.82, and 0.85; Cr 0 and 0.65

xxBxx Leaded steels

B denotes boron steel

xxLxx Vanadium steels

L denotes leaded steel

xxVxx

V denotes vanadium steel

a

The xx in the last two digits of these designations indicates that the carbon content (in hundredths of a weight percent) is to be inserted

Turning to the mechanical properties, it should be emphasized that the microstructure has a decisive influence on the properties of all steels. Therefore the composition and the prior thermal, mechanical, or thermomechanical treatments which determine the phase transformations and ensuing microstructural state of a steel will always have to be taken into account. Accordingly, tabulated property data will invariably be given with reference to mechanical and thermal treatments applied. The terms used and their specific definitions are outlined in Sect. 3.1.5.1. In plain carbon steels the C content and microstructure are determining the mechanical properties. Manganese is providing moderate solid solution

strengthening and increases the hardenability. The properties of plain carbon steels are also affected by the other common residual elements Si, P, and S. Furthermore, the gasses O, N, and H and their reaction products may play a role. Their content depends largely on the melting, deoxidizing and pouring practice. While Fig. 3.1-109 illustrates the general effect of C content on the mechanical properties if the austenite grain size and transformation microstructure are held essentially constant. Tables 3.1-44 and 3.1-45 list the mechanical properties of representative carbon and low alloy steels in specified states as a function of deformation and heat treatment.

Metals

1.5 Iron and Steels

conditions [1.80] AISI

Treatment

Austenitizing temperature (◦ C)

Tensile strength (MPa)

Yield strength (MPa)

Elongation

As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed As-rolled Normalized Annealed Normalized Annealed Normalized Annealed

– 925 870 – 870 870 – 925 870 – 925 845 – 900 790 – 900 790 – 900 790 – 900 790 – 900 790 – 900 855 – 925 790 – 900 790 – 900 815 – 900 790 870 800 870 815

420.6 424.0 386.1 448.2 441.3 394.7 503.3 482.6 429.2 551.6 520.6 463.7 620.5 589.5 518.8 723.9 748.1 636.0 813.6 775.7 625.7 965.3 1010.1 615.4 965.3 1013.5 656.7 486.8 467.1 429.5 521.2 477.8 450.2 627.4 668.8 584.7 675.7 706.7 598.5 703.3 667.4 584.7 836.3 703.3 891.5 689.5

313.7 324.1 284.4 330.9 346.5 294.8 358.5 358.5 317.2 344.7 344.7 341.3 413.7 374.0 353.4 413.7 427.5 365.4 482.6 420.6 372.3 586.1 524.0 375.8 572.3 499.9 379.2 305.4 303.4 279.2 316.5 319.2 284.8 379.2 396.4 344.7 358.5 405.4 353.0 420.6 399.9 346.8 558.5 436.4 599.8 422.6

No.a 1015

1020

1022

1030

1040

1050

1060

1080

1095

1117

1118

1137

1141

1144

1340 3140

Hardness

(%)

Reduction in area (%)

39.0 37.0 37.0 36.0 35.8 36.5 35.0 34.0 35.0 32.0 32.0 31.2 25.0 28.0 30.2 20.0 20.0 23.7 17.0 18.0 22.5 12.0 11.0 24.7 9.0 9.5 13.0 33.0 33.5 32.8 32.0 33.5 34.5 28.0 22.5 26.8 22.0 22.7 25.5 21.0 21.0 24.8 22.0 25.5 19.7 24.5

61.0 69.6 69.7 59.0 67.9 66.0 67.0 67.5 63.6 57.0 60.8 57.9 50.0 54.9 57.2 40.0 39.4 39.9 34.0 37.2 38.2 17.0 20.6 45.0 18.0 13.5 20.6 63.0 63.8 58.0 70.0 65.9 66.8 61.0 48.5 53.9 38.0 55.5 49.3 41.0 40.4 41.3 62.9 57.3 57.3 50.8

126 121 111 143 131 111 149 143 137 179 149 126 201 170 149 229 217 187 241 229 179 293 293 174 293 293 192 143 137 121 149 143 131 192 197 174 192 201 163 212 197 167 248 207 262 197

(HB)

Part 3 1.5

Table 3.1-44 Mechanical properties of selected carbon and low-alloy steels in the hot-rolled, normalized, and annealed

231

232

Part 3

Classes of Materials

Part 3 1.5

Table 3.1-44 Mechanical properties of selected carbon and low-alloy steels [1.80], cont. AISI

Treatment

No. a

Austenitizing temperature (◦ C)

Tensile strength (MPa)

Yield strength (MPa)

Elongation

Hardness

(%)

Reduction in area (%)

(HB)

4130

Normalized Annealed

870 865

668.8 560.5

436.4 360.6

25.5 28.2

59.5 55.6

197 156

4140

Normalized Annealed

870 815

1020.4 655.0

655.0 417.1

17.7 25.7

46.8 56.9

302 197

4150

Normalized Annealed

870 815

1154.9 729.5

734.3 379.2

11.7 20.2

30.8 40.2

321 197

4320

Normalized Annealed

895 850

792.9 579.2

464.0 609.5

20.8 29.0

50.7 58.4

235 163

4340

Normalized Annealed

870 810

1279.0 744.6

861.8 472.3

12.2 22.0

36.3 49.9

363 217

4620

Normalized Annealed

900 855

574.3 512.3

366.1 372.3

29.0 31.3

66.7 60.3

174 149

4820

Normalized Annealed

860 815

75.0 681.2

484.7 464.0

24.0 22.3

59.2 58.8

229 197

5140

Normalized Annealed

870 830

792.9 572.3

472.3 293.0

22.7 28.6

59.2 57.3

229 167

5150

Normalized Annealed

870 825

870.8 675.7

529.0 357.1

20.7 22.0

58.7 43.7

255 197

5160

Normalized Annealed

855 815

957.0 722.6

530.9 275.8

17.5 17.2

44.8 30.6

269 197

6150

Normalized Annealed

815 815

722.6 667.4

275.8 412.3

17.2 23.0

30.6 48.4

197 197

8620

Normalized Annealed

915 870

632.9 536.4

357.1 385.4

26.3 31.3

59.7 62.1

183 149

8630

Normalized Annealed

870 845

650.2 564.0

429.5 372.3

23.5 29.0

53.5 58.9

187 156

8650

Normalized Annealed

870 795

1023.9 715.7

688.1 386.1

14.0 22.5

40.4 46.4

302 212

8740

Normalized Annealed

870 815

929.4 695.0

606.7 415.8

16.0 22.2

47.9 46.4

269 201

9255

Normalized Annealed

900 845

932.9 774.3

579.2 486.1

19.7 21.7

43.4 41.1

269 229

9310

Normalized Annealed

890 845

906.7 820.5

570.9 439.9

18.8 17.3

58.1 42.1

269 241

a

All grades are fine-grained except for those in the 1100 series, which are coarse-grained. Heat-treated specimens were oil quenched unless otherwise indicated

Metals

1.5 Iron and Steels

AISI No. a 1030 b

1040 b

1040

1050 b

1050

1060

1080

1095 b

1095

Tempering temperature (◦ C)

Tensile strength (MPa)

Yield strength (MPa)

Elongation

Hardness

(%)

Reduction in area (%)

205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650

848 800 731 669 586 896 889 841 779 669 779 779 758 717 634 1124 1089 1000 862 717 – 979 938 876 738 1103 1103 1076 965 800 1310 1303 1289 1131 889 1489 1462 1372 1138 841 1289 1262 1213 1089 896

648 621 579 517 441 662 648 634 593 496 593 593 552 490 434 807 793 758 655 538 – 724 655 579 469 779 779 765 669 524 979 979 951 807 600 1048 1034 958 758 586 827 813 772 676 552

17 19 23 28 32 16 18 21 23 28 19 20 21 26 29 9 13 19 23 28 – 14 20 23 29 13 13 14 17 23 12 12 13 16 21 10 11 13 15 20 10 10 12 15 21

47 53 60 65 70 45 52 57 61 68 48 53 54 57 65 27 36 48 58 65 – 47 50 53 60 40 40 41 45 54 35 35 36 40 50 31 33 35 40 47 30 30 32 37 47

495 401 302 255 207 514 444 352 269 201 262 255 241 212 192 514 444 375 293 235 – 321 277 262 223 321 321 311 277 229 388 388 375 321 255 601 534 388 293 235 401 375 363 321 269

HB

Part 3 1.5

Table 3.1-45 Mechanical properties of selected carbon and alloy steels in the quenched-and-tempered condition, heat treated as 25 mm rounds [1.80]

233

234

Part 3

Classes of Materials

Part 3 1.5

Table 3.1-45 Mechanical properties of selected carbon and alloy steels, cont. AISI No. a 1137

1137 b

1141

1144

1330 b

1340

4037

4042

4130 b

Tempering temperature (◦ C)

Tensile strength (MPa)

Yield strength (MPa)

Elongation

Hardness

(%)

Reduction in area (%)

205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650

1082 986 876 758 655 1496 1372 1103 827 648 1634 1462 1165 896 710 876 869 848 807 724 1600 1427 1158 876 731 1806 1586 1262 965 800 1027 951 876 793 696 1800 1613 1289 986 793 1627 1496 1282 1034 814

938 841 731 607 483 1165 1124 986 724 531 1213 1282 1034 765 593 627 621 607 572 503 1455 1282 1034 772 572 1593 1420 1151 827 621 758 765 731 655 421 1662 1455 1172 883 689 1462 1379 1193 910 703

5 10 15 24 28 5 9 14 19 25 6 9 12 18 23 17 17 18 20 23 9 9 15 18 23 11 12 14 14 – 6 14 20 23 29 12 13 15 20 28 10 11 13 17 22

22 33 48 62 69 17 25 40 60 69 17 32 47 57 62 36 40 42 46 55 39 44 53 60 63 35 43 51 58 66 38 53 60 63 60 37 42 51 59 66 41 43 49 57 64

352 285 262 229 197 415 375 311 262 187 461 415 331 262 217 277 262 248 235 217 459 402 335 263 216 505 453 375 295 252 310 295 270 247 220 516 455 380 300 238 467 435 380 315 245

(HB)

Metals

1.5 Iron and Steels

AISI No. a 4140

4150

4340

5046

50B46

50B60

5130

5140

5150

Tempering temperature (◦ C)

Tensile strength (MPa)

Yield strength (MPa)

Elongation

Hardness

(%)

Reduction in area (%)

205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650

1772 1551 1248 951 758 1931 1765 1517 1207 958 1875 1724 1469 1172 965 1744 1413 1138 938 786 – 1779 1393 1082 883 – 1882 1510 1124 896 1613 1496 1275 1034 793 1793 1579 1310 1000 758 1944 1737 1448 1124 807

1641 1434 1138 834 655 1724 1593 1379 1103 841 1675 1586 1365 1076 855 1407 1158 931 765 655 – 1620 1248 979 793 – 1772 1386 1000 779 1517 1407 1207 938 689 1641 1448 1172 862 662 1731 1586 1310 1034 814

8 9 13 18 22 10 10 12 15 19 10 10 10 13 19 9 10 13 18 24 – 10 13 17 22 – 8 11 15 19 10 10 12 15 20 9 10 13 17 25 5 6 9 15 20

38 43 49 58 63 39 40 45 52 60 38 40 44 51 60 25 37 50 61 66 – 37 47 51 60 – 32 34 38 50 40 46 51 56 63 38 43 50 58 66 37 40 47 54 60

510 445 370 258 230 530 495 440 370 290 520 486 430 360 280 482 401 336 282 235 560 505 405 322 273 600 525 435 350 290 475 440 379 305 245 490 450 365 280 235 525 475 410 340 270

(HB)

Part 3 1.5

Table 3.1-45 Mechanical properties of selected carbon and alloy steels, cont.

235

236

Part 3

Classes of Materials

Part 3 1.5

Table 3.1-45 Mechanical properties of selected carbon and alloy steels, cont. AISI No. a 5160

51B60

6150

81B45

8630

8640

86B45

8650

8660

Tempering temperature (◦ C)

Tensile strength (MPa)

Yield strength (MPa)

Elongation

Hardness

(%)

Reduction in area (%)

205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650 205 315 425 540 650

2220 1999 1606 1165 896 – – 1634 1207 965 1931 1724 1434 1158 945 2034 1765 1407 1103 896 1641 1482 1276 1034 772 1862 1655 1379 1103 896 1979 1696 1379 1103 903 1937 1724 1448 1172 965 – – 1634 1310 1068

1793 1772 1462 1041 800 – – 1489 1103 869 1689 1572 1331 1069 841 1724 1572 1310 1027 793 1503 1392 1172 896 689 1669 1517 1296 1034 800 1641 1551 1317 1034 876 1675 1551 1324 1055 827 – – 1551 1213 951

4 9 10 12 20 – – 11 15 20 8 8 10 13 17 10 8 11 16 20 9 10 13 17 23 10 10 12 16 20 9 9 11 15 19 10 10 12 15 20 – – 13 17 20

10 30 37 47 56 – – 36 44 47 38 39 43 50 58 33 42 48 53 55 38 42 47 54 63 40 41 45 54 62 31 40 41 49 58 38 40 45 51 58 – – 37 46 53

627 555 461 341 269 600 540 460 355 290 538 483 420 345 282 550 475 405 338 280 465 430 375 310 240 505 460 400 340 280 525 475 395 335 280 525 490 420 340 280 580 535 460 370 315

(HB)

Metals

1.5 Iron and Steels

AISI

Tempering temperature (◦ C)

Tensile strength (MPa)

Yield strength (MPa)

Elongation

8740

205 315 425 540 650

1999 1717 1434 1207 986

1655 1551 1358 1138 903

9255

205 315 425 540 650

2103 1937 1606 1255 993

9260

205 315 425 540 650

94B30

205 315 425 540 650

No. a

a b

Hardness

(%)

Reduction in area (%)

10 11 13 15 20

41 46 50 55 60

578 495 415 363 302

2048 1793 1489 1103 814

1 4 8 15 20

3 10 22 32 42

601 578 477 352 285

– – 1758 1324 979

– – 1503 1131 814

– – 8 12 20

– – 24 30 43

600 540 470 390 295

1724 1600 1344 1000 827

1551 1420 1207 931 724

12 12 13 16 21

46 49 57 65 69

475 445 382 307 250

(HB)

All grades are fine-grained except for those in the 1100 series, which are coarse-grained. Heat-treated specimens were oil quenched unless otherwise indicated Water quenched

Hardenability Hardening of steels is the heat treatment consisting of heating to the range of austenite, cooling in water, oil, or air, and subsequent tempering. The term hardenability refers to the suitability of a steel to be transformed partially or completely from austenite to martensite to a specified depth below the free surface of a workpiece when cooled under specified conditions. This definition reflects that the term hardenability does not only refer to the magnitude of hardness which can be attained for a particular steel, but it relates the extent of hardening achievable to the macroscopic or local cooling rate or isothermal holding time in the transformation range and, thus, to the mechanisms, kinetic phase transformations, and their effects on the mechanical properties. The amount of martensite formed upon cooling is a function of C content and total steel composition. This behavior is due to two decisive factors of influence:

• •

The temperature range of transformation of austenite to martensite depends on the C content, as shown in Fig. 3.1-101 of Sect. 3.1.5.1, and The diffusion-dependent transformations of austenite (to ferrite, pearlite, and bainite) compete with the martensitic transformation such that the volume fraction available for the latter will decrease as the volume transformed by the former increases. This transformation kinetics of the diffusional phase transformations is strongly dependent on alloy composition.

The lower the cooling rate may be while still permitting one to obtain a high fraction of martensite, the higher the hardenability of steel. This can best be tested by varying the cooling rate and analyzing the resulting microstructure and its hardness (and other mechanical properties). The method used most widely is an ingeniously simple testing procedure, the Jominy end-quench test illustrated in Fig. 3.1-110. The mater-

Part 3 1.5

Table 3.1-45 Mechanical properties of selected carbon and alloy steels, cont.

237

238

Part 3

Classes of Materials

Part 3 1.5

Air-cooled end

Hardness (HRC) 70

315 110 55

60 Specimen

50

Waterquenched end

22 11

40

5

30

Water spray

Approximate cooling rate at 705 °C, Ks–1

3

20 10

Nozzle

0 0

10

20 30 40 50 Distance from quenched end (mm)

Fig. 3.1-111 Plot of end-quench hardenability data of an Drain

Water inlet

AISI 8650 steel (0.49 wt% C, 0.98 wt% Mn, 0.29 wt% Si, 0.59 wt% Ni, 0.47 wt% Cr, 0.19 wt% Mo) [1.80]

Fig. 3.1-110 Jominy end-quench apparatus

ial to be tested is normalized and a test bar 100 mm long and 25 mm in diameter is machined. This specimen is austenitized and transferred to the fixture (shown in Fig. 3.1-110) holding it vertically 13 mm above the nozzle through which water is directed against the bottom face of the specimen. While the bottom end is quenched by water, the top end is slowly cooled in air and intermediate cooling rates occur at intermediate positions. After the test, hardness readings and microstructural analyses may be taken along the bar. They can be correlated to the pre-determined approximate cooling rate at a given temperature, as shown for a characteristic example in Fig. 3.1-111. The hardenability of numerous commonly used steels has been characterised quantitatively by extensive investigations of their transformation behavior as a function of temperature and time. These investigations have been carried out in two modes of heat treatment:

•

Quenching from the austenite range to a temperature in the transformation range at which the specimen is held isothermally in a salt or a lead bath for different times, and finally quenched to room temperature to be investigated regarding the transformation products by microstructural and supplementary measurements. The resulting plots of the beginning of formation of the different transforma-

•

tion products (sometimes including the fractional amounts and end of transformation) are termed time-temperature-transformation (TTT) or isothermal transformation (IT) diagrams. An example is shown as Fig. 3.1-112. Cooling from the austenite range through the transformation range at different cooling rates, and investigating the temperature of onset of transformation of the different products for different cooling rates by microstructural and supplementary measurements, e.g., dilatometry. The resulting plot is called a continuous-cooling-transformation (CCT) diagram. An example is shown in Fig. 3.1-113. The critical cooling rate means the lowest rate for which a fully martensitic state can be obtained.

Apart from empirical determinations of these transformation diagrams, methods of prediction based on nucleation theory and phenomenological growth theory using the Johnson–Mehl–Avrami equation have been devised to estimate TTT diagrams [1.83]. The hardenability increases with increasing carbon and metallic alloy element concentration (with the exception of Co). The transformation kinetics and ensuing hardenability properties are documented extensively in compilations of TTT and CCT diagrams such as [1.84].

Metals

T(°C) T(°F) 1600

Hardness (HRC) A1

800

A

1400 As

700

12 F+C

1200

18

A+F

600

24

1000

24

A+F+C

500

28

A

800

37

50 %

M*s

400

44 M *50 M *90

600 300

I – T diagram

400

200

200

100

* Estimated temperature

0 0.1

0

1 min

1

10

1h 103

100

1 day 104

1 week 105

106 Time (s)

Fig. 3.1-112 Time-temperature-transformation (TTT) diagram of a 4130 grade low-alloy steel. A – austenite; F – ferrite; C – cementite; M – Martensite (the suffix indicates the amount of martensite formed in vol.%)

900

T(°C)

T (°F) 1500

800 Ac3 Ac1 700

10 % 50 % 90 %

Start

A F

Finish

P

600

1250

1000 500 B 400

750

Ms

300 500

M 200 104

100 0

0.1

5000

1

2000

1000

500

200

10

100

50

20

100

10

5 2 1 Cooling rate (° C/min)

250

103 Bar diameter (air cooling) (mm)

Fig. 3.1-113 Continuous-cooling-transformation (CCT) diagram for a 4130 grade low-alloy steel. Ac3 and Ac1 signify the temperatures of the γ/(γ + α) and eutectoid reation, respectively. A – austenite, F – ferrite, B – bainite, P – pearlite, M – martensite. The cooling rate is measured at 705 ◦ C. The calculated critical cooling rate is 143 K/s [1.80]

239

Part 3 1.5

900

1.5 Iron and Steels

240

Part 3

Classes of Materials

Part 3 1.5

3.1.5.3 High-Strength Low-Alloy Steels High-strength low-alloy (HSLA) steels are designed to provide higher mechanical property values and/or higher resistance to atmospheric corrosion than conventional low-alloy steels of comparable level of alloy content. Higher yield stress is achieved by adding ≤ 0.1 wt% N, Nb, V, Ti, and/or Zr (micro-alloying) which form carbide or carbonitrite precipitates, and by special, closelycontrolled processing which yields mostly fine-grained microstructures. HSLA steels contain 0.05 to 0.25 wt% C, ≤ 2 wt% Mn and mainly Cr, Ni, Mo, and Cu as further alloying elements. Their yield stress is in the range ≥ 275 MPa. They are primarily hot-rolled into usual wrought product forms and commonly delivered in the as-rolled condition. The particular processing methods of HSLA steels include [1.80]:

•

• •

• •

Controlled rolling of micro-alloyed, precipitation hardening variants to obtain fine equiaxial and/or highly deformed, pancake-shaped austenite grains. During cooling these austenite grains transform into fine ferrite grains, providing an optimum combination of high yield strength and ductility. Accelerated cooling of controlled-rolled steels to enhance the formation of fine ferrite grains. Quenching of steels containing ≤ 0.08 wt% C such that acicular ferrite or low-carbon bainite is formed. This microstructural state provides an excellent combination of high yield strengths of 275 to 690 MPa, ductility, formability, and weldability. Normalizing of V-alloyed steel, thus increasing yield strength and ductility. Intercritical annealing, i. e., annealing in the γ + α phase field to obtain a dual-phase microstructure which, after cooling, consists of martensite islands dispersed in a ferrite matrix. This microstructure exhibits a somewhat lower yield strength but a high rate of work-hardening, providing a better combination of tensile strength, ductility, and formability than conventional HSLA steels.

HSLA steels include numerous standard and proprietary grades designed to provide specific desirable combinations of properties such as strength, ductility, weldability, and atmospheric corrosion resistance. Table 3.1-46 lists characteristic compositions and Table 3.1-47 lists mechanical properties of these characteristic variants.

In view of the multitude of compositional and processing variants of HSLA steels it is useful to have a summarizing overview as provided in Table 3.1-48.

3.1.5.4 Stainless Steels Stainless steels are treated extensively in [1.79]. Compared to carbon or low-alloy steels, they are characterized by an increased resistance against corrosion in aggressive media. The corrosion resistance is achieved basically by an alloy content of at least 11–12 wt% Cr. This content is required to form a dense, pore-free protective surface layer consisting mainly of chromium oxides and hydroxides. The corrosion resistance can be further increased by additional alloying with elements such as Ni, Mo, W, Mn, Si, Cu, Co, Al, or N. Since chromium has a high affinity to carbon, the formation of chromium carbides may reduce the local concentration of Cr in solution and thus deteriorate the corrosion resistance. This can be avoided by

• • •

Low carbon content of the steel. Suitable heat treatment. Bonding of carbon by other elements with higher carbon affinity, such as Ti and Nb, so-called stabilization.

Similar effects can be attained by the formation of chromium nitrides. Thus, in addition to the chemical composition of the steel, its corrosion properties are strongly influenced by its heat treatment condition. Depending on the intended field of application, the corrosion resistance of the steel must often be combined with other useful properties such as high strength or hardness, high temperature strength, good formability, low temperature fracture toughness, weldability or machinability. However, since optimization of one property is generally only possible at the expense of others, the property spectrum of a stainless steel is often the result of a compromise. Consequently, a large number of steel grades has been developed to meet different property requirements. Some steels have been developed just for a single application. The following section gives typical representatives of the various types of stainless steel grades. Depending on alloy composition and cooling conditions from elevated temperature, stainless steels may occur in different types of microstructure: ferritic (bcc), austenitic (fcc), martensitic, or mixtures of two or all three of these phases. The bcc structure is promoted by the ferrite forming elements Cr, Mo, W, Ti, V, Nb, Al, and Si, whereas the fcc structure is promoted by the austenite

Table 3.1-46 Compositional limits of HSLA steel grades according to ASTM standards [1.80] Heat compositional limits (wt%) b Si Cr Ni

Mn

P

S

A 242

Type 1

K11510

0.15

1.00

0.45

0.05

–

–

A 572

Grade 42 Grade 50 Grade 60 Grade 65

– – – –

0.21 0.23 0.26 0.23 c

1.35 c 1.35 c 1.35 c 1.65 c

0.04 0.04 0.04 0.04

0.05 0.05 0.05 0.05

0.30 c 0.30 c 0.30 0.30

– – – –

Grade A Grade B Grade C Grade D

K11430 K12043 K11538 K11552

0.10–0.19 0.20 0.15 0.10–0.20

0.90–1.25 0.75–1.25 0.80–1.35 0.75–1.25

0.04 0.04 0.04 0.04

0.05 0.05 0.05 0.05

0.15–0.30 0.15–0.30 0.15–0.30 0.50–0.90

0.40–0.65 0.40–0.70 0.30–0.50 0.50–0.90

Grade K

–

0.17

0.50–1.20

0.04

0.05

A 606

–

–

0.22

1.25

–

A 607

Grade 45 Grade 50 Grade 55 Grade 60 Grade 65 Grade 70

– – – – – –

0.22 0.23 0.25 0.26 0.26 0.26

1.35 1.35 1.35 1.50 1.50 1.65

0.04 0.04 0.04 0.04 0.04 0.04

A 618

Grade Ia Grade Ib Grade II Grade III

– – K12609 K12700

0.15 0.20 0.22 0.23

1.00 1.35 0.85–1.25 1.35

A 633

Grade A Grade C Grade D Grade E

K01802 K12000 K02003 K12202

0.18 0.20 0.20 0.22

A 656

Type 3

–

Type 7

–

V

Other

–

0.20 min

–

–

– – – –

0.20 min d 0.20 min d 0.20 min d 0.20 min d

– – – –

e

– 0.25–0.50 0.25–0.50 –

0.25–0.40 0.20–0.40 0.20–0.50 0.30

0.02–0.10 0.01–0.10 0.01–0.10 –

0.25–0.50 0.40–0.70 0.40

0.30–0.50

–

– – – 0.04 Nb, 0.05–0.35 Zr 0.10 Mo, 0.005–0.05 Nb

0.05

–

–

–

–

–

–

0.05 0.05 0.05 0.05 0.05 0.05

– – – – – –

– – – – – –

– – – – – –

0.20 min d 0.20 min d 0.20 min d 0.20 min d 0.20 min d 0.20 min d

– – – – – –

e

0.15 0.04 0.04 0.04

0.05 0.05 0.05 0.05

– – 0.30 0.30

– – – –

– – – –

0.20 min 0.20 min f – –

– – 0.02 min 0.02 min

– – – 0.005 Nb min g

1.00–1.35 1.15–1.50 0.70–1.60 c 1.15–1.50

0.04 0.04 0.04 0.04

0.05 0.05 0.05 0.05

0.15–0.30 0.15–0.50 0.15–0.50 0.15–0.50

– – 0.25 –

– – 0.25 –

– – 0.35 –

– – – 0.04–0.11

0.05 Nb 0.05–0.05 Nb 0.08 Mo 0.01–0.05 Nb d , 0.01–0.03 N

0.18

1.65

0.025

0.035

0.60

–

–

–

0.08

0.18

1.65

0.025

0.035

0.60

–

–

–

e e e

e e e e e

0.020 N, 0.005–0.15 Nb 0.005–0.15 0.020 N, 0.005–0.10 Nb

241

Part 3 1.5

A 588

Cu

1.5 Iron and Steels

UNS designation C

Metals

ASTM speci- Type or fication a grade

242

Part 3 1.5

Part 3

ASTM speci- Type or fication a grade

UNS designation C

A 690

–

K12249

0.22 0.60–0.90 0.08–0.15 0.05

A 709

Grade 50, type 1 Grade 50, type 2 Grade 50, type 3 Grade 50, type 4

– – – –

0.23 0.23 0.23 0.23

A 715

–

–

A 808

–

A 812

Mn

P

S

Heat compositional limits (wt%) b Si Cr Ni

Cu

V

Other –

0.10

–

0.40–0.75 0.50 min

–

0.04 0.04 0.04 0.04

0.05 0.05 0.05 0.05

0.40 0.40 0.40 0.40

– – – –

– – – –

– – – –

– 0.005–0.05 Nb 0.01–0.15 – h 0.05 Nb max i 0.015 Nb max

0.15 1.65

0.025

0.035

–

–

–

–

Added as necessary

Ti, Nb added as necessary

–

0.12 1.65

0.04

0.05 max or 0.15–0.50

–

–

–

0.10

0.02–0.10 Nb, V + Nb = 0.15 max

65

–

0.23 1.40

0.035

0.04

0.15–0.50 j –

–

–

80

–

0.23 1.50

0.035

0.04

0.15–0.50

0.35

–

–

V + Nb = 0.05 Nb max 0.02–0.15 V + Nb = 0.05 Nb max 0.02–0.15

A 841

–

–

0.20

0.030

0.030

0.15–0.50

0.25

0.25

0.35

0.06

0.08 Mo, 0.03 Nb, 0.02 Al total

A 871

–

–

0.20 1.50

0.04

0.05

0.90

0.90

1.25

1.00

0.10

0.25 Mo, 0.15 Zr, 0.05 Nb, 0.05 Ti

1.35 1.35 1.35 1.35

0.010 max

a b c d e f g h i j k

k

For characteristics and intended uses, see Table 3.1-48; for mechanical properties, see Table 3.1-47. If a single value is shown, it is a maximum unless otherwise stated. Values may vary, or minimum value may exist, depending on product size and mill form. Optional or when specified May purchased as type 1 (0.005–0.05 Nb), type 2 (0.01–0.15 V), type 3 (0.05 Nb, max, plus 0.02–0.15 V) or type 4 (0.015 N, max, plus V ≥ 4 N). If chromium and silicon are each 0.50% min, the copper minimum does not apply. May be substituted for all or part of V. Niobium plus vanadium, 0.02 to 0.15%. Nitrogen with vanadium content of 0.015% (max) with a minimum vanadium-to-nitrogen ratio of 4:1. When silicon-killed steel is specified. For plate under 40 mm (1.5 in.), manganese contents are 0.70 to 1.35% or up to 1.60% if carbon equivalents do not exceed 0.47%. For plate thicker than 40 mm (1 to 5 in.), ASTM A 841 specifies manganese contents of 1.00 to 1.60%

Classes of Materials

Table 3.1-46 Compositional limits of HSLA steel grades according to ASTM standards [1.80], cont.

Metals

1.5 Iron and Steels

ASTM specification a

Type, grade or condition

A242

Type 1

A572

Grade 42 Grade 50 Grade 60 Grade 65 Grades A–K

A588

Minimum tensile strength c (MPa)

Minimum yield strength c (MPa)

Minimum elongation (%) c in 200 mm in 50 mm

Bend radius c Longitudinal

Transverse

480 460 435

345 315 290

18 18 18

– 21 21

– – –

– – –

150 100 32 32

415 450 520 550

290 345 415 450

20 18 16 15

24 21 18 17

d

– – – –

100 100–125 125–200

485 460 435

345 315 290

18 – –

21 21 21

d

Product thickness b (mm)

20 20–40 40–100

d d d

d d

– – –

A606

Hot rolled Hot rolled and annealed or normalized Cold rolled

sheet sheet

480 450

345 310

– –

22 22

t t

2t − 3t 2t − 3t

sheet

450

310

–

22

t

2t − 3t

A607

Grade 45 Grade 50 Grade 55 Grade 60 Grade 65 Grade 70

sheet sheet sheet sheet sheet sheet

410 450 480 520 550 590

310 345 380 415 450 485

– – – – – –

22–25 20–22 18–20 16–18 15–16 14

t t 1.5t 2t 2.5t 3t

1.5t 1.5t 2t 3t 3.5t 4t

A618

Ia, Ib, II Ia, Ib, II, III

485 460

345 315

19 18

22 22

t − 2t t − 2t

– –

A633

A C, D C, D E E

430–570 485–620 450–590 550–690 515–655

290 345 315 415 380

18 18 18 18 18

23 23 23 23 23

d

– – – – –

19 19–38 100 65 65–100 100 100–150

d d d d

50 60 70 80

50 40 25 20

415 485 550 620

345 415 485 550

20 17 14 12

– – – –

d

A690

–

100

485

345

18

–

2t

–

A709

50 50W

100 100

450 450

345 345

18 18

21 21

– –

– –

A715

Grade 50 Grade 60 Grade 70 Grade 80

sheet sheet sheet sheet

415 485 550 620

345 415 485 550

– – – –

22–24 20–22 18–20 16–18

0 0 t t

t t 1.5t 1.5t

A808

–

450 450 415

345 315 290

18 18 18

22 22 22

– – –

– – –

A656

40 40–50 50–65

d d d

– – – –

Part 3 1.5

Table 3.1-47 Tensile properties of HSLA steel grades specified in ASTM standards [1.80]

243

244

Part 3

Part 3 1.5

Table 3.1-47 Tensile properties of HSLA steel grades specified in ASTM standards [1.80], cont.

Classes of Materials

ASTM specification a

Type, grade or condition

Product thickness b (mm)

Minimum tensile strength c (MPa)

Minimum yield strength c (MPa)

Minimum elongation (%) c in 200 mm in 50 mm

Bend radius c Longitudinal

Transverse

A812

65 80 –

sheet sheet 65 65–100 5–35 5–20

585 690 485–620 450–585 520 550

450 550 345 310 415 450

– – 18 18 16 15

– – – – – –

– – – – – –

A841 A871 a b c d

60, as-hot-rolled 65, as-hot-rolled

13–15 11–13 22 22 18 17

For characteristics and intended uses, see Table 3.1-48; for specified composition limits, see Table 3.1-46 Maximum product thickness exept when a range is given. No thickness are specified for sheet products. May vary with product size and mill form Optional supplementary requierement given in ASTM A6

Table 3.1-48 Summary of characteristics and uses of HSLA steels according to ASTM standards [1.80] ASTM specification a

Title

Alloying elements b

Avalible mill forms

Special characteristics

Intended uses

A 242

High-strength low-alloy structural steel

Plate, bar, and shapes ≤ 100 mm in thickness

A 572

High-strength low-alloy niobium-vanadium steels of structural quality

Cr, Cu, N, Ni, Si, Ti, V, Zr Nb, V, N

Atmospheric-corrosion resistance four times of carbon steel Yield strength of 290 to 450 MPa in six grades

A 588

High-strength low-alloy structural steel with 345 MPa minimum yield point ≤ 100 mm in thickness

Nb, V, Cr, Ni, Mo, Cu, Si, Ti, Zr

Plate, bar, and shapes ≤ 200 mm in thickness

Atmospheric-corrosion resistance four times of carbon steel; nine grades of similar stregth

A 606

Steel sheet and strip hot-rolled steel and cold-rolled, high-strength low-alloy with improved corrosion resistance Steel sheet and strip hot-rolled steel and cold-rolled, high-strength low-alloy niobium and/or vanadium

Not specified

Hot-rolled and cold-rolled sheet and strip

Nb, V, N, Cu

Hot-rolled and cold-rolled sheet and strip

Hot formed welded and seamless high-strength low-alloy structural tubing

Nb, V, Si, Cu

Square, rectangular round and specialshape structural welded or seamless tubing

Atmospheric-corrosion twice that of carbon steel (type 2) or four times of carbon steel (type 4) Atmospheric-corrosion twice that of carbon steel, but only when copper content is specified; yield strength of 310 to 485 MPa in six grades Three grades of similar yield strength; may be purchased with atmospheric-corrosion resistance twice that of carbon steel

Structural members in welded, bolted, or riveted construction Welded, bolted, or riveted structures, but many bolted or riveted bridges and buildings Welded, bolted, or riveted structures, but primarily welded bridges and buildings in which weight savings or added durability is important Structural and miscellaneous purposes for which weight savings or added durability is important Structural and miscellaneous purposes for which greater strength or weight savings is important

A 607

A 618

Plate, bar, and sheet piling ≤ 150 mm in thickness

General structural purposes include welded, bolted or riveted bridges and buildings

Metals

1.5 Iron and Steels

ASTM specificationa

Title

Alloying elementsb

Avalible mill forms

Special characteristics

Intended uses

A 633

Normalized high-strength low-alloy structural steel

Nb, V, Cr, Ni, Mo, Cu, N, Si

Plate, bar, and shapes ≤ 150 mm in thickness

A 656

High strength low-alloy, hot rolled structural vanadium-aluminiumnitrogen and titaniumaluminium steels High-strength low-alloy steel H-piles and sheet piling

V, Al, N, Ti, Si

Plate, normally ≤ 16 mm in thickness

Enhanced notch toughness; yield strength of 290 to 415 MPa in five grades Yield strength of 552 MPa

Ni, Cu, Si

Structural-quality H-pills and sheet piling

Welded, bolted, or riveted structures for service at temperatures at or above −45 ◦ C Truck frames, brackets, crane booms, rail cars and other applications for witch weight savings is important Dock walls, sea walls Bulkheads, excavations and similar structures exposed to seawater

A 709, grade 50 and 50W

Structural steel

V, Nb, N, Cr, Ni, Mo

A 714

High-strength low-alloy welded and seamless steel pipe

V, NI, Cr, Mo, Cu, Nb

All structural-shape groups and plate ≤ 100 mm in thickness Pipe with nominal pipe size diameters of 13 to 660 mm

A 715

Steel sheet and strip hot-rolled. high-strength low-alloy with improved formability

Nb, V, Cr, Mo, N, Ti, Zr, B

Hot-rolled sheet and strip

A 808

High-strength low-alloy steel with improved notch toughness

V, Nb

Hot-rolled plate ≤ 65 mm in thickness

A 812

High-strength low-alloy steels Plate produced by themomechanical controlled processes Cold formed welded and seamless high-strength low-alloy structural rubing with improved atmospheric corrosion resistance

V, Nb

Steel sheet in coil form

V, Nb, Cr Mo, Ni

Plates ≤ 100 mm in thickness

Cu, Cr, Ni, Si, V, Ti, Zr, Nb

Welded rubing with maximum periphery of 1625 mm and wall thickness of 16 mm or seamless tubing with maximum periphery of 810 mm and wall thickness of 13 mm

A 690

A 841

A 847

Corrosion resistance two to three times greater than that of carbon steel in the splash zone of marine marine structures Minimum yield strength of 345 MPa, Grade 50W is a weathering steel Minimum yield strength of ≤ 345 MPa and corrosion resistance two or four times that of carbon steel Improved formabilityc compared to a A 606 and A 607; yield strength of 345 to 550 MPa in four grades

Charpy V-notch impact energies of 40–60 J (40 – 60 ft lfb) at −45 ◦ C Yield strength of 450– 550 MPa Yield strength of 310– 345 MPa Minimum yield strength ≤ 345 MPa with atmosphieric-corrosion twice that of carbon steel

Bridges

Piping

Structural and miscellaneous applications for which high strength, weight savings, improved formability and good weldability are important Railway tank cars

Welded layered pressure vesels Welded pressure vessels

Round, square, or specially shaped structural tubing for welded, riveted or bolted construction of bridges and buildings

Part 3 1.5

Table 3.1-48 Summary of characteristics and uses of HSLA steels according to ASTM standards [1.80], cont.

245

246

Part 3

Part 3 1.5

Table 3.1-48 Summary of characteristics and uses of HSLA steels according to ASTM standards [1.80], cont.

Classes of Materials

ASTM specificationa

Title

Alloying elementsb

Avalible mill forms

Special characteristics

Intended uses

A 860

High-strength buttwelding fittings of wrought high-strength low-alloy steel High-strength low-alloy steel with atmospheric corrosion resistance

Cu, Cr, Ni, Mo, V, Nb, Ti

Normalized or quenched-andtempered wrought fittings As-rolled plate ≤ 35 mm in thickness

Minimum yield strength ≤ 485 MPa

High-pressure gas and oil transmission lines

Atmosperic-corrosion resistance four times that of carbon structural steel

Tubular structures and poles

A 871

a b c

V, Nb, Ti Cu, Mo, Cr

For grades and mechanical properties, see Table 3.1-47. In addition to carbon, manganese, phosphorus, and sulfur. A given grade may contain one or more of the listed elements, but not necessarily all of them; for specified compositional limits, see Table 3.1-46. Obtained by producing killed steel, made to fine grain practice, and with microalloying elements such as niobium, vanadium titanium, and zirconium in the composition.

forming elements C, N, Ni, Mn, Cu, and Co. All alloying elements suppress the austenite to martensite transformation by reducing the Ms temperature, so that the steel may remain fcc at and below room temperature at a sufficiently high alloy content. For a rough estimate of the structural components of a stainless steel as a function of alloy composition, the so-called Schaeffler diagram (initially determined by M. Strauss and E. Maurer in 1920) can be used (see Fig. 3.1-114 [1.77]). It relates the equivalent Cr and Ni content to the observed fractions of martensite, austenite, and ferrite. One of the formulas of the Ni and Cr equivalent used most frequently is that of Schneider [1.85] (in wt%): Crequ = Cr + 2 Si + 1.5 Mo + 5 V + 5.5 Al + 1.5 Ti + 0.7 W Nickel equivalence (wt %) Austenite 20 Austenite + Ferrite

A.+ M. 10

0

Martensite

10

A.+M.+F. M. + F.

Ferrite

20 30 Chromium equivalence (wt %)

Fig. 3.1-114 Structure of iron-based alloys as a function of

the concentrations of the chromium and nickel equivalent elements. A: austenite (face centered cubic); F: ferrite (body centered cubic); M: martensite (tetragonal-body centered cubic) [1.77]

and Niequ = Ni + Co + 0.5 Mn + 0.3 Cu + 25 N + 30 C . Ferritic Chromium Steels High chromium (≥ 18 wt% Cr) and low carbon concentrations result in a fully ferritic structure of the steels at all temperatures, i. e., with a bcc delta ferrite structure and no phase transformations. Therefore these steels cannot be strengthened by quenching and tempering. The possibility to increase strength by cold deformation is limited since it decreases ductility and toughness. Steels containing < 18 wt% Cr form some austenite during heating which can be transformed into martensite by fast cooling, thus strengthening the steel. A tempering treatment just below Ar1 results in a mixture of δ-ferrite, α-ferrite, and carbides formed from tempered martensite. In general the toughness of the conventional stainless ferritic chromium steels is not very high, the impact transition temperature often being at or above room temperature and reaching 100 ◦ C after welding (see curve (e) in Fig. 3.1-115). This is due to (i) the tendency of the ferritic stainless steels to pronounced grain coarsing on heat treatments, leading to a relatively large grain size (which cannot be refined by phase transformation) and (ii) the precipitation of chromium carbides at the grain boundaries. Both effects render the steel rather brittle after welding. Furthermore, precipitation of chromium carbides at the grain boundaries causes susceptibility to intergranular corrosion due to the formation of zones with local chromium depletion along the grain boundaries. Some improvement can be achieved

Metals

1.5 Iron and Steels

Cr-Superferrite

150

CrNi-Austenite CrNi-Superferrite CrNi-Martensite Cr-Ferrite

100 13 Cr-Martensite 50 17 Cr-Martensite 0 –300

–200

–100

0

100 200 Test Temperature (° C)

Fig. 3.1-115 Notched bar impact energy as a function of test temperature of various types of stainless steels (DVM

samples: dimension 10 × 10 × 55 mm3 , notch depth 3 mm, notch root radius 1 mm)

(i) by quenching or a suitable diffusion heat treatment for equilibration of the chromium distribution, and (ii) by a stabilization of the steels with small amounts of Ti and/or Nb which are added to bind the carbon and nitrogen in more stable compounds. In unstabilized steels the carbon content is generally restricted to ≤ 0.1 wt%. Up to 2 wt% Mo improves the corrosion resistance of ferritic chromium steels, especially in chloride-containing media. In Table 3.1-49 the chemical composition of a number of ferritic stainless steels is given. The most common representative is the grade X6Cr17/AISI 430. Table 3.1-50 presents some information on hot deformation and recommended heat treatment parameters. Tables 3.1-51 and 3.1-52 show typical data of the mechanical and physical properties, respectively, and Table 3.1-53 reviews the weldability of these steels. Good ductility and toughness at sub-zero temperatures can be achieved when the carbon and nitrogen content in ferritic steels is reduced to very low concentrations (below 100 ppm) (see curve (a) in

Fig. 3.1-115). With higher alloy concentrations on the order of 26–30 wt% Cr, up to 2 wt% Mo, and up to 4 wt% Ni, these so-called superferritic steels exhibit excellent corrosion properties, i. e., high resistance against transcrystalline stress corrosion cracking and chlorideinduced pitting corrosion, as well as intercrystalline and general corrosion. However, in order to maintain the low C and N contents even after welding, an effective inert gas shielding is required during welding as it is known for welding of Ti. Obviously, the high purity requirements which have to be observed during melting, hot forming and welding, and some embrittling effects which occur in high Cr steels after lengthy high temperature exposure (475◦ embrittlement and σ-phase formation) have precluded as yet a wider application of these steels, in spite of their attractive properties. In addition to their good corrosion resistance these steels possess a higher thermal conductivity than austenitic stainless steels, which is of special interest in heat exchanger applications, and a lower rate of work hardening on cold deformation.

Part 3 1.5

Notched bar impact (J) 200

247

248

Part 3

Part 3 1.5

Table 3.1-49 Chemical composition of ferritic stainless steels

Classes of Materials

Grade no. Steel designation (EN 10088)

ASTM Chemical composition (wt%) A 276/ C Si Mn AISI grade

1.4016

X6Cr17

430

1.4104

X12CrMoS17

430F

1.4105

X4CrMoS18

1.4509

X2CrTiNb18

1.4510

X3CrTi17

1.4511

X3CrNb17

1.4113

X6Cr Mo17-1

1.4520

X2CrTi15

1.4521

X2CrMoTi18-2

≤0.08

≤1

≤1

0.10–0.17 ≤1.5

S

P

Cr

≤0.03

Mo

Others

15.5–17.5

≤1

0.15–0.35 ≤0.06

15.5–17.5 0.2–0.6

0.15–0.35 ≤0.06

16.5–18.5 0.2–0.6

≤0.06

≤1.5

≤1

441

≤0.03

≤1

≤1

≤0.015

430Ti

≤0.08

≤1

≤1

≤0.03

≤0.045 16–18

Ti ≥ 7x% C up to 1.20%

≤0.08

≤1

≤1

≤0.03

≤0.045 16–18

Nb ≥ 12x% C up to 1.20%

≤0.08

≤1

≤1

≤0.03

≤0.045 16–18

≤0.015

≤0.5

≤0.5

≤0.020

≤0.025 14–16

444

≤0.025

≤1

≤1

≤0.03

≤0.045 17–19

434

17.5–18.5

Ti 0.1–0.6 Nb 9x% C+ 0.3–1.0

0.9–1.3 Ti 0.25–0.40 1.8–2.3 Ti ≥ 7x% (C+N) up to 0.8, (C+N) ≤ 0.04

X20Cr20

442

≤0.2

≤1

≤1

≤0.03

≤0.04

18–23

1.3810

X20Cr25

446

≤0.25

≤0.5–2.0

≤0.5

≤0.03

≤0.04

23–27

a

X1CrMo26-1

0.002

0.1

0.3

0.015

0.01

26

1

a

X1CrMo29-4

0.003

0.1

0.04

0.01

0.01

29.5

4

a

X1CrMoNi29-4-2

0.002

0.1

0.1

0.01

0.01

29.5

4

Ni 2.2

a

X2CrMoNiTi25-4-4

0.012

0.04

0.3

0.006

25

4

Ni 4, Ti 0.4

a

N 0.006

Typical values

Table 3.1-50 Heat treatment conditions of ferritic stainless steels Grade no.

Rolling and forging (◦ C)

Soft annealing Temperature (◦ C)

1.4016

1100–800

750–850

20–30

1.4104

1100–800

750–850

120–180

1.4105

1100–800

750–850

1.4510

1100–800

750–850

20–30

Air/water

1.4511

1050–750

750–850

20–30

Air/water

1.4113

1050–750

750–850

20–30

Air/water

1.4521

1150–750

750–900

X1CrMo26-1

1150–750

750–900

X1CrMo29-4

1100–800

750–800

120–360

X1CrMoNi29-4-2

1150–750

750–800

15–30

X2CrMoNiTi25-4-4

1100–800

730–780

120–360

Time (min)

Cooling Air/water Air/furnace Air/water

Air/water Air/water Air/furnace Air Air/furnace

Metals

1.5 Iron and Steels

Grade no.

1.4016 1.4104 1.4105 1.4510 1.4511 1.4113 1.4521 X1CrMo26-1 X1CrMo29-4 X1CrMoNi29-4-2 X2CrMoNiTi25-4-4 a

Tensile properties of flat products ≤ 25 mm in thickness

Heat treatment condition

Annealed Annealed Annealed Annealed Annealed Annealed Annealed Annealed Annealed Annealed Annealed

Min. yield strength or 0.2% proof strength (MPa)

Ultimate tensile strength (MPa)

Min. fracture elongation A5 (%)

270 300 270 270 250 260 320 275 a 415 a 415 a 550 a

450–600 540–740 450–650 450–600 450–600 480–630 450–650 450 a 550 a 550 a 650 a

20 16 20 20 20 20 20 22 a 20 a 20 a 20 a

Typical values

Table 3.1-52 Physical properties of ferritic stainless steels Grade no.

1.4016 1.4104 1.4105 1.4510 1.4511 1.4113 1.4521

Mean thermal expansion coefficient between 20 ◦ C and T (◦ C) in 10−6 K−1 100 200 300 400

Density (kg/dm3 )

10.0 10.0 10.0 10.0 10.0 10.0 10.4

7.7 7.7 7.7 7.7 7.7 7.7 7.7

10.0 10.5 10.5 10.0 10.0 10.0 10.8

10.5 10.5 10.5 10.5 10.5 10.5 11.2

10.5 10.5 10.5 10.5 10.5 10.5 11.6

Thermal conductivity at 20 ◦ C (W/K m)

Specific heat at 20 ◦ C

Modulus of elasticity

(J/g K)

Electrical resistvity at 20 ◦ C (
mm2 /m)

25 25 25 25 25 25 15

0.46 0.46 0.46 0.46 0.46 0.46 0.43

0.60 0.70 0.70 0.60 0.60 0.70 0.80

220 216 216 220 220 216 220

Magnetizable

(kN/mm2 ) yes yes yes yes yes yes yes

Table 3.1-53 Weldability of ferritic stainless steels Grade no.

1.4016 1.4104 1.4105 1.4510 1.4511 1.4113 1.4521 X2CrMoTi29-4 X1CrMo26-1 X1CrMo29-4 X1CrMoNi29-4-2

Weldable

Yes No No Yes Yes Yes Yes Yes Yes Yes Yes

Welding method SAW/MIG/TIG welding

Arc welding

Resistance welding

Autogenous welding

+ − − + + + + + + + +

+ − − + + + − − − − −

+ − − + + − − − − − −

(+) − − − − − − − − − −

Preheating (◦ C)

After-treatment Annealing at T (◦ C)

200 − − 200 200 − −

(+) − − (+) (+) + −

700 − − 750 750 750 −

Part 3 1.5

Table 3.1-51 Mechanical properties of ferritic stainless steels

249

250

Part 3

Classes of Materials

Part 3 1.5

Martensitic and Martensitic-Ferritic Chromium Steels Steels with 11.5 to 18 wt% Cr and up to 1.2 wt% C are austenitic at high temperatures and can be transformed into martensite by fast cooling. Due to the high chromium content, the hardenability of these steels is relatively high, so a fully martensitic transformation can be achieved even with relatively large cross sections and moderate cooling rates. They are normally used for applications requiring a combination of high hardness with good corrosion and wear resistance. With carbon contents below about 0.35 wt% C the steels are hypo-eutectic, and some ferrite will be present after heat treatment. They can be austenitized at ≥ 960 ◦ C. Steels with ≥ 0.40 wt% C and 13 wt% Cr are already hyper-eutectic and will contain some undissolved primary carbides after quenching. To dissolve more carbon, these steels are usually quenched from a higher austenitization temperature around 1050 ◦ C. The steels cannot be hardened if the carbon concentration is below 0.12 wt% C and the chromium content ≥ 16 wt% Cr. Hardness (HV) 700 600 500 400 300

0.1

0.2

In some grades a small content of 0.5–1 wt% Mo (and sometimes some W, V, or Nb) is used to increase the tempering resistance, i. e., to retain higher hardness on tempering by means of precipitation reactions. Increased S contents or Se additions improve the machinability of the steels. About 1–2.5 wt% Ni together with reduced carbon content is applied if hardenabilty of higher cross sections and an improved weldability are required. The hardness after quenching depends on the carbon content, as illustrated in Fig. 3.1-116 for a 12 wt% Cr steel [1.77]. In the as-quenched state the steels are hard but very brittle. Thus a tempering treatment is necessary to adjust toughness and strength to the level required for a specific application. For high hardness, annealing temperatures of about 100–300 ◦ C are applied, whereas increases in ductility and toughness require tempering at or above 650 ◦ C. The chemical composition for a number of martensitic Cr steels is given in Table 3.1-54. Tables 3.1-55 – 3.1-58 review data on recommended heat treatment conditions, mechanical properties, physical properties, and weldability, respectively. It should be noted that a different way to produce stainless steels with high hardness is by precipitation hardening. Such steels have a low carbon content and contain in addition to chromium a few wt% of Ni and Cu. The hardening is caused by Cu precipitates. Others use precipitation hardening by intermetallic phases such as NiTi, TiAl, or NiAl.

0.3 Carbon (wt %)

Fig. 3.1-116 As-quenched hardness as a function of the

carbon content of a martensitic 12 wt% Cr steel Table 3.1-54 Chemical composition of martensitic and martensitic-ferritic chromium steels Grade no. (EN 10088)

Steel designation

ASTM Chemical composition (wt%) A 276/ C Si Mn AISI grade

1.4006

X12Cr13

410

1.4005

X12CrS13

416

1.4021

X20Cr13

420

1.4028

X30Cr13

420

1.4104

P

Cr

Mo

Ni

≤0.030

12.0–14.0

–

–

≤0.045

12.0–13.0

–

–

≤1.0

≤1.0

≤1.0

≤1.0

0.17–0.25

≤1.0

≤1.0

≤0.045

≤0.030

12.0–14.0

–

–

0.28–0.35

≤1.0

≤1.0

≤0.045

≤0.030

12.0–14.0

–

–

X12CrMoS17-2 430F

0.10–0.17

≤1.0

≤1.5

≤0.060

15.5–17.5

0.2–0.6

1.4057

X20CrNi17-2

431

0.14–0.23

≤1.0

≤1.0

≤0.045

≤0.030

15.5–17.5

–

1.4109

X70CrMo15

440A

0.60–0.75

≤1.0

≤1.0

≤0.045

≤0.030

13.0–15.0

0.50–0.60 –

1.4125

X105CrMo17

440C

0.95–1.20

≤1.0

≤1.0

≤0.045

≤0.030

16.0–18.0

0.40–0.80

0.08–0.12 ≤0.15

≤0.045

S

0.15–0.25

0.15–0.35

1.50–2.50

1.5 Iron and Steels

Metals

Grade no.

Rolling and forging T (◦ C)

Soft annealing

Quenching

T (◦ C)

Time (min)

Cooling

1.4006

1100–800

750–800

120–360

Air/furnace

1.4005

1150–750

750–800

15–30

Air

1.4021

1100–800

730–780

120–360

1.4028

1100–800

730–780

1.4104

1100–800

750–850

1.4057

1100–800

650–750

1.4109

1100–900

1.4125

1100–900

T (◦ C)

Annealing Medium

Hardness HRC ca.

T (◦ C)

950–1000

Air/oil

31

780–680

950–1000

Oil

31

700–600

Air/furnace

980–1030

Air/oil

47

750–650

Air/furnace

980–1030

Air/oil

120–180

Air/furnace

980–1030

Air/oil

27

650–550

180–240

Air/furnace

980–1030

Air/oil

47

720–620

790–840

120–360

Furnace

1020–1060

Oil

59

200–150

800–850

160–240

Furnace

1000–1050

Oil

61

300–100

740–640

Table 3.1-56 Mechanical properties of martensitic and martensitic-ferritic chromium steels Grade no.

Heat treatment condition

Tensile properties of flat products ≤25 mm thickness Min. yield strength or 0.2% proof strength (MPa)

Ultimate tensile strength (MPa)

Fracture elongation A5 (%) long./transv.

CVN impact energy at room temperature (J) longitudinal/ transversal

Min. yield strength or 0.2% proof strength at T (◦ C) in MPa

100

200

300

400

1.4006

Annealed Quenched and tempered

250 420

450–650 600–800

20/15 16/12

−/− −/−

235 420

225 400

220 365

195 305

1.4005

Quenched and tempered

440

590–780

12/−

−/−

−

−

−

−

1.4021

Annealed Quenched and tempered

− 450 550

≤740 650–800 750–950

− 15/11 13/10

−/− 30/− 25/−

420

400

365

305

1.4028

Annealed Quenched and tempered

−

≤780

−

−/−

600

800–1000

−

11/−

1.4104

Annealed Quenched and tempered

300

540–740

−

−/−

640–840

−

−/−

1.4057

Annealed Quenched and tempered

−

−

−/−

14/10

20/−

495

460

430

345

450

550

≤950 750–950

Part 3 1.5

Table 3.1-55 Heat treatment conditions of martensitic and martensitic-ferritic chromium steels

251

252

Part 3

Classes of Materials

Part 3 1.5

Table 3.1-57 Physical properties of martensitic and martensitic-ferritic chromium steels Grade no.

Mean thermal expansion coefficient between 20 ◦ C and T (◦ C) in 10−6 K−1 100 200 300 400

Density (kg/dm3 )

Thermal conductivity at 20 ◦ C (W/K m)

Specific heat at 20 ◦ C

Modulus of elasticity

(J/g K)

Electrical resistvity at 20 ◦ C (
mm2 /m)

1.4006

10.5

11.0

11.5

12.0

1.4005

10.5

11.0

11.5

12.0

7.7 7.7

1.4021

10.0

10.0

10.5

10.5

1.4028

10.5

11.0

11.5

1.4104

10.0

10.5

1.4057

10.0

1.4109 1.4125

Magnetizable

30

0.46

0.60

216

yes

30

0.46

0.60

216

yes

7.7

30

0.46

0.60

216

yes

12.0

7.7

30

0.46

0.65

220

yes

10.5

10.5

7.7

25

0.46

0.70

216

yes

10.5

11.0

11.0

7.7

25

0.46

0.70

216

yes

10.5

11.0

11.0

11.5

7.7

30

0.46

0.65

210

yes

10.4

10.8

11.2

11.6

7.7

15

0.43

0.80

220

yes

(kN/mm2 )

Table 3.1-58 Weldability of martensitic and martensitic-ferritic chromium steels Grade no.

Weldable

Welding method SAW/MIG Arc TIG welding welding

Resistance welding

Autogenous welding

Preheating (◦ C)

After-treatment Annealing at T (◦ C)

Q+T anew −

1.4006

Yes

+

+

+

(+)

250

+

750

1.4005

No

−

−

−

−

−

−

−

−

1.4021

Condit.

+

+

−

−

350

+

720

(+)

1.4028

Yes

−

+

−

−

−

+

720

−

1.4104

No

−

−

−

−

−

−

−

−

1.4057

Condit.

+

+

−

−

200

+

700

(+)

1.4109

No

−

−

−

−

−

−

−

−

1.4125

No

−

−

−

−

−

−

−

−

Austenitic Stainless Steels By adding of austenite forming elements, mainly Ni, the range of stability of the fcc phase is extended down to and below room temperature. The favorable combinations of ductility, toughness, hot and cold formability, weldability, and corrosion resistance have made the austenitic CrNi steels by far the most important and popular stainless steels. The most widespread representatives are the steel grades AISI 304 (X5CrNi18-10, 1.4301) and AISI 316 (X5CrNiMo17-12-2, 1.4401). The austenitic steels are applied in the solution-annealed (at 1000–1100 ◦ C) and fast-cooled state which yields a microstructure that is free of carbide precipitates and has a homogeneous distribution of the alloying elements necessary for good corrosion resistance. Compared to the bcc ferrite phase the fcc austenite phase is characterized by a higher solubility but a lower diffusivity of almost all alloying elements. The first fact allows the production of single phase fcc alloys with a broad composition spectrum. This permits adjustment of the properties of the steel to specific requirements of

corrosion and oxidation resistance, cold and hot strength etc. The low diffusivity makes precipitation processes rather sluggish. The austenite of the quenched steels can be unstable and can transform into martensite as a result of cold deformation or cooling to sub-zero temperatures, especially if these steels are relatively weakly-alloyed. This transformation leads to increased strength and reduced ductility. Martensite can be detected by magnetization measurements because the austenite is paramagnetic whereas the martensite is ferromagnetic. Since the fcc austenitic steels do not exhibit the ductile-brittle transition characteristic of ferritic alloys, the austenitic steels stay sufficiently ductile even at liquid He temperature (4.2 K) and are thus preferred materials for cryogenic applications. Their yield strength of 200–250 MPa is lower than that of the ferritic steels, but due to their pronounced work hardening by cold deformation (making extensive cold-forming operations difficult and often requiring intermediate soft annealing heat treatments), they have a higher tensile strength and fracture elon-

Metals

able effect are the same as for the ferritic steels: bonding of the carbon (and nitrogen) atoms by an overstoichiometric alloying with Nb, Ta, or Ti (so-called stabilization of the steels), or the reduction of the carbon content to below 0.03 wt% C resulting in the development of the extra low carbon (ELC) steels. However, in strongly oxidative media (such as concentrated nitric acid) even steels that have been sufficiently stabilized by Ti may exhibit intergranular corrosion due to selective dissolution of the TiC. Under less severe corrosion conditions, the Ti stabilized steels are as stable as the Nb stabilized grades but at somewhat lower costs. Chemical compositions, heat treatment conditions, physical properties, and hints to weldability of austenitic stainless steels are presented in Tables 3.1-59 – 3.1-63.

Table 3.1-59 Heat treatment conditions of austenitic stainless steels Grade no.

Rolling and forging temperature (◦ C)

Cooling

Quenching temperature (◦ C)

Cooling

1.4541 1.4401 1.4402 1.4406 1.4436 1.4571 1.4580

1150–750

Air

1020–1100

Air, > 2 mm water

1.4301 1.4303 1.4305 1.4306 1.4311

1150–750

Air

1000–1080

Air, > 2 mm water

1.4550

1150–750

Air

1050–1150

Air, > 2 mm water

1.4429 1.4438 1.4439

1150–750

Air

1040–1120

Air, > 2 mm water

1.4435

1150–750

Air, below 600 ◦ C furnace

1020–1100

Air, > 2 mm water

253

Part 3 1.5

gation. A pronounced solid solution strengthening is possible, especially by higher concentrations of nitrogen (up to about 0.4 wt% N). The nitrogen-alloyed CrNi steels are characterized by particularly favorable combinations of mechanical and corrosion properties. As mentioned above, after fast cooling from ≥ 1000 ◦ C, the austenitic stainless steels are free of carbide precipitates. But since steels with ≥ 0.05 wt% C are already carbon-supersaturated at temperatures below 900 ◦ C, holding the material at temperatures between about 400 and 900 ◦ C will lead to preciptation of chromium carbides (mainly M23 C6 type), preferentially at the grain boundaries. This will result in an increased susceptibility to intergranular corrosion due to local chromium depletion. The means to avoid this undesir-

1.5 Iron and Steels

254

Part 3 1.5

Part 3

Grade no. (EN 10088)

Steel designation

ASTM A 276/ AISI grade

Chemical composition (wt%) C Si Mn

P

S

Cr

Ni

1.4310 1.4301 1.4303 1.4305 1.4306 1.4311 1.4541

X12CrNi17-7 X5CrNi18-10 X5CrNi18-12 X10CrNiS18-9 X2CrNi19-11 X2CrNiN18-10 X6CrNiTi18-10

301 304 305, 308 303 304L 304LN 321

≤0.12 ≤0.07 ≤0.07 ≤0.12 ≤0.03 ≤0.03 ≤0.08

≤1.5 ≤1.0 ≤1.0 ≤1.0 ≤1.0 ≤1.0 ≤1.0

≤2.0 ≤2.0 ≤2.0 ≤2.0 ≤2.0 ≤2.0 ≤2.0

≤0.045 ≤0.045 0.15–0.25 ≤0.060 ≤0.045 ≤0.060 ≤0.045

0.030 ≤0.030 ≤0.045 0.15–0.35 ≤0.030 0.15–0.35 ≤0.030

16.0–18.0 17.0–19.0 17.0–19.0 17.0–19.0 18.0–20.0 17.0–19.0 17.0–19.0

6.0–9.0 8.5–10.5 11.0–13.0 8.0–10.0 10.0–12.5 8.5–11.5 9.0–12.0

1.4550

X6CrNiNb18-10

347

≤0.08

≤1.0

≤2.0

≤0.045

≤0.030

17.0–19.0

9.0–12.0

1.4401 1.4404 1.4406 1.4571

X5CrNiMo17-12-2 X2CrNiMo17-13-2 X2CrNiMoN17-12-2 X6CrNiMoTi17-12-2

316 316L 316LN 316Ti

≤0.07 ≤0.03 ≤0.03 ≤0.08

≤1.0 ≤1.0 ≤1.0 ≤1.0

≤2.0 ≤2.0 ≤2.0 ≤2.0

≤0.045 ≤0.045 ≤0.045 ≤0.045

≤0.030 ≤0.030 ≤0.030 ≤0.030

16.5–18.5 16.5–18.5 16.5–18.5 16.5–18.5

10.5–13.5 11.0–14.0 10.5–13.5 10.5–13.5

2.0–2.5 2.0–2.5 2.0–2.5 2.0–2.5

1.4580

X6CrNiMoNb17-12-2

316Cb

≤0.08

≤1.0

≤2.0

≤0.045

≤0.030

16.5–18.5

10.5–13.5

2.0–2.5

1.4429 1.4435

X2CrNiMoN17-13-3 X2CrNiMo18-14-3

≤0.03 ≤0.03

≤1.0 ≤1.0

≤2.0 ≤2.0

≤0.045 ≤0.045

≤0.025 ≤0.025

16.5–18.5 17.0–18.5

11.5–14.5 12.5–15.0

2.5–3.0 2.5–3.0

1.4436 1.4438 1.4439

X5CrNiMo17-13-3 X2CrNiMo18-16-4 X2CrNiMoN17-13-5

(X15CrNiSi20-12) (X12CrNi25-21)

≤0.07 ≤0.03 ≤0.03 ≤0.15 ≤0.15 ≤0.20 ≤0.25

≤1.0 ≤1.0 ≤1.0 ≤1.0 ≤1.0 ≤1.0 ≤1.5

≤2.0 ≤2.0 ≤2.0 5.5–7.5 7.5–10.0 ≤2.0 ≤2.0

≤0.045 ≤0.045 ≤0.045 ≤0.06 ≤0.06 ≤0.045 ≤0.045

≤0.025 ≤0.025 ≤0.025 ≤0.03 ≤0.03 ≤0.03 ≤0.03

16.5–18.5 17.5–19.5 16.5–18.5 16.8–18.0 17.0–19.0 22.0–24.0 24.0–26.0

11.0–14.0 14.0–17.0 12.5–14.5 3.5–5.5 4.0–6.0 12.0–15.0 19.0–22.0

2.5–3.0 3.0–4.0 4.0–5.0

(1.4828) (1.4845)

316LN 316L 317L 316 317L F48 201 202 309 310

Mo

Others

N 0.12–0.22 Ti 5x% C up to 0.80 Nb 10x% C up to 1.0

N 0.12–0.22 Ti 5x% C up to 0.80 Nb 10x% C up to 1.0 N 0.14–0.22

N 0.12–0.22 N 0.25 N 0.25

Classes of Materials

Table 3.1-60 Chemical composition of austenitic stainless steels

Metals

1.5 Iron and Steels

Grade no.

Heat treatment condition

1.4310 1.4301 1.4303 1.4305 1.4306 1.4311 1.4541 1.4550 1.4401 1.4404 1.4406 1.4571 1.4580 1.4429 1.4435 1.4436 1.4438 1.4439 AISI 201 AISI 202 AISI 309 AISI 310 a

Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched Quenched

Tensile properties of flat products ≤ 25 mm thickness

Min. CVN impact energy at room temperarture (J)

Min. yield strength or 0.2% proof strength (MPa)

Ultimate tensile strength (MPa)

Min. fracture elongation A5 (%)

260 195 185 195 180 270 200 205 205 190 280 210 215 295 190 205 195 285 370a 359a 334a 319a

600–950 500–700 490–690 500–700 460–680 550–760 500–730 510–740 510–710 490–690 580–800 500–730 510–740 580–800 490–690 510–710 490–690 580–800 1125a 1110a 691a 678a

35 45 45 35 45 40 40 40 40 40 40 35 35 40 35 40 35 35 57a 55a 48a 50a

105 85 85 – 85 85 85 85 85 85 85 85 85 85 85 85 85 85

Min. yield strength or 0.2% proof strength at T (◦ C) in MPa

100

200

300

400

500

– 157 155 – 147 205 176 177 177 166 211 185 186 225 166 177 172 225

– 127 127 – 118 157 157 157 147 137 167 167 167 178 137 147 147 185

– 110 110 – 100 136 136 136 127 118 145 145 145 155 118 127 127 165

– 98 98 – 89 125 125 125 115 108 135 135 135 145 108 115 115 150

– 92 92 – 81 119 119 119 110 100 129 129 129 138 100 110 110 –

Typical values

Table 3.1-62 Physical properties of austenitic stainless steels Grade no.

1.4310 1.4301 1.4303 1.4305 1.4306 1.4311 1.4541 1.4550

Mean thermal expansion coefficient between 20 ◦ C and T (◦ C) in 10−6 K−1

100

200

300

400

500

16.4 16.0 16.0 16.0

16.9 17.0 17.0 17.0

17.4 17.0 17.0 17.0

17.8 18.0 18.0 18.0

18.2 18.0 18.0 18.0

600

700

800

18.5

18.5

19.0

18.5

18.5

19.0

Density (kg/dm3 )

Thermal conductivity at 20 ◦ C (W/K m)

Specific heat at 20 ◦ C (J/g K)

Electrical resistivity at 20 ◦ C (
mm2 /m)

Modulus of elasticity at 20 ◦ C (kN/mm2 )

Magnetizable

8.0 7.9 7.9 7.9

15 15 15 15

0.45 0.50 0.50 0.50

0.80 0.73 0.73 0.73

198 200 200 200

No No No No

Part 3 1.5

Table 3.1-61 Mechanical properties of austenitic stainless steels

255

256

Part 3

Part 3 1.5

Table 3.1-62 Physical properties of austenitic stainless steels, cont. Grade no.

Classes of Materials

Mean thermal expansion coefficient between 20 ◦ C and T (◦ C) in 10−6 K−1

100

200

300

400

500

600

700

800

Density Thermal (kg/dm3 ) conductivity at 20 ◦ C (W/K m)

Specific heat at 20 ◦ C (J/g K)

Electrical resistivity at 20 ◦ C (
mm2 /m)

Modulus of elasticity at 20 ◦ C (kN/mm2 )

Magnetizable

1.4401 16.5 1.4404 1.4406 1.4435 1.4436 1.4571 1.4580

17.5

17.5

18.5

18.5

19.0

19.5

19.5

7.98

15

0.50

0.75

200

No

1.4429

16.5

17.5

17.5

18.5

18.5

7.98

15

0.50

0.75

200

No

1.4438

16.5

17.5

18.0

18.5

19.0

19.0

19.5

19.5

8.0

14

0.50

0.85

200

No

1.4439

16.5

17.5

17.5

18.5

18.5

8.02

14

0.50

0.85

200

No

Table 3.1-63 Weldability of austenitic stainless steels welding methods not in parentheses are to be preferred Grade no.

Weldable

Welding method SAW/MIG/TIG welding

Arc welding

Resistance welding

Autogenous welding

Preheating (◦ C)

After-treatment

1.4310

Yes

+

+

+

+

−

−

1.4301 1.4303 1.4306 1.4438 1.4541 1.4550 1.4401 1.4404 1.4406 1.4571 1.4580

Yes

+

+

+

(+)

−

−

1.4305

No

−

−

−

−

−

−

1.4311 1.4429 1.4435 1.4436 1.4439

Yes

+

+

+

−

−

−

1.5 Iron and Steels

Metals

Part 3 1.5

intergranular corrosion. With respect to optimum toughness, the δ-ferrite content of duplex steels should be below 60 vol%. The influence of annealing temperature and cooling conditions on the ferrite content of a steel with 0.05 wt% C, 25 wt% Cr, 8 wt% Ni, 2.5 wt% Mo, and 1.5 wt% Cu is illustrated in Table 3.1-69 [1.78]. During the partial phase transformation of ferrite into austenite below 1350 ◦ C, a redistribution of the alloying elements occurs with the ferrite-forming elements Cr, Mo, and Ti enriched in the α-phase and the austeniteforming elements C, N, Ni, and Mn enriched in the γ -phase. The reduced C content in the α-phase delays the formation of chromium carbides. The relatively high Mo and N contents ensure good resistance against pitting corrosion. The formation of the brittle Cr-rich σ-phase, which can form in the temperature range of 1000–500 ◦ C and can lead to a drastic reduction of toughness and corrosion resistance, requires special attention. Therefore, duplex steels are usually water quenched from a solution treatment at 1100–1150 ◦ C.

Duplex Stainless Steels Duplex steels have a mixed structure of ferrite and austenite. They contain the ferrite-forming elements Cr and Mo at levels of 20–29 wt% Cr and up to 4 wt% Mo, respectively, and the austenite-forming elements of about 4–9 wt% Ni and up to 0.3 wt% N. Typical examples are presented in Table 3.1-64. These steels solidify as δ-ferrite which will partly transform into austenite upon cooling. Thus, the phase fractions of ferrite and austenite depend not only on the chemical composition, but also on the annealing and cooling conditions. The advantages of the duplex steels compared to the austenitic steels are a substantially higher yield and tensile strength (cf. Table 3.1-66) and a better resistance against stress corrosion cracking. A few data on heat treatment conditions, physical properties, and weldability are given in Tables 3.1-65, 3.1-67, and 3.1-68. In comparison with ferritic stainless steels, the duplex steels have a better weldability, a higher low temperature toughness, and a lower susceptibility to general and

Table 3.1-64 Chemical composition of duplex stainless steels Grade no. (EN 10088)

Steel designation

ASTM A 276/ AISI grade

Chemical composition (wt%) C Si Mn S

1.4460 1.4462

X4CrNiMoN27-5-2

329

≤0.05

≤1

≤2

≤0.03 ≤0.045

X2CrNiMoN22-5-3

F51

≤0.03

≤1

≤2

≤0.02 ≤0.03

P

Cr

Ni

Mo

N

25.0–28.0 4.5–6.0

1.3–2.0

0.05–0.20

21.0–23.0 4.5–6.5

2.5–3.5

0.08–0.20

Table 3.1-65 Heat treatment conditions of duplex stainless steels Grade no.

Rolling and forging temperature (◦ C)

Cooling

Quenching temperature (◦ C)

Cooling

1.4460

1150–900

Air

1020–1100

Air, water

1.4462

1150–900

Air

1020–1100

Air, water

Table 3.1-66 Mechanical properties of duplex stainless steels Grade no.

Heat treatment condition

Tensile properties of flat products ≤ 25 mm thickness Min. yield strength or 0.2% proof strength (MPa)

Ultimate tensile strength (MPa)

Min. CVN impact energy at room temp. (J)

257

Min. yield strength or 0.2% proof strength at T (◦ C) in MPa

Min. fracture elongation A5 (%) 100

200

300

400

500

1.4460

Quenched

450

600–800

20

55

360

310

–

–

–

1.4462

Quenched

450

640–900

30

120

360

310

280

–

–

258

Part 3

Part 3 1.5

Table 3.1-67 Physical properties of duplex stainless steels

Classes of Materials

Grade Mean thermal expansion coefficient between 20 ◦ C no. and T (◦ C) in 10−6 K−1

100

200

300

400

500

600

700

800

Density Thermal Specific (kg/dm3 ) conduc- heat tivity at at 20 ◦ C 20 ◦ C (W/K m) (J/g

1.4460 12.0 1.4462 12.0

12.5 12.5

13.0 13.0

13.5 –

– –

– –

– –

– –

7.8 7.8

15 15

0.45 0.45

Electrical resistivity at 20 ◦ C (
mm2 /m)

Modulus of elasticity at 20 ◦ C (kN/mm2 )

Magnetizable

0.80 0.80

200 200

Yes Yes

Table 3.1-68 Weldability of duplex stainless steels Grade no.

1.4460 1.4462

Weldable

Yes Yes

Welding method SAW/MIG/TIG welding

Arc welding

Resistance welding

Autogenous welding

+ +

+ +

+ +

+ −

Preheating (◦ C)

Aftertreatment

− −

1020 ◦ C −

Table 3.1-69 Influence of annealing temperature and cooling conditions on the ferrite content of a steel with 0.05 wt% C,

25 wt% Cr, 8 wt% Ni, 2.5 wt% Mo and 1.5 wt% Cu [1.10] Annealing temperature (◦ C) (holding time 15 min)

Ferrite content (vol.%) after water quenching

air cooling

1350 1300 1250 1150 1050 1000

93.0 70.2 43.5 35.7 24.0 7.6

78.8 61.8 37.5 34.2 23.7 7.6

3.1.5.5 Heat-Resistant Steels Heat-resistant steels are treated extensively in [1.52], creep data are compiled in [1.86]. Steels are considered heat-resistant if they possess–in addition to good mechanical properties at ambient temperature–special resistance against short or long term exposure to hot gases, combustion products and melts of metals or salts at temperatures above about 550 ◦ C where non- or lowalloyed steels are no longer applicable due to extensive scaling and creep. Thus, heat-resistant steels are characterized by a combination of good high temperature strength, scaling resistance, a sufficient hot and cold formabilty, and weldability. They are sufficiently stable against embrittling processes at the high application temperatures. The resistance against scaling and hot gas corrosion is affected by the formation of a protective dense, pore-free, and tightly adherent oxide layer at the surface. The main alloying elements leading to such an oxide layer are Cr, Al, and Si. The oxidation and scaling resistance increases with increasing Cr content between about 6 and 25 wt% Cr. Higher Cr concentrations do not lead to fur-

ther improvement. Additions of up to 2 wt% Al and up to 3 wt% Si enhance the effect of Cr. Small additions of rare earth metals, e.g., of Ce, can improve the adherence and the ductility of the oxide layer. In order to keep the protective oxide layer intact during temperature changes, the steels should exhibit low volume changes and, if possible, no phase transformations during heating and cooling. Consequently, there are two main groups of heat resistant steels: ferritic and austenitic steels, both showing no phase transformations. The ferritic Cr (or Cr−Al−Si) steels are less expensive but have a lower creep strength above 800 ◦ C. They may suffer from three embrittling mechanisms:

• • •

The “475 ◦ C embrittlement” due to decomposition in the metastable miscibility gap of the Fe−Cr solid solution, occuring between about 350 and 550 ◦ C at Cr contents above 15 wt% Cr (Fig. 3.1-107); The formation of the brittle intermetallic FeCr σphase at temperatures between about 550 and 900 ◦ C (Sect. 3.1.5.1, Fig. 3.1-106); Grain coarsening at temperatures above about 900 ◦ C.

– Ti 0.15–0.6

Ti ≥ 4xwt% C up to 0.8 – – –

9.0–12.0 11.0–13.0 12.0–15.0 19.0–22.0 19.0–22.0 33.0–37.0 30.0–34.0 17.0–19.0 19.0–21.0 21.0–23.0 24.0–26.0 24.0–26.0 15.0–17.0 19.0–23.0 – – – – – – 0.15–0.6 ≤0.03 ≤0.03 ≤0.03 ≤0.03 ≤0.03 ≤0.02 ≤0.02 ≤0.045 ≤0.045 ≤0.045 ≤0.045 ≤0.045 ≤0.030 0.030 ≤2.0 ≤2.0 ≤2.0 ≤2.0 ≤2.0 ≤2.0 ≤2.0 ≤1 1.5–2.5 ≤1 ≤0.75 1.5–2.5 1.0–2.0 ≤1 According to SEW [1.87] a

321 309 309S 310S 310/314 330 B163 1.4878 1.4828 1.4833 1.4845 1.4841 1.4864 1.4876

X10CrNiTi18-10 X15CrNiSi20-12 X12CrNi23-12 X8CrNi25-21-12 X15CrNiSi25-20 X12NiCrSi36-18 X10NiCrAlTi32-21

327 1.4821 X15CrNiSi25-4 Austenitic steels

≤0.12 ≤0.20 ≤0.08 ≤0.15 ≤0.20 ≤0.15 ≤0.12

– 3.5–5.5 24.0–27.0 ≤0.03 0.8–1.5

2.0

≤0.04

–

– – – – – 6.0–8.0 10.5–12.5 12.0–14.0 17.0–19.0 23.0–26.0 0.5–1.0 – 0.7–1.2 0.7–1.2 1.2–1.7 ≤0.03 ≤0.03 ≤0.03 ≤0.03 ≤0.03 ≤0.04 ≤0.04 ≤0.04 ≤0.04 ≤0.04 ≤1 ≤1 ≤1 ≤1 ≤1 0.5–1.0 ≤1.0 0.7–1.4 0.7–1.4 0.7–1.4 ≤0.12 ≤0.08 ≤0.12 ≤0.12 ≤0.12 – – 405 430 446 1.4713 X10CrAlSi7 1.4720 X7CrTi12 1.4724 X10CrAlSi13 1.4742 X10CrAlSi18 1.4762 X10CrAlSi25 Ferritic–austenitic steels

Ferritic steels

0.10–0.20

Others Ni Cr Al S P Chemical composition (wt%) C Si Mn ASTM/ AISI grade Grade a Steel designation

Table 3.1-70 Chemical composition of heat-resistant steels according to SEW [1.87]

1.5 Iron and Steels

259

Part 3 1.5

However, these embrittling mechanisms will not impair the behavior at high operating temperatures if taken into account properly, but will deteriorate the toughness after cooling to room temperature. Heating to temperatures above the range of occurrence of the embrittling phases followed by sufficiently fast cooling will suppress the embrittling effects. The Cr and Ni alloyed austenitic steels possess a higher temperature strength and better ductility, toughness, and weldability. The susceptibility to embrittling effects is considerably lower. At Ni contents above 30 wt% Ni, they are outside the stability region of the brittle σ-phase. The properties of the ferritic-austenitic steels lie between those of the ferritic and austenitic steels. They are characterized by a higher fracture toughness, cold formability, high temperature strength, and weldability than the fully ferritic grades, and by a higher chemical resistance in sulphurous gases than the austenitic grades. It is obvious that the scaling resistance of the heat-resisting steels will be detrimentally influenced by any other corrosion mechanism which may be destroying the oxide layer, e.g., by chemical reactions with other metal oxides, chlorine, or chlorides. Thus in general, the heat resistance cannot be characterized by a single test method or measuring parameter but will depend on the specific environmental conditions. In Table 3.1-70 chemical compositions of the most important grades of heat resistant steels are presented [1.87]. Table 3.1-71 contains some information about recommended temperature ranges for heat treatment and hot forming. In Tables 3.1-72 and 3.1-73 the mechanical properties at room temperature and at high temperatures are listed, respectively. Table 3.1-74 shows some physical properties. The ferritic and ferriticaustenitic steels are magnetisable while the austenitic grades are nonmagnetic. Qualitative data on the high temperature behavior in special gas atmospheres are given in Table 3.1-75. In carburizing atmospheres carbon can diffuse into the steel, reacting with the chromium to form chromium carbides which can lead to embrittlement and reduced scaling resistance due to chromium depletion in the matrix. Higher Ni and Si contents reduce the carburization susceptibility. In sulfur-containing atmospheres, which contain the sulfur mostly in the form of SO2 or H2 S, the formation of sulfides at the surface may inhibit the formation of the protecting oxide layer. Under oxidizing conditions this process will proceed rather slowly, but under reducing conditions the pick-up of sulfur occurs very

– Ti ≥ 6xwt% C up to 1.0 – – –

Metals

260

Part 3

Part 3 1.5

Table 3.1-71 Recommended conditions for heat treatment and hot forming of heat-resistant steels

Classes of Materials

Hot forming temperature (◦ C)

Soft annealing (◦ C) Cooling in air (water)

Quenching temperature (◦ C) Cooling in water (air)

1.4713

1100–750

750–800

–

620

1.4720

1050–750

750–850

–

800

1.4724

1100–750

800–850

–

850

1.4742

1100–750

800–850

–

1000

1.4762

1100–750

800–850

–

1150

1150–800

–

1000–1050

1100

1.4878

1150–800

–

1020–1070

850

1.4828

1150–800

–

1050–1100

1000

1.4833

1150–900

–

1050–1100

1000

1.4845

1150–800

–

1050–1100

1050

1.4841

1150–800

–

1050–1100

1150

1.4864

1150–800

–

1050–1100

1100

1.4876

1150–800

900–980 (recrystallization annealing)

1100–1150 (solution annealing)

1100

Grade a

Limiting scaling temperature in air (◦ C)

Ferritic steels

Ferritic–austenitic steels 1.4821 Austenitic steels

a

According to SEW [1.87]

Table 3.1-72 Mechanical properties of heat-resistant steels at 20 ◦ C Grade a

Heat treatment condition

Hardness (HB) max.

0.2% proof stress (MPa) min.

Ultimate tensile strength (MPa)

Elongation Lo = 5do min. (%) long. transv.

Ferritic steels 1.4713

Annealed

192

220

420–620

20

15

1.4720

Annealed

179

210

400–600

25

20

1.4724

Annealed

192

250

450–650

15

11

1.4742

Annealed

212

270

500–700

12

9

1.4762

Annealed

223

280

520–720

10

7

235

400

600–850

16

12

Ferritic–austenitic steels 1.4821

Quenched

Austenitic steels 1.4878

Quenched

192

210

500–750

40

30

1.4828

Quenched

223

230

500–750

30

22

1.4833

Quenched

192

210

500–750

35

26

1.4845

Quenched

192

210

500–750

35

26

1.4841

Quenched

223

230

550–800

30

22

1.4864

Quenched

223

230

550–800

30

22

1.4876

Recryst. annealed Solution annealed

192 192

210 170

500–750 450–700

30 30

22 22

a

According to SEW [1.87]

1.5 Iron and Steels

Metals

bands Temperature (◦ C)

Grade a

Ferritic and ferritic-austenitic steels ⎫ 1.4713 ⎪ 500 ⎪ ⎪ 1.4720 ⎪ 600 ⎪ ⎪ ⎪ ⎬ 1.4724 700 1.4742 ⎪ 800 ⎪ ⎪ ⎪ ⎪ 1.4762 ⎪ 900 ⎪ ⎭ 1.4821

1% creep limit (MPa) at t = 1000 h 10 000 h 80 27.5 8.5 3.7 1.8

Creep rupture strength (MPa) at t = 1000 h 10 000 h 100 000 h

50 17.5 4.7 2.1 1.0

160 55 17 7.5 3.6

100 35 9.5 4.3 1.9

55 20 5 2.3 1.0

Austenitic steels 1.4878

600 700 800

110 45 15

85 30 10

185 80 35

115 45 20

65 22 10

600 700 800 900

120 50 20 8

80 25 10 4

190 75 35 15

120 36 18 8.5

65 16 7.5 3.0

600 700 800 900

150 53 23 10

105 37 12 5.7

230 80 35 15

160 40 18 8.5

80 18 7 3.0

1.4864

600 700 800 900

105 50 25 12

80 35 15 5

180 75 35 15

125 45 20 8

75 25 7 3

1.4876 (solution annealed)

600 700 800 900

130 70 30 13

90 40 15 5

200 90 45 20

152 68 30 11

114 47 19 4

1.4828 1.4833

1.4845 1.4841

a

⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭ ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭

According to SEW [1.87]

Table 3.1-74 Physical properties of heat-resistant steels Grade a Density at Average coefficient of thermal expansion 20 ◦ C between 20 ◦ C and T (◦ C) (× 10−6 K−1 ) 3 (g cm ) 200 400 600 800 1000

1200

Thermal conductivity at T (◦ C) (W m−1 K−1 ) 20 500

Specific heat at 20 ◦ C (J g−1 K−1 )

Specific electrical resistivity at 20 ◦ C (
mm2 m−1 )

Ferritic steels 1.4713

7.7

11.5

12.0

12.5

13.0

–

–

23

25

0.45

0.70

1.4720

7.7

11.0

12.0

12.5

13.0

–

–

25

28

0.45

0.60

1.4724

7.7

11.0

11.5

12.0

12.5

13.5

–

21

23

0.45

0.90

1.4742

7.7

10.5

11.5

12.0

12.5

13.5

–

19

25

0.45

0.95

1.4762

7.7

10.5

11.5

12.0

12.5

13.5

15.0

17

23

0.45

1.10

13.5

14.0

14.5

15.0

15.5

17

23

0.50

0.90

Ferritic–austenitic steels 1.4821

7.7

13.0

Part 3 1.5

Table 3.1-73 Long-term mechanical properties of heat-resistant steels at high temperatures; average values of scatter

261

262

Part 3

Classes of Materials

Part 3 1.5

Table 3.1-74 Physical properties of heat-resistant steels, cont. Grade a Density at Average coefficient of thermal expansion 20 ◦ C between 20 ◦ C and T (◦ C) (× 10−6 K−1 ) 3 (g cm ) 200 400 600 800 1000 Austenitic steels 1.4878 7.9 1.4828 7.9 1.4833 7.9 1.4845 7.9 1.4841 7.9 1.4864 8.0 1.4876 8.0 a

17.0 16.5 16.0 15.5 15.5 15.0 15.0

18.0 17.5 17.5 17.0 17.0 16.0 16.0

18.5 18.0 18.0 17.5 17.5 17.0 17.0

19.0 18.5 18.5 18.0 18.0 17.5 17.5

– 19.5 19.5 19.0 19.0 18.5 18.5

1200

Thermal conductivity at T (◦ C) (W m−1 K−1 ) 20 500

Specific heat at 20 ◦ C (J g−1 K−1 )

Specific electrical resistivity at 20 ◦ C (
mm2 m−1 )

– – – – 19.5 – –

15 15 15 14 15 13 12

0.50 0.50 0.50 0.50 0.50 0.50 0.50

0.75 0.85 0.80 0.85 0.90 1.00 1.00

21 21 19 19 19 19 19

According to SEW [1.87]

Table 3.1-75 Resistance of heat-resistant steels in various media Grade a

Resistance to Carburization

Sulphurous gases Oxidizing

Reducing

Nitrogenous and low-oxygen gases

Maximum operating temperature in air (◦ C)

1.4713 Medium 1.4762 Medium Ferritic–austenitic steels

Very high Very high

Medium High

Low Low

800 1150

1.4821 Austenitic steels

Medium

High

Medium

Medium

1100

1.4878 1.4828 1.4841 1.4864

Low Low Low High

Medium Medium Medium Medium

Low Low Low Low

High High High High

850 1000 1150 1100

Ferritic steels

a

According to SEW [1.87]

fast. This is especially true with Ni-alloyed steels due to the formation at about 650 ◦ C of a low-melting Ni/NiS eutectic. Thus under such conditions the ferritic steels are more stable than the austenitic grades. In sulfur-containing atmospheres the maximum service temperatures will be about 100 to 200 ◦ C lower than in air. The heat-resistant steels are weldable by the usual processes, with arc welding preferred over gas fusion welding. For the ferritic steels, the tendency to grain coarsening in the heat affected zone has to be kept in mind. The application of austenitic filler metals will lead to better mechanical properties of the weld connection than those of the base metal (however, with respect to the scaling resistance, different thermal expansions of the ferritic and austenitic materials may be a problem). Filler materials should be at least as highly alloyed as the base metal. In sulfurizing atmospheres it is advisable to use ferritic electrodes for the cap passes only in order

to ensure a tough weld. Post-weld heat treatments are generally not necessary.

3.1.5.6 Tool Steels Tool steels are the largest group of materials used to make tools for cutting, forming, or otherwise shaping a material into a part or component. An extensive account is given in [1.88]. Other major groups of tool materials are cemented carbides (Sect. 3.1.6.6), and ceramics including diamond (Chapt. 3.2). The most commonly used materials are wrought tool steels, which are either carbon, alloy, or high-speed steels capable of being hardened by quenching and tempering to hardness levels ≤ 70 HRC. High-speed tool steels are so named because of their suitability to machine materials at high cutting speed. Other steels used for metalworking applications include steels produced by powder metallurgy, medium-carbon alloy steels,

Metals

Hardness (HRC) 70

Hardness (HRC) 69 67

900 Cobalt-base type 800

64

700

60

600

Noncobaltbase type

55

500

49

400

41

300

30

200

11

100 0 –18

93

204

316 427

538

649 760

871 T (°C)

Fig. 3.1-118 Comparison of the hot hardness of Co-bearing versus non-Co bearing high-speed tool steels [1.88] 4

60 50

3 2

40 30 20

Hardness HV (DPH) 1000

0

100

200

300

1 400 500 600 700 Tempering temperature (°C)

Fig. 3.1-117 Isothermal (1 h) tempering curves of 4 typical

tool steels. Curves 1 and 2: softening of AISI grade W (water-hardening) and O (oil-hardening) steels; Curves 3 and 4: softening and secondary hardening of AISI grade A2 (air-hardening medium alloy) and M2 (Mo high-speed) steels [1.88]

Co is an alloying element which raises the high temperature stability of tool steels by raising their melting temperature. Figure 3.1-118 shows this effect by a comparison of the hardness vs. temperature data for non-Co-based and Co-based high-speed tool steels. Table 3.1-77 gives composition ranges for the tool steels most commonly used. According to the AISI classification, each group of similar composition and properties is given a capital letter, somewhat related to the major alloying element. Thus, high-speed steels are classified by M for molybdenum and T for tungsten. Within each group individual types are assigned code numbers. The basic properties of tool steels that determine their performance in service are hardness, wear

Table 3.1-76 Alloy carbides occurring in tool steels Type of carbide

Prototype

Lattice type

Occurrence, composition a

M7 C3 M23 C6 M6 C M2 C MC

Cr7 C3 Cr23 C6 W6 C W2 C VC

Hexagonal Face-centered cubic Face-centered cubic Hexagonal Face-centered cubic

In Cr alloy steels M = Cr In high-Cr steels M = Cr, Fe, W, Mo M = W, Mo, Cr, V, Co M = W, Mo, Cr VC

a

Bold letters indicate major components

263

Part 3 1.5

high-carbon martensitic stainless steels, and maraging steels. Wrought tool steels are essentially hardenable alloy steels with relatively high contents of the carbide forming elements Cr, Mo, W, and V. If the steels are quenched and tempered, the dependence of their hardness on tempering temperature indicates the level of hardening achieved as well as its temperature stability, (Fig. 3.1-117). The rate of effective softening at tempering temperatures up to about 300 ◦ C is mainly due to the competing effects of recovery and the precipitation of iron carbides (Table 3.1-40). The hardening at higher temperatures is associated with the precipitation of alloy carbides which can form at elevated temperatures only because of their high melting points and transformation kinetics. They give rise to a second maximum on isothermal tempering curves, as curves 3 and 4 in Fig. 3.1-117, which is referred to as secondary hardening. The alloy carbide phases which precipitate and give rise to secondary hardening are listed in Table 3.1-76.

1.5 Iron and Steels

264

Part 3 1.5

Part 3

Designation AISI

Composition b (wt%) UNS No. C

Mn

Si

Cr

Ni

Mo

W

V

Co

Molybdenum high-speed steels M1

T11301

0.78–0.88

0.15–0.40

0.20–0.50

3.50–4.00

0.30 max

8.20–9.20

1.40–2.10

1.00–1.35

–

M2

T11302

0.78–0.88; 0.95–1.05

0.15–0.40

0.20–0.45

3.75–4.50

0.30 max

4.50–5.50

5.50–6.75

1.75–2.20

–

M3, class 1

T11313

1.00–1.10

0.15–0.40

0.20–0.45

3.75–4.50

0.30 max

4.75–6.50

5.00–6.75

2.25–2.75

–

M3, class 2

T11323

1.15–1.25

0.15–0.40

0.20–0.45

3.75–4.50

0.30 max

4.75–6.50

5.00–6.75

2.75–3.75

–

M4

T11304

1.25–1.40

0.15–0.40

0.20–0.45

3.75–4.75

0.30 max

4.25–5.50

5.25–6.50

3.75–4.50

–

M7

T11307

0.97–1.05

0.15–0.40

0.20–0.55

3.50–4.00

0.30 max

8.20–9.20

1.40–2.10

1.75–2.25

–

M10

T11310

0.84–0.94; 0.95–1.05

0.10–0.40

0.20–0.45

3.75–4.50

0.30 max

7.75–8.50

–

1.80–2.20

–

M30

T11330

0.75–0.85

0.15–0.40

0.20–0.45

3.50–4.25

0.30 max

7.75–9.00

1.30–2.30

1.00–1.40

4.50–5.50

M33

T11333

0.85–0.92

0.15–0.40

0.15–0.50

3.50–4.00

0.30 max

9.00–10.00

1.30–2.10

1.00–1.35

7.75–8.75

M34

T11334

0.85–0.92

0.15–0.40

0.20–0.45

3.50–4.00

0.30 max

7.75–9.20

1.40–2.10

1.90–2.30

7.75–8.75

M35

T11335

0.82–0.88

0.15–0.40

0.20–0.45

3.75–4.50

0.30 max

4.50–5.50

5.50–6.75

1.75–2.20

4.50–5.50

M36

T11336

0.80–0.90

0.15–0.40

0.20–0.45

3.75–4.50

0.30 max

4.50–5.50

5.50–6.50

1.75–2.25

7.75–8.75

M41

T11341

1.05–1.15

0.20–0.60

0.15–0.50

3.75–4.50

0.30 max

3.25–4.25

6.25–7.00

1.75–2.25

4.75–5.75

M42

T11342

1.05–1.15

0.15–0.40

0.15–0.65

3.50–4.25

0.30 max

9.00–10.00

1.15–1.85

0.95–1.35

7.75–8.75

M43

T11343

1.15–1.25

0.20–0.40

0.15–0.65

3.50–4.25

0.30 max

7.50–8.50

2.25–3.00

1.50–1.75

7.75–8.75

M44

T11344

1.10–1.20

0.20–0.40

0.30–0.55

4.00–4.75

0.30 max

6.00–7.00

5.00–5.75

1.85–2.20

11.00–12.25

M46

T11346

1.22–1.30

0.20–0.40

0.40–0.65

3.70–4.20

0.30 max

8.00–8.50

1.90–2.20

3.00–3.30

7.80–8.80

M47

T11347

1.05–1.15

0.15–0.40

0.20–0.45

3.50–4.00

0.30 max

9.25–10.00

1.30–1.80

1.15–1.35

4.75–5.25

M48

T11348

1.42–1.52

0.15–0.40

0.15–0.40

3.50–4.00

0.30 max

4.75–5.50

9.50–10.50

2.75–3.25

M62

T11362

1.25–1.35

0.15–0.40

0.15–0.40

3.50–4.00

0.30 max

10.00–11.00

5.75–6.50

1.80–2.10

–

–

8.00–10.00

Tungsten high-speed steels T1

T12001

0.65–0.80

0.10–0.40

0.20–0.40

3.75–4.50

0.30 max

17.25–18.75

0.90–1.30

–

T2

T12002

0.80–0.90

0.20–0.40

0.20–0.40

3.75–4.50

0.30 max

1.0 max

17.50–19.00

1.80–2.40

–

T4

T12004

0.70–0.80

0.10–0.40

0.20–0.40

3.75–4.50

0.30 max

0.40–1.00

17.50–19.00

0.80–1.20

T5

T12005

0.75–0.85

0.20–0.40

0.20–0.40

3.75–5.00

0.30 max

0.50–1.25

17.50–19.00

1.80–2.40

7.00–9.50

T6

T12006

0.75–0.85

0.20–0.40

0.20–0.40

4.00–4.75

0.30 max

0.40–1.00

18.50–21.00

1.50–2.10

11.00–13.00

T8

T12008

0.75–0.85

0.20–0.40

0.20–0.40

3.75–4.50

0.30 max

0.40–1.00

13.25–14.75

1.80–2.40

4.25–5.75

T15

T12015

1.50–1.60

0.15–0.40

0.15–0.40

3.75–5.00

0.30 max

1.00 max

11.75–13.00

4.50–5.25

4.75–5.25

4.25–5.75

Intermediate high-speed steels M50

T11350

0.78–0.88

0.15–0.45

0.20–0.60

3.75–4.50

0.30 max

3.90–4.75

–

0.80–1.25

–

M52

T11352

0.85–0.95

0.15–0.45

0.20–0.60

3.50–4.30

0.30 max

4.00–4.90

0.75–1.50

1.65–2.25

–

Classes of Materials

Table 3.1-77 Composition ranges of principle types of tool steels according to AISI and UNS classifications [1.88]

Table 3.1-77 Composition ranges of principle types of tool steels according to AISI and UNS classifications [1.88], cont. Designation AISI UNS No.

Composition b (wt%) C Mn

Si

Cr

Ni

Mo

W

V

Co

Chromium hot-worked steels H10

T20810

0.35–0.45

0.25–0.70

0.80–1.20

3.00–3.75

0.30 max

2.00–3.00

–

0.25–0.75

–

H11

T20811

0.33–0.43

0.20–0.50

0.80–1.20

4.75–5.50

0.30 max

1.10–1.60

–

0.30–0.60

–

H12

T20812

0.30–0.40

0.20–0.50

0.80–1.20

4.75–5.50

0.30 max

1.25–1.75

0.50 max

–

H13

T20813

0.32–0.45

0.20–0.50

0.80–1.20

4.75–5.50

0.30 max

1.10–1.75

0.80–1.20

–

H14

T20814

0.35–0.45

0.20–0.50

0.80–1.20

4.75–5.50

0.30 max

–

4.00–5.25

–

–

H19

T20819

0.32–0.45

0.20–0.50

0.20–0.50

4.00–4.75

0.30 max

0.30–0.55

3.75–4.50

1.75–2.20

4.00–4.50

1.00–1.70 –

Tungsten hot-worked steels H21

T20821

0.26–0.36

0.15–0.40

0.15–0.50

3.00–3.75

0.30 max

–

8.50–10.00

0.30–0.60

–

H22

T20822

0.30–0.40

0.15–0.40

0.15–0.40

1.75–3.75

0.30 max

–

10.00–11.75

0.25–0.50

–

H23

T20823

0.25–0.45

0.15–0.40

0.15–0.60

11.00–12.75

0.30 max

–

11.00–12.75

0.75–1.25

–

H24

T20824

0.42–0.53

0.15–0.40

0.15–0.40

2.50–3.50

0.30 max

–

14.00–16.00

0.40–0.60

–

H25

T20825

0.22–0.32

0.15–0.40

0.15–0.40

3.75–4.50

0.30 max

–

14.00–16.00

0.40–0.60

–

H26

T20826

0.45–0.55b

0.15–0.40

0.15–0.40

3.75–4.50

0.30 max

–

17.25–19.00

0.75–1.25

–

0.15–0.40

–

3.75–4.50

0.30 max

4.50–5.50

5.50–6.75

1.75–2.20

–

Molybdenum hot-worked steels H42

T20842

0.55–0.70b

Air-hardening, medium-alloy, cold-worked steels A2

T30102

0.95–1.05

1.00 max

0.50 max

4.75–5.50

0.30 max

0.90–1.40

–

0.15–0.50

–

A3

T30103

1.20–1.30

0.40–0.60

0.50 max

4.75–5.50

0.30 max

0.90–1.40

–

0.80–1.40

–

A4

T30104

0.95–1.05

1.80–2.20

0.50 max

0.90–2.20

0.30 max

0.90–1.40

–

–

–

A6

T30106

0.65–0.75

1.80–2.50

0.50 max

0.90–1.20

0.30 max

0.90–1.40

–

–

–

A7

T30107

2.00–2.85

0.80 max

0.50 max

5.00–5.75

0.30 max

0.90–1.40

0.50–1.50

3.90–5.15

–

A8

T30108

0.50–0.60

0.50 max

0.75–1.10

4.75–5.50

0.30 max

1.15–1.65

1.00–1.50

–

–

A9

T30109

0.45–0.55

0.50 max

0.95–1.15

4.75–5.50

1.25–1.75

1.30–1.80

–

0.80–1.40

–

A10

T30110

1.25–1.50b

1.60–2.10

1.00–1.50

–

1.55–2.05

1.25–1.75

–

–

–

–

1.10 max

–

1.00 max

–

High-carbon, high-chromium, cold-worked steels 1.40–1.60

0.60 max

0.60 max

11.00–13.00

0.30 max

0.70–1.20

T30403

2.00–2.35

0.60 max

0.60 max

11.00–13.50

0.30 max

–

D4

T30404

2.05–2.40

0.60 max

0.60 max

11.00–13.00

0.30 max

0.70–1.20

–

1.00 max

–

D5

T30405

1.40–1.60

0.60 max

0.60 max

11.00–13.00

0.30 max

0.70–1.20

–

1.00 max

2.50–3.50

D7

T30407

2.15–2.50

0.60 max

0.60 max

11.50–13.50

0.30 max

0.70–1.20

–

3.80–4.40

–

265

Part 3 1.5

1.00 max

1.5 Iron and Steels

T30402

D3

Metals

D2

266

Part 3 1.5

Part 3

Designation AISI UNS No.

Composition b (wt%) C Mn

Si

Cr

Ni

Mo

W

V

Co

Oil-hardening cold-worked steels O1 T31501 O2 T31502 O6 T31506 O7 T31507 Shock-resisting steels

0.85–1.00 0.85–0.95 1.25–1.55 c 1.10–1.30

1.00–1.40 1.40–1.80 0.30–1.10 1.00 max

0.50 max 0.50 max 0.55–1.50 0.60 max

0.40–0.60 0.50 max 0.30 max 0.35–0.85

0.30 max 0.30 max 0.30 max 0.30 max

– 0.30 max 0.20–0.30 0.30 max

0.40–0.60 – – 1.00–2.00

0.30 max 0.30 max – 0.40 max

– – – –

S1 T41901 0.40–0.55 S2 T41902 0.40–0.55 S5 T41905 0.50–0.65 S6 T41906 0.40–0.50 S7 T41907 0.45–0.55 Low-alloy special-purpose tool steels

0.10–0.40 0.30–0.50 0.60–1.00 1.20–1.50 0.20–0.90

0.15–1.20 0.90–1.20 1.75–2.25 2.00–2.50 0.20–1.00

1.00–1.80 – 0.50 max 1.20–1.50 3.00–3.50

0.30 max 0.30 max – – –

0.50 max 0.30–0.60 0.20–1.35 0.30–0.50 1.30–1.80

1.50–3.00 – – – –

0.15–0.30 0.50 max 0.35 max 0.20–0.40 0.20–0.30 d

– – – – –

L2 T61202 0.45–1.00 b L6 T61206 0.65–0.75 Low-carbon mold steels

0.10–0.90 0.25–0.80

0.50 max 0.50 max

0.70–1.20 0.60–1.20

– 1.25–2.00

0.25 max 0.50 max

– –

0.10–0.30 0.20–0.30 d

– –

P2 T51602 0.10 max P3 T51603 0.10 max P4 T51604 0.12 max P5 T51605 0.10 max P6 T51606 0.05–0.15 P20 T51620 0.28–0.40 P21 T51621 0.18–0.22 Water-hardening tool steels

0.10–0.40 0.20–0.60 0.20–0.60 0.20–0.60 0.35–0.70 0.60–1.00 0.20–0.40

0.10–0.40 0.40 max 0.10–0.40 0.40 max 0.10–0.40 0.20–0.80 0.20–0.40

0.75–1.25 0.40–0.75 4.00–5.25 2.00–2.50 1.25–1.75 1.40–2.00 0.50 max

0.10–0.50 1.00–1.50 – 0.35 max 3.25–3.75 – 3.90–4.25

0.15–0.40 – 0.40–1.00 – – 0.30–0.55 –

– – – – – – –

– – – – – – 0.15–0.25

– – – – – – 1.05–1.25Al

0.10–0.40 0.10–0.40 0.10–0.40

0.10–0.40 0.10–0.40 0.10–0.40

0.15 max 0.15 max 0.40–0.60

0.20 max 0.20 max 0.20 max

0.10 max 0.10 max 0.10 max

0.15 max 0.15 max 0.15 max

0.10 max 0.15–0.35 0.10 max

– – –

W1 W2 W3 a

T72301 T72302 T72303

0.70–1.50 e 0.85–1.50 e 1.05–1.15

All steels except group W contain 0.25 max Cu, 0.03 max P, and 0.03 max S; group W steels contain 0.20 max Cu, 0.025 max P, and 0.025 max S. Where specified, sulfur may be increased to 0.06 to 0.15% to improve machinability of group A, D, H, M and T steels. b Available in several carbon ranges. c Contains free graphite in the microstructure. d Optional. e Specified carbon ranges are designated by suffix numbers.

Classes of Materials

Table 3.1-77 Composition ranges of principle types of tool steels according to AISI and UNS classifications [1.88], cont.

Metals

room temperature as a function of hardening treatment are listed for group L and group S steels in Table 3.1-78.

Table 3.1-78 Mechanical properties of group L and group S tool steels at room temperature as a function of hardening

treatment [1.88] Elongationa (%)

Reduction in area (%)

Hardness (HRC)

510

25

50

96 HRB

2000 1790 1550 1275 930 655

1790 1655 1380 1170 760 380

5 10 12 15 25 25

15 30 35 45 55 55

54 52 47 41 30 93 HRB

2000 1585 1345 965 690

1790 1380 1100 830 415

4 8 12 20 24

9 20 30 48 52

54 46 42 32 96 HRB

2070 2025 1790 1680 1345 725

1895 1860 1690 11 525 1240 440

– 4 5 9 12 25

– 12 17 23 37 50

57.5 54 50.5 47.5 42 96 HRB

2345 2240 1895 1515 1035 640

1930 1860 1690 1380 1170 380

5 7 9 10 15 25

20 24 28 30 40 55

59 58 52 48 37 95 HRB

2170 1965 1895 1820 1240

1450 1585 1410 1380 1035

7 9 10 10 14

20 25 29 33 45

58 55 53 51 39

Type

Condition

Tensile strength (MPa)

L2

Annealed Oil quenched from 855 ◦ C and single tempered at: 205 ◦ C 315 ◦ C 425 ◦ C 540 ◦ C 650 ◦ C Annealed Oil quenched from 845 ◦ C and single tempered at: 315 ◦ C 425 ◦ C 540 ◦ C 650 ◦ C Annealed Oil quenched from 925 ◦ C and single tempered at: 205 ◦ C 315 ◦ C 425 ◦ C 540 ◦ C 650 ◦ C Annealed Oil quenched from 870 ◦ C and single tempered at: 205 ◦ C 315 ◦ C 425 ◦ C 540 ◦ C 650 ◦ C Annealed Oil quenched from 940 ◦ C and single tempered at: 205 ◦ C 315 ◦ C 425 ◦ C 540 ◦ C 650 ◦ C

710

L6

S1

S5

S7

a

In 50 mm

0.2% yield strength (MPa)

267

Part 3 1.5

resistance, ductility and fracture toughness, and in many applications stability against softening at elevated temperatures. Characteristic mechanical properties at

1.5 Iron and Steels

268

Part 3

Classes of Materials

Part 3 1.5

3.1.5.7 Cast Irons

Microstructure of Metallic Matrix Phases. Ferritic,

pearlitic, austenitic, bainitic (austempered). More details are presented in Fig. 3.1-119 and Table 3.1-79.

The term cast iron pertains to a large family of multi-component Fe−C−Si alloys which solidify according to the eutectic of the Fe−C system (Sect. 3.1.5.1; Fig. 3.1-99). They are treated extensively in [1.89]. Their comparatively high C and Si contents lead to solidification either according to the metastable equilibria involving Fe3 C or according to the stable equilibria involving graphite, depending, also, on the content of further alloying elements, melt treatment, and rate of cooling. Since, in addition, the metallic phases can be alloyed and their microstructures varied by annealing and transformation treatments as in other ferrous alloys, a multitude of microstructural states and associated properties result.

Iron–Carbon–Silicon Equilibria and Carbon Equivalent Since C and Si are the alloying elements which dominate the solidification behavior and the resulting microstructures of cast irons, their phase equilibria need to be taken into account. Figure 3.1-120 shows a section through the metastable ternary Fe−C−Si diagram at 2 wt% Si which approximates the Si content of many cast irons. Compared to the binary Fe−C system, the addition of Si decreases the stability of Fe3 C and increases the stability of ferrite, as indicated by the expansion of the α-phase field. With increasing Si concentration, the C concentrations of the eutectic and the eutectoid equilibria decrease while their temperatures increase. These relations are the basis for correlating the C and Si concentrations with the ranges of formation of steels and of the main groups of cast irons as shown in Fig. 3.1-121. The relations are expressed in terms of the carbon equivalent CE = (wt% C) + (1/3) (wt% Si). The concentration of the eutectic (upper dashed line) is given by CEe = 4.3. Accordingly, alloys with CE < 4.3 are hypoeutectic and alloys with CE > 4.3 are hypereutectic. In P-containing cast irons the relation is CE = (wt% C) + (1/3) (wt% Si + wt% P). In addition, Fig. 3.1-121 shows the limit of solubility of C in austenite (lower dashed line), which is the upper limit of the range of steels. It is given by CEγmax = 2.1 = (wt% C) + (1/6) (wt% Si).

Classification The C rich phases determine the basic classification of cast irons. According to the color of their facture surfaces, Fe3 C-containing grades are called white, graphite-containing grades are called gray, and alloys which solidify in mixed states are called mottled. In addition, the shape of the graphite phase particles and the microstructure of the metallic matrix phases are taken into account since they are also characterizing the mechanical properties. Shape of Graphite Phase Particles. Lamellar (flake)

graphite (FG) is characteristic of cast irons with nearzero ductility; spheroidal (nodular) graphite (SG) is characteristic of ductile cast iron; compacted (vermicular) graphite (CG) is a transition form between flake and nodule shape; temper graphite (TG) results from a tempering treatment and consists of small clusters of branched graphite lamellae.

Grades of Cast Irons Table 3.1-80 lists the composition ranges of typical unalloyed cast irons, indicating that they are classified mainly by the type of carbon-rich phase formed and by the basic mechanical behavior.

Table 3.1-79 Classification of cast irons according to commercial designation, microstructure and color of fracture surface [1.89] Commercial designation

Carbon-rich phase

Matrixa

Fracture

Final structure after

Gray iron

Lamellar graphite

P

Gray

Solidification

Ductile iron

Spheriodal graphite

F, P, A

Silver-gray

Solidification or heat treatment

Compacted graphite iron

Compacted (vermicular) graphite

F, P

Gray

Solidification

White iron

Fe3 C

P, M

White

Solidification and heat treatmentb

Mortled iron

Lamellar Gr + Fe3 C

P

Mottled

Solidification

Malleable iron

Temper graphite

F, P

Silver-gray

Heat treatment

Austempered ductile iron

Spheroidal graphite

At

Silver-gray

Heat treatment

a b

F, ferrite; P, pearlite; A, austenite; M, martensite; At, austempered (bainite) White irons are not usually heat treated, exept for stress relief and to continue austenite transformation

1.5 Iron and Steels

Metals

Classification by structure Alloys with eutectic (>2 % C on Fe-C diagram)

Cast irons White iron

With carbides Wear resistant High-temperature applications

Ferritic

M3C

Pearlitic

M4C3

Martensitic

M7C3

Austenitic

MC

Mottled iron

With carbides and graphite

Gray iron

With graphite

High-alloy irons

Flake (lamellar) graphite

Ductile iron

Compacted (vermicular) graphite

Malleable iron

Spheroidal graphite Temper carbon

Fig. 3.1-119 Classification of cast irons [1.89] Table 3.1-80 Range of composition, microstructural and mechanical characteristics of typical unalloyed cast irons [1.89] Type

Carbon phase

Concentration range (wt%) C Si

Mn

P

S

Gray Compacted graphite Ductile White Malleable

FG CG SG Fe3 C Fe3 C/TG

2.5–4.0 2.5–4.0 3.0–4.0 1.8–3.6 2.2–2.9

0.2–1.0 0.2–1.0 0.1–1.0 0.25–0.8 0.15–1.2

0.002–1.0 0.01–0.1 0.01–0.1 0.06–0.2 0.02–0.2

0.02–0.25 0.01–0.03 0.01–0.03 0.06–0.2 0.02–0.2

Gray Iron. This most common type of cast iron is char-

acterised by flake graphite and requires a high CE to ensure a sufficient graphitization potential which is also increased by Al addition. Gray irons may be moderately alloyed, e.g., by 0.2–0.6 wt% Cr, 0.2–1 wt% Mo, and 0.1–0.2 wt% V which promote the formation of alloy carbides and pearlite. Upon plastic deformation the flake form of graphite promotes early internal crack

1.0–3.0 1.0–3.0 1.8–2.8 0.5–1.9 0.9–1.9

formation and, thus, causes the low ductility of gray iron. Ductile Iron. This cast iron is characterized by the spheroidal graphite phase (SG) in its microstructure. Spheroidal graphite is formed during solidification if the melt has been treated by the addition of a component which promotes the particular nucleation and

Part 3 1.5

Ferrous alloys Classification by commercial name or application

269

270

Part 3

Classes of Materials

Part 3 1.5

Carbon content (wt %)

T(°C) 1500

(δ –Fe + γ – Fe + L) CEe

1400 L 1300

Ductile irons

4.0

(δ –Fe Delta ferrite)

1200

3.0

(γ –Fe Austenite)

1100

Gray irons

(γ – Fe + Fe3C + L)

White irons Malleable irons

2.0

1000 900

CE x max

1.0 800 (α –Fe) Ferrite

700 600

0

1

Steels

(α – Fe + γ –Fe + Fe3C) 0

2

3 4 5 Carbon content (wt %)

Fig. 3.1-120 Section through the metastable Fe−C−Si phase diagram at 2 wt% Si [1.89]

growth behavior of graphite in the form of nodules. The most common alloying component added to nucleate spheroidal graphite is Mg, but Ca, Ce, La, and Y have also been found to favour spheroidal graphite formation. Basically this microstructural modification leads to higher yield strength and higher ductility because the plastic deformation of the metallic matrix phases can be extended to higher strains than in gray iron before fracture sets in. Malleable Irons. The melt treatment of malleable cast

irons involves Mg, Ca, Bi, or Te additions. But malleable irons have an as-cast structure consisting of Fe3 C in a pearlitic matrix. By heat treatment in the range of 800–970 ◦ C the cementite phase is transformed into graphite (TG). The cooling is controlled in such a way as to promote pearlite formation, ferrite formation, or a mixture of the two.

0

1.0

2.0

3.0 Silicon content (wt %)

Fig. 3.1-121 Approximate C and Si concentrations for the composition ranges of steels and different grades of cast irons [1.89]

Alloy Cast Irons. Alloying elements beyond the levels mentioned above are added to cast irons almost exclusively to enhance resistance to abrasive wear or chemical corrosion, or to extend their stability for application at elevated temperature. The function of the alloying elements is essentially the same as in steels. Table 3.1-81 lists the groups of grades with typical compositions and the microstructural constituents present in the as-cast state.

Mechanical Properties of Cast Irons Due to the multitude of as-cast structures as a function of alloy composition, melt treatment, cooling rate (as influenced by the cooling conditions and the cross section of the work piece), and subsequent heat treatment, there is a wide range of mechanical properties which can be achieved according to the requirements of the application. Table 3.1-82 gives a survey in terms of characteristic examples.

Metals

1.5 Iron and Steels

Composition (wt%) a TC b Mn P

S

Low-carbon white iron d High-carbon, low-silicon white iron Martensitic nickel-chromium iron Martensitic nickel, high-chromium iron Martensitic chromium-molybdenum iron High-chromium iron Corrosion-resistant irons

2.2–2.8 2.8–3.6 2.5–3.7 2.5–3.6

0.15 0.15 0.15 0.15

High-silicon iron f High-chromium iron Nickel-chromium gray iron g Nickel-chromium ductile iron h High-resistant gray iron

0.4–1.1 1.2–4.0 3.0 3.0

1.5 0.3–1.5 0.5–1.5 0.7–4.5

0.15 0.15 0.08 0.08

0.15 0.15 0.12 0.12

Medium-silicon iron i Nickel-chromium iron g Nickel-chromium-silicon iron j High-aluminium iron Heat resistant ductile irons

1.6–2.5 1.8–3.0 1.8–2.6 1.3–2.0

0.4–0.8 0.4–1.5 0.4–1.0 0.4–1.0

0.30 0.15 0.10 0.15

0.10 0.15 0.10 0.15

Medium-silicon ductile iron Nickel-chromium ductile iron h Heat-resistant white irons Ferritic grade Austenitic grade

2.8–3.8 0.2–0.6 0.08 0.12 3.0 0.7–2.4 0.08 0.12 1.0–2.5 0.3–1.5 – 1.0–2.0 0.3–1.5 –

Description

Si

Ni

Cr

Mo

Cu

0.5 1.0 1.0 1.0

e

Matrix structure as-cast c

Abrasion-resistant white irons

a b c d e f g h i j

0.2–0.6 0.3–2.0 1.3 1.3

0.15 0.30 0.30 0.10

1.0–1.6 0.3–1.0 0.8 1.0–2.2

1.5 2.5 2.7–5.0 5.0–7.0

2.0–3.6 0.5–1.5 0.10 0.06

1.0

1.5

11.0–23.0

0.5–3.5

1.2 M, A

2.3–3.0 0.5–1.5 0.10 0.06

1.0

1.5

23.0–28.0

1.5

1.2 M

14.0–17.0 – 5.0 0.5–3.0 5.0 12.0–35.0 1.0–2.8 13.5–36.0 1.5–6.0 1.0–3.0 18.0–36.0 1.0–5.5

1.0 4.0 1.0 1.0

0.5 3.0 7.5 –

F M, A A A

– 1.0 1.0 –

– 7.5 10.0 –

F A A F

2.5–6.0 1.5 – 1.75–5.5 18.0–36.0 1.75–3.5

2.0 1.0

– –

F A

0.5–2.5 0.5–2.5

– –

– –

F A

– –

4.0–7.0 1.0–2.75 5.0–6.0 1.3–6.0

1.0 3.0 1.1–4.0 7.0–11.0

– – 13.5–36.0 1.8–6.0 13.0–43.0 1.8–5.5 – 20.0–25.0 Al

– 30.0–35.0 10.0–15.0 15.0–30.0

e

– –

CP CP M, A M, A

Where a single value is given rather than a range, that value is a maximum limit Total carbon CP, coarse pearlite; M, martensite; A, austenite; F, ferrite Can be produced from a malleable-iron base composition Copper can replace all or part of the nickel Such as Durion, Durichlor 51, Superchlor Such as Ni-Resist austenitic iron (ASTM A 436) Such as Ni-Resist austenitic ductile iron (ASTM A 439) Such as Silal Such asd Nicrosilal

Table 3.1-82 Mechanical properties of cast irons Material

Gray cast irons (FG) DIN 1691 Ductile cast irons (SG) DIN 1693

Rp0.2 (N mm−2 ) (min.)

Rm (N mm−2 ) (min.)

250 c 360 c 400 c

100 b 200 b 350 b 390 c 600 c 700 c

A5 (%) (min.)

Matrix microstructure

Short code a

0.6010 0.6020 0.6035 0.7040 0.7060 0.7070

GG-10 GG-20 GG-35 GGG-40 GGG-60 GGG-70

Unspecified Mainly ferritic

15 d 2d 2d

Material number a

Pearlitic-ferritic Mainly pearlitic Wide variation permissable

Part 3 1.5

Table 3.1-81 Ranges of alloy content of typical alloy cast irons [1.89]

271

272

Part 3

Classes of Materials

Part 3 1.6

Table 3.1-82 Mechanical properties of cast irons, cont. Material

White malleable irons (TG) DIN 1692 Black malleable irons (TG) DIN 1692

a b

c d

Short code a

Core: ganular pearlite Core: lamellar to granular pearlite Ferrite

0.8035 0.8045 0.8040

GTW-35-04 GTW-45-07 GTW-40-05

Pearlite, ferrite Pearlite Hardened

0.8135 0.8145 0.8165 0.8170

GTS-35-10 GTS-45-06 GTS-65-02 GTS-70-02

– 12 –

0.6652 0.6661 0.6680

GGL-NiMn13-7 GGL NiCr20-3 GGL-NiSiCr30-5-5

15 d 7d – 7d

0.7652 0.7661 0.7680 0.7685

GGG-NiMn13-7 GGG NiCr20-3 GGG-NiSiCr30-5-5 GGG-NiCr35-3

Rm (N mm−2 ) (min.)

260 b 220 b

350 d 450 d 400 d

4 7 5

200 c 270 c 430 c 530 c

350 d 450 d 650 d 700 d

10 6 2 2

140/220 190/240 170/240 390 390 390 370

Austenitic alloy cast irons (FG) DIN 1694 Austenitic cast iron (SG) DIN 1694

Material number a

Rp0.2 (N mm−2 ) (min.)

210 210 240 210

A5 (%) (min.)

Matrix microstructure Unspecified

According to German Materials Standard The values refer to a cylindrical test specimen of 30 mm in diameter corresponding to a wall thickness of 15 mm. The tensile strength values to be expected depend on the wall thickness Example: GG-20. Wall thickness (mm) 2.5–5.5 5.5–10 10–20 20–40 40–80 80–150 Rm (N/mm2 ) 230 205 180 155 130 115 Diameter of the test rod: 12 or 15 mm. For cast parts with a thickness < 6 mm tensile test specimens. For a cylindrical test specimen of 12 mm in diameter. The mechanical properties depend on the diameter of the test specimen Example: GTW-45-07 Diameter of the test rod (mm) 9 12 15 Rm (N/mm2 ) 400 450 480 Rp0.2 (N/mm2 ) 230 260 280

3.1.6 Cobalt and Cobalt Alloys Cobalt is applied as a base metal for a number of alloys, as an alloying element, and as a component of numerous inorganic compounds. Table 3.1-83 lists its major applications. Cobalt and cobalt-based materials are treated extensively in [1.90, 91]. Data on the electronic structure of Co and Co alloys may be found in [1.92]. Phase diagrams, crystal structures, and thermodynamic data of binary Co alloys may be found in [1.93].

3.1.6.1 Co-Based Alloys Cobalt-based alloys with a carbon content in the range of 1 to 3 wt% C are widely used as wear-resistant

solid materials and weld overlays. Depending on the alloy composition and heat treatment, M23 C6 , M6 C, and MC carbides are formed. Materials with lower carbon content are mostly designed for corrosion resistance and for heat resistance, sometimes combined with wear resistance. The metals W, Mo, and Ta are essentially added for solid solution strengthening. In a few alloys Ti and Al are added. They serve to form a coherent ordered Co3 (Ti, Al) phase which precipitates and leads to strengthening by age hardening. The Cr content is generally rather high to provide oxidation and hot corrosion resistance. Table 3.1-84 presents a survey of Co-based alloys.

1.6 Cobalt and Cobalt Alloys

Metals

Application

Co consumption (%)

Form

Section

Co-based alloys, Co-based superalloys, steels

24.3

Base and alloying element

Sects. 3.1.5, 3.1.6, 3.1.7

Hard facing and related materials

6.9

Base and alloying element

Sect. 3.1.6

Soft and hard magnetic materials, and controlled thermal expansion alloys

8.5

Base and alloying element, oxide

Chapt. 4.3

15.2

Metal, binder

Sect. 3.1.6

8.0

Metal, sulfates

−

Oxides, salts

−

9.5

Powder, hydroxide, LiCoO2

−

11.0

Soaps, complexes made from metal powder

−

Sulphate, carbonate, hydroxide

−

Cemented carbides, diamond tooling Catalysts Colorizer for glass, enamel, ceramics, plastics, fabrics

11.6

Batteries Tire adhesives, soaps, driers Feedstuff, anodizing, electrolysis, copper winning

5.0

Table 3.1-84 Compositions of Co-based alloys Alloy tradename

Nominal composition (wt%) UNS No. Co Cr W Mo

C

Fe

Ni

Si

Mn

Others

2.5

3

1.5

2.4

5 (max)

3.5 (max) 2 (max)

1.3

0.5

−

2 (max)

0.57

3 (max)

3 (max)

2 (max)

1 B (max)

1 (max)

−

Cast, P/M and weld overlay wear-resistant alloys Stellite 1

R30001

bal

30

13

Stellite 3 (P/M) R30103

bal

30.5

12.5

Stellite 4

R30404

bal

30

14

Stellite 6

R30006

bal

29

4.5

1.5 (max) 1.2

3 (max)

3 (max)

1.5 (max) 1 (max)

−

Stellite 6 (P/M) R30106

bal

28.5

4.5

1.5 (max) 1

5 (max)

3 (max)

2 (max)

2 (max)

1 B (max)

Stellite 12

R30012

bal

30

1.4

3 (min)

1.5

0.7

2.5

−

Stellite 21

R30021

bal

27

−

5.5

0.25

3 (max)

2.75

1 (max)

1 (max)

0.007 B (max)

Stellite 98M2 (P/M)

−

bal

30

18.5

0.8 (max) 2

5 (max)

3.5

1 (max)

1 (max)

4.2 V, 1 B (max)

Stellite 703

−

bal

32

−

12

2.4

3 (max)

3 (max)

1.5 (max) 1.5 (max) −

Stellite 706

−

bal

29

−

5

1.2

3 (max)

3 (max)

1.5 (max) 1.5 (max) −

Stellite 712

−

bal

29

−

8.5

2

3 (max)

3 (max)

1.5 (max) 1.5 (max) −

Stellite 720

−

bal

33

−

2.5

3 (max)

3 (max)

1.5 (max) 1.5 (max) 0.3 B

Stellite F

R30002

bal

25

12.3

1.75

3 (max) 22

2 (max)

1 (max)

−

Stellite Star J (P/M)

R30102

bal

32.5

17.5

−

2.5

3 (max)

2.5 (max) 2 (max)

2 (max)

1 B (max)

Stellite Star J

R31001

bal

32.5

17.5

−

2.5

3 (max)

2.5 (max) 2 (max)

2 (max)

−

Tantung G

−

bal

29.5

16.5

−

3

3.5

7 (max)

−

2 (max)

4.5 Ta/Nb

Tantung 144

−

bal

27.5

18.5

−

3

3.5

7 (max)

−

8.3

0.5 − 1 (max)

−

18 1 (max)

5.5 Ta/Nb

Laves-phase wear-resistant alloys Tribaloy T-400 R30400

bal

9

−

29

−

−

−

2.5

−

−

Tribaloy T-800 −

bal

18

−

29

−

−

−

3.5

−

−

Wrought wear-resistant alloys Stellite 6B

R30016

bal

30

4

1.5 (max) 1

3 (max)

2.5

0.7

1.4

−

Stellite 6K

−

bal

30

4.5

1.5 (max) 1.6

3 (max)

3 (max)

2 (max)

2 (max)

−

Part 3 1.6

Table 3.1-83 Applications of cobalt [1.91]

273

274

Part 3

Classes of Materials

Part 3 1.6

Table 3.1-84 Compositions of Co-based alloys, cont. Alloy tradename

Nominal composition (wt%) UNS No. Co Cr W Mo

C

Fe

Ni

Si

Mn

Others

Wrought heat-resistant alloys (see Table 3.1-86 for cast alloy compositions) R30605

bal

20

15

−

0.1

R30188 R30783

bal bal

22 3

14 −

− −

0.1 3 (max) 22 0.03 (max) 25.5 28

UMCo-50 − bal S-816 R30816 40 (min) Corrosion-resistant alloys

28 20

− 4

− 4

0.02 (max) 21 − 0.37 5 (max) 20

0.35 1.25 0.03 La 0.5 (max) 0.5 (max) 5.5 Al, 3 Nb, 3.4 Ti (max) 0.75 0.75 − 1 (max) 1.5 4 Nb

Ultimet (1233) MP 159

bal bal

26 19

2 −

5 7

0.06 −

9 25.5

0.3 −

0.8 −

MP35N R30035 Duratherm 600 R30600

35 41.5

20 12

− 3.9

− − 0.05 (max) 8.7

35 bal

− 0.4

− 0.75

Elgiloy Havar

40 42.5

20 20

− 2.8

0.15 (max) bal 0.2 bal

15.5 13

− −

2 1.6

Haynes 25 (L605) Haynes 188 Inconel 783

R31233 R30159

R30003 R30004

10 4 7 2.4

3 (max) 10

3 9

0.4 (max) 1.5

−

0.08 N 3 Ti, 0.6 Nb, 0.2 Al − 2 Ti, 0.7 Al, 0.05 Be 1 Be (max) 0.06 Be (max)

P/M: powder metallurgy; bal: balance

3.1.6.2 Co-Based Hard-Facing Alloys and Related Materials

3.1.6.3 Co-Based Heat-Resistant Alloys, Superalloys

The behavior of Co-based wear resistant alloys is based on a coarse dispersion of hard carbide phases embedded in a tough Co-rich metallic matrix. The volume fraction of the hard carbide phase is comparatively high: e.g., at 2.4 wt% C the carbide content is 30 wt%. The carbide phases are M7 C3 (Cr7 C3 type) and M6 C (W6 C type). Table 3.1-85 lists characteristic properties of Co-based hard facing alloys the compositions of which are listed Table 3.1-83.

Both wrought and cast Co-based heat resistant alloys, listed in Tables 3.1-84 and 3.1-86, respectively, are also referred to as Co superalloys. They are based on the face-centered cubic high temperature phase of Co which is stabilized between room temperature and the solidus temperature by alloying with ≥ 10 wt% Ni. They are solid-solution strengthened by alloying with W, Ta, and Mo. Furthermore, they are dispersion strengthened by carbides.

Table 3.1-85 Properties of selected Co-based hard-facing alloys Property

Stellite 21

Stellite 6

Stellite 12

Stellite 1

Tribaloy T-800

Density, g cm−3 (lb in−3 ) Ultimate compressive strength, MPa (ksi) Ultimate tensile strength, MPa (ksi) Elongation, % Coefficient of thermal expansion, ◦ C−1 (◦ F−1 )

8.3 (0.30) 1295 (188) 710 (103) 8 14.8 × 10−6 (8.2 × 10−6 )

8.3 (0.30) 1515 (220) 834 (121) 1.2 15.7 × 10−6 (8.7 × 10−6 )

8.6 (0.31) 1765 (256) 827 (120) 1 14 × 10−6 (7.8 × 10−6 )

8.6 (0.31) 1930 (280) 620 (90) 1 13.1 × 10−6 (7.3 × 10−6 )

8.6 (0.31) 1780 (258) 690 (100) 3.0 mm per year. Oxidation Behavior Refractory metals require protection from oxidizing environment as they do not form protective oxide layers. Oxidation of Mo and W leads to a loss of material by the formation of volatile oxides above 600 ◦ C, but without any significant impact on the mechanical properties. The low temperature oxidation of Mo and W often causes problems in practical use as thin corrosion films are formed during storage in moist air. The surface topography of Mo has a strong impact on the reaction rate. The corrosion film contains oxygen but also chemically-bonded nitrogen, which is incorporated in the film during film growth. Cx H y residues are the nuclei for the oxidative attack in the early stage of film growth [1.132]. There is extensive evidence that between 300 and 500 ◦ C, oxide-dispersion-strengthened (ODS) refractory metal alloys (e.g., Mo−La2 O3 and Mo−Y2 O3 grades) possess markedly reduced oxidation rates compared to the pure metals [1.133]. In-situ oxidation and evaluation of the binding state reveal that MoO2 dominates over MoO3 both for Mo and Mo–

Table 3.1-109 Metal loss of Mo, W, Nb and Ta in millimeter per year (mm/yr) in acids, alkalis and salt solutions Corroding agent (aqueous solution)

Temperature

10% HCl 10% H2 SO4 10% HNO3 3% HF 10% CH3 COOH 10% KOH 3% NaCl 10% HCl 10% H2 SO4 10% HNO3 3% HF 10% CH3 COOH 10% KOH 3% NaCl

20 ◦ C 20 ◦ C 20 ◦ C 20 ◦ C 20 ◦ C 20 ◦ C 20 ◦ C 100 ◦ C 100 ◦ C 100 ◦ C 100 ◦ C 100 ◦ C 100 ◦ C 100 ◦ C

Metal loss (mm/yr) Mo W < 0.003 < 0.005 18.6 < 0.001 0.07 < 0.1 < 0.1 < 0.025 0.17 150 0.18 0.033 0.054 < 0.1

0.002 < 0.1 < 0.25 < 0.1 < 0.05 < 0.1 < 0.1 0.005 < 0.25 < 0.25 0.15 < 0.05 0.01 < 0.1

Nb

Ta

0 < 0.1 < 0.013 > 3.0 < 0.1 < 0.2 < 0.1 0.005 (embrittlement) < 0.001 < 0.076 > 3.0 < 0.1 1.2 (embrittlement) < 0.1

< 0.001 < 0.1 < 0.013 > 3.0 < 0.013 < 0.1 < 0.1 < 0.025 0 < 0.025 > 3.0 < 0.013 < 0.003 (embrittlement) < 0.1

Metals

1.9 Refractory Metals and Alloys

temperatures the solubility of the refractory metal in the metal melts and vice versa is negligible) Maximum resistance temperature (◦ C) Mo W

Nb

Ta

Al

Not resistant

Not resistant

Not resistant

Pb

1100

1100

Fe

Not resistant

Not resistant

Metal melt

680

850 Not resistant

1000 Not resistant

Ga

300

K

1200

Cu

1300

Mg

1000

600

950

1150

Na

1030

900

1000

1000

Hg

600

600

600

600

Zn

500

750

Not resistant

Sn

550

980

Not resistant

Ag

Resistant

800

400

450

900

1000

1000

Resistant

Resistant

Resistant

Resistant

Resistant

500 260 1200

Table 3.1-111 Maximum temperatures for the resistance of Mo, W, Nb, and Ta against gaseous media at atmospheric

pressure Gaseous media

Maximum resistance temperature Mo W

Nb

Ta

Air and oxygen

see Sect. 3.1.9.2

Hydrogen

Resistant

Resistant

250 ◦ C (T > 250 ◦ C embrittlement owing to dissolved hydrogen)

300 ◦ C (T > 300 ◦ C embrittlement owing to dissolved hydrogen)

Nitrogen

Resistant

Resistant

300 ◦ C (T > 300 ◦ C embrittlement owing to dissolved nitrogen)

400 ◦ C (T > 400 ◦ C embrittlement owing to dissolved nitrogen)

Ammonia

Resistant (except 1000–1100 ◦ C: nitration)

Resistant (except 700– 1150 ◦ C: nitration)

300 ◦ C (T > 300 ◦ C embrittlement owing to dissolved nitrogen)

700 ◦ C (T > 700 ◦ C embrittlement owing to dissolved nitrogen)

Water vapor

700 ◦ C

700 ◦ C

200 ◦ C

200 ◦ C

Carbon monoxide

800 ◦ C

1000 ◦ C

800 ◦ C

1100 ◦ C

Carbon dioxide

(T > 800 ◦ C carburization) (T > 800 ◦ C carburization) 1200 ◦ C 1200 ◦ C 400 ◦ C (T > 1200 ◦ C oxidation) (T > 1200 ◦ C oxidation)

0.47 wt%Y2 O3 –0.08 wt%Ce2 O3 (Fig. 3.1-146). These results are confirmed when comparing the thickness of the oxide layer formed at 500 ◦ C in air (Fig. 3.1-147). The enhanced oxidation resistance of doped samples cannot be attributed to a chemical but rather to a morphological-mechanical effect. Investigations of the surface of pure Mo samples subjected to long-term oxidation reveal a network of cracks in the MoO2 layer which drastically diminishes the passivating effect of

500 ◦ C

this layer by facilitating a further attack by O. Such cracks cannot be found on the surface of oxidized Mo−La2 O3 and Mo−Y2 O3 samples [1.133]. Above 700 ◦ C for Mo and approximately 900 ◦ C for W, evaporation of the volatile oxides MoO3 and WO3 is the rate-controlling process and the oxidation follows a linear time dependence. Above 2000 ◦ C for Mo and 2400 ◦ C for W, the metal loss increases because of the increasing vapor pressure of the pure metals. The time

Part 3 1.9

Table 3.1-110 Maximum temperatures for the resistance of Mo, W, Nb, and Ta against metal melts (up to the stated

309

310

Part 3

Classes of Materials

Part 3 1.9

(%) 100

Mo/percentage Mo Mo/percentage Mo2 Mo/percentage Mo3 MY/percentage Mo MY/percentage MoO2

80 60 40 20

MY/percentage MoO3

0 0

5000

15 000 20 000 Langmuir (L)

10 000

Fig. 3.1-146 ESCA measurements and evaluation of Mo/MoO2 /MoO3 fraction versus in-situ oxidation conditions in Langmuir (1 L = 10−6 Torr s). Mo: 4N5 Mo ribbon, electro-polished surface; MY: Mo–0.47 wt%Y2 O3 – 0.08 wt%Ce2 O3 ribbon, electro-polished surface, test conditions: 500 ◦ C/air [1.133] Oxide layer thickness (µm) 60 Mo (oxide layer thickness) MY (oxide layer thickness) 50 Mo (crack length) MY (crack length) 40 30 20

T (°C) 2400 2100 2 ∆d 10 (µm/h) 86

a)

10 1800

1600

1400 1300 1008

4

6

0.67 Pa

2

101

4 2

0.27 Pa

8 6

10–1 8

0.13 Pa

4

6

0.07 Pa

2

∆g (mg/ cm2 min)

4

0 0

100

200

300

Crack length/ area (mm / mm2) 50 45 40 35 30 25 20 15 10 5 0 400 500 600 Time (h)

Fig. 3.1-147 Thickness of oxide layer and crack length per area versus testing time. Mo: 4N5 Mo ribbon, electropolished surface; MY: Mo–0.47 wt%Y2 O3 – 0.08 wt%Ce2 O3 ribbon, electropolished surface, test conditions: 500 ◦ C/air [1.133]

2

100

8 6 –1

0.03 Pa

Mo

10–2 8

4 ×10

3.6

4.4

5.2

6.0

T(°C) 3000 2400 2100 1800 1600 ∆d 1 10 (µm/h) 8

6 ×10–3 6.8 104 / T (K–1)

b)

1400 1200

6

0.53 Pa

4

10–1 6 4

0.13 Pa

1008

∆g (mg/ cm2 min)

8

0.27 Pa

2

2× 10–1

2

6

0.07 Pa

4

10–2 2

8

W

0.03 Pa

6

–1

10

3

4

5

6

4 ×10–3 7 104 / T (K–1)

Fig. 3.1-148a,b Metal loss in air for Mo (a) and W (b) at T ≥

1200 ◦ C [1.134]

dependence of metal loss for Mo and W at T ≥ 1200 ◦ C is shown in Fig. 3.1-148 [1.134]. The oxidation rates of Nb and Ta strongly depend on temperature, pressure, and time. Different mechanisms causing different oxidation rates can be observed and metastable sub-oxides are formed during use in O-containing atmospheres [1.131, 134]. Oxygen is dissolved in the metal matrix which leads to significant changes of the mechanical properties. A poorly adherent, porous pentoxide is formed on the metal surface which does not protect the metal from further attack. Oxygen which has penetrated the porous oxide layer diffuses along the grain boundaries of the metal, leading to drastic embrittlement. The metal loss at 1100 ◦ C due to oxidation in air is shown for Mo, W, Nb, and Ta in Fig. 3.1-149 [1.135]. The embrittled zone caused by oxygen diffusion into the substrate is not considered in this diagram. Only a few coating systems have been found to prevent the refractory metals from oxidation. In the case of Mo, Pt-cladded components with a diffusion barrier interlayer on the basis of alumina, which prevents the formation of brittle intermetallic molybdenum–platinum

Metals

Metal loss (mm)

5 4 Mo 3 2

W

1

Nb Ta

0 0

2

4

6

8

10

12 Time (h)

Fig. 3.1-149 Oxidation behavior of Mo, W, Nb, and Ta at

1100 ◦ C [1.135]

phases, are used; e.g., for stirrers used to homogenize special glasses. Mo components for glass tanks and glass melting electrodes are protected from oxidation by coatings based on silicides, such as silicon–boron [1.136]. Silicon–boron and other silicide based coatings, such as silicon–chromium–iron or silicon–chromium–titanium, are also used to protect Mo and Nb based alloys from oxidation in aerospace applications [1.135, 137–139]

3.1.9.3 Recrystallization Behavior The mechanisms and kinetics of recovery and recrystallization processes significantly affect the processing and application of refractory metals. The homologous temperatures for obtaining 50% recrystallized structure during annealing for one hour, range from 0.39 for Mo, 0.41 for W, 0.42 for Nb, to 0.43 for P/M Ta. The fraction of recrystallized structure as a function of the annealing temperature of Mo, W, P/M Ta, TZM, and Mo–0.7 wt%La2 O3 sheets of 1-mm thickness is shown in Fig. 3.1-150. Experimental data on the evolution of grain size with the annealing temperature for pure Mo and Ta sheets of 1-mm thickness are shown in Fig. 3.1-151 [1.126,140]. A recrystallization diagram for Mo is published in [1.141], and for P/M Ta in [1.142]. Compared to pure Mo, the recrystallization temperature of the carbide-precipitation-hardened alloy TZM is increased by 450 ◦ C and that of Mo–0.7 wt%La2 O3 by 550 ◦ C. The data listed in Table 3.1-112 show that all those alloys containing particles, which deform together with the matrix metal (ML, K−Si−Mo, WL10, WL15, WT20, and AKS−W−ThO2 ), reveal a significantly increased recrystallization temperature in the highly de-

Percentage of recrystallized structure 100 Mo 90 Ta 80 W 70 TZM 60 50 40 Mo – 0.7 wt % 30 La2O3 20 10 0 600 800 1000 1200 1400 1600 1800 Annealing temperature (°C)

Fig. 3.1-150 Fraction of recrystallized structure versus annealing temperature (annealing time ta = 1 h) for Mo, P/M Ta, W, TZM, and Mo–0.7 wt% La2 O3 sheets with a thickness of 1 mm, degree of deformation, th −th ϕ = pth p s 100[%], where th p = thickness of sintered plate, and th s = thickness of rolled sheet. Mo: ϕ = 94%, P/M Ta: ϕ = 98%, W: ϕ = 94%, TZM: ϕ = 98%, Mo– 0.7 wt% La2 O3 : ϕ = 99% [1.126] Average grain size (µm) 10 000 P / M Mo 1000 100

EB Ta P / M Ta

10 1

600 800 1000 1200 1400 1600 1800 2000 2200 Annealing temperature (°C)

Fig. 3.1-151 Grain size versus annealing temperature (annealing time ta = 1 h) for Mo, P/M Ta, and EB (electronbeam melted) Ta sheets with a thickness of 1 mm. Mo: ϕ = 94%, P/M Ta: ϕ = 98%, EB Ta: ϕ = 98% [1.126, 140]

formed state. Increasing the degree of deformation from ϕ = 90% to ϕ = 99.99% leads to a further increase of the recrystallization temperature (100% recrystallized structure, 1 h annealing time) ranging from 600 ◦ C for K−Si−Mo, 700 ◦ C for ML, 950 ◦ C for WT20, 1000 ◦ C for WL10, to 1050 ◦ C for WL15 and WC20. This can be explained by particle refinement. During the deformation process the particles are elongated. During annealing they break up and rows of smaller particles

311

Part 3 1.9

6

1.9 Refractory Metals and Alloys

312

Part 3

Classes of Materials

Part 3 1.9

Table 3.1-112 Typical recrystallization temperature and ultimate tensile strength of commercial Mo and W based rod and

wire materials with a defined degree of total deformation ϕ [1.118] Alloy designation Pure Mo TZM MHC ML MY K−Si−Mo Mo50Re Mo30W Pure W AKS-W WL10 WL15 WC20 WT20 AKS-W−ThO2 W5Re W26Re

Composition (wt%)

Mo, 0.5% Ti, 0.08% Zr, 0.025% C Mo, 1.2% Hf, 0.08% C Mo, 0.3% La2 O3 Mo, 0.48% La2 O3 , 0.07% Ce2 O3 Mo, 0.05% Si, 0.025% K Mo, 47.5% Re Mo, 30% W W, 0.005% K W, 1.0% La2 O3 W, 1.5% La2 O3 W, 1.9% Ce2 O3 W, 2% ThO2 W, 1% ThO2 , 0.004% K W, 5 Re W, 26 Re

Temperature for 100% recrystallized structure (t = 1 h) (◦ C)

Typical ultimate tensile strength at 1000 ◦ C (MPa)

1100 (ϕ = 90%) 1400 (ϕ = 90%) 1550 (ϕ = 90%) 1300 (ϕ = 90%), 2000 (ϕ = 99.99%) 1100 (ϕ = 90%), 1350 (ϕ = 99.99%) 1200 (ϕ = 90%), 1800 (ϕ = 99.99%) 1300 (ϕ = 90%) 1200 (ϕ = 90%) 1350 (ϕ = 90%) 2000 (ϕ = 99.9%) 1500 (ϕ = 90%), 2500 (ϕ = 99.99%) 1550 (ϕ = 90%), 2600 (ϕ = 99.99%) 1550 (ϕ = 90%), 2600 (ϕ = 99.99%) 1450 (ϕ = 90%), 2400 (ϕ = 99.99%) 2400 (ϕ = 99.9%) 1700 (ϕ = 90%) 1750 (ϕ = 90%)

250 (ϕ = 90%) 600 (ϕ = 90%) 800 (ϕ = 90%) 300 (ϕ = 90%) 300 (ϕ = 90%) 300 (ϕ = 90%) 600 (ϕ = 90%) 350 (ϕ = 90%) 350 (ϕ = 90%) 800 (ϕ = 99.9%) 400 (ϕ = 90%) 420 (ϕ = 90%) 420 (ϕ = 90%) 400 (ϕ = 90%) 1000 (ϕ = 99.9%) 500 (ϕ = 90%) 900 (ϕ = 90%)

are formed. With the increase in number of particles, the subgrain boundaries are pinned more effectively, resulting in an increase of the recrystallization temperature [1.119]. Experiments with various oxide-dispersion-strengthened (ODS) Mo materials with 2 vol.% of oxide, mean oxide particle sizes in the as-sintered state of around 0.8 µm, and a degree of deformation ln(A0 /A) = 8.5 (A0 = cross section as-sintered, A = cross section asdeformed), revealed differences in the recrystallization temperature of up to 750 ◦ C depending on the oxide used. It could be shown that this effect is caused by particle refinement during deformation and subsequent heat treatment. Particles which increase the recrystallization temperature very effectively, as is the case with La2 O3 , show a high particle deformability [1.143]. Whether oxide particles deform in a pseudo-plastic manner or not depends on a multitude of parameters, such as the yield stress of the particles, the yield stress of the matrix, the particle/matrix bonding strength, the crystallite size, the defect density, or the state of stresses. Most of these parameters are unknown or difficult to measure. Good correlation could be found between the particle deformability, with its effect on the increase of the recrystallization temperature, and the fraction of ionic bonding character of the oxide, following the definition of Pauling [1.143]. Figure 3.1-152 shows that

compounds with a high fraction of ionic bonding character, such as La2 O3 or SrO, raise the recrystallization temperature very effectively. Slight particle multiplication could also be found for Al2 O3 , ZrO2 , and HfO2 compounds with a marked covalent bonding character, but because of breakage of the particles during the deformation process. The recrystallization temperature can be tailored by varying both the type and the content of the oxide, the latRecrystallization start temperature (°C) 2000 Sr O 1750 MgO

1500 1250

ZrO2 HfO2

Al2O3 1000 50

La2 O3 Ce2 O3

55

60

Y2O3

65

70 75 Ionic bonding (%)

Fig. 3.1-152 Recrystallization start temperature of various

ODS Mo materials versus fraction of ionic bonding (according to Pauling) of the respective oxides. Oxide content = 2 vol.%, wire diameter = 0.6 mm [1.143]

Metals

1600

Recrystallization start temperature (°C)

1500

Mo – 0.3 wt % La2O3

1400 1300 1200 1100 Mo – 0.03 wt % La2O3

1000 900 800

6

6.5

7

7.5

8

8.5

9

9.5

10 10.5 In (A0 / A)

Fig. 3.1-153 Recrystallization start temperature of Mo–

0.03 wt% La2 O3 and Mo–0.3 wt% La2 O3 wires versus degree of deformation ln(A0 /A) [1.133]

Table 3.1-113 Recrystallization mechanisms for AKS-W wires [1.120, 144, 145]

Microstructural state Evolution of the microstructure during wire drawing Coarsening of the microstructure during annealing

Processes

• •

• •

Exaggerated grain growth

Formation of a dislocation cell structure by static and dynamic recovery processes Annealing temperature 800 to 1400 ◦ C: – Reduction of the dislocation density within the cell walls; – Break-up of the K-containing stringers into pearl rows of bubbles; – Migration of longitudinal grain boundaries is strongly reduced by pearl rows of bubbles; – Similar 110 texture as in the as-worked state. For low heating rates, partial or even entire bubble rows can be dragged by the boundaries moving in the transverse direction. As a result, row/row collision and bubble coalescence can occur The temperature up to which the coarsened substructure remains stable depends on the degree of deformation (e.g., diameter 0.18 mm: 2100 ◦ C/15 min). The coarsened substructure has a significant portion of high-angle grain boundaries (misorientation angles higher than 15◦ )

Nucleation and growth of large interlocking grains occur by primary recrystallization, whereby a subgrain begins to grow laterally at the expense of neighboring polygonized subgrains.

• • • •

313

Part 3 1.9

ter shown in Fig. 3.1-153 for Mo–0.03 wt%La2 O3 (ILQ) and Mo–0.3 wt%La2 O3 (ML). AKS–W shows a similar effect where the Kcontaining bubbles are effective pinning centers. The recovery and recrystallization mechanisms of AKS–W as a function the annealing temperature are summarized in Table 3.1-113. The recrystallization temperature of AKS–W is determined by the relation of the driving to dragging forces. The driving forces are determined by the thermomechanical treatment (TMT), the dragging forces depend on the number, size, and distribution of the K bubbles. With increasing degree of deformation, both the driving forces (increasing dislocation density and lowangle/high-angle boundary volume) and dragging forces (increasing length of stringers of K-filled pores and, as a consequence, increasing number of K bubbles formed) become larger. During the first deformation steps the

1.9 Refractory Metals and Alloys

Because of the pearl row of bubbles, the rate of grain boundary movement is higher in the axial, than in the transverse direction Because of the interaction between the bubbles and the growing grains, the grain boundaries possess a wave-like, interlocking structure The grain aspect ratio of the recrystallized structure increases with increasing number of K bubbles. The number of K bubbles is a function of the K-content, the degree of deformation and the TMT. Highly deformed, recrystallized wires reveal a 531 texture.

314

Part 3

Classes of Materials

Part 3 1.9

Recrystallization onset temperature (°C)

GAR-value / grain size *0.1 (µm)

2000 28

1900

25

1800

22

1700

Grain size Recrystallization onset temperature

1600

19 16 13

1500

10 1400

GAR- 7 value 4

1300 1200

3

3.5

4

4.5

5

5.5

6

1 6.5 7 in (A0 / A)

Fig. 3.1-154 Recrystallization onset temperature, grain size, and grain aspect ratio (GAR) versus ln(A0 /A). AKS-W grade with K content of 42 µg/g; deformation temperature below the onset temperature of recrystallization; no intermediate heat treatments above recrystallization temperature; annealing time = 15 min; heating rate = 3 K/s; annealing atmosphere = hydrogen; annealing temperature for GAR evaluation = 2200 ◦ C (ta = 5 min); grain size measured in transverse direction [1.133]

increase of the driving forces outweighs that of the dragging forces. Then the rise of the dragging forces starts to dominate, resulting in an increase of the recrystallization temperature (see Fig. 3.1-154). With increasing length of the potassium stringers/number of potassium bubbles, the significance of the dragging effect in the transverse direction increases, resulting in an increase of the grain aspect ratio (GAR) in the recrystallized state. A marked increase of the GAR starts at a degree of deformation that coincides with a pronounced increase of the transverse grain size, as illustrated in Fig. 3.1-154.

3.1.9.4 Mechanical Properties Influence of Thermomechanical Treatment (TMT) and Impurities Molybdenum and Tungsten Alloys [1.133]. The formation of a cellular dislocation structure increases both strength and fracture toughness [1.146, 147]. Additionally, the mechanical properties depend on the type of deformation process, purity, and heat treatment. The thermomechanical treatment (TMT) serves to obtain the specified shape, to eliminate the porosity, and to adjust the mechanical and structural properties. In particular,

the evolution of the density distribution, pore size and shape, and its interaction with the mechanical properties are of high importance [1.120, 148–150]. During hot deformation which is usually the primary working step for both Mo and W, high-angle grain boundaries are formed and migrate, grains are subdivided by low-angle boundaries, and new large-angle boundaries are formed by coarsening of the substructure [1.151]. Grains with an aspect ratio close to one and a low dislocation density are formed. Following this hot deformation, the material is processed at temperatures below the recrystallization onset temperature, but above the onset temperature of polygonization, leading to a cellular dislocation structure. The cell boundaries become impenetrable for slip dislocations and behave like grain boundaries, when the misorientation between neighboring cells is higher than a critical value of about 4◦ for Mo and W [1.146]. The formation of a misoriented cellular dislocation structure results both in an increase of strength and a decrease of the ductile-brittletransition temperature (DBTT). Both effects become more and more significant with increasing degree of deformation which results in a smaller effective grain size [1.146]. The size of the misoriented cellular dislocation structure depends sensitively on the deformation temperature. A high deformation temperature implies large grains [1.152]. It is essential to control the deformation temperature carefully. The control of the microstructure at intermediate steps has also been recommended [1.153]. The production yield is mainly decreased by the formation of grain boundary cracks. The cohesion of the grain boundaries is believed to be the controlling factor limiting the ductility of Mo and W [1.154]. Impurities segregated at the grain boundaries can lead to a strong decrease in ductility. Based on both semiempirical and first principle modeling of the energetics and the electronic structures of impurities on a Σ3 (111) grain boundary in W, it was concluded that the impurities N, O, P, S, and Si weaken the intergranular cohesion, while B and C enhance the interatomic interaction across the grain boundary [1.154]. The amount of O in Mo (≈ 10 µg/g) and W (≈ 5 µg/g) is sufficient to form a monolayer of O on the grain boundaries as long as the grain size is not smaller than 10 µm. During recrystallization a migrating grain boundary can be saturated by collecting impurities while sweeping the volume. Based on the investigation of arccast Mo samples, a beneficial effect of C was found and attributed to the following mechanisms [1.155]:

Metals

•

Suppression of oxygen segregation Precipitation of carbides, acting as dislocation sources Formation of an epitaxial relationship between precipitates and bulk crystals at grain boundaries

From these findings it was proposed that a C/O atomic ratio of >2 should improve the mechanical properties of Mo. The results obtained with arc-cast samples published in [1.155] could not be reproduced for samples produced by a P/M route [1.157]. As a consequence of the above mentioned effects, but in contrast to many other metallic materials, the fracture toughness of molybdenum and tungsten is strongly reduced with increasing degree of recrystallization. With increasing plastic deformation, the fracture toughness increases (see Sect. 3.1.9.4), combined with a transition from intercrystalline to transcrystalline cleavage and to a transcrystalline ductile fracture [1.147, 158, 159]. With increasing degree of deformation the working temperature can be progressively reduced. In particular, products with a high degree of deformation such as wires, thin sheets, and foils can be subjected to a high degree of deformation at a temperature below the polygonization temperature. The reduction of grain boundaries oriented transversely to the drawing direction increases the bending ductility of W [1.160]. Tungsten wire with an optimum ductility can only be obtained, when deformed in such a way that dynamic recovery processes occur without polygonization [1.161]. Other recovery phenomena, besides polygonization, are described in [1.162]. However a high degree of deformation below the onset temperature for dynamic polygonization favors the formation of longitudinal cracks. Thin sheets and foils, annealed under conditions resulting in a small fraction of primarily recrystallized grains, can show a very specific fracture behavior, i. e., cracks running at an angle of 45◦ to the rolling direction [1.163, 164]. Such 45◦ embrittlement is caused by the nucleation of critical cracks at isolated grains formed by recrystallization of weak secondary components of the texture. Cracks propagate under 45◦ to the rolling direction owing to the alignment of the cleavage planes in the rolling texture.

the ingot has to be protected to prevent an interaction with the atmosphere. The mechanical behavior of pure annealed niobium and tantalum is characterized by a high ductility and low work-hardening rate. The influence of deformation on the yield strength and fracture elongation of pure tantalum is shown in Fig. 3.1-155. Mechanical properties of niobium- and tantalumbased alloys are strongly influenced by interstitial impurities, e.g., oxygen, nitrogen, carbon, and hydrogen. The generally lower content of impurities and the larger grain size are the reasons why melt-processed niobium and tantalum have a lower room-temperature tensile strength compared to sintered material. As an example, the influence of oxygen on the mechanical properties of tantalum is presented in Fig. 3.1-156. After deformation both niobium- and tantalumbased alloys are usually heat treated in high vacuum before delivering in order to achieve a fine grained primarily recrystallized microstructure. Static Mechanical Properties Properties at Low Temperatures and Low Strain Rates. The flow stress of the transition metals

Mo, W, Nb, and Ta is strongly dependent on temperature and a strain rate below a characteristic transition temperature TK (corresponding to 0.1 to 0.2 of the absolute melting temperature) and plastic strain rates below 1 × 10−5 s−1 [1.165]. As an example, experimental data on the temperature dependence of the flow stress of recrystallized Ta are shown in Fig. 3.1-157. This dependence has Yield strength (MPa) 600 500 400 300 200 100 15

30

45

60

75 90 97.5 Deformation (%)

30

45

60

75 90 97.5 Deformation (%)

Elongation (%) 40 20

Niobium and Tantalum Alloys. Contrary to Mo and W,

pure Nb and Ta are deformed at room temperature. Only highly-alloyed materials require breaking down the ingot microstructure either by forging or extrusion at elevated temperatures. In these cases

15

Fig. 3.1-155 Yield strength and fracture elongation of as-

worked tantalum versus degree of deformation [1.156]

315

Part 3 1.9

• •

1.9 Refractory Metals and Alloys

316

Part 3

Classes of Materials

Part 3 1.9

Elongation/reduction in area (%)

Tensile strength (MPa) 500

100

1000

90

900

80

Tensile strength

70

Reduction in area

40

700

400

Elongation

20

200 100

10

0 200 400 600 800 1000 1200 1400 1600 1800 2000

0

Oxygen concentration (wt ppm)

Fig. 3.1-156 Tensile strength, fracture elongation, and reduction in area versus oxygen concentration of tantalum specimens tested at room temperature [1.168] Flow stress (MPa) Macroplastic range Microplastic range

4 ×10–6 s–1

350 300

σ*

200

Pk

150 100 50 σ G 0 150

200

250

300

350

Nb

350

400 300

30

250

Ta

450

800

500

50

400

Mo

Mo

600

60

0

Tk (K)

400 T (K)

Fig. 3.1-157 Temperature dependence of the flow stress (at

εpl = 1 × 10−5 ) of recrystallized Ta under monotonic loading and dε/ dt = 2 × 10−6 s−1 , TK = “knee” temperature, σG = athermal range, σ ∗ = thermal range [1.140]

been attributed to the characteristic behavior of screw dislocations [1.166]. The transition temperature TK was shown to depend on the strain rate (Fig. 3.1-158) [1.140, 167]. For test temperatures T < TK the flow stress increases markedly. Borderlines between elastic/anelastic strain (σA ) and microstrain/macrostrain deformation ranges can be deduced, subdivided into athermal (σG ) and thermal (σ ∗ ) ranges. The lower borderline of the microplastic region is almost independent of tem-

300 250 –6 10

10–5

10–4

10–3

10–2 10–1 Stain rate (1 / s)

Fig. 3.1-158 Dependence of TK on strain rate [1.140, 167]

perature and may be called the intrinsic flow stress which is much lower than the conventionally determined flow stress (technical flow stress). In the stress range between the intrinsic and the technical flow stress below TK , strains of up to several percent were observed after extended loading times for Mo and Ta [1.169, 170]. The effect of temperature and strain rate on the monotonic microflow behavior of bcc metals as functions of temperature and strain rate was presented schematically [1.171]. Experimental data for Mo and Ta in constant load tests (low temperature creep tests) for stresses considerably below the technical flow stress are shown in Figs. 3.1-159 and 3.1-160. After a considerable incubation period, depending on the test temperature and stress, a rapid increase in strain can be noticed approaching a saturation strain which depends on the stress level. The effect of the loading rate on the instantaneous plasCreep strain (%) 90 °C

0.8 0.7

80°C 70 °C

30 °C

0.6 50 °C

0.5 0.4 0.3 0.2 0.1 0.0 1

σ = 150 MPa 10

100

1000

10 000 100 000 Time (min)

Fig. 3.1-159 Creep elongation of recrystallized Mo at σ = 150 MPa for 30 ◦ C ≤ T ≤ 90 ◦ C [1.126]

Metals

P /M Ta recrystallized (1240°C/ 2 h) T = 30 °C

3.00

125 MPa 2.00 110 MPa 150 MPa

1.00

0.00 1

10

100

1000

10 000 Time (min)

Fig. 3.1-160 Creep elongation of recrystallized Ta sheets

(thickness = 2 mm) at 30 ◦ C for 110 MPa ≤ σ ≤ 150 MPa [1.126]

tic strain can be revealed with high resolution in loading–unloading tests under various constant loading rates [1.140, 170]. This microflow behavior may be significant for components at low temperatures and low loads, e.g., under storage conditions. Internal stresses in semi-finished products may be reduced even at room temperature to levels corresponding to the intrinsic flow stress [1.170]. A significant influence of the strain rate on the tensile properties at room temperature was determined for recrystallized Mo and Ta (Fig. 3.1-161) [1.140], in close agreement with literature data [1.172]. This strain rate effect makes it imperative for comparison of test data to list the test conditions.

Properties at Elevated Temperatures. A rough ranking of the high temperature strength of Mo and W alloys can be obtained from the comparison presented in Table 3.1-112 (Sect. 3.1.9.3). Carbide-precipitationstrengthened Mo-based alloys (MHC, TZM) and alloys high in Re (Mo–50 wt%Re, W–26 wt%Re) have the highest tensile strength. Alloys containing potassium (AKS–W, AKS−W−ThO2 ) exhibit high strength only in the case of a high preceding plastic deformation. A comparison of the high-temperature strength of rods made of Mo, W, Nb, and Ta in their usual state of delivery is given in Fig. 3.1-162. The typical microstructure of stress-relieved Mo is a highly polygonized structure with up to 5% recrystallized grains. Depending on the product shape W is delivered in the as-worked state, especially in case of sheet material and wires, or stress-relieved with a polygonized microstructure. The decrease of tensile strength and the increase of reduction in area with increasing test temperature can be related to changes in the fracture mode (Fig. 3.1-163), i. e., cleavage fracture, brittle grain boundary failure, and ductile transcrystalline failure [1.158]. Ultimate tensile strength (MPa)

800 700 600

Mo W Ta Nb

500 400

700

300

Stress (MPa)

600

200

ReH ReL Rm

Mo

100

500

00

400 Ta

300 200 100 0 –5 10

10–4

10–3

10–2 10–1 100 –1 Total strain rate (s )

Fig. 3.1-161 Effect of strain rate on tensile properties at

room temperature of recrystallized Mo and recrystallized Ta [1.140]

200 400 600 800 1000 1200 1400 1600 18002000 Testing temperature (°C)

Fig. 3.1-162 Ultimate tensile strength versus test tem-

perature for Mo, W, Ta, and Nb rods in their usual delivering condition. Mo, W: diameter = 25 mm (stress relieved); Ta, Nb: diameter = 12 mm (recrystallized); technical strain rates = 1.0 × 10−4 s−1 up to the 0.2% yield strength followed by 3.3 × 10−3 s−1 (Mo, room temperature), 1.7 × 10−3 s−1 (Mo, elevated temperatures), 8.3 × 10−4 s−1 (W, elevated temperatures), 6.7 × 10−4 s−1 up to the 0.2% yield strength followed by 3.3 × 10−3 s−1 (Nb, Ta for all test temperatures) [1.118]

317

Part 3 1.9

Creep strain (%) 4.00

1.9 Refractory Metals and Alloys

318

Part 3

Classes of Materials

Part 3 1.9

a) Ultimate tensile strength (MPa)

Fracture mode, Area fraction (%)

800

100

P/M Ta P/M Ta 2.5 W P/M Ta 10 W

700 Transcrystalline ductile failure

Cleavage failure

80

600 500

Recrystallization Brittle grain boundary failure

60

400 300 200

40

100 Fibrous failure

20

0

0

200

400

600

800

0

Ductile grain boundary failure

1000 1200 1400 1600 1800 Test temperature (°C)

Fig. 3.1-163 Effect of test temperature on fracture modes of pure W,

stress relieved at 1000 ◦ C/6 h [1.158]

Fig. 3.1-164a,b The ultimate tensile strength Rm (a) and the yield strength Rp0.2 (b) versus test temperature of

P/M Ta, P/M Ta2.5W, and P/M Ta10W sheets that are 1 mm thick, with impurity content (µg/g) Ta: O = 60, N = 10, H = 1.8, C < 5; Ta2.5W: O = 70, N = 12, H = 2.4, C = 5; Ta10W: O = 31, N < 5, H < 1, C = 21; material condition = recrystallized, technical strain rates = 6.7 × 10−4 s−1 up to Rp0.2 , followed by 3.3 × 10−3 s−1 [1.126]

0

200 400 600 800 1000 1200 1400 1600 1800 2000 Testing temperature (°C) 0.2 % yield strength (MPa) 800 P/M Ta 700 P/M Ta 2.5 W P/M Ta 10 W 600

b)

500 400 300 200 100 0

0

500

200 400 600 800 1000 1200 1400 1600 1800 2000 Testing temperature (°C)

Yield stress 0.2 % (MPa) C – 103 Wc – 3009 FS – 85 Nb – 1 Zr

400

The influence of alloying Ta with W is illustrated in Fig. 3.1-164 for Ta2.5W and Ta10W, which are the main commercial Ta-based alloys. Figure 3.1-165 summarizes values of Rp0.2 of the most common Nb-based alloys at elevated temperatures. All of these alloys are hardened primarily by solid solution strengthening; however, small amounts of precipitates are present. For comparison, the high-temperature strength of stress-relieved 1-mm sheets made of Mo- and W-based materials is shown in Fig. 3.1-166. For short-term application under high stresses, the precipitationstrengthened Mo alloys TZM and MHC offer the best performance up to a service temperature of 1500 ◦ C. For higher temperatures, W-based materials should be applied. Tantalum-based alloys are used only if additional high ductility is required after cooling to room temperature.

300 200 100 0 800

900

1000

1100

1200

1300

1400 1500 T (°C)

Fig. 3.1-165 Effect of temperature on Rp0.2 for common Nb-based alloys [1.173]

Dynamic Properties Microplasticity Effects under Cyclic Loading at Low Temperatures. Microplasticity effects under monotonic

loading have been reported in the literature for singleand polycrystalline Mo and Ta [1.171, 174]; information regarding effects of strain rate and temperature on the cyclic stress–strain response is given in [1.140,170]. Most experiments on cyclic stress–strain behavior have

Metals

Plastic strain 2 × 10–3 Stress cycle Mo TZM W

1200 1000

Stress (MPa) 120

ε pl for 0.042 MP a / s ε pl for 0.42 MP a / s

1 × 10

–3

60

800 600

0.0

0

–1 × 10–3

–60

400 200

ε pl for 4.2 MP a / s

0 0

200 400 600 800 1000 1200 1400 1600 1800 2000 Testing temperature (°C) b) 0.2 % yield strength (MPa) 1400 Mo TZM W

1200 1000 800 600 400 200 0

0

200 400 600 800 1000 1200 1400 1600 1800 2000 Testing temperature (°C)

Fig. 3.1-166a,b The ultimate tensile strength Rm (a) and the yield strength Rp0.2 (b) versus test temperature for Mo,

TZM, and W sheets that are 1 mm thick. Material condition = stress relieved, technical strain rates = 2.0 × 10−3 s−1 (Mo, TZM, room temperature), 1.3 × 10−3 s−1 (Mo, TZM, elevated temperatures), 3.3 × 10−4 s−1 up to Rp0.2 , followed by 6.7 × 10−4 s−1 (W, elevated temperatures) [1.126]

been carried out at room temperature. When bcc metals are deformed at T < 0.2 Tm , microstrain (ε ≤ 10−3 ) is characterized as the plastic strain, accommodated by the motion of non-screw dislocations [1.166, 169]. These differences are manifested in the temperature and strain-rate dependence of the flow behavior [1.171,175]. Investigations of Mo and Ta showed that a true microplastic deformation can only be considered at plastic strains of less than 5 × 10−4 [1.140]. The critical temperature below which the marked increase in the cyclic flow stress occurs is in the range of 25 ◦ C to 80 ◦ C for Ta and between 200 ◦ C and 280 ◦ C for Mo, depending on the strain rate. The experimental results for Ta showed that the highest cyclic plastic strains are obtained under strain rates between 1 × 10−8 s−1 and 2 × 10−6 s−1 . As an example, the effect of the loading rate on the

–2 × 10–3 –0.2

0.0

0.2

0.4

0.6

–120 0.8 1.0 1.2 Normalized cycle

Fig. 3.1-167 Effect of loading rate on cyclic plastic strain of recrystallized Ta during a tension-compression cycle (R = −1). Stress amplitude = 120 MPa; test temperature = 25 ◦ C; duration of a cycle at 0.042 MPa/s = 190 min, at 4.2 MPa/s = 1.9 min; maximum plastic strain rate at all loading rates = approx. 3 × 10−6 s−1 [1.140]

cyclic plastic strain of recrystallized tantalum during tension–compression cycles at loading rates between 0.042 MPa/s (duration of one cycle = 190 min) and 4.2 MPa/s (duration of one cycle = 1.9 min) is shown in Fig. 3.1-167 [1.140]. High-Cycle Fatigue Properties. Most of the fatigue data are reported in form of stress vs. number of cycles (S–N) curves. For Mo a fatigue limit may be approached for N > 107 under stress-controlled conditions [1.176]. Experiments were conducted at test frequencies up to 20 kHz. The results of such tests should be considered with caution, taking into account the temperature and strain-rate sensitivity of bcc metals. Representative S–N curves for as-worked and recrystallized Mo, and a comparison of push–pull- and bending–fatigue-tested Mo sheet specimens are shown in Figs. 3.1-168 [1.126] and 3.1-169 [1.126]. The reported fatigue test data for various test methods are summarized in Table 3.1-114 with the fatigue limit (Se) and the ratio of fatigue limit to tensile–stress (Se/Rm) as characteristic parameters. Methods of statistical evaluation of test data were published [1.176, 177]. A decrease in fatigue limits with decreasing cyclic frequency was found. Cyclic hardening/softening was deduced and cyclic stress–strain curves over wide ranges of plastic strain amplitudes were published in [1.178, 179] for Mo, in [1.172, 180, 181] for Ta, and in [1.182] for Nb and

319

Part 3 1.9

a) Ultimate tensile strength (MPa) 1400

1.9 Refractory Metals and Alloys

320

Part 3

Classes of Materials

Part 3 1.9

Stress amplitude (MPa) 800

Stress amplitude (MPa) 400 1. Anelastic stress-strain range

700

2. Microplastic stress-strain-range 3. Onset of macroplasticity 4. Macroplastic inter300 actions 2

600

As worked

2

500 1

400 300

3 2

1

200

Recrystallized

193 K 3

4 3

200

363 K 423 K

4

2

100

100

245 K 300 K

4

3

1

1

3 218 K

3 2

0 4 10

10 5

10 6

10 7 10 8 Number of loading cycles

Region I 0 1 × 10–5

Region II 1 × 10 1 × 10 1 × 10–2 Cyclic plastic strain at saturation (∆ ε plas ) –4

Fig. 3.1-168 Rotating–bending fatigue test results for as-

received and recrystallized Mo rods (diameter = 25 mm) at room temperature [1.126]

–3

Fig. 3.1-170 Cyclic-stress–plastic-strain curves of recrystallized Mo at different temperatures at a loading rate of 60 MPa/s [1.140]

Stress amplitude (MPa) 1000

Stress amplitude (MPa) 400 1. Anelastic σ-ε -range

800

2. Microplastic σ-ε -range 3. Onset of macroplasticity 4. Macroplastic inter300 actions

25 Hz bending loading

2

Region I

600

Region II 3

2

300 K 4

400

3 100

200

0 2 10

223 K

3

200 8 Hz push-pull loading

4

173 K

2

4

373 K

3 2

10

3

10

4

10

5

10 10 10 Number of loading cycles 6

7

8

Fig. 3.1-169 Comparison of test results of bending (at

25 Hz) and push–pull fatigue (at 8 Hz) tests of stressrelieved Mo sheet specimens (800 ◦ C/6 h) [1.126] at room temperature

Nb1Zr. Cyclic stress–plastic-strain curves are given in Figs. 3.1-170 and 3.1-171 for Mo and Ta at various test temperatures. The ranges of microplastic and macroplastic strain can be differentiated, based on the different slopes. The elevated temperature fatigue behavior of TZM was investigated for test temperatures between 300 ◦ C and 500 ◦ C [1.183]. Brittle failure under high cycle fatigue conditions was found over the entire temperature range, with a significant decrease in fatigue strength with increasing temperature.

0 1 × 10–5

1 × 10–4 1 × 10–3 1 × 10–2 Cyclic plastic strain at saturation (∆ε plas)

Fig. 3.1-171 Cyclic-stress–plastic-strain curves of recrys-

tallized Ta at different temperatures at a loading rate of 0.42 MPa/s [1.140] Low-Cycle Fatigue Properties. Results of low-cycle fatigue experiments under strain control on asworked W plate material at 815 ◦ C are shown in Fig. 3.1-172. Low-cycle fatigue tests of pure W were performed in the temperature range between 1650 ◦ C and 3300 ◦ C [1.184]. A relationship Nfailure = exp(−αT ) was found to be valid up to test temperatures of 2700 ◦ C [1.185]. In all cases the failure mode was intercrystalline. Similar results were also obtained at a test temperature of 1232 ◦ C [1.186]. The deformation behavior of Nb and Nb1Zr under plastic-strain control at room temperature was investigated and cyclic stress–strain curves published [1.182].

Metals

1.9 Refractory Metals and Alloys

recrystallized. RT = room temperature

Production Dimension (mm) Pretreatment process (plate: thick- T(◦ C)/ta (h) ness, bar: diameter)

Mo

P/M

bar 12

Mo5Re

P/M

bar 12

Mo41Re

P/M

bar 12

TZM

P/M

bar 12

W

P/M

bar 12

W5Re

P/M

bar 12

W26Re

P/M

bar 12

W2ThO2 Nb

P/M P/M

bar 12 bar 5.9

Ta

P/M

bar 5.9

P/M P/M

plate 1 bar 50

Push-pull fatigue, R = −1, fatigue limit Se for N = 1 × 107

Material

Mo TZM

Bending fatigue, R = −1, fatigue limit Se for 50% fracture probability at N = 1 × 107

Rotating bending fatigue, R = −1, fatigue limit Se for 50% probability at N = 5 × 107

Test mode

Mo

P/M

plate 2

Mo5Re Mo41Re TZM

P/M P/M P/M

plate 1.6 plate 1.6 plate 2

W

P/M

plate 2

Ta

P/M

plate 1

Ta

EB

plate 1

Ta2.5W Ta2.5W Ta10W

P/M EB EB

plate 1 plate 1 plate 0.64

Ta

plate 2

Aw Rxx Aw Sr Rxx Aw Sr Rxx Aw Sr Rxx Aw Rxx Aw Rxx Aw Rxx Rxx Aw Rxx Aw Rxx Rxx Aw Aw Aw Aw Aw Rxx Rxx Aw Sr Rxx Sr Sr Aw Sr Rxx Aw Rxx Aw Rxx Aw Rxx Rxx Rxx Aw

Test conditions, temperature,

Se (MPa)

Se /Rm

Ref.

450 220 450 400 230 690 620 320 550 560 340 760 310 770 440 820 450 365 225 220 290 270 195 440 500 250 205 225 180 210 520 540 280 460 680 650 750 460 520 225 335 240 270 220 310 270 480

0.68 0.44 0.68 0.68 0.48 0.62

[1.126]

frequency

RT, 100 Hz 1200/1 RT, 100 Hz RT, 100 Hz 900/6 RT, 100 Hz 1300/1 RT, 100 Hz RT, 100 Hz 1050/6 RT, 100 Hz 1400/1 RT, 100 Hz RT, 100 Hz RT, 100 Hz 1500/1 RT, 100 Hz RT, 100 Hz 1600/1 RT, 100 Hz RT, 100 Hz 1800/1 RT, 100 Hz RT, 100 Hz 1700/1 RT, 100 Hz 1900/1 RT, 100 Hz RT, 100 Hz RT, 100 Hz RT, 100 Hz RT, 100 Hz 1200/1 RT, 0.05 Hz RT, 25 Hz RT, 25 Hz 850 ◦ C, 25 Hz RT, 0.05 Hz RT, 10 Hz 1200/2 RT, 0.05 Hz 1200/2 RT, 10 Hz RT, 25 Hz 780/6 RT, 25 Hz 1200/1 RT, 25 Hz RT, 25 Hz RT, 25 Hz RT, 25 Hz 1150/6 RT, 25 Hz 1500/1 RT, 25 Hz RT, 25 Hz 1600/1 RT, 25 Hz RT, 25 Hz 1200/1 RT, 25 Hz RT, 25 Hz 1200/1 RT, 25 Hz 1300/1 RT, 25 Hz 1300/1 RT, 25 Hz RT, 25 Hz

0.36 0.62 0.57 0.48 0.70 0.71 0.65 0.54 0.39 0.64 0.42 0.51 0.92 0.95

[1.126]

[1.126]

[1.126]

[1.126] [1.126] [1.126] [1.126] [1.190] [1.190] [1.179] [1.191]

[1.179]

[1.126]

0.56 0.61

[1.126] [1.126] [1.126]

[1.126] 0.56 0.75 0.61 0.96 0.79 0.69

[1.126] [1.126] [1.126] [1.126] [1.168]

Part 3 1.9

Table 3.1-114 Summary of fatigue data of refractory metals, pretreatment: Aw = as worked, Sr = stress relieved, Rxx =

321

Part 3

Classes of Materials

Part 3 1.9

Table 3.1-114 Summary of fatigue data of refractory metals, pretreatment: Aw = as worked, Sr = stress relieved, Rxx =

recrystallized, cont. Test mode High-frequency push– pull fatigue, R = −1, fatigue limit Se for 50% fracture probability at N = 108

322

10

2

Material

Production Dimension (mm) Pretreatment process plate: thickness, T(◦ C)/ta (h) bar: diameter

Mo TZM Ta

P/M P/M EB

bar 11 bar 11 bar 3

Ta2.5W Ta10W Nb

P/M P/M

plate 2 bar 12 bar 3

Rxx Rxx Aw Sr Rxx Rxx Aw Rxx

101

1

10–2 1 10

1088 K As-received Recrystallized 102

Room temperature As-received Recrystallized 103

104

105 106 Cycles to failure Nf

Fig. 3.1-172 Low-cycle fatigue data of as-received and re-

crystallized W at room temperature and 815 ◦ C [1.186]

Low-cycle fatigue test data of Mo at high test temperatures were reported in [1.187]. The influence of microstructural changes in cold-worked molybdenum on the low-cycle fatigue behavior was reported for test temperatures between 300 ◦ C and 950 ◦ C [1.188]. Deformation experiments under low-cycle fatigue conditions between room temperature and 100 ◦ C showed that recrystallized Mo, in spite of the low temperature and stress level, exhibits considerable plastic strains which depend sensitively on the loading frequency [1.189]. Data on the high temperature (350 ◦ C and 500 ◦ C) isothermal mechanical fatigue behavior of TZM were reported and a model for lifetime prediction was proposed [1.183]. Fig. 3.1-173 K IC of forged Mo rods (ϕ = 74%) versus de-

gree of recrystallization [1.147]

1300/4 RT, 20 kHz 1600/2 RT, 20 kHz RT, 20 kHz RT, 20 kHz RT, 20 kHz RT, 20 kHz RT, 20 kHz RT, 20 kHz

Se (MPa)

Se /Rm

Ref.

278 383 383 286 300 580 230 220

0.56 0.69 0.72 0.92

[1.176] [1.176] [1.126]

0.80 0.65

[1.126] [1.126] [1.177]

Fracture Mechanics Properties Fracture Toughness. Fracture toughness properties are

Total strain range ∆ ε t (%)

10–1

Test conditions, temperature, frequency

affected by many parameters (thermomechanical pretreatments, microstructure, specimen and crack plane orientation; testing procedures as well as the preparation of the starting notch and of the fatigue precrack). Due to the peculiarities of the P/M production process, it is frequently not possible to introduce sufficient deformation into products of larger dimension in order to completely eliminate sinter pores which may affect the dynamic properties. The increase of fracture toughness with increasing degree of hot working of disc-shaped compact tension specimens, cut from a hot forged Mo bar is shown in Fig. 3.1-173 and the decrease of fracture toughness with increasing fraction of recrystallized microstructure in Fig. 3.1-174 [1.147]. Fracture toughness data for Mo, TZM, and W materials are summarised in Table 3.1-115. Data taken at elevated temperature for Mo and W are shown in Fig. 3.1-175 [1.192], and for TZM in Fig. 3.1-176 [1.193]. Data for Nb could only be Fracture toughness KIC (MPa m1/2 ) 14 12 10 8 6 4 2 0

0

20

40

60 80 100 Degree of recrystallization (%)

Metals

1.9 Refractory Metals and Alloys

Fracture toughness data

Specimen type: CT compact tension, SCT center surface cracked tension, DCT disk-shaped compact tension, SNB side notched bend CNT center through-thickness notched tension

Material

Production process

Dimension (mm) plate: thickness, bar: diameter

Pretreatment T (◦ C)/ta (h)

Mo

P/M

plate 6.5

Rxx

1300/2 CNT

L-T

RT

Mo

P/M

bar 50

Sintered DCT Hot forged DCT Rxx 1400/2 DCT

R-C R-C R-C

RT RT RT

6 12 5

[1.147]

Mo

VAC

plate 6.4

Sr Rxx Sr Rxx

L-T/T-L L-T/T-L L-T/T-L L-T/T-L

RT RT 300 ◦ C 300 ◦ C

20/21 18/19 74/70 60/67

[1.195]

bar 54

Rxx

R-C

RT/450 ◦ C

Mo5Re

Specimen type

CT CT CT CT

Fracture toughness (MPa m1/2 ) 9.5

Ref.

[1.126]

18/27

[1.193]

Mo–0.3 wt% La2 O3

P/M

plate

Sintered

CT

L-T

RT

25

[1.196]

TZM

VAC

plate 6.4

Sr Rxx Sr Rxx

CT CT CT CT

T-L/L-T T-L/L-T T-L/L-T T-L/L-T

RT RT 300 ◦ C 300 ◦ C

19/15 15/18 85/89 59/68

[1.195]

TZM

P/M

bar 54 Machined to 12 Swaged to 12

Aw Aw Rxx

R-C L-C L-C

RT RT RT

19 37 19

[1.159, 197]

SNB SNB

C-R/L-R C-R/L-R

−196 ◦ C RT

11/6 13/8

[1.198]

SNB

R-L

RT/150 ◦ C/ 300 ◦ C/500 ◦ C

9/10/13/14

[1.199]

SNB SNB SNB

−196 ◦ C/RT −196 ◦ C/RT −196 ◦ C/RT

9/31 4/20 3/9

[1.198]

W

bar 10

W

bar 25

W

1300/1 DCT

Crack plane Test ASTM 399 temperature

DCT SCT 1400/2 SCT

Aw

Single crystal bar 16 (111)[011] bar 16 (011)[100] bar 16 (100)[001]

W

Aw

SNB

RT/400/600/ 800

15/21/26/39

[1.200]

W5Re

Aw

SNB

RT/400 ◦ C/ 600 ◦ C

11/26/58

[1.200]

bar 25

Aw

SNB

R-L

RT/150 ◦ C/ 300 ◦ C/500 ◦ C

plate 1.25

Sr Rxx

CNT CNT

L-T L-T

−253 ◦ C −253 ◦ C

40 72

[1.192]

Rxx Rxx

SNB SNB

−196 ◦ C RT

37 37

[1.194]

W-1 wt% La2 O3 Nb Nb

P/M

determined below −200 ◦ C [1.192]. Data on the impact and dynamic toughness of Nb between −196 ◦ C and 25 ◦ C were reported in [1.194]. The dy-

9/10/11/13

[1.199]

namic cleavage fracture toughness was shown to be 37 MPa m1/2 , relatively independent on grain size and test temperature.

Part 3 1.9

Table 3.1-115 Fracture mechanical data for various refractory metals, pretreatment: Aw = as worked, Sr = stress relieved, Rxx = recrystallized. RT = room temperature

323

Table 3.1-115 Fracture mechanical data for various refractory metals, pretreatment: Aw = as worked, Sr = stress relieved, Rxx = recrystallized. RT = room temperature, cont.

P/M P/M

P/M

P/M P/M

Production process

bar 12 bar 12

bar 12

plate 6.5 bar 12

Rxx Aw Rxx Sr Rxx Rxx Rxx Rxx

Specimen type

1300/2 CNT SCT 1400/2 850/1 SNT 1400/2 1700/2 SNT 1300/1 SCT 1450/1 CCT

Dimension Pretreatment (mm) T (◦ C)/ta (h) plate: thickness, bar: diameter

Test conditions, temperature, frequency RT, 20 kHz RT, 20 kHz RT, 20 kHz RT, 20 kHz RT, 20 kHz RT

Crack plane ASTM 399 L-T L-C C-R C-R L-C

20 kHz resonance test method, crack growth monitored by traveling light microscope, ∆K th corresponding to a crack growth rate of da/ dN < 10−13 m/cycle, ∆K th,eff calculated from crack closure measurements based on strain gauge method

TZM Mo5Re Ta10W

Mo

Mo Mo

Material

10−13 –10−9 10−13 –10−9 10−13 –10−9 10−9 –10−5

−1 −1 0.4

10−13 –10−9 10−13 –10−9

−1

−1 −1

Stress da/dNratio R range, (m/cycle) 5.8 11.3 10.7 10.3 8.5 10.1 11.4

K th

11 11 7.0 6.6 6.3 9.9

K th,eff

E647 E647

E647

E647 E647

ASTM

[1.201] [1.126] [1.202]

[1.201]

[1.126] [1.159]

Ref.

SCT center surface cracked tension SNT side notched tension

Part 3 1.9 Specimen type: CNT center through-thickness notched tension CCT corner cracked tension

Part 3

Fatigue crack growth and threshold data

324 Classes of Materials

14 Fracture toughness KIC (MPa m1/2 )

12

10 8

6

4

2

0

30

0

0 0.5

0 –273 –200 –100

0

100

1

100 80

60

0

200

1.5

20

100

5

300

2 In (A0 / A)

Fig. 3.1-174 K IC of forged Mo rods versus ln(A0 /A)

[1.147] Kc × 1000 (psi in. 1/2) Wrought, Recrystalstress relieved lized Tungsten Molybdenum Columbium

Columbium

40 Molybdenum

Tungsten

200 300 400 500 Test temperature (°C)

Fig. 3.1-175 Effect of test temperature on fracture

toughness of unalloyed W, Mo, and Nb sheet specimens [1.192] KIc (MPa m 1/2)

25

20

15

10

TZM Mo5Re

400

500 T (°C)

Fig. 3.1-176 Effect of test temperature on static fracture toughness of TZM and Mo5Re specimens [1.193]

Metals

Threshold Stress Intensity for Fatigue Crack Growth.

The fatigue crack growth behavior of Mo, TZM, and W in the region near the threshold stress intensity, ∆K th , considered to correspond to fatigue crack growth rates of da/ dN < 10−13 m/cycle, is shown in Fig. 3.1-178 [1.126]. The available crack growth and threshold data are included in Table 3.1-115. An effective threshold value for fatigue crack growth, ∆K th,eff , can be computed. Methods for the determination of this effective threshold stress intensity range are described in [1.197]. The available data on ∆K th,eff of Mo and TZM are listed in Table 3.1-115.

10–9

dc / dN (m / cycle)

10–10

10–11

10–12 dKth = 11.4 MPa m1/2 10–13 1

10

100 ∆ K (MPa m1/2)

Fig. 3.1-178 Crack growth curve near threshold stress

Short Fatigue Crack Growth Behavior. The nucle-

ation and growth behavior of short fatigue cracks is of considerable practical and theoretical significance. Differences in the growth behavior exist between initial short cracks (length comparable with microstructural features) and long cracks of macroscopic dimensions. The irregular growth rate of such short cracks

10–3

Crack growth rate da/ d N (mm / cycle) Ta – 10W

10–4

8 mm

10–5 Eroded notch

Fatigue crack

10–6

10–7

Condition: recrystallized and aged, tests at RT, stress ratio R=0.4 5

10

50 ∆ K (MPa m 1/2)

Fig. 3.1-177 Crack propagation behavior of recrystallized

P/M Ta10W specimens at room temperature at a stress ratio of R = 0.4 [1.202]

325

Part 3 1.9

Fatigue Crack Growth. Few data on the linear region of crack growth were published for Ta10W (Fig. 3.1-177), and a Nb−W−Zr alloy [1.202, 203].

1.9 Refractory Metals and Alloys

intensity of a center surface cracked specimen machined from a recrystallized Mo5Re rod, tested at a stress ratio of R = −1, test temperature = 50 ◦ C, and 20 kHz cyclic frequency; open symbols test under increasing load, solid symbols tests under decreasing load [1.126]

(Fig. 3.1-179) may pose problems for a conservative prediction of fatigue life [1.201]. Microscopic observations during fatigue exposure of specimens, loaded at stress amplitudes slightly above the fatigue limit, show initially a surface deformation very early in fatigue life, followed by short crack initiation and growth up to the final long crack growth. The number of fatigue cycles of the various stages depends on the microstructure and the presence of second phase particles (Fig. 3.1-180) [1.204]. It is known that fatigue failures occur in defectcontaining materials after a high number of loading cycles (N > 108 ) at stresses considerably below the fatigue limit determined by conventional test procedures (N < 107 ). A fracture mechanics approach to this problem was proposed by Kitagawa et al. [1.205]. Based on a diagram relating a cyclic stress amplitude with crack length, a critical defect size (ct ) can be deduced which, when exceeded, causes a reduction of the fatigue strength. A modification of this diagram by introducing the value of the effective stress intensity range is shown in Fig. 3.1-181 [1.201]. Good agreement between predicted values and experimental results are obtained for hemispherical surface notches of various sizes [1.206, 207].

326

Part 3

Classes of Materials

Part 3 1.9

a)

Number of loading cycles N

3 × 107 D

C 2 × 107

Fig. 3.1-179a,b Growth behavior of short surface cracks in a TZM specimen, tested at a stress amplitude of 375 MPa [1.201,204]. (a) Crack length as function of number of loading cycles. (b) Crack growth rate as function of crack length

B 100

1 × 107

N / Nf (%) Failure Macro crack growth

A 80 0

b)

100

200

300 400 Crack length c (µm)

SC-growth 60

Crack growth rate dc / dN (m / cycle)

Microcrack initiation

40 1 × 10–10

Surface deformation No visible damage

20 0

1 × 10–11

a

b

c

d

Fig. 3.1-180 Fraction of total fatigue life spent on damage

accumulation and crack growth in specimens of stress relieved Mo, recrystallized Mo, TZM with fine particles, and TZM with coarse particles [1.204]

1 × 10–12

1 × 10–13 0

1000

100

200

300 400 Crack length c (µm)

Cyclic stress amplitude σ (MPa) Mo stress relieved Mo recrystallized TZM recrystallized

Region of microcracks Short crack growth behavior (Stage I propagation) 500

Fatigue limit (σ FL )

Region of short cracks with crystallographic stage II growth

ct Region of long cracks

Region of non-propagating microcracks

∆ Kth

∆ Kth, eff

100 100

1000

10 000 Crack length c (µm)

Fig. 3.1-181 Effect of crack length on stress amplitude for crack growth in specimens of stress relieved Mo, recrystallized Mo, and recrystallized TZM (modified Kitagawa diagram) [1.201]

Metals

Stress for 1% elongation in 10 000 h (MPa) 1000

100

10

1

0.1 600

W

TZM

800

Mo

1000

1200

1400

1600

1800 2000 2200 Temperature (°C)

Fig. 3.1-182 Comparison of 10 000 h/1% creep data for Mo, TZM, and W based on [1.107] Stress (MPa) 1000

TZM 100

W-25Re

Ta Mo

W

10

Nb

1 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 Test temperature (°C)

Fig. 3.1-183 Comparison of 100 h of rupture data for selected refractory metals based on [1.107] Stress for steady-state creep rate of 10 – 4/h 1000

100

10

1

Mo

Fig. 3.1-184

Stress for steady state creep rate of 1 × 10−4 /h

versus 1/T for Mo and TZM, deformed samples, various shapes [1.208]

0.1

327

Part 3 1.9

Creep Properties Creep-rupture data available up to 1970 were collected in [1.107]. The fairly wide scatter results from minor differences in microstructure, thermomechanical pretreatment, and impurity levels, but possibly also from impurities picked up from the environment in the hightemperature test systems. A summary of 10 000 h/1% creep data for Mo, W, and TZM is given in Fig. 3.1-182; the 100 h creep-rupture data for Mo, W, Nb, Ta, W25Re and TZM are given in Fig. 3.1-183, based on [1.107]. Up to 1100 ◦ C the carbide-precipitation-hardened material TZM reveals the highest creep strength, only outperformed by Mo and W alloys precipitation hardened with hafnium carbide, which are not considered in these figures. Comparing the stress causing a steady state creep rate of 1 × 10−4 /h, as illustrated in Fig. 3.1-184, it can be concluded that precipitation hardening is effective up to 1600 ◦ C. At higher temperatures, the creep strength of TZM deteriorates to the level of Mo or even below. Above 1600 ◦ C, W-based materials offer the best performance. The influence of the microstructure on the creep mechanisms of Mo is illustrated in Fig. 3.1-185 for 1450 ◦ C [1.208]. For a test stress of 35 MPa the steady state creep rate is almost independent of the grain size. In this stress regime a stress exponent of 5.4 was obtained, indicating dislocation creep as the rate-controlling mechanism. Lowering the test stress to 14 MPa and 7 MPa, grain-size-dependent creep mechanisms, such as diffusion creep and grain boundary sliding, become active, and as a consequence, the steady state creep rate increases with decreasing grain size [1.208]. The steady state creep rates of Mo rods made of VAC ingots, VAC and P/M Mo sheets, and P/M Mo– 0.7 wt%La2 O3 sheets are summarized in Fig. 3.1-186. Stress exponents of 4.3 (P/M Mo sheet/1800 ◦ C), 4.5–4.7 (VAC Mo sheet/1600 ◦ C), 4.6 (VAC Mo rod/1600 ◦ C), 5.0 (Mo–0.7 wt% La2 O3 /1800 ◦ C), and 5.5 (VAC Mo sheet/2200 ◦ C) indicate that dislocationcontrolled creep is rate-controlling in the stress regime investigated. For AKS–W wires, used as lamp filaments, creep resistance is one of the most important requirements. The fine, potassium filled bubbles act as an effective barrier against dislocation movement, thereby reducing the deformation rate in the power-

1.9 Refractory Metals and Alloys

TZM

0.00045 0.00055 0.00065 0.00075 0.00085 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 1/T (1/K)

328

Part 3

Classes of Materials

Part 3 1.9

Steady state creep rate (1/h) 1 10 –1 10 –2 10 –3 10 –4 10 –5 10 –6 10 –7 0.01

3.5 MPa 7 MPa 14 MPa 35 MPa 0.1

1

10 Grain size (mm)

Fig. 3.1-185 Steady state creep rate of molybdenum sheets ver-

sus grain size. Sheet thickness = 2 mm/6 mm; test temperature = 1450 ◦ C; test atmosphere = hydrogen [1.208]

1

Steady-state creep rate of (1/h)

10 –1 10 –2 10 –3

with different grain aspect ratios (GAR) is given in Fig. 3.1-187. In the high stress regime (> 60 MPa) and at temperatures between 2500 ◦ C and 3000 ◦ C, stress exponents between 8 and 25 were found [1.162,209,210]. This high stress dependence led to the introduction of a threshold stress (σth ) below which a component does not reveal any measurable creep deformation under usual service conditions. For this threshold stress, which is lower than the Orowan stress, the detachment of the dislocations from the second phase particles or bubbles is the controlling factor [1.211, 212]. In the second phase particle/metal matrix interface, the dislocation line energy is lower compared to the dislocation line energy in the metal matrix. Of all dispersion strengthened materials investigated, potassium bubbles in AKS–W exert the most attractive interaction on dislocations [1.213]. For material produced in the 1970s with a mean, but strongly scattered, grain aspect ratio of around 35, dislocation creep dominated at stresses > 60 MPa (stress exponent = 25), as can be seen in Fig. 3.1-188. For material produced 20 years later with a similar grain aspect ratio of 31, a stress exponent of 1.2 was found in the stress regime from 30 to 80 MPa, indicating a diffusion-controlled creep process [1.214]. The evaluation of the strain rate/stress dependence of the values

10 –4 Stress (MPa)

10 –5 10 –6

1

10

T=1600°C; arc-cast Mo sheet, th.=0,5mm T=1600 °C; arc-cast Mo (M9) sheet, th.=0,5mm T= 1600°C; arc-cast Mo rod, dia.=4,1mm T= 2200°C; arc-cast Mo sheet, th.=0,5mm T= 2200°C; arc-cast Mo (M9) sheet, th.=0,5mm T=2200°C; arc-cast Mo rod, dia.= 4,1mm T=1800 °C; PM-Mo sheet, th.=6mm, grain size=0,1 mm T= 1800°C, MLR sheet,th.=1mm

100 Test stress (MPa)

90 80 70 60

AKS-W (GAR > 12)

AKS-W (GAR = 4)

50 40 30

Fig. 3.1-186 Steady state creep rate at various test temperatures

of vacuum-arc-cast (VAC) Mo sheet (thickness = 0.5 mm), VAC Mo rod (diameter = 4.1 mm), P/M Mo sheet (thickness = 6 mm), and Mo–0.7 wt% La2 O3 sheet (thickness = 1 mm) versus test stress [1.107, 208]

pure W

20 15 10

law creep regime. Nabarro–Herring and/or Coble creep is suppressed because of the large diffusion distances in a structure with large, highly elongated grains. Grain boundaries resist sliding because of the interlocking structure. A comparison of creep rupture data of pure tungsten and two AKS–W grades

100 Time to rupture (min)

Fig. 3.1-187 Creep rupture data for AKS–W wires in com-

parison with pure tungsten. Wire diameter = 0.183 mm; 4 < GAR < 12; test temperature = 2527 ◦ C; atmosphere = vacuum better than 7 × 10−5 Pa; heating rate = approximately 2000 ◦ C/s [1.162]

Metals

Time to rupture (min)

Strain rate (1/s)

Zilberstein 1998 Wright 1978

1000

Stress exponent= 25

10 –7

10 –8

10 –9

Stress exponent= 1.2

10

100

100 Stress (MPa)

Fig. 3.1-188 Strain rate versus stress for AKS–W wires tested at 2527 ◦ C. Wright 1978 [1.162]: AKS–W wire with a diameter of 0.183 mm; atmosphere = vacuum better than 7 × 10−5 Pa; heating rate = approximately 2000 ◦ C/s; GAR = 35±10; pre-recrystallized at 2527 ◦ C/10 min. Zilberstein 1998 [1.215]: AKS–W wire with a diameter of 0.178 mm; atmosphere = vacuum; GAR = 31±1; pre-recrystallized at 2527 ◦ C/15 min Fig. 3.1-189 Time-to-rupture versus grain aspect ratio for AKS–W wires with a diameter of 0.183 mm. Test temperature = 2527 ◦ C; test stress = 73.6 MPa; atmosphere = vacuum better than 7 × 10−5 Pa; heating rate = approximately 2000 ◦ C/s [1.162]

generated under vacuum also reveals a stress exponent close to 1 [1.215]. Data for the stress exponents are summarized in [1.113]. By lowering the grain aspect ratio, the transition temperature between dislocation and diffusion creep is shifted towards lower stresses. In the low

10

0

10

20

30

40

70 60 50 Grain aspect ratio

GAR regime a strong dependence of the creep resistance on microstructural features can be observed, as grain boundary related phenomena, such as grain boundary sliding and diffusion creep resulting in cavitations become rate-controlling. The influence of the GAR on time to creep rupture is demonstrated in Fig. 3.1-189.

3.1.10 Noble Metals and Noble Metal Alloys The noble metals Ag, Au, Pd, Pt, Rh, Ir, Ru, and Os are characterized by their positive reduction potentials against hydrogen, high densities, high melting temperatures, high vapor pressures (Fig. 3.1-190), high electrical and thermal conductivities, optical reflectivity (Fig. 3.1-191), and catalytic properties. The electronic density of states (DOS) near the Fermi surface is nearly the same for all noble metals. Individual differences of electrical conductivity, magnetic, and optical behavior are related to different posi-

329

Part 3 1.10

10 –6

1.10 Noble Metals and Noble Metal Alloys

tions of the Fermi level relative to the DOS function (Fig. 3.1-192). Small energy differences between their outer s and d electronic states result in multiple oxidation states. Silver, Au, Pd, and Pt are comparatively soft and ductile. Their hardness increases in the order Rh < Ir < Ru < Os. Strengthening of the alloys is affected by solid solution and dispersion hardening. The corrosion resistance against different agents decreases in the order Ir > Ru > Rh > Os > Au > Pt > Pd > Ag.

Part 3

Classes of Materials

Part 3 1.10

Vapour pressure (Torr)

Density of state N (E) Ag

103

Au Pd

Rh Pt

Ru Ir

Os

d-band

5

Fermi level

102 10

Ru, Os Rh, Ir Pd, Pt

330

4

1

Fermi level

10 –1

Au Ag

3

10 –2 10 –3

2

10 –4

Hole

10 –5 1

10 –6 10 –7

s-band

Electron

10 –8

0 –8

10 –9

–6

–4

–2

0 2 4 Electronic energy E (eV)

10 –10 10 –11 400

4400 4000 4800 Temperature (°C)

Fig. 3.1-192 Schematic density of states (DOS) curve of

Fig. 3.1-190 Vapour pressures of the noble metals [1.216, p. 43]

The pure elements and their alloys are key materials in electronics and electrical engineering (Ag, Au, Pd, Pt, and Ru) and serve to manufacture high strength, corrosion-resistant, high temperature, and highly oxidation-resistant structural parts (Pt, Au, Rh, and Ir). The platinum group metals, Ag, and Au, in both the metallic state and in the form of chemical compounds are effective heterogeneous or homogeneous catalysts for a wide variety of chemical reactions. Traditional applications of noble metals and their alloys are in dentistry (Au, Pt, Ag, Pd, and Ir), jewellery (Au, Ag, Pt, Pd, Rh, and Ir), and in coins and medals (Au and Ag).

800

1200

1600

2000

2400

2800

3200

3600

Reflectivity R 1 Ag 0.9 Rh 0.8 Ru 0.7 Ir Pt 0.6

Pd

3.1.10.1 Silver and Silver Alloys

0.5 Au 0.4 400

the noble metals [1.218, p. 30]

460

520

580

640

700 760 Wavelength (nm)

Fig. 3.1-191 Optical reflectivity in the visible spectral range [1.217,

p. 173]

The purity grades of the elements are standardized according to ASTM (American Society for Testing and Materials) standards from 99.8 to 99.999 wt%: Ag (B 413–69), Au (B 562–86), Pd (B 589–82), Pt (B 561–86), Rh (B 616–78), Ir (B 671–91), Ru (B 717).

Application Silver and silver alloys are used for electrical contacts, connecting leads in semiconductor devices, solders and brazes, corrosion-resistant structural parts, batteries, oxidation catalysts, optical and heat reflecting mirrors, table ware, jewellery, dentistry, and coins. Silver halides are base components in photographic emulsions. Production Silver is extracted from ores through lead melts and precipitation with zinc by the Parkes process. Zinc is removed by distillation, while the remaining lead

1.10 Noble Metals and Noble Metal Alloys

Metals

Phases and Phase Equilibria Selected phase diagrams are shown in Figs. 3.1-193– 3.1-198 [1.219, 220]. Silver forms continuous solid solutions with Au and Pd, with miscibility gaps occuring in alloy systems with Mn, Ni, Os, P, Rh. Data for the solubility of oxygen are given in Table 3.1-117 [1.216]. Thermodynamic data are given in Tables 3.1-118– 3.1-121. The entropy of fusion (L/T ) of completely disordered intermetallic phases can generally be calculated by fractional addition from those of the components. For the completely ordered state the term − 19.146 (N1 log N1 + N2 log N2 ) is to be added to the calculated entropy of fusion [1.216–218, 221, 222]. The molar heat capacity of the homogeneous alloy phases and intermetallic compounds, as calculated approximately from the atomic heat capacities of the components using Neumann–Kopps’ rule, is obeyed to within ±3% in the temperature range 0–500 ◦ C in the Ag−Au, Ag−Al, Ag−Al, and Ag−Mg alloy systems. The heat capacities of heterogeneous alloys may be calculated by fractional addition from those of the components by the empirical relation c p = 4.1816(a + 10−3 bT + 105 cT −2 )J/(K mol) to satisfactory accuracy.

T (K) 5

1400

10 15 20 25 30 35 40 45 50

60

Cu (wt %) 70 80 90 1356 K

Ag-Cu 1300 1233.5 K

1200 1100

1052 K

(Ag)

14.1

1000

(Cu)

39.9

95.1

900 800 700 600 500 Ag

10

20

30

40

50

60

70

80

90 Cu Cu (at. %)

Fig. 3.1-193 Binary phase diagram: Ag−Cu [1.219, p. 38] T (K) 1900

5

10

20

30

40

50

60

Ni (wt %) 70 80 90

Two liquids

Ag-Ni 1800

1728 K 1708 K

1700 1600 1500 1400 1300

1600 T (K)

≈ 97

Liquid L

(Ni) 1500

1400

L + (Ni)

1300

1233 K 1200 Ag 1

2

3 Ni (at. %)

1233 K

1200 1233.5 K 1100 Ag

10

20

30

40

50

60

70

80

90 Ni Ni (at. %)

Fig. 3.1-194 Binary phase diagram: Ag−Ni [1.219, p. 88]

Table 3.1-116 Specifications Designation

Grade (wt%) Impurity

Maximum content (ppm)

of fine silver grades [1.217, p. 51]

> 99.9 > 99.97 > 99.99 < 99.999

1000 300/10/10/5/5 100/10/10/5/5 2/1/1/1/0.5/0.5/0.5/0.5/0.5

“Good delivery” Fine silver Fine silver 999.9 F. silver high pure

any, Cu Cu/Pb/Bi/Se/Te Cu/Pb/Bi/Se/Te Fe/Pb/Au/Cu/Cd/Bi/Se/Te

Part 3 1.10

and base metals are removed by oxidation (cupellation) up to ≈ 99% Ag. True silver ores are extracted by cyanide leaching. High purity grades are produced by electrolysis. Bars, sheets, and wires are produced by classical metallurgical processing, powder by chemical and by electrolytic precipitation from solutions, and nano-crystalline powder grades by dispersion in organic solutions. Coatings and laminate structures are produced by cladding, by electroplating, in thick film layers by applying pastes of silver or in silver alloy powder with organic binder and glass frits onto ceramic surfaces and firing, in thin film coatings by evaporation, and by sputtering Composite materials are made by powder technology, or by infiltration of liquid Ag into sintered refractory metals skeletons. Commercial grades of Ag are listed in Table 3.1-116. Standard purities of crystal powder and bars range from 99.9% to 99.999 wt% (ASTM B 41369) [1.217].

331

332

Part 3

Classes of Materials

Part 3 1.10

T (K) 10 20 30 40 50 1250

60

Pb (wt %) 80 85 90 95

70

1235 K

Ag-Pb

1200

T (K) 10 20 30 40 50 2100 Ag-Pt 2000 Ag3Pt

60

Pt (wt %) 70 75 80 85 90 95 2042 K

AgPt

AgPt3

1150 1900 1100 1800

1050

1700

1000 2.8

950

1600 (Pt)

900 1500

1459 K

850

22

800 750

1300

700

1200 1100

600 K

600

577 K 95.5

550 500 Ag 10

20

30

40

50

60

70

80

90 Pb Pb (at. %)

Fig. 3.1-195 Binary phase diagram: Ag−Pb [1.219, p. 92]

5

1235 K

(Ag)

650

T (K) 1300

83.3

42.9

1400

10 15 20

30

40

50

Zn (wt %) 60 70 80 90

1000 Ag 10

20

30

40

50

60

70

80

90 Pt Pt (at. %)

Fig. 3.1-196 Binary phase diagram: Ag−Pt [1.219, p. 101] Table 3.1-117 Solubility L (ppm) of oxygen in solid and liquid Ag (O2 pressure 1 bar) [1.216, p. 57] T (◦ C) L ppm

200 0.03

400 1.4

600 10.6

800 38.1

973 3050

1000 3000

1200 2500

Ag-Zn

1233.5 K

1200 1100 983 K 37.5

1000

904 K

61.8 58.6

900 800

934 K

32.1 36.7

71 61

α

64.7 69.4

β

(Ag)

98

γ

ε

700 600

531K 40.2

500

45.6

89

704 K 95 692 K

η

547K 58.8 50.4

(Zn)

ζ 400 Ag

10

20

30

40

50

60

70

80

90 Zn Zn (at. %)

Fig. 3.1-197 Binary phase diagram: Ag−Zn [1.219, p. 144]

Metals

c p = 4.1868 (a + 10−3 bT + 10−5 T −2 ) J/K [1.222, p. 219] Element Ag Au ∗

a 5.09 5.66

b 2.04 1.24

c

Temperature range (K)

0.36 –

298–mp∗ 298–mp∗

= melting point

Table 3.1-120 Latent heat and temperatures of transition of

Table 3.1-118 Thermodynamic data of Ag [1.217, p. 107] T (K)

cp (J/K mol)

H (J/K mol)

S (J/mol)

G (J/mol)

p (at)

298.15 400 800

25.397 25.812 28.279

42.551 50.069 68.661

0 2.606 13.392

−12.687 −17.421 −41.537

1.09 × 10−43 5.02 × 10−31 1.45 × 10−12

T = Temperature, c p = specific heat capacity, S = Entropy, H = Enthalpy, G = free Enthalpy, p = partial pressure of the pure elements

Ag and Au intermediate compounds [1.222, p. 189] N2

Transition

Tt

Lt

β-AgCd AgZn AuCu AuCu3 AuSb2

50 50 50 75 66.7

β  –β order–disorder order–disorder order–disorder β–γ

211 258 408 390 355

712 2449 1779 1214 335

Cu ) -Zn Cu α(

Phase

20

Tt = transition temperature, L t = latent heat of transition, N2 = mole fraction of the second component

80 c

40

60

Table 3.1-121 Latent heats and temperatures of fusion of

Ag and Au intermediate compounds [1.222, p. 188] Phase

N2

Tm (◦ C)

Lm (hJ/g-at.)

β-AgCd γ -AgZn AgZn δ-AuCd AuSn β-AuZn

67.5 61.8 72.1 50.0 50.0 50.0

592 664 632 627 418 760

8.46 7.79 8.75 8.96 12.81 12.31

0.42 0.33 0.42 0.50 0.33 0.54

N2 = mole fraction of the second component, Tm = melting point, L m = Latent heat of fusion.

For compositions and crystal structures, see Tables 3.1-122–3.1-124 [1.217, 218, 223, 224]. Primary solid solutions have the fcc structure of Ag and the lattice parameters correspond roughly to Vegard’s rule with a few exceptions. Alloys with Pt, In, Mg, Cd, and Zn form superlattice phases with tetrahedral and rhombo-

60

40 b

β

80

20

γ δ

α (Ag-Zn) Ag

a 20

ε 40

60

η 80

Zn (at. %)

Fig. 3.1-198 Ternary phase diagram: Ag−Cu−Zn [1.220, p. 153]

hedral symmetry. A characteristic series of structures of intermetallic phases are formed with B-metals at compositions corresponding to e/a values (valence electrons per atom) of 3/2, 21/13, and 7/4 (Hume-Rothery phases) [1.225].

333

Part 3 1.10

Table 3.1-119 Molar heat capacities of solid Ag and Au,

1.10 Noble Metals and Noble Metal Alloys

334

Part 3

Classes of Materials

Part 3 1.10

Phase

Pearson symbol

a (nm)

Ag−Al Ag2 Al Ag−Cd AgCd AgCd Ag−Cu Ag−Mg Ag−Mg AgO AgO Ag−O Ag−O Ag−Zn Ag−Zn

cF4 hP2 hP2 cP2 hP2 cF4 cF4 hP2 cF8 mP8 cP6 hP3 hP2 hP9

0.4064 0.28777 0.2987 0.3332 0.3016 0.3603 0.4116 0.3197 0.4816 0.5852 0.4728 0.3072 0.28227 0.7636

b (nm)

c (nm)

c/a

Remarks

Concentration x: A(1 − x)B(x) 0.18

0.46223 0.553

0.3478

1.6062 1.8514

0.4863

1.6124

0.51838

1.6215

293 K 673 K

0.97 0.5 0.5 0.95 0.26 0.98

Table 3.1-122

Structure and lattice parameter of intermediate Ag compounds [1.217, p. 112]

0.5495 0.4941 0.44274 0.28179

1.6084 1.5685 0.369

HP/HT 0.775 0.38–0.52

HT = High-temperature modification, HP = High-pressure modification Atomic ratio

Composition

3:1 or 1:3

Pd3 Fe Pt3 Fe Pt3 Ti Rh3 Mo Rh3 W Ir3 Mo Ir2 W Pd3 V Pd3 Nb Pt3 V

2:1

1:1

Pd2 V Pt2 V Pt2 Mo PdFe PtFe PtV PtNi PtCo PtCu PdCu

RhMo IrMo PtMo IrW PtNb

PdCu3 PtCu3 PtNi3 PtMn3

Au3 Cu Au3 Pd Ag3 Pt

Superlattice structure

Fundamental structure

L12

fcc

AuCu3

Ag3 In DO14 (Au2 Mn)

DO22

fcc

Au3 Cd Au3 Zn Ag3 Mg

DO23

fcc

Ni2 Cr

fcc

L10

fcc

AuCu

AuMn AgCd AgZn

L11 L20 or B2

fcc bcc

hcp B19

Table 3.1-123

Composition and structures of superlattices in NM-alloy systems [1.218, p. 105]

Metals

1.10 Noble Metals and Noble Metal Alloys

Electron: atom ratio = 3:2 Complex cubic Body-centered (β-manganese) structure cubic structure AgMg AgZn AgCd Ag3 Al Ag3 In AuMg AuZn AuCd

AgHg Ag3 Al Au3 Al

Close-packed hexagonal structure AgZn AgCd Ag3 Al Ag3 Ga Ag3 In Ag5 Sn Ag7 Sb Au3 In Au5 Sn

Mechanical Properties In Tables 3.1-125–3.1-135 and Figs. 3.1-199–3.1-204 characteristic data are shown [1.217,220,225–229]. References for data of elastic constants of Ag alloys are given in [1.222]. Pure silver is very soft. Strengthening is affected by solid solution and by dispersion hardening [1.216,230]. Alloying with 0.15 wt% Ni affects grain refinement and stabilizes against recrystallization. The high solubility of oxygen in silver (Table 3.1-117) permits the inducement of dispersion hardening by internal oxidation of Ag alloys containing Al, Cd, Sn, and/or Zr.

Electron: atom ratio = 21:13 γ -brass structure

Electron: atom ratio = 7:4 Close packed hexagonal structure

Ag5 Zn8 Ag5 Cd8 Ag5 Hg8 Ag9 In4 Au3 Zn8 Au5 Cd8 Au9 In4 Rh5 Zn21 Pd5 Zn21 Pt5 Be21 Pt5 Zn21

AgZn3 AgCd3 Ag3 Sn Ag5 Al3 AuZn3 AuCd3 Au3 Sn Au5 Al3

Table 3.1-127 Mechanical properties of Ag (99.97%) at different temperatures (◦ C) [1.217, p. 204] T (◦ C)

E (GPa) Rm (MPa) A (%)

Rp0.2 (MPa) HV

20 200 400 800

82 77 67 46

28 25 20 17

150 130 100 35

50 – 30 –

26 22 17 5

A = Elongation, E = Module of elasticity, Rp = Limit of proportionality, HV = Vickers hardness, Rm = Tensile strength

Table 3.1-128 Tensile strength Rm (MPa) of binary Ag

alloys [1.217, p. 207] Table 3.1-125 Module of elasticity of Ag in crystal direc-

tions (GPa) [1.217, p. 204] E100

E110

E111

44

82

115

Table 3.1-126 Elastic constants of Ag (GPa) [1.217, p. 204] T (◦ C)

c11

c12

c14

−273 +20

131.4 124.0

97.3 93.4

51.1 46.1

Content (wt%) Alloying elements

2

5

10 Rm (MPa)

Au Cd Cu Pd Sb Sn

160 160 190 160 190 190

170 170 240 180 240 240

180 180 280 21 300 300

20 200 210 310

Table 3.1-129 Hardness of Ag−Mn alloys [1.226, p. 473] wt% Mn

0.5

4.9

6.2

12.0

HV (kg/mm2 )

31

39

40

58

Composition (wt%) Cu P Ag

BS a 1845

Density (g/cm3 )

Melting range (◦ C)

Tensile strength (kg/mm2 )

Elongation (%)

15 5 2

CP1 CP4 CP3

8.40 8.20 8.15

645–719 645–750 645–770

25 25 25

10 5 5

a

80 89 91

5 6 7

= British standard (1966/1971) designation

Table 3.1-130

Mechanical properties of Ag−Cu−P alloys [1.226, p. 477]

Part 3 1.10

Table 3.1-124 Compositions and structures of e/a (Hume-Rothery) compounds [1.225, p. 197]

335

336

Part 3

Classes of Materials

Part 3 1.10

Composition (wt%) Cu Zn Ag

Specific weight (cast)

Tensile strength (kg/mm2 )

Elongation (%)

Electrical conductivity (% of Cu)

36 25 22 16

9.11 9.52 10.35 10.05

40.5 45.0 29.3 35.1

6.2 7.7 5.3 16.0

19.7 20.5 53.4 45.8

24 15 3.0 4.0

40 60 75 80

Alloy Ag−X (wt%)

HV5 s

Pd27.5 Pd27.4Cu10.5 Pd39.9Zn4

55 140 160

h

Ron (MPa) s h

A (%) s

h

310 270

80 320 285

230 510 560

33 31 18

3 6

950 790

Mechanical properties of Ag−Cu−Zn alloys [1.220, p. 154]

Table 3.1-132

Rp0.2 (MPa) s h 940 595

Table 3.1-131

Mechanical properties of Ag−Pd alloys in annealed (s) and hard (h) condition [1.217, p. 208]

s = soft, h = hard Alloy AgX (wt%)

Temperature (◦ C) 20 200

Cd 4 Cd 8 Cu 3 Cu 7.5 Ni 0.3 Si 3

170/60 480/5 190/35 250.46 190/60 260/39

Table 3.1-133 400

600

800

– 200/55 140/40 180/47 130/65 180/35

– – 90/80 120/55 100/65 90/52

– – 30/150 60/78 60/50 20/55

Tensile strength Rm (MPa) and elongation A (%) of Ag alloys at different temperatures [1.217, p. 207]

Rm /A 150/50 260/20 170/40 220/48 170/60 220/33

Table 3.1-134 Strengthening of Ag (99.975%) by cold forming as a function of reduction in cross section in % [1.217, p. 204] V (%)

Rm (MPa)

A (%)

HV

0 10 30 80

150 180 260 90

50 30 5

26 54 70

2

V = reduction of cross section

E (GPa) 140 Ag1–xPdx 120

Table 3.1-135 Strengthening of Ag alloys by cold forming

100

(HV 10) (reduction in % of thickness) [1.217, p. 207]

Ag

Reduction (%) Alloying element

0

40

80

Cu 5 Cu 15 Cu 28 Cu 50 Ni 0.15 Pd 30 Pd 30 Cu 5

58 76 98 84 40 70 92

108 126 136 130 86 132 174

134 158 177 166 100 164 2165

Cu Pd

Ag1–xCux

60 40 20 0

0

20

40

60

80

100 x (at. %)

Fig. 3.1-199 Module of elasticity of Ag−Pd and Ag−Cu

alloys [1.217, p. 206]

Hardness (HV) Ag1– xMx

100

Mo Pt

Brinell hardness

Si

20

Ni

150

Mn Au Zn

10

20

0 MPa

Sn Sb

50

W

Cd Pd

Cu

Al

0

337

40 Mg

0

1.10 Noble Metals and Noble Metal Alloys

Part 3 1.10

Metals

30

40

50 x (wt %)

Fig. 3.1-200 Influence of alloying elements on the hard-

ness of binary Ag alloys [1.217, p. 206]

Tensile strength

100 50 0 (%) 90 80

Reduction in area

70

HV3 200 AgCu20 160 120

60 Elongation

AgCu10 AgCu5 AgCu3

50

Ag

30 0

80

40 4

8

12

16 20 Zn content (at. %)

Fig. 3.1-202 Plastic properties of Ag−Zn crystals [1.220,

40

p. 135] 0

0

20

40

60

80 100 Cold forming (%)

HB

Fig. 3.1-201 Hardening of Ag−Cu alloys by cold form-

ing [1.217, p. 432]

Cold formed

160

Hot formed

120

d

80

c

40

0

a

0

200

400

b

600

1000 800 Temperature T (°C)

Fig. 3.1-203 Hardness of fine grain and dispersionhardened Ag [1.216, p. 36]

338

Part 3

Classes of Materials

Part 3 1.10

Electrical Properties Tables 3.1-136–3.1-139 and Fig. 3.1-205 [1.217, 231– 233] show characteristic data. The residual resistivity ratio (RRR) of pure Ag ranges up to 2100. Ag alloys with Pb and Sn show superconductivity in the composition ranges: Ag0.95 – 0.66 Pb0.05 – 0.34 with Tc = 6.6–7.3 K and Ag0.72 – 0.52 Sn0.28 – 0.48 with Tc = 3.5–3.65 K [1.234].

Rp 0.2 /Rm(MPa)

500

Rm

400 R p 0.2

d

Table 3.1-136 Specific electrical resistivity ρ(T ) = ρ0 + ρi (T ) of Ag (ρ0 = 0.0008 µΩ cm) at different temperatures [1.217, p. 156]

300

ρ(T ) (µ
cm)

T (K) Rp 0.2

c b

Rm

10

0.0001

50

0.1032

Rm

120

0.5448

273

1.470

500

2.860

700

4.172

900

5.562

1100

7.031

100 Rm

Rp0.2

0

a

Rp0.2

0

200

400

600 800 Temperature T (°C)

Fig. 3.1-204 Tensile strength and 0.2% proof stress of

silver grades at different temperatures [1.216, p. 37]

Table 3.1-137 Increase of atomic electrical resistivity of

Ag by alloying elements ∆ρ/C (µΩ cm/at.%) [1.217, p. 157] Base element

Alloying elements

Ag

Al 1.87, As 8, Au 0.36, Cd 0.35, Cr 6.5, Cu 0.07, Fe 3.2, Ga 2.3, Ge 5, Hg 0.8, In 1.6, Pb 4.6, Pd 0.44, Pt 1.5, Sn 4.5, Zn 0.63

ρ (µΩ cm) Sb

Table 3.1-138 Specific electrical resistivity ρi and coefficient of electrical resistivity (TCR) of noble metal solid solution alloy phases [1.217, p. 158]

20

15

Base/ solute-metal

Mn Sn

10 Ga 5 Ag 0

Pd

Pt

0

Rh/Ni

ρi TCR

Ag/Au

ρi TCR

8.3 0.93

11.0 0.83

Ag/Pd

ρi TCR

11 0.58

22 0.40

Ag/Pt

ρi

33

Au/Pd

ρi TCR

9.8 0.88

Au/Pt

ρi TCR

28 0.28

Au 2

4

6 8 10 Alloying addition (at. %)

Fig. 3.1-205 Influence of alloying elements on the electrical conductivity of binary Ag alloys [1.231, p. 20]

Solute content 20 40 21 3.8

37 1.8

60

80

51 < 0.1 11.0 0.84

50 3 8.1 1.1

41

34 0.75

60

46

35

17 0.61

30 0.45

26 1.2

44 0.26

0.82 0.82

0.8 0.8

–

Metals

1.10 Noble Metals and Noble Metal Alloys

Part 3 1.10

Table 3.1-139 Specific electrical resistivity ρ25 of annealed (8 h at 550 ◦ C) Ag−Cu wire at 25 ◦ C

and 100 ◦ C (ρ100 ) and temperature coefficient of resistivity (TCR) α for 25–100 ◦ C [1.226, p. 380] at.% Ag × 10−6

ρ25 (µΩ cm) ρ100 × 10−6 (µΩ cm) TCR ×105

5

15

45

75

96

1.832 2.369 389

1.895 2.320 387

1.913 2.411 380

1.645 2.308 365

1.822 2.297 381

Thermoelectric Properties In Tables 3.1-140–3.1-142 and Fig. 3.1-206, characteristic data are shown: absolute thermoelectric power, thermo-electromotive force of pure Ag as well as Ag−Au, Ag−Pd, and Ag−Pt alloys at different temperatures against a reference junction at 0 ◦ C [1.217, 235, 236].

Table 3.1-140 Thermal electromotive force E Ag,Pt (mV) force of Ag

at different temperatures; reference junction at 0 ◦ C [1.217, p. 159] T (◦ C)

−200

E Ag,Pt (mV)

−0.39 −0.21 −0.10 0.74

+100

+200

+400

+800

1.77

4.57

13.36

at 100 ◦ C and 700 ◦ C reference junction at 0 ◦ C [1.217, p. 160]

100 700

Composition (wt%) 0 20 40

60

80

100

0.74 10.75

0.42 6.8

0.49 7.3

0.78 10.15

0.47 7.7

0.42 6.7

Cu

0.8

Magnetic Properties Silver is diamagnetic (Table 3.1-143). The magnetic susceptibility remains constant from 0 K to the melting point. Alloying with B metals causes only minor variations compared to pure Ag. In the continuous solid solution range the molar susceptibilities remain negative and the alloys are diamagnetic. Ni, Pd, and Pt dissolve up to 25 at.% diamagnetically. Cr, Fe, and Mn give rise to paramagnetism, while Co causes ferromagnetism [1.216, 217].

Cd

0.6 Zn

Au 0.4 t2 = 100°

Table 3.1-143 Atom susceptibility of Ag and Au alloys at room

t1 = 100°

temperature [1.216, p. 90]

0.2 Pd

0.0 Ag

−50

Table 3.1-142 Thermal electromotive force of Ag−Au alloys in mV T (◦ C)

Thermal electromotive force EA, Pf (mV)

−100

95

Pt

90

85 Ag (at. %)

Base metal

Alloying element

Base metal content (at.%) 100 99 95 90

80

Ag

Au Pd Cu Ni Pd Pt

−19 −20 −26 −28 −28 −28

−22.2 −22 −22.4 − −15 ±0

Au

Fig. 3.1-206 Thermal electromotive force of binary Ag

alloys [1.216, p. 98]

Table 3.1-141 Absolute thermoelectric power of Ag at different temperatures [1.216, p. 94] Temperature (◦ C)

−255

Thermoelectric power (µV/◦ C)

+0.62 +0.82 +1.00 –

−200

−100

−20

0

100

300

500

800

+1.4

+1.9

+3.0

+4.6

+8.3

−20.2

−22

339

−25.2 ±0

−20.8 −21 −24.2 +16 −20 −6

340

Part 3

Classes of Materials

Part 3 1.10

Thermal Properties Selected data of thermal expansion, thermal conductivity, and melting temperatures of Ag alloys are given in Tables 3.1-144–3.1-150 and in Fig. 3.1-207 [1.216, 220].

∆ Trecryst. (°C) Cu

200

Bi

Pb Sb Al Ge

Table 3.1-144 Recrystallization temperatures (◦ C) of Ag

99.95 and 99.995% purity after different degrees of deformation V ; annealing time 1 h [1.217, p. 205] V (%)

40 60 99

Trecryst. Purity 99.95%

99.995%

190 160 127

125 100 70

0

In

Pd

α (10−6 K−1 ) Ag

Au

17.9 19.1 19.9 21.1 23.6

13.9 14.8 15.3 15.7 16.2

Table 3.1-146 Mean coefficients of thermal expansion α (10−6 K−1 ) of Ag and Au alloys [1.217, p. 154] Base metal 2nd metal

Au Ag

Au Ag

Au Cu

Au Ni

Ag Pd

Temp. range (K)

273 373

293 1073

273 593

273 373

373 473

wt% of 2nd metal

α (10−6 K−1 )

20 40 50 60 80

15.5 16.5 17.0 17.5 18.2

14.9 – 15.7 15.8 15.9

14.4 13.9 14.0 13.9 13.4

16.2 – 14.7 – 12.4

17.0 18.7 – 20.1 20.8

0

0.2

0.4

Cd

Au

0.6 0.8 1.0 1.2 1.4 1.6 1.8 Amount of solute elements added (at. %)

Fig. 3.1-207 Increase of the recrystallization temperature of Ag by solute elements [1.218, p. 452]

(10−6 K−1 ) of Ag and Au [1.217, p. 154]

373 473 673 873 1073

Sn

Mg

Table 3.1-145 Mean coefficients of thermal expansion α T (K)

100

Be

Table 3.1-149 Thermal conductivity λ (W/m K) of Ag and Au at different temperatures [1.217, p. 153] T (K)

λ (W/m K) Ag

Au

40 100 273 600 800

1050 475 435 411 397

420 360 318 296 284

Table 3.1-150 Melting range of Ag−Cu−Sn and Ag−

Cu−In solder alloys Composition (wt%) Ag Cu Sn 60 50 47 50 49 50 45 25

23 30 20 10 19 25 17 45

Melting range (◦ C) In

17 20 33 40

557–592 555–578 472–515 435–456 549–556 594–601 534–548 581–610

32 25 38 30

Table 3.1-147 Specific heat of Ag at different temperatures [1.220, p. 9] T (◦ C)

−259.46

−240.86

−141.93

−67.90

+98.7

+249.0

+399.5

+652.2

c p (cal/g)

0.001177

0.01259

0.04910

0.05334

0.0569

0.0583

0.0600

0.0635

Table 3.1-148 Vapor pressure of liquid Ag [1.220, p. 8] T (◦ C)

1550

1611

1742

1838

1944

2152

Vapour pressure (mm Hg)

8.5

15.7

54

100

190

760 (extrapol.)

1.10 Noble Metals and Noble Metal Alloys

Metals

Reflectivity R (%) 100 60 40 20 0.1 R 10 8 6

Ag Au

Temperature (◦ C)

Spectral degree of emission

Solid Liquid Solid Liquid

940 1060 1000 1067

0.044 0.0722 0.154 0.222

Table 3.1-152 Colored noble metal alloys [1.237, p. 178] Alloy

Color

Ag−Zn (β-phase) Ag−Au(70) Al2 Au KAu2 Au−Zn−Cu−Ag AuIn2 Zintl Phases Li2 AgAl Li2 AgGa Li2 AgIn Li2 AgTl Li2 AuTl Li2 AgSi Li2 AgGe Li2 AgSn Li2 AgPb Li2 AuPb

Rose Green-yellow Violet Violet Green Blue

Remarks

3.8 4.0 eV

4

Table 3.1-151 Spectral emissivity of Ag and Au at different temperatures [1.217, p. 171] Surface

Part 3 1.10

Optical Properties Table 3.1-151 and Figs. 3.1-208, 3.1-209 [1.237] show characteristic data of optical properties. Ag has the highest reflectivity of all noble metals. An interband transition takes place in the ultraviolet range at 3.9 eV. Ag−Al alloys between 10 at.% and 28 at.% Ag show higher reflectance in the low wavelength range than the pure elements. In Ag−Pd alloys, the threshold energy at 3.9 eV for the interband transition remains constant up to ≈ 34 at.% Pd. Examples of colored Ag alloys are given in Table 3.1-152 [1.237].

2 1

0

2

4

6

8

10

12

14

16

18

20 22 24 Energy (eV)

Fig. 3.1-208 Reflectance versus radiation energy of Ag [1.237,

p. 158] Reflectivity (%) 90 (Ag 10%) (Ag 28%) 80 (Al) 70 60 50

Yellow-rose Yellowish Gold-yellow Violet-rose Green-yellow Rose-violet Rose-violet Violet Blue-violet Violet

VEC = Valence electron concentration

VEC 1.5 VEC 1.5 VEC 1.5 VEC 1.5 VEC 1.5 VEC 1.75 VEC 1.75 VEC 1.75 VEC 1.75 VEC 1.75

40 30 20

(Ag)

10 0

341

2000 2500 3000 3500 4000 4500 5000 5500 6000 λ (Å)

Fig. 3.1-209 Reflectivity of Ag−Al alloys [1.220, p. 142]

342

Part 3

Classes of Materials

Part 3 1.10

Diffusion Data for self-diffusion of Ag in Ag alloys and diffusion of tracer impurity elements are shown in Tables 3.1-153– 3.1-158 and Figs. 3.1-210–3.1-212. Diffusion of H and O is of importance for annealing treatments and dispersion hardening [1.217, 220, 226, 235].

D (m2 s –1) 1012 8 6

Ag-Cu

4

6.56 at. % Cu

2

4.16 at. % Cu 1.75 at. % Cu

10 –13

Table 3.1-153 Self-diffusion

in

binary

8

homogeneous

6

Ag−Au alloys [1.217, p. 150] Au (at.%)

T (K)

Ag−Au (110m Ag diffusion) 8 927–1218 17 908–1225 83 923–1284 94 936–1234 Ag−Au (198 Au diffusion) 8 991–1213 17 991–1220 83 985–1274 94 991–1283

Lattice

Surface

Grainboundary a

D0 (104 m2 /s)

Q (kJ/mol)

0.52 0.32 0.09 0.072

187.5 184.4 171.7 168.5

4

2

10 –14 8 6

0.82 0.48 0.12 0.09

202.2 198.0 180.2 176.1

4 × 10 –15 0.85

0.88

0.91

Element

D0 (m2 /s)

Q (kJ/mol)

Ag Ag(s) a Au Au(s) a Ag Ag Au(110) Au Ag Au

0.278 0.67 0.107 0.027 1 × 104 3 × 10−5 1 × 102 8 × 102 7.24 × 10−5 9.10 × 10−6

181.7 190.1 176.9 165 264 49 227 272 190.4 174.6

T (K) 1038–1218 913–1221 623–733 603–866 873 –1173 (H2 ) 580 –730 (Vac.) 1138–1329 (H2 ) 1200–1300 (Vac.) ∼790–680 625–521

Table 3.1-155 Diffusion of Ag in Cu and Cu in Ag [1.226, p. 365f.] Ag in Cu 485 4.9 × 10−14 ±0.1

574 8.2 × 10−13 ±0.6

625 2.91 × 10−12 ±0.08

731 7.7 × 10−11

794 1.65 × 10−10

D = D0 exp(−E A /RT ) with D0 = 0.61 cm2 /s, E A = 46.5 kcal/g-at. Cu in Ag T (◦ C) DCu

498 2.87 × 10−13 ±0.45

597 5.08 × 10−12 ±0.54

D0 = 1.23 cm2 /s, E A = (46.1 ± 0.9) kcal/g-at.

760 3.55 × 10−10

0.97

1.00 1.03 1/ T (10 –3K–1)

Fig. 3.1-210 Self-diffusion of Ag(110w) in Ag−Cu (1.75–6.56 at.% Cu) alloys [1.238, p. 189]

(s) = single crystal

T (◦ C) DAg

0.94

800 5.9 × 10−10

895 9.4 × 10−10

Table 3.1-154 Selfdiffusion in pure Ag and Au [frequency factor D0 (10−4 m2 /s)], activation energy Q (kJ/mol) [1.217, p. 149]

1.10 Noble Metals and Noble Metal Alloys

Metals

D0 (10−4 m2 /s)

Tracer

Q (kJ/mol)

Matrix: Silver (Ag) Cu 1.23 0.029 Au 0.262 0.41 0.85 0.62 Pd 9.57 Pt 6.0 1.9 Ru 180

193.0 164.1 190.5 194.3 202.1 199.0 237.6 238.2 235.7 275.5

T (K) 990–1218 699–897 923–1223 929–1178 991–1198 1009–1212 923–1223 1094–1232 1066–1219

Table 3.1-157 Grain boundary tracer diffusion in pure

Ag [1.217, p. 150] Matrix metal

Tracer

Ag

Cd In Sb Sn Te

D0 (m2 /s)

Q (kJ/mol)

T (K)

5.04 × 104 5.50 × 104 2.34 × 104 4.72 × 104 2.10 × 104

176.6 174.8 163.5 170.9 154.7

772–557 764–469 771–471 776–527 970–650

Table 3.1-158 Diffusion of hydrogen and oxygen in Ag,

Pd, Pt, and Au [1.217, p. 151] Matrix

Gas

D0 (10−4 m2 /s) Q (kJ/mol)

T (K)

Ag Ag Pd

H O H D T H H

8.55 × 10−3 3.66 × 10−3 2.9 × 10−3 1.7 × 10−3 7.2 × 10−3 6 × 10−3 5.6 × 10−4

947–1123 680–1140 473–1548 218–233 273–323 600–900 773–1213

Pt Au

30.11 46.1 22.19 19.88 23.8 24.70 23.61

D0 (10−4 m2 /s)

Tracer

Matrix: Gold (Au) Pd 0.076 Pt 0.095 Ag 0.072 0.08 0.086 Hg 0.116 Matrix: Platin (Pt) Ag 0.13 Au 0.13 Matrix: Palladium (Pd) Fe 0.18 D

4 × 10 –12 (m2 s–1)

1200 (K) 1100

Q (kJ/mol)

T (K)

195.1 201.4 168.3 169.1 169.3 156.5

973–1273 973–1273 943–1281 1046–1312 1004–1323 877–1300

258.1 252.0

1473–1873 850–1265

260

1373–1523

1000

900

800 T (K)

Tm = 1235 K

Matrix: Ag

10 –12

Ge

Sb

Al

10 –13

Co Fe

10 –14

Cr Ag Hg Au

10 –15

Pd 10 –16

Pt 10 –17

D (10–13m2 s–1) 1.6

Ag-Au 10 –18

1.2

2 × 10 –19 0.80

0.8

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

1.25 1.30 (10 –3 K–1) 1/T

Fig. 3.1-211 Diffusion of impurities in Ag [1.238, p. 244] 0.4

0

0

20

40

60

80

100 Au (at. %)

Fig. 3.1-212 Self-diffusion of Ag(110w) (brown circles) and Au(198) (gray circles) in Ag−Au (8–94 at.%) Ag−Au alloys [1.238, p. 190]

Part 3 1.10

Table 3.1-156 Diffusion of impurities in Ag, Au, Pt and Pd [1.217, p. 151]

343

344

Part 3

Classes of Materials

Part 3 1.10

Chemical Properties Silver has the reduction potential of E 0 = +0.8 V for Ag/Ag+ . It is resistant against dry oxygen, air, nonoxidizing acids, organic acids, and alkali. Water and water vapor do not attack Ag up to 600 ◦ C. Ag is dissolved in alkaline cyanidic solutions in the presence of oxidizing agents, air, and oxygen. H2 S attacks Ag readily at room temperature, forming black Ag2 S layers (tarnish) [1.217]. Metallic Ag and Ag−Au alloys are heterogeneous catalysts for oxidation processes, e.g., in the production of ethylene oxide and formaldehyde applied as grids or as powder preparations on Al2 O3 or carbon substrates [1.217]. Ag-Based Materials Binary alloys (Tables 3.1-159–3.1-161) [1.218]: Ag−Ni alloys are grain-stabilized materials usually containing 0.15 wt% Ni. Ag−Cu alloys have manifold applications in jewelry, silverware, brazes, and solders. Jewelry, sil-

Table 3.1-161 Physical properties of noble-metal-contain-

ing vacuum braze alloys [1.217, p. 560]

Ag−Cu

Ag−Mn Ag−Pd

Pd−Cu Pd−Ni Au−Cu Au−Ni a

Composition

Solidus (◦ C)

Ag40Cu19Zn21Cd20 Ag60Cu27In13 Ag44Cu30Zn26 Ag72Cu28 Ag85Mn15 Ag68.4Pd5Cu26.6 Ag54Pd25Cu21 Ag75Pd20Mn5 Pd18Cu72 Pd60Ni40 Au80Cu20 Au33Cu65 Au82Ni18

595 605 675 779 E a 950 807 901 100 1080 1237 890 990 950

Liquidus (◦ C) 630 710 735 950 810 950 1120 1090 1237 890 1010 950

E = Eutectic composition

Table 3.1-159 Noble metal containing soft solders [1.217] Alloy (wt%)

Melting range (◦ C)

Density (g/cm3 )

Tensile strength (N/mm2 )

Elongation (%)

Eleasticity module (N/mm2 )

Thermal expansion (10−6 K−1 )

Electrical conductivity (m/
mm2 )

Thermal conductivity (W/m K)

AuSn20 AuGe12 AuSi2 SnAg25Sb10 SnAg3.5 PbSn5Ag2.5 PbIn5Ag2.5

280 356 363–740 228–395 221 280 307

14.57 14.70 14.50 7.86 7.38 11.70 11.60

275 150–200 500–600 a 80–120 25–35 25–35 35–40

823 K

Tc (ordered)

(α-Fe) Tc (γ)

400

Phases and Phase Equilibria. Selected phase diagrams

C (wt %) 40

2042 K

1200

Production. Platinum sponge or powder are compacted by pressing and sintering. Melting and alloying is done in electrical heated furnaces in Al2 O3 or MgO crucibles, by vacuum arc and by electron beam melting 99.98%.

2

200 0 Fe

(Fe3Pt)

10

20

30

40

(α-Fe)

50

60

70

80

90 Pt Pt (at. %)

Fig. 3.1-278 Binary phase diagram Pt−Fe (dash-dotted

line: Curie temperature) [1.219]

1.10 Noble Metals and Noble Metal Alloys

Metals

T (K)

c p (J/K mol)

S (J/K mol)

298.15

25.857

41.631

H (J/mol) 0

400

26.451

49.314

800

28.593

1400

31.731

G (J/mol)

Part 3 1.10

Table 3.1-220 Thermodynamic data of Pt [1.217, p. 109] p (at)

12.412

8.26 × 10−92

2.664

−17.961

1.30 × 10−66

68.313

13.677

−40.973

9.75 × 10−30

85.111

31.776

−87.38

5.84 × 10−14

T = Temperature, c p = specific heat capacity, S = Entropy, H = Enthalpy, G = free Enthalpy, p = partial pressure of the pure elements

T (K)

20 40 60 10 30 50

80

Pt (wt %) 95

90

70 85 2100 2042 K Co-Pt 2000 1900 1768 K 1800 1703 K 1700 ≈15 1600 (α-Co, Pt) 1500 1394 K 1400 1300 Tc CoPt CoPt3 1200 1098 K 1100 ≈1023 K 1000 On heating 900 695 K 800 700 On cooling 600 500 (ε-Co) 400 300 Co 10 20 30 40 50 60 70 80 90 Pt Pt (at. %)

a) T (K)

20 40 60 10 30 50

2100 2000

80

70

Pt (wt %) 95

90

85

2042 K

Cu-Pt

1900

L

1800 1700

(Cu, Pt)

1600 1500 1400

1357.87 K

1300

b) 1200 1100 1000

Cu-Pt

≈1085 K

(Cu, Pt)

≈1005 K (CuPt)

900 800 700 600 Cu

?

≈691 K

(Cu3Pt)

1D-LPS

10

20

30

40

50

60

70

80

90 Pt Pt (at. %)

Fig. 3.1-280a,b Binary phase diagrams Pt−Cu. (a) Liquid– solid. (b) Solid–solid (1-D LPS = one-dimensional

Fig. 3.1-279 Binary phase diagram Pt−Co [1.219]

long-period superstructure) [1.219] Temperature (°C)

Platinum (at. %) 20

10 1700

40

50

60

70

80 100 90

1300 1100

(Ni, Pt)

900 700

Magnetic transformation

500

361°C

Ni3Pt

NiPt

300 100

0

Ni

10

20

30

40

50

Table 3.1-221 Crystal structure and lattice parameters of intermediate phases of Pt oxides [1.219]

1769.0°C

L

1455°C

1500

30

60

70

80

90

100

Pt (wt %)

Fig. 3.1-281 Binary phase diagram Pt−Ni [1.219]

377

Phase

Structure

PtO Pt3 O4 PtO2 PtO2

tetragonal PtO cubic Pt3 O4 orthorhombic Fe2 O3 hexagonal

Type

a (nm) b (nm) c (nm) 0.304 0.6226 0.4533 0.310

0.534 0.4488

0.3138 0.435

solutions with all other noble metals and with Co, Cu, Fe, and Ni. Miscibility gaps exist with C, Co, Ir, Pt, and Rh. Primary solid solutions have fcc structure and the lattice parameters correspond with few exceptions roughly to Vegard’s law. Numerous intermediate phases exist in al-

378

Part 3

Classes of Materials

Part 3 1.10

Table 3.1-222 Structure and lattice parameter of selected intermediate Pt compounds [1.217, p. 119] Phase

Pearson Symbol

a (nm)

b (nm)

c (nm)

CoPt CoPt3 CuPt CuPt3 Cu3 Pt Cu3 Pt Fe−Pt FePt Fe3 Pt NiPt PtZr Pt3 Zr

tP4 cP4 hR32 cF4 o∗∗ cP4 cF4 tP4 cP4 tP4 oC8 hP16

0.3806 0.3831 0.7589 0.3849 0.7596 0.3682 0.376 0.3861 0.3727 0.3823 0.3409 0.5624

0.3684

0.9679

0.2745

0.245

1.0315

0.3788

0.9811

0.3589 0.4277 0.9213

0.9388

in Tables 3.1-223 – 3.1-226 [1.217], Figs. 3.1-282 – 3.1-290 [1.217, 228, 228, 231]. For elastic properties of PGMs at different temperatures, see [1.217]. Strengthening is affected by solid solution hardening, order hardening (Pt−Co, Pt−Cu), and dispersion hardening. Dispersion-strengthened Pt and Pt alloys are remarkably resistant to creep at high temperatures. They are proTable 3.1-223 Elastic constants of Pt [1.217, p. 219] c11

c12

c44

347

173

76.5

Table 3.1-224 Mechanical properties of Pt (99.9%) at different temperatures (◦ C) [1.217, p. 220] T (◦ C)

E (GPa) Rm (MPa) A (%)

Rp0.2 (MPa) HV

20 250 500 750 900

173 169 159 140 126

50 40 30 20 17 a

a

Concentration x A(1 − x)B(x)

0.777

Mechanical Properties. Characteristic data are shown

41 40 42 46 44

Remarks

0.5

loy systems with rare earth metals. The formation and crystal structures of the intermediate phases have been related to the electron configuration of the alloy components (Engel–Brewer correlation) [1.283, 284]. Phases with superlattice structures are formed with Co, Cu, Fe, Nb, and V in atomic ratios of 1:1, 2:1, and 3:1 (Tables 3.1-123, 3.1-197). The ordered CuPt phase has a long-range ordered rhombohedral structure.

135 110 78 44 34

c/a

55 53 50 35 23

interpolation A = Elongation, E = Modulus of elasticity, Rp = Limit of proportionality, HV = Vickers hardness, Rm = Tensile strength

1.6328

Table 3.1-225 Mechanical properties of Pt as function of reduction in thickness (%) by cold rolling [1.217, p. 220] Reduction (%) 0 20 59

Rm (MPa) 250 350 400

Rp (MPa) 140 310 380

HV a

b

50 70 84

40 63 73

a = Pt > 99.5%, b = Pt > 99.99%

Table 3.1-226 Tensile strength Rm (MPa) and elongation A (%) of binary Pt alloys at different temperatures [1.217, p. 217, 220] Alloy compound

Temperature (◦ C) 20 400

(wt%)

Rm /A

Au5 Ir10 Ni5 Pd20Rh5 Rh5 Rh10

340/18 260/33 470/26 370/30 225/44 287/39

290/10 240/27 420/26 290/18 150/40 200/33

600

250/10 180/33 320/25 240/23 120/43 170/38

duced either by co-precipitation with refractory oxides (e.g., 0.16 vol% ZrO2 ) or by internal oxidation of alloys with 0.2 wt% Cr or 0.8 wt% Zr. Rh additions improve the solubility for oxygen. TiC powder affects dispersion strengthening in concentrations of 0.04–0.08 wt% (Fig. 3.1-291) [1.277].

1.10 Noble Metals and Noble Metal Alloys

Metals

Rh

Pt1–x Mx

Sn

Ru

1) Au

Sb

Ga, In

Ir

300

Part 3 1.10

a) Hardness (Hv) 200 Ge, Be

Modulus of elasticity E (GPa) 400

Cu

150

Ag

2) Au 200

100 Cu

100

Pd 0

20

40

60

80

100 x (at. %)

50

Fig. 3.1-282 Modulus of elasticity of binary Pt al-

Pt1– x Mx

loys [1.217, p. 222] 0 Tensile strength (MPa)

Tensile strength (ksi)

1750 Hard

250

b) Hardness (Hv) 200

1500 200 1250

Ni

Ti, Ma, W, Os V, Ru Zr Nb

Re

Ta

Cr Ir

150 Fe

Annealed 750

100

100

Rh

500 Mn

50

Pd

250 0 Pt

Co

150

1000

4

8

12

0 16 20 Nickel (%)

Fig. 3.1-284 Tensile strength of Pt−Ni alloys as a function of Ni content [1.228, p. 695]

50

Pt1– x Mx 0

0

10

20

379

30 x (mass %)

Fig. 3.1-283a,b Solid solution hardening of binary Pt alloys (a) de-alloyed at 900 ◦ C; (b) solution annealed at 1200 ◦ C [1.217, p. 223]

380

Part 3

Classes of Materials

Part 3 1.10

Tensile strength (MPa)

Tensile strength (ksi)

1250 160

Elongation Tensile δ (%) strength σB (N / mm2) 1400 64

Vickers hardness HV 10 350

HV 10

1000 Hard

120

750 80

500

Annealed 40

250

0 Pt

4

0

6

0 8 10 Ruthenium (%)

56

1300

330

48

1200

310

40

1100

290

32

1000

270

24

900

250

16

800

230

8

700

210

0

600

190

σB

δ 0

20

40

60 80 100 Cold forming (%)

Fig. 3.1-285 Tensile strength of Pt−Ru alloys as a function

Fig. 3.1-287 Mechanical properties of PtNi8 by cold form-

of Ru content [1.228, p. 694]

ing as a function of reduction of cross section [1.231, p. 69] Tensile strength (ksi) or hardness (HV)

Tensile strength (MPa) 2500

Tensile strength 2000

350

400

300 350

Hardness

250

1500 Hardness

200

300

150

1000 Tensile strength

250 100

500

0 Pt

Vickers hardness (kg/mm2)

Hard Annealed

2

4

6

50

0 8 Tungsten (%)

Fig. 3.1-286 Tensile strength of Pt−W alloys as a function

of W content [1.228, p. 697]

150 Quenched value 0 0.1

1.0

10.0

100.0 Time (h)

Fig. 3.1-288 Order hardening of stoichiometrc CuPt alloy [1.285, p. 49]

1.10 Noble Metals and Noble Metal Alloys

Metals

Resistivity at 20 °C (68 °F) (n Ω m)

440

450

400 *16 Pt Rh 10

400

360

350

W

Part 3 1.10

Tensile strength (MPa)

Ru

Cu Os

*40 Pt 320

300

280 *16 Pt

250

Ir

240

200

Pd

Ni

Rh

Pt Rh 10 200

150

160

100

120 Pt

0

2

4

6

8

10 12 14 16 Alloying element (%)

Fig. 3.1-291 Effect of various alloying additions on the

electrical resistivity of binary Pt alloys [1.231, p. 67]

80 40 0 RT

200

400

600

800

1000 1200 Temperature (°C)

Fig. 3.1-289 Tensile strength of dispersion hardened Pt and PtRh10 (∗ grain stabilized with 0.16 and 0.40 vol.% ZrO2 , respectively) [1.217, p. 222]

Electrical Properties. Characteristic data are shown in Tables 3.1-203, 3.1-205, 3.1-227 [1.217], and Figs. 3.1-292 – 3.1-294 [1.217,228,231]. Mo–28 at.% Pt (A15 structure) shows superconductivity at Tc ≈ 4.2–5.6 K [1.286]. Coefficient (% / K)

True creep strain

Resistivity (nΩ m)

0.5

0.35

Pure platinum

0.30

10 % Rhodium – Platinum

400

0.4

300 Electrical resistivity 20 °C (68 °F)

0.25

0.3

200

0.20 Temperature coefficient of resistivity 0 to 100 °C (32 to 212 °F)

0.2 0.15 0.10

0.1

0.05 0

0

1

10

100

0 Pt 1000 Time (h)

Fig. 3.1-290 Creep curves of TiC-dispersion-strengthened

Pt and PtRh wire at 1400 ◦ C in air [1.277]

100

0 Hard Annealed

Dispersion – Strengthened Pt

4

8

12

381

16

20 Ni (%)

Fig. 3.1-292 Electrical resistivity and temperature coefficient of resistivity (TCR) of Pt−Ni alloys as a function of composition [1.228, p. 696]

382

Part 3

Classes of Materials

Part 3 1.10

Table 3.1-227 Specific electrical resistivity (µΩ cm) of Pt at temperature (K) [1.217, p. 157] T (K)

10

50

120

273

673

1273

1673

ρ (µΩ cm)

0.0029

0.719

3.565

9.83

24.57

37.45

53.35

Coefficient (nΩ m / K) 0.4

0.3

Thermal electromotive force EA, Pt (mV)

Resistivity (nΩ m)

Temperature coefficient of resistivity 0 to 100 °C (32 to 212 °F)

Electrical resistivity 20 °C (68 °F)

800

t2 = 1200 °C t1 = 0 °C

Fe 20

600

Ni Cr 10

Co

400

Cu

0.2 0

200 0.1

Mo

30

0

t2 = 1200 °C t1 = 0 °C

Nb 0 Pt

1

2

3

Ru

20

4 Tungsten (%)

Rh

Fig. 3.1-293 Electrical resistivity and temperature coeffi-

10

Zr Sb

cient of resistivity (TCR) of Pt−W alloys as a function of composition [1.228, p. 697]

Sn

Pd

Ag In

0

Re

30 W

Thermoelectric Properties. Selected values of thermal

20

electromotive force of Pt and Pt alloys are given in Tables 3.1-206, 3.1-207, 3.1-228 – 3.1-231 [1.216, 217, 222], and Fig. 3.1-295 [1.216]. Thermocouples that are Pt−Rh-based are especially suited for high temperatures (see Fig. 3.1-296).

10

Ta

Ir

Os

t2 = 1200 °C t1 = 0 °C 0

Pt

90

95

Table 3.1-228 Pt−Rh thermocouples according IEC 5845

Fig. 3.1-294 Thermal electromotive force of binary Pt alloys [1.216, p. 97]

(see Fig. 3.1-296) [1.217, p. 472] Class

Alloy

Maximum applicable temperature (◦ C)

Type R: Type S: Type B:

PtRh(87/13)–Pt PtRh(90/10)–Pt PtRh(70/30)–Pt

1500–1600 1500–1600 1750–1800

85 Pt (wt %)

Table 3.1-229 Absolute thermoelectric power of Pt [1.222, p. 1009] Temperature (K)

300

400

500

600

700

800

900

1000

1100

1200

Thermoelectric power (µV/K)

−5.05

−7.66

−9.69

−11.33

−12.87

−14.38

−15.97

−17.58

−19.03

−20.56

Metals

70

80

−0.4 6.8

Ag

100 900

Au

100 900

Ir

100 1000

1.3 15.7

1.2 19.1

19.4

Rh

100 1000 1300

0.64 9.57 13.1

0.62 12.3 17.9

0.60 13.3 19.0

90

−0.1 4.0

0.2 4.5

0.8 11.9

0.4 13.5

Table 3.1-230 Thermal electromotive force of Pt alloys (mV) at different temperatures, reference junction at 0 ◦ C [1.217, p. 160]

Table 3.1-231 Basic values of thermal electromotive force (mV) of common PGM-based thermocouples [1.216, p. 100] T1 (◦ C)

T2 (◦ C)

0

Pt − Rh10/Pt

Pt − Rh20/Pt − Rh5

Rh − Ir60

100

0.643

0.074

0.371

3.31

4.6

500

4.221

1.447

2.562

20.20

27.9

5.495

41.65

59.6

1000

9.570

4.921

T1 (K)

T2 (K)

Au − Co2.1/Cud

Au − Fe0.02/Cud

4.2

10

0.044

0.093

20

0.173

0.208

40

0.590

0.423

Pt-elb

Pd-orc

Pt-el = Platinel, Pd83Pt14Au3/AuPd35 c Pd-or = Pallador, PtIr10/AuPd40 d at.% b

Thermal electromotive force (mV)

Thermal electromotive force (mV)

15

20

Typ R

1000 °C

Typ S

900 °C 800 °C

10

15

700 °C 600 °C 500 °C

5

400 °C 300 °C

0

Typ B 10

0

20

40

60

80 100 Rhodium (at. %)

Fig. 3.1-295 Influence of the Rh content on the thermal

emf of Pt−Rh alloys against Pt [1.217, p. 473]

5

0

0

500

1000

1500 2000 Temperature (°C)

Fig. 3.1-296 Thermal electromotive force of Pt−Rh thermocouples according to IEC 5845 (Type R: PtRh(87/13)– Pt; type S: PtRh(90/10)–Pt; type B: PtRh(70/30)– PtRh(94/6)) [1.217, p. 473]

383

Part 3 1.10

Composition (wt%Ir) 10 30 40

T (◦ C)

Alloy const.

1.10 Noble Metals and Noble Metal Alloys

384

Part 3

Classes of Materials

Part 3 1.10

Magnetic Properties. Selected data are shown in Tables

3.1-211, 3.1-232 [1.217,222], and Figs. 3.1-297 [1.220] and 3.1-298. The paramagnetic susceptibility of Pt (25.2 × 10−10 m3 mol−1 at 0 K) rises by alloying with 0.1 at.% Rh to 42.5 × 10−10 m3 mol−1 . CoPt is a hard magnetic material (Hc = 3500–4700 Oe) but has been replaced by rare-earth transition metal magnetic materials in recent years. Superlattice phases in PtCr-alloys in the composition ranges of 17–65 wt% Cr are ferromagnetic, with the maximum of Tc at ∼ 30 at.% Cr. The superlattice structure in FePt and CoPt with tetragonal crystal symmetry gives rise to high values of magnetic anisotropy. The coercivity of sputtered Pt−Co multilayers is increased by annealing in air, caused by the formation of cobalt oxide at the grain boundaries. The

Potential, V Pt O3 × H2O

5

2.0 1.6

8 Corrosion 4 3

1.2

Passive Pt O2 × H2O

0.8 7

2

6

τO = O

Pt (OH)2

0.4 0

Immune

Pt

1

– 0.4

Table 3.1-232 Characteristic properties of technical perma-

nent magnet alloys [1.222, p. 1053] Alloy (wt%)

Hmax (kJ/m3 )

Hc (kA/m)

Br (T)

Pt77Co23 Sm34Co66 Co52Fe35V13

75.0 110–160 22.4

380 560 36

0.60 0.80 1.00

–1.2 –1.6 –2

B = magnetic flux density, H = magnetic field, Br = Remanence

Saturation and residual magnetism (G)

Resistance per cm and cm2 6 (10 Ω) 45

3000

Brinell hardness 2 (kg/ mm )

5000

2500

250

4000 Hardness

2000

200

40

3000

1500

150

35

2000

1000

30

1000

500

Resistance

Coercivity force 25

0 550 0 Quenched

600 650 700 Starting temperature

750

6

8

10

12

14

16 pH

Table 3.1-233 Thermal conductivity λ of Pt–(Au, Rh, Ir) alloys (W/m K) [1.217, p. 153]

3500

Residual magnetism

4

oxide layer gives rise to domain pinning and to magnetic isolation of the grains, thus leading to a high perpendicular anisotropy [1.217].

Saturation 6000

2

at 25 ◦ C (see Table 3.1-232) [1.217, p. 201]

4000

7000

0

Fig. 3.1-298 Potential pH-diagram of the system Pt/H2 O

Coercivity force (Oe)

8000

τH = O – 0.8

800 Final state (°C)

Fig. 3.1-297 Change of magnetic properties of PtCo50 alloy by annealing [1.220, p. 263]

PtAu5

PtRh5

PtRh10

PtRh20

PtIr5

PtIr10

43

33 a

30

28 a

42

31

= calculated with Wiedemann-Franz’ law λ = LσT , Lorenz number L = 2.45 × 10−6 W/K from λ(PtRh10) and the specific electrical conductivity of PtRh-alloys

a

Table 3.1-234 Thermal expansion coefficient α (10−6 K−1 )

of Pt−Rh alloys at different temperature ranges [1.217, p. 155] Temperature range (K) Rh-content (wt%)

α (10−6 /K) 273–983 (10−6 /K)

293–1473 (10−6 /K)

6 10 20 30

10.7 10.7 10.9 10.8

11.3 11.2 11.5 11.4

Metals

Optical Properties. Values of the spectral degree of

Corrosion (mm / a) 40 20 10

1

emission and the optical reflectivity are given in Table 3.1-216 [1.217] and Fig. 3.1-275 [1.220]. Diffusion. Data for self-diffusion, diffusion of tracer

elements and of hydrogen and oxygen are shown in Tables 3.1-158, 3.1-216, 3.1-217 [1.217]. Chemical Properties. Platinum has the reduction potential of E 0 = +1.118 for Pt/Pt2+ . It is resistant against reducing acids in all pH ranges, but is attacked by alkali and oxidizing media. Alloying with 30 at.% Rh improves the corrosion resistance against alkali hydroxides. Figure 3.1-298 and Table 3.1-235 [1.217] give the potential pH diagram of the system Pt/H2 O at 25 ◦ C. Dry Chlorine attacks with rising temperature (Fig. 3.1-299 [1.217]). Detailed information about chemical behavior is given in [1.217]. Platinum reacts with ZrC to form Pt3 Zr. It also reacts in the presence of hydrogen with ZrO2 , Al2 O3 , and rare earth oxides at temperatures between 1200 and 1500 ◦ C [1.283, 284]. The solubility of oxygen in platinum is very low. Thin coatings of Pt on reactive materials are an effective protection against oxidation. Alloying of Pt with 2 wt% or higher Al improves the oxidation resistance up to 1400 ◦ C by forming protective dense oxide coatings [1.287]. Superalloys that are Pt−Al-based have high compression strength at high temperatures. Third alloying elements (e.g., Ru) stabilize the high-temperature phase down to room temperature and affects solid-solution strengthening [1.288].

0.1 0.03 250

500

750

1000 Temperature (°C)

Fig. 3.1-299 Corrosion of Pt in dry Cl2 gas [1.217,

p. 186] Catalysis. Platinum and Pt alloys are preferably ap-

plied in heterogeneous catalysis as wire nets or powders with a high specific surface area ranging from 20 to 1000 m2 /g (“platinum black,” “palladium black”) on carbon or Al2 O3 supports. The catalytic effectivity is structure-sensitive. Figure 3.1-300 show an example of the catalytic action of Pt for the reaction rate and the product selectivity on different crystal planes [1.218]. Pt−Pd−Rh alloys are the main active constituents of catalytic converters for automobile exhaust gas cleaning. Special Alloys. Molybdenum clad with Pt serves as glass

handling equipment up to 1200 ◦ C. Binary Pt alloys with Cu(4), Co(5), W(5), and Ir(10) at.%; and ternary alloys of Pt−Pd−Cu and Pt−Pd−Co are standard jewelry alloys. Alloys of Pt−Au and Pt−Au−Rh surpass the strength of pure Pt at 1000 ◦ C and resist wetting of molten glass. The materials PtIr3, PtAu5 are suitable for laboratory crucibles and electrodes with high mechanical stability.

Number

Reaction equation

Potential E0 (V)

1 2 3 4 5 6 7 8

2H+ + 2e−

0.000 − 0.0591 pH 1.228 − 0.0591 pH 0.980 − 0.0591 pH 1.045 − 0.0591 pH 2.000 − 0.0591 pH log[Pt++ ] = −7.06 − 2 pH 1.188 + 0.0259 log[Pt++ ] 0.837 − 0.1182 pH − 0.0259 log[Pt++ ]

→ H2 2H2 O → O2 + 4H+ + 4e− Pt + 2H2 O → Pt(OH2 ) + 2H+ + 2e− Pt(OH)2 → PtO2 + 2H+ + 2e− PtO2 + H2 O → PtO3 + 2H+ + 2e− Pt + H2 O → PtO + 2H+ Pt → Pt++ + 2e− Pt++ + 2H2 O → PtO2 + 4H+ + 2e−

385

Part 3 1.10

Thermal Properties. Tables 3.1-212 – 3.1-215, 3.1-233, and 3.1-234 [1.217,217] provide selected data of thermal conductivity and thermal expansion. In the disordered state the Fe−Pt alloy system exhibits a negative thermal expansion coefficient at room temperature near Fe3 Pt (Invar effect) [1.281, 282].

1.10 Noble Metals and Noble Metal Alloys

Table 3.1-235 Reaction and potentials corresponding to graphs of Fig. 3.1-298 [1.217, p. 200]

386

Part 3

Classes of Materials

Part 3 1.10

a) Toluene (108 mol / cm2) 12

Pt (111)

Fig. 3.1-300 (a) Rate of reaction of n-heptane dehydrocyclization to toluol on Pt(111) and Pt(100). (b) Variation of selectivity at different crystal planes [1.218, p. 279]

8 4 Pt (100) 0

0

180 120 Reaction time (min)

60

b) Dehydrocyclization Hydrogenolysis 6

Selectivity

4 2 0

(111)

(557)

(10, 8, 7)

(25, 10, 7) Crystal plane

3.1.10.4 Rhodium, Iridium, Rhutenium, Osmium, and their Alloys Rhodium and Rhodium Alloys Applications. Rhodium is an essential component of

catalysts in numerous chemical reactions and automobile exhaust-gas cleaning. In heterogeneous catalysis it is applied in alloyed form, in homogeneous catalysis as complex organic compounds. Rhodium is an alloy component of corrosion- and wear-resistant tools in the glass industry and a constituent in platinum-group-metalbased thermocouples. Rhodium coatings on silverware and mirrors protect them against corrosion. Commercial grades available are powder, shot, foil, rod, plate, and wires with purity from 98–99.5% (ASTM B 616-78; reappraised 1983).

Production. Rhodium is produced as powder and

sponge by chemical reduction or thermal decomposition of the chloro–ammonia complex (NH4 )3 [RHCl6 ]. Bars, rods, and wires are produced by powder compacting and extrusion, while coatings are produced galvanically, by evaporation or by sputtering. Phases and Phase Equilibria. Selected phase dia-

grams of Rh are shown in Fig. 3.1-301a–c. Rhodium forms continuous solid solutions with Fe, Co, Ni, Ir, Pd, and Pt. Miscibility gaps exist in alloys with Fe, Co, Ni, Cu, Ag, Au, Pd, Pt, Ru, and Os. Thermodynamic data are given in Table 3.1-236 (see also

Table 3.1-236 Thermodynamic data of Rh [1.217, p. 110] T (K)

c p (J/K mol)

S (J/K mol)

H (J/mol)

298.15

24.978

31.506

0

400

26.044

38.993

2.598

800

39.155

58.333

1400

35.195

76.556

G (J/mol) −9.393

p (atm.) 1.43 × 10−89

−13

6.59 × 10−65

13.853

−32.813

7.21 × 10−29

33.532

−73.646

1.71 × 10−13

T = Temperature, c p = specific heat capacity, S = Entropy, H = Enthalpy, G = free Enthalpy, p = partial pressure of the pure elements

Metals

10

0 2100

20

30

(at. %) 50 60 70 80 90 100

40

1963 °C

Table 3.1-190) and the maximum hydrogen inclusion is listed in Table 3.1-194. The compositions and crystal structures of intermediate compounds are shown in Table 3.1-237 (see Table 3.1-197 for superlattice structures).

L

1700

1300

1150 °C

1084.87 °C (Cu, Rh) 900 (Cu) + (Rh) 500

0 10 Cu

20

30

40

50

60

b) Temperature (°C) 0

10

20

30

70

80

90 100 (wt %) Rh

(at. %) 50 60 70 80 90100

40

1963 °C

2000 L 1600 1538 °C 1200

1521 + 4 °C (δFe) 1394°C

~1300 °C (γFe, Rh)

912 °C 800

a) Young’s modulus

Modulus of rigidity G (GPa)

E (GPa)

770 30, 605 °C

400 (αFe)

Tc

α'

0 Fe

10

20

30

40

50

60

70

80

90 100 (wt %) Rh

c) Temperature (°C) 0 10 20 30 40 50 2000

60

70

165

65

160

53

155

α'' 0

1600

Mechanical Properties. Characteristic mechanical data of Rh are given in Tables 3.1-238–3.1-241 and Figs. 3.1-302–3.1-307. The modulus of rigidity G = 153 GPa; Poisson’s ratio is 0.26; the elastic constants are c0 = 413, c12 = 194, and c44 = 184. Rhodium is very hard but can be deformed at temperatures above 200 ◦ C. For strong hardening by deformations, repeated annealing is needed at temperatures higher than 1000 ◦ C. Rh is an effective hardener in Pd and Pt alloys.

80

90

L

(at. %) 100

1963 °C

1769.0 °C

E Pt

51

G Pt

49

150 145 135

47

130

45

b) Poisson’s ratio ν 0.52 0.50

(Pt, Rh)

0.48

1200

νE/GPt

0.46 0.44

~760 °C

800 (Pt)

(Rh) (Pt) + (Rh)

400 0

0 Pt

0.42 0.38 0

10

20

30

40

50

60

70

80

90 100 (wt %) Rh

Fig. 3.1-301a–c Phase diagrams of Rh alloys with (a) Cu, (b) Fe, and (c) Pt [1.216, p. 101, 104]

νGPt

0.40 100 200 300 400 500 600 700 800 900 Temperature (°C)

Fig. 3.1-302 (a) Young’s modulus E (GPa) and modu-

lus of rigidity G (GPa) of Pt at different temperatures. (b) Poisson’s ratio for Pt at different temperatures [1.289,

p. 76]

387

Part 3 1.10

a) Temperature (°C)

1.10 Noble Metals and Noble Metal Alloys

388

Part 3

Classes of Materials

Part 3 1.10

Table 3.1-237 Structure and lattice parameter of selected Rh compounds [1.217, p. 117ff.] Phase

Pearson symbol

a (nm)

b (nm)

Cu−Rh Fe−Rh Fe−Rh FeRh Fe−Ru Ni−Rh

cF4 cI2 cF4 cP2 hP2 cF4

0.3727 0.288885 0.374 0.2998 0.258 0.36845

Concentration x A(1 − x)B(x)

c (nm)

0.5 0.5 0.414

0.2 0.494

Table 3.1-238 Mechanical properties of Rh (99%) at different temperatures [1.217, p. 227] T (◦ C)

E (GPa)

Rm (MPa)

A (%)

Rp0.2 (MPa)

HV

20 500 700 1000

386 336 315 −

420 370 340 120

9 19 16 10

70 80 40 30

130 91 73 52

A = elongation of rupture, E = modul of elasticity, Rp = limit of proportionality, HV = Vickers hardness, Rm = tensile strength

Table 3.1-239 Increase of Rh hardness by cold forming [1.217, p. 227]

Table 3.1-241 Hardness of Rh−Ni alloys at 300 K [1.217,

p. 228]

V (%)

HV

Alloy

HV 5

0 10 30 50

130 275 50 400

RhNi27 RhNi40 RhPd20 RhPt20

275 220 178 165

Table 3.1-240 Hardness of Pd/Rh and Pt/Rh alloys as

a funtion of composition [1.217, p. 218] 2nd metal

Pd Pt

HV 5 Content (mass%) 0 20 130 130

178 165

a) Young’s modulus

Modulus of rigidity G (GPa)

E (GPa) 380

150

360 40

60

80

340

235 164

229 145

138 123

320

140 E Rh

270 250 230 210 190 170 150 130

400 °C 800 °C 1200 °C 10

20 30 Rhodium concentration (wt %)

Fig. 3.1-303 Young’s modulus of as cast Pt/Rh-alloys at

various temperatures [1.289, p. 80]

260

110

240

100

b) Poisson’s ratio ν

25 °C

0

120

GRh

280 Young’s modulus E (GPa)

130

300

0.30 0.29 0.28 0.27 0.26 0.25 0.24 0.23 0.22

νDRh

νE/GRh

0

100

200

300

400

500

600

700

800

900 1100 1000 1200 Temperature (°C)

1.10 Noble Metals and Noble Metal Alloys

Metals

Part 3 1.10

Fig. 3.1-305 Vickers hardness of Pt/Rh-10 as a function of reduction (%) and various annealing temperatures [1.218, p. 608]

Vickers hardness % Reduction

a) Young’s Modulus E (GPa) 280

E 30 %Rh

250 90 %

260 240 220 200

E 20 %Rh

200 80 %

E 10%Rh 60 %

180 160

b) Modulus of rigidity G (GPa) 105 G 30%Rh 100 95 90 85 G 20%Rh 80 75 G 10 %Rh 70 65 60 c) Poisson’s ratio ν 0.39 0.38 νD10%Rh 0.37 0.36 νE/G10 %Rh νD20 % Rh 0.35 νE/G20 % Rh 0.34 νD30%Rh 0.33 0.32 νE/G30 %Rh 0.31 100 300 500 700 900 1100 0 200 400 600 800 1000 1200 Temperature (°C)

Fig. 3.1-306 (a) Young’s modulus E (GPa) of Pt/Rh-10, Pt/Rh-20 and Pt/Rh-30 alloys at different temperatures. (b) Modulus of rigidity G (GPa) of Pt/Rh-10,Pt/Rh-20 and Pt/Rh-30 alloys at different temperatures. (c) Poisson’s ratio of Pt/Rh 10, Pt/Rh 20 and Pt/Rh-30 alloys at different temperatures [1.289, p. 79]

40 %

150 20 % 15 % 10 % 5%

100 1h 0

500

Stress (kg / mm2)

1000 1400 Temperature (°C)

Elongation (%) 50

100 90

Tensile strength

Elongation 40

80 70

30

60 50

20

40 30

J

Fig. 3.1-304 (a) Young’s modulus E (GPa) and the mod-

20

ulus of rigidity G (GPa) of forged Rh at different temperatures. (b) Poissons ratio for forged Rh at different temperatures [1.289, p. 77]

10

Fig. 3.1-307 Mechanical properties of Pt/Rh-10 alloy [1.218, p. 609]

10

1h 0

389

500

1000 1400 Temperature (°C)

390

Part 3

Classes of Materials

Part 3 1.10

Electrical Properties. Characteristic electrical proper-

Electrical resistance

ties are given in Tables 3.1-242 and 3.1-243 (see also Table 3.1-203). Rhodium shows superconductivity below 0.9 K [1.216]. Superconducting Rh alloys are shown in Table 3.1-244. Among the three-element alloys containing precious metals there exists a special group known as magnetic superconductors [1.218]. Figure 3.1-308shows as example the alloy ErRh4 B4 with the coexistence of superconductivity and magnetic order changing in the region below the critical temperature of beginning superconductivity [1.218]. Data for light and thermoelectric emission are given in Table 3.1-245 [1.290].

Magnetic susceptibility 1

0

–1 0

Tc1

Tc2

Temperature (K)

Fig. 3.1-308 Coexistence of superconductivity and magnetic order in ErRh4B4 [1.218, p. 637]

Table 3.1-242 Increase of atomic resistivity ∆ρ/C of

Rh [1.217, p. 158] Base element

ρ/C (µ
cm/at.%)

Rh

Co 0.34, Cr 4, Fe 0.6, Mn 1.4

Table 3.1-243 Specific electric resistivity ρi (T ) (µΩ cm) of Rh at temperature T (ρ0 = 0.0084) [1.217, p. 156] T (K)

25

70

160

273

500

1250

1750

ρi (T )

0.0049

0.34

2.12

4.3

9.20

26.7

40.9

Table 3.1-244 Superconducting Pd, Pt, and Rh al-

loys [1.218, p. 636] Pd, Pt Compound

Tc (K)

PtNb3 Pd1.1Te PdTe1.02 PdTe2

10.6 4.07 2.56 1.69

Rh Compound

Tc (K)

Rh2P Rh4P3 ErRhB4

1.3 2.5 8.5

Table 3.1-245 Light and thermoelectric emission of Rh, Pd, and Pt [1.220, p. 79] Metal Rh Pd Pt

Light-electric constants Wavelength limit (Å) Work function (V)

Temperature (◦ C)

2500 2700 2490 1962

20 240 RT RT

4.57 − 4.96 6.30

Thermoelectric work function (V) 4.58 (at 1550◦ abs.) 4.99 (at 1550◦ abs.) 6.37 (at 1550◦ abs.)

Metals

3.1-207 give data for the absolute thermoelectric power; Tables 3.1-246 and 3.1-247 give the thermal electromotive force of Rh and of Rh/Ni alloys at different temperatures. Rh is also used as a component in Pt-based thermocouples (Tables 3.1-230–3.1-228, Fig. 3.1-295).

χg (10–9 m3 kg–1) 300 250

Rh-Ni

200 150

Magnetical Properties. Data of the magnetic suscepti-

100

bility of Rh and Rh alloys are given in Figs. 3.1-271, 3.1-272, and 3.1-309–3.1-312. For magnetostriction data see Table 3.1-211. The superlattice alloy FeRh shows a transition from the antiferro- to the ferromagnetic state near room temperature Fig. 3.1-312 [1.218] where small additions of Pd, Pt, Ir, Ru, or Os enhance this effect.

50 0

0 Ni

20

40

60

80 100 Rhodium (at. %) Rh

Fig. 3.1-310 Mass susceptibility of Rh−Ni alloys as a function of alloy composition at 4.2 K [1.217, p. 166] χg (10–9 m3 kg–1)

–9

3

χg (10 m /kg) 20 19 18 17 16 15 14 13 12 11

180 160 140

Rh

Pd1-x Rhx x = 0.050 x = 0.030

120 100 80

x = 0.015 x = 0.001

60 0 0

400

800

1200

1600

2000 T (K)

Fig. 3.1-309 Temperature dependence of the mass suscep-

50

100

150

200

250

300 T (K)

Fig. 3.1-311 Mass susceptibility of Pd−Rh alloys as a function of alloy composition [1.217, p. 169]

tibility of Rh [1.217, p. 163] Table 3.1-246 Thermal electromotive force of Rh at different temperatures [1.217, p. 159] T (◦ C)

−200

−100

+100

+400

+800

+1000

+1300

E Rh/Pt

− 0.23

− 0.32

+ 0.70

+ 3.92

+ 10.16

+ 14.05

+ 20.34

Table 3.1-247 Thermal electromotive force of Rh/Ir alloys at different temperatures [1.217, p. 160] T (◦ C) 1000

Composition (wt% Ir) 10 30 15.15

391

Part 3 1.10

Thermoelectrical Properties. Tables 3.1-206 and

1.10 Noble Metals and Noble Metal Alloys

50

70

90

17.40

18.40

17.75

15.45

392

Part 3

Classes of Materials

Part 3 1.10

Chemical Properties. Rhodium is not attacked by acids or alkali even under oxidizing conditions (aqua regia) (Fig. 3.1-313). Sodium hypochlorite attacks in the order of increasing strength: Pt = Rh = Ir = Ru < Pd < Os. Heating in air causes the formation of thin oxide layers above 600 ◦ C which decompose above 1100 ◦ C (Fig. 3.1-314). Pt alloys with 5–40 wt% Rh are corrosion-resistant against H2 F2 . A detailed survey about these chemical properties is given in [1.216]. Rhodium is the effective component of the threeway Pt/Pd/Rh alloy autocatalyst for the reduction of

a) Magnetization (emu g–1) 140 120

Calculated for S = 1

100 80 σ 60 40

Potential (V) 20

2.0

0

200

800 600 Temperature (K)

400

b) Magnetization (emu g ) –1

120 FeRh Pd 0.0833 FeRh Ru 0.0833 FeRh Ir 0.0833 FeRh Pt 0.0833 FeRh Os 0.0833

100 80 60 40

Passive b

1.2 0.8 0.4 0

Immune

a –0.4

20 0

1.6

–0.8 – 200

0

200

400

800 600 Temperature (°C)

Fig. 3.1-312a,b Metamagnetic behavior of (a) FeRh superlattice alloy [1.218, p. 102]. (b) Variation by addition of small amounts of Pd, Ru, Ir, Pt, Os [1.218, p. 102]

–1.2 –1.6 –2

0

2

4

6

8

10

12

14

16 pH

Fig. 3.1-313 Potential

Thermal Properties. Tables 3.1-212–3.1-214 show

the recrystalization temperature, thermal conductivity and thermal expansion at different temperatures. Vapor pressure at different temperatures is shown in Fig. 3.1-273.

pH diagram for the system Rh−H2 O [1.217, p. 202] Weight change (10 –2mg cm–2) + 20 1100 °C 0

Optical Properties. Rhodium has the highest optical re-

flectivity of all ranging about It is used as ing on silver Data of the Table 3.1-216.

platinum-group metals (Fig. 3.1-274), 20% below the reflectivity of Ag. hard and corrosion-resistant coatjewelry and for optical reflectors. spectral emissivity are given in

Diffusion. Data for self-diffusion are given in

Table 3.1-217 (see [1.216] for further data).

– 20

1200 °C

– 40 1300 °C – 60

0

4

8

12

16

20 Time (h)

Fig. 3.1-314 Weight change of Rh in oxygen [1.217, p. 185]

1.10 Noble Metals and Noble Metal Alloys

Metals

15

Rh

10

Iridium and Iridium Alloys Applications. Iridium is used for crucibles to grow high-

5

purity crystals for lasers, medical scanners etc., anodes to prevent corrosion of shipping vessels and under-water structures, coatings of electrodes for the manufacturing of chlorine and caustic soda, as an alloy component of automotive exhaust catalysts, and as alloy component and compounds of chemical process catalysts for the production of acetic acid and complex organic compounds. Iridium is an effective hardener for materials used at high temperature, high wear, and high corrosion conditions (e.g., spark plugs). It is also used as finegrain forming addition in jewelry and dental gold alloys. Commercial grades available are powder, shot, ingot, and wire in a purity ranging from 98–99.9% (ASTM 671-81, reappraised 1987).

Pd 400

500

600 Temperature (K)

b) N2 formation rate (1013 molecule cm–2 s–1) 3 Rh 2 1 Pd 600

800

1000

1200 Temperature (K)

Fig. 3.1-315a,b Product formation rates in N = −H2 reactions on Pd- and Rh-catalyst foils. (a) NH3 forma-

Production. Iridium is produced as powder and sponge

tion rates p(NO) = 9.4 × 10−5 Pa, p(H2 ) = 4.9 × 10−5 Pa. (b) N2 formation rates p(NO) = 1.1 × 10−5 Pa, p(H2 ) = 1.9 × 10−5 Pa [1.218, p. 287]

by chemical reduction or thermal decomposition of the chloro–ammonia compound (NH4 )2 [IrCl6 ]. Bars, rods, ingot, and wires are produced by compacting of powder followed by extrusion. Coatings are produced galvanically, by evaporation, or by sputtering.

NOx of exhaustion gases (Figs. 3.1-315a,b). Rhatalysts surpass the group homolog, Co-based catalysts, with lower reaction pressures and temperatures and higher yields [1.216]. Complex organic rhodium compounds on the basis of RhCl (PPH3 ) with different substitute ligands are important homogeneous catalysts in the technical production processes for hydrogenation and hydroformulation (“oxo”-processes, e.g., synthesis a) MeO AcO

COOH NHAc

Phases and Phase Equilibria. Figures 3.1-317–

3.1-319 [1.216] show the binary phase diagrams of Ir alloys with Pt, Rh, and Ru. Miscibility gaps exist in the solid state also in the alloy systems with Cu, Os, Re, and Ru. Iridium alloyed in Fe lowers the α–λ transition temperature considerMeO

[Rh ((R, R)-(DiPAMP) COD] BF4 10 bar H2, 25 °C ton 20 000, tof 1000 h–1

AcO

COOH H NHAc

100 % yield; 95 % ee

b)

100 °C [Rh-(–)-BINAP(COD)]CIO4 NEt2 … allylamine

ton 400 000 tof 440 h–1

HO HO

COOH H NHAc L-DOPA

3 steps NEt2 … enamine

OH 94 % ee L-menthol

Fig. 3.1-316a,b Examples of organic synthesis of chiral compounds catalysed by complex Rh compounds. (a) L-DOPA. (b) L-menthol [1.291, p. 83]

Part 3 1.10

of aldehydes and acetic acid). Replacement of PPH3 by complex chiral phosphan ligands enables the synthesis of asymmetric compounds, e.g., L-DOPA and L-menthol (Fig. 3.1-316a,b) [1.291].

a) NH3 formation rate (1011 molecule cm–2 s–1)

393

394

Part 3

Classes of Materials

Part 3 1.10

Temperature (°C) 0 10 20 2600 2447 °C

30

40

50

60

Platinum (at. %) 70 80 90 100

Fig. 3.1-317 Phase diagram of Ir−Pt [1.217, p. 88] Temperature (°C) Ruthenium (at. %) 0 10 20 30 40 50 60 70 80 90 100 2600 2447 °C L 36.3 30 35.4 2334 °C 2395 °C 2000

L

2200 1800

1769 °C

(Ir, Pt)

1400

(Ir)

(Ru)

1000 (Ir) + (Pt) 600

0 Ir

10

20

30

40

Temperature (°C) 0 10 20 30 40 50 2600 2447 °C

50

60

60

70

70 80 90 100 Platinum (wt %) Pt

80

Rhodium (at. %) 90 100

1963 °C (Ir, Rh)

1000

10

20

30

40

50

60 70 80 90 100 Ruthenium (wt %) Ru

Fig. 3.1-319 Phase diagram of Ir−Ru [1.217, p. 89]

ably (Fig. 3.1-343). Thermodynamic data are given in Table 3.1-248 [1.216]. Structure and lattice parameters of selected intermediate compounds are given in Table 3.1-249 [1.216].

L 2000

1000 800 0 Ir

~ 850 °C (Ir) + (Rh)

400 0 Ir

10

20

30

40

50

60

70 80 90 100 Rhodium (wt %) Rh

Fig. 3.1-318 Phase diagram of Ir−Rh [1.217, p. 89]

Table 3.1-248 Thermodynamic data of Ir [1.217, p. 109] T (K)

c p (J/K mol)

S (J/K mol)

H (J/mol)

G (J/mol)

p (atm)

298.15 400 800 1400

24.979 25.695 28.51 32.733

35.505 42.946 61.62 78.647

0 2.581 13.442 31.795

−10.586 −14.598 −35.875 −78.311

6.70 × 10−80 2.81 × 10−36 1.15 × 10−17

T = Temperature, c p = specific heat capacity, S = Entropy, H = Enthalpy, G = free Enthalpy, p = partial pressure of the pure elements

Table 3.1-249 Structure and lattice parameter of intermediate compounds [1.217, p. 117ff,] Phase

Pearson symbol

a (nm)

Cu−Ir Ir−Os Ir−Os Ir−Rh Ir−Ru Ir−Ru

cF4 hP2 cF4 cF4 hP2 cF4

0.3629 0.27361 0.38358 0.3824 0.2718 0.3818

b (nm)

HT = high temperature modification, LT = low temperature modification

c (nm)

Concentration x A(1 − x)B(x)

0.43417

0.65 0.2 0.5 0.56 0.47

0.4331

Metals

can only be deformed at temperatures above 600 ◦ C, with repeated annealing steps at temperatures higher than 1200 ◦ C. The Young’s modulus is different for different crystal directions (Table 3.1-250) [1.216], the modulus of rigidity is 214 GPa, and the Poisson’s ratio amounts to 0.26. Characteristic data of mechanical properties of Ir and Pt/Ir alloys are given in Tables 3.1-251– 3.1-253 [1.216] and Figs. 3.1-320–3.1-322 [1.289]. Two-phase Ir-based refractory superalloys with fcc and L12 structure of the components (Ir−12Zr and Ir−17Nb, Ir−15Nb−5Ni) have resist temperatures up to 1200 ◦ C and exhibit marked creep resistance (Figs. 3.1-323– 3.1-325) [1.292, 293].

a) Young’s modulus E (GPa) 250

E 30 % Ir E 20 % Ir

200

150

E 10 % Ir

0

E 110

E 111

47.4 GPa

662 GPa

c11 = 580

c12 = 242

a) Young’s modulus E (GPa) 520 500 480 460 440 420 400 380

1200

95 G 30 % Ir

85 G 20 % Ir

80

60

G 10 % Ir

0

100 200 300 400 500 600 700 800 900 1000 1100

Temperature (°C)

c44 = 256

Fig. 3.1-321 (a) Young’s modulus of Pt−Ir alloys at different temperatures. (b) Modulus of rigidity of as cast Pt−Ir

200 190 180 170

b) Poisson’s ratio v 0.30

alloys at different temperatures [1.289] Young’s modulus E (GPa) 270 250 230 210 190 170 150 130

25 °C 400 °C 800 °C 1200 °C

0

10

20 30 Iridium concentration (wt %)

Fig. 3.1-322 Young’s modulus of as cast Pt−Ir alloys at

different temperatures [1.289]

vD Ir 0.25 vE/G Ir 0.20 0

1000

Temperature (°C)

65

210

G Ir

800

100

70

Modulus of rigidity G (GPa) 220

E Ir

600

75

Table 3.1-251 Elastic constants of Ir [1.217, p. 212] T = 300 K

400

b) Modulus of rigidity G (GPa)

90

Table 3.1-250 Modulus of elasticity in crystal direction [1.217, p. 212]

200

200

400

600

800

1000 1200 Temperature (°C)

Fig. 3.1-320 (a) Young’s modulus of Ir at different temperatures. (b) Poisson’s ratio for as cast Ir at different temperatures [1.289]

395

Part 3 1.10

Mechanical Properties. Iridium is extremely hard and

1.10 Noble Metals and Noble Metal Alloys

396

Part 3

Classes of Materials

Part 3 1.10

Table 3.1-252 Mechanical properties of Ir at different temperatures [1.217, p. 213] T (◦ C)

E (GPa)

Rm (MPa)

A (%)

Rp0.2 (MPa)

HV

20 500 800 1000

538 488 456 434

623 530 450 331

6.8 9 18 −

234 12.7 234 51 142 80.6 43.4

200 138 112 97

A = elongation of rupture, E = modul of elasticity, Rp = limit of proportionality, HV = Vickers hardness, Rm = tensile strength

Table 3.1-253 Change of hardness of Ir by degree cold

forming V (%) [1.217, p. 312]

Specific strength (MPa g-1cm3) 140

V (%)

HV

0 10 20 30 59

240 425 485 475 590

(Ir0.75 Rh0.25)75 Nb15 Ni10 (Ir0.5 Rh0.5)75 Nb15 Ni10 (Ir0.25 Rh0.75)75 Nb15 Ni10 Ir75 Nb15 Ni10 Rh75 Nb15 Ni10

120 100 80 60 40

0.2% flow stress (MPa)

20

2000

500

Ir-Zr

1000

1500 2000 Temperature (°C)

Fig. 3.1-324 Specific strength of Ir−Rh−Nb alloys [1.293, 1500

p. 78] Ir-Nb

1000

0.2 % flow stress (MPa) 2000

CMSX-10

Ir-Ta Ir-Hf

Ir-12Zr

Mar-M247 1500 500

Ir-17Nb

Ni-Al-Cr Ir-Ti

W alloy

Ir-V 500

Ir-15Nb-5Ni

Nb-Si-Mo-W

1000 1000

Fig. 3.1-323 High-temperature compression strength of se-

lected Ir-based alloys [1.292, p. 159]

CMSX-10

1500 2000 Temperature (°C) 500

Ir-13.5Nb-8Ni-2Al W alloy

500

1000

1500 2000 Temperature (°C)

Fig. 3.1-325 Comparison of compressive strength of Ir

alloys versus W and Nb/Mo alloys at various temperatures [1.293, p. 77]

1.10 Noble Metals and Noble Metal Alloys

Metals

p. 157] T (K)

15

40

140

273

700

1100

1500

ρi (T )

0.0013

0.10

1.96

4.65

13.90

23.20

34.02

Electrical Properties. The residual resistance ratio

Thermoelectric voltage (mV)

(RRR) amounts to 85 (Table 3.1-203). The specific electrical resistivity at different temperatures and the dependence of the atomic resistivity are given in Tables 3.1-254, and 3.1-255 [1.216]. The RRR is listed in Table 3.1-203. Iridium becomes superconducting below 0.11 K. Some ternary alloys show critical transition temperatures between 3 K and above 8 K (Table 3.1-256) [1.218]. Thermoelectrical Properties. Data for the absolute ther-

moelectric power and the thermoelectric voltage of Ir, and the thermoelectric voltage of Ir/Rh alloys are shown in Tables 3.1-206–3.1-208, 3.1-257 [1.216] and Fig. 3.1-326 [1.217].

45 WRe(97/3)WRe(75/25)

40 35 30 25

MoRe(95/5) MoRe(59/41)

20 Mo-MoRe(59/41)

15 10

IrRh(60/40)Ir

5

Magnetic Properties. Iridium is paramagnetic. Figures

3.1-271, 3.1-327, 3.1-328 [1.216] show the mass susceptibility of Ir and Pt/Ir alloys at different temperatures. Iridium exhibits magnetostriction according the equation ∆l/l = Sl H 2 , with Sl = +3.8 (Table 3.1-211).

0

0

500

1000

1500

2000 2500 Temperature (°C)

Fig. 3.1-326 Thermoelectric voltage of Ir−Rh alloys compared to Mo−Re and W−Re alloys [1.217, p. 474] χg (10–9 m3 / kg) 3 2.5 Ir

Table 3.1-255 Increase of atomic resistivity [1.217, p. 158]

2

Base element

ρ/C (µ
cm/at.%)

Ir

Pt 1.33, Re 2.7, Cr 2, Mo 3.65, W 3, Fe 0.6

1.5

Table 3.1-256 Superconducting Ir alloys [1.218, p. 636]

1

Ir Compound

Tc (K)

IrTe3 Sc5Ir4Si10 Y5Ir4Si10 Lu5Ir4Si10

1.18 8.46–8.38 3.0–2.3 3.76–3.72

0

300

600

900

1200

1500

1800 T (K)

Fig. 3.1-327 Mass susceptibility of Ir at different tempera-

tures [1.217, p. 164]

Table 3.1-257 Thermoelectric voltage of Ir at different temperatures [1.216, p. 95] T (◦ C)

−200

−100

−50

+100

+200

+400

+800

E Ir,Pt (mV)

−0.20

−0.35

−0.20

0.66

1.525

3.636

9.246

Part 3 1.10

Table 3.1-254 Specific electrical resisitivity [ρi (T ) = ρ0 + ρi (T )] of Ir at temperatures T (ρ0 = 0.10 µΩ cm) [1.217,

397

398

Part 3

Classes of Materials

Part 3 1.10

χg (10–9 m3 / kg) 16 Pt1-x Irx 14 12 10 8 6 4 2 0 0 50

a) Weight loss (10–2 mg cm–2) 0 1000° C

Pt

1100 °C

x = 0.0512 x = 0.1987

30

x = 0.3008 x = 0.5002

1200 °C

60 x = 0.6870 Ir

100

150

200

250

300 T (K)

90

1300 °C

Fig. 3.1-328 Mass susceptibility of Pt−Ir alloys at different

temperatures [1.217, p. 68]

120

Thermal Properties. Tables 3.1-212–3.1-214 give se-

lected data for the recrystallization temperature (varying by purity, degree of cold forming, and annealing time), thermal conductivity, and thermal expansion coefficient. Optical Properties. The optical reflectivity of Ir is

markedly lower than that of Rh increasing in the wavelength range from 0.4 to 0.8 µm (Figs. 3.1-191 and 3.1-274). Data of the spectral emissivity are given in Table 3.1-216.

0

6

12

18

30 Time (h)

24

b) Weight loss (mg cm ) –2

0 10 % 2 20 %

4

Diffusion. Table 3.1-217 gives only one value for self

diffusion of iridium but further information may be obtained from Landolt–Börnstein [1.238].

30 %

6

Chemical Properties. Iridium is not attacked by acids

or alkali even under oxidizing conditions (aqua re-

8 40 %

Weight change (mg cm–2)

(wt % Ir)

70

10

20

10

20

30

40 Time (h)

Fig. 3.1-329a,b Evaporation losses. (a) Pt loss in oxygen. (b) Pt−Ir clad loss in oxygen at 900 ◦ C [1.217, p. 184]

–30 Ir sheet IrCr5 IrNb4Ce IrTi20 IrAl9 IrAl12 RuAl21

–80 –130 –180

0

0

10

20

30

40

50 Time (h)

Fig. 3.1-330 Oxidation behavior of various Ir alloys at

1000 ◦ C in air [1.294, p. 100]

gia). It forms volatile oxides in air above 1000 ◦ C but it can be heated up to 2300 ◦ C without danger of catastrophic oxidation. Pt alloys with 1–30 wt% Ir are corrosion-resistant against H2 F2 . Figures 3.1-329 and 3.1-330 [1.216, 294] show data of the evaporation and oxidation behavior of Ir alloys. A detailed survey on the chemical properties is given in [1.216, 294].

Metals

1

50

2

Ruthenium (at. %) 4 5

3

980 40

L1 + L2

Ir / Ru 960

30 20

Rh only

10

L

962°C

L+?

940 920°C

920 5

10 15 20 Water concentration (% w/w)

Fig. 3.1-331 Carbonylation rates for Ir−Ru and Rh catalysts in methylacetat reactions [1.295, p. 100]

Metal-organic Ir compounds are effective homogeneous catalysts for organo-chemical reactions such as hydrogenation and carbonylation. The technical production of acetic acid (“Cativa” process). Figure 3.1-331 shows an example for different carbonylation rates of Rh- and Ir/Ru-based catalysts [1.295]. Complex organic Ir catalysts have high stereoselectivity in hydrating cyclic alcohols [1.216]. Ruthenium and Ruthenium Alloys Applications. Ruthenium is a component of alloys

and compounds of chemical process catalysts, and Ptbased catalysts for proton-exchange fuel cells (PEFC). Because of its corrosion resistance, it is used for corrosion-preventing anodes in shipping vessels and under-water structures, pipelines, in geothermal industries, and as coating of electrodes in chlorine and caustic soda production. Ruthenium oxide (RuO2 ) and complex Bi/Ba/Pt oxides are materials for electrical resistors. Ruthenium layers on computer hard discs are used for high density data storage improvement of data-storage densities. Ruthenium is an effective hardener of Pd and Pt. Commercial grades available are sponge, powder, grains, and pellets in purity ranging from 99–99.95% (ASTM B 717).

2.9 (Ag)

900 880

0 Ag

b) T (K)

(Ag) + ?

0.5

1

1.5

2

10

20

30

40

2.5

50

3

60

3.5 4 4.5 Ruthenium (wt %) 70

2600

80

Ru (wt %) 90

(2553 K)

Ag – Ru 2400 2200 2000 1800 1600 Two liquids 1400

1235 K

(?)

1243 K

1200

1193 K

1000 Ag

10

20

30

40

50

60

70

80

90 Ru Ru (at. %)

Fig. 3.1-332a,b Phase diagram of Ag−Ru (a) and phase diagram of Ag−Ru in the high-temperature range (b) [1.217,

245] Temperature (°C) 0 10 20 30 2400 2000 1800

ical reduction of chloro compounds to powder, followed by compacting to pellets. Coatings are produced by galvanic processing, evaporation or sputtering.

1600

Phases and Phase Equilibria. Selected phase diagrams

1000

are shown in Figs. 3.1-332 – 3.1-334, thermodynamic data are listed in Table 3.1-258, and molar heat capacities can be found in Table 3.1-190. Ruthenium alloyed

800

1400

50

60

Ruthenium (at. %) 70 80 90 100 2334°C

L

2200

Production. Production of ruthenium starts with chem-

40

1555°C 1583°C

~ 82 (Ru)

~16.5 (Pd)

1200

600

0 Pd

10

20

30

40

50

60 70 80 90 100 Ruthenium (wt %) Ru

Fig. 3.1-333 Phase diagram of Pd/Ru [1.217]

399

Part 3 1.10

a) Temperature (°C)

Carbonylation rate (mol dm–3 h–1)

1.10 Noble Metals and Noble Metal Alloys

400

Part 3

Classes of Materials

Part 3 1.10

Table 3.1-258 Thermodynamic data of Ru [1.217, p. 110] T (K)

c p (J/K mol)

S (J/K mol)

H (J/mol)

G (J/mol)

p (at)

298.15 400 800 1400

23.705 24.345 26.516 30.97

28.535 35.595 53.121 69.01

0 2.449 12.611 29.77

− 8.508 − 11.79 − 29.885 − 66.844

1.50 × 10−77 4.83 × 10−35 7.73 × 10−17

T = Temperature, c p = specific heat capacity, S = Entropy, H = Enthalpy, G = free Enthalpy, p = partial pressure of the pure elements

T(K) 1

10

20

30

40

Table 3.1-261 Hardness (HV 5) of Pd/Ru and Pt/Ru alloys

Ru (wt %) 50 60 70 90

at 300 K [1.217, p. 230] Alloying metal

2800 2600

2607 K

Pt– Ru L

2400

2042 K

Pd Pt

2200

HV 5 alloy conc. (wt%) 0 20 350 350

412 330

40

60

80

425 446

284 293

243 253

2000 (Ru)

(Pt)

pounds. The superlattice structures can be found in Table 3.1-197.

1800 1600

Mechanical Properties. Ruthenium has a Young’s mod-

1400 1200 Pt

10

20

30

40

50

60

70

80

90 Ru Ru (at. %)

Fig. 3.1-334 Phase diagram of Pt/Ru [1.245]

to Fe lowers the γ –α transition temperature considerably (Fig. 3.1-343). Table 3.1-259 gives the structure and lattice parameters of intermediate Co and Fe com-

ulus of 485 GPa, the Poisson’s ratio amounts to 0.29, and the modulus of rigidity is 172 GPa. Characterisitic properties of Ru are given in Tables 3.1-260 and 3.1-261. The mechanical properties are marked anisotropic. The hardness of different single crystal faces varies between 100 HV and 250 HV [1.216]. High compression-strength alloys are formed by two-phase Ru−Al intermetallic structures. Figure 3.1-335 gives

Table 3.1-259 Structure and lattice parameter of intermediate compounds [1.217, p. 117ff.] Phase

Pearson symbol

a (nm)

Co−Ru Co−Ru Fe−Ru Fe−Ru Os−Ru

hP2 cF4 cI2 hP2 hP2

0.261 0.3592 0.2883 0.258 0.27193

b (nm)

c (nm)

Concentration x A(1 − x)B(x)

0.4181

0.5 0.2 0.06 0.2 0.5

0.414 0.4394

Table 3.1-260 Mechanical properties of Ru at different temperatures [1.217, p. 229], [1.216, p. 31] T(◦ C)

Rm (MPa)

A (%)

Rp0.2 (MPa)

HV

20 750 1000

500 300 220 (430)

3 15 14

380 230 190

250–500 a 160–280 b 100–200 a

a

at different crystal planes, at 600 ◦ C A = Elongation of rupture, Rp = Limit of proportionality, HV = Vickers hardness, Rm = Tensile strength b

Metals

1.10 Noble Metals and Noble Metal Alloys

3.1-336 present data of the magnetic mass susceptibility of Ru and of Ru/Cr alloy at different temperatures.

1400 Ru – RuAl (melt)

1200 1000 800 600 400

Ru – RuAl (RHIP) RuAl

Table 3.1-263 Increase of atomic resisitivity by alloying Ru

(∆ρ/C (µΩ cm/at.%)) [1.217, p. 158]

200 200

400

600

800

1000 1200 1400 Temperature (°C)

Fig. 3.1-335 High-temperature compression strength of eutectic Ru-70/Al-30 in relation to its constituent phases [1.288, p. 164]

an example of molten and hot isostatic-pressed eutectic Ru (Ru-70/Al-30) in relation to the constituent phases [1.296]. Electrical Properties. The residual resistance ratio

(RRR) amounts to 25 000 (Table 3.1-203). Characteristic electrical properties of Ru are given in Tables 3.1-203, 3.1-262, and 3.1-263. The specific electrical resistivity of RuO2 is 3.5 × 10−5 Ω cm (1 Ω cm for PdO for comparison). Together with its low temperature dependence of the coefficient of resistance, Ru is suited for the production of resistors in sintered form or as thick-film layers covering resistors ranging from ≈ 1.5to10 MΩ. Conductive components are either RuO2 , Pb2 Ru2 O6 , or Bi2 Ru2 O7 together with additions of doping oxides [1.218]. Ruthenium shows superconductivity below 0.47 K [1.218]. Ternary alloys have critical transition temperatures up to 12.7 K (Table 3.1-264). Thermoelectric Properties. Data of thermoelectric

properties of Ru are given in Tables 3.1-206 and 3.1-265.

Base element

ρ/C (µ
cm/at.%)

Ru Os

Fe 0.21, Re 2, Y 1.5 Y 10

Table 3.1-264 Critical transition temperature of supercon-

ducting Ru alloys [1.218, p. 636] Ru Composit

Tc (K)

TiRuP ZrRuP HrRuP TiRuAs ZrRuAs HfRuAs Y3Ru4Ge13 Lu3Ru4Ge13

1.33 12.34–10.56 12.70–11.08 >0.35 11.90–1.03 4.93–4.37 1.7–1.4 2.3–2.2

χg (10–9 m3 kg–1) 60 50 40 30 20 10 0

0 Cr

Ru – Cr

20

40

60

100 80 Ru (at. %) Ru

Fig. 3.1-336 Temperature dependence of the mass suscep-

tibility of Ru/Cr alloy [1.217, p. 166] Table 3.1-262 Specific electrical resistivity ρi (T ) (µΩ cm) of Ru at different temperatures (ρ0 = 0.016 µΩ cm) ρ(T ) = ρ0 + ρi (T ) [1.217, p. 156] T (K)

25

50

100

200

273

300

500

ρi (T )

0.005

0.105

1.25

4.38

6.69

7.43

13.2

Table 3.1-265 Thermal electromotive force of Ru at different temperatures [1.217, p. 159] T (◦ C)

+100

+200

+300

+500

+800

+1000

+1200

E Ru/Pt

0.684

1.600

2.673

5.119

9.519

13.003

16.864

Part 3 1.10

Magnetic Properties. Figures 3.1-271, 3.1-337, and

0.2% Proof stress (MPa)

401

402

Part 3

Classes of Materials

Part 3 1.10

Chemical Properties. Ruthenium is not attacked by

χg (10–9 m3 kg–1)

acids or alkali even under oxidizing conditions (aqua regia). By heating in air above 800 ◦ C Ru forms the oxides RuO and RuO2 ; above 1100 ◦ C Ru forms RuO3 which vaporizes. Detailed survey about the chemical properties is given in [1.218, 218]. Complex organic Ru compounds are catalysts for the enantioselective hydrogenation of unsaturated carboxylic acids, used in pharmaceutical, agrochemical, flavors and fine chemicals (Fig. 3.1-338) [1.291].

7 6.5 6 5.5 5 4.5

0

200

400

600

800 1000 Temperature (K)

Osmium and Osmium Alloys Applications. Osmium is used as a component in hard,

Fig. 3.1-337 Temperature dependence of the mass suscep-

tibility of Ru [1.217, p. 163] Thermal Properties. Characteristic data of thermal expansion and thermal conductivity are given in Tables 3.1-213 and 3.1-266. Figure 3.1-273 shows the vapor pressure data for Ru. Optical Properties. The optical reflectivity of Ru is near that of Rh (Fig. 3.1-333). Ruthenium alloyed to Pd enhances the optical reflectivity by 4–5% (Fig. 3.1-275).

wear- and corrosion-resistant alloys, as surface coatings of W-based filaments of electric bulbs, cathodes of electron tubes, and thermo-ionic sources. Osmium itself, Os alloys, and Os compounds are strong and selective oxidation catalysts. Commercial grades available are powder in 99.6% and 99.95% purity, OsO4 , and chemical compounds. Production. The production of Os starts from the

mineral osmiridium via soluble compounds and the reduction to metal powder followed by powdermetallurgical compacting.

Diffusion. Table 3.1-217 gives some values for self

diffusion of Ru.

Phases and Phase Equilibria. Selected phase diagrams

COOH [Ru(OAc)2 ((S) – BINAP)] MeO

COOH

MeO (S)-(+)-naproxen (92% yield; 97% ee)

Fig. 3.1-338 Synthesis of (S)-(+)-Naproxen catalysed by Ru-cplx

compound [1.291, p. 83]

are shown in Figs. 3.1-339–3.1-342 [1.216]. Continuous series of solid solution are formed with Re and Ru. Miscibility gaps exist with Ir, Pd and Pt. The solid solubility in the Os−W system are 48.5 at.% for W and ≈ 5 at.% for Os. Osmium alloyed to Fe lowers the γ –α transition temperature considerably (Fig. 3.1-343 [1.297]). Thermodynamic data are given in Table 3.1-267 [1.216] and molar heat capacities in Table 3.1-190. Table 3.1-268 gives structures and lattice parameters of intermediate compounds with Ir, Ru, Pt, and W [1.216].

Table 3.1-266 Thermal expansion coefficients of Ru and Os at different temperatures [1.217, p. 154] Temperature (◦ C)

(10−6 K−1 ) Rua

Rub

Rup

Osa

Osb

Osp

323 423 623 723 823

5.9 6.1 6.8 7.2 7.6

8.8 9.3 10.5 11.0 11.7

6.9 7.2 8.0 8.4 8.8

4.0 4.3 4.0 5.3 5.8

5.8 6.2 7.1 7.6 8.3

4.8 5.0 5.7 6.2 6.9

a b p

vertical to the crystal c axis parallel to the crystal c axis polycrystalline

Metals

30

40

50

60

Os (at. %) 80 90 100

70

Fig. 3.1-339 Phase diagram of Os−Ir [1.217, p. 87] T (K) 10

3033°C

L

3000

20

30

40

50

60

70

80

2660°C

2500

3695 K

3800

61.8

3400

L 3218 K

3305 K

3000

2000 (Ir)

W (wt %) 90

4200 Os– W

2447°C

≈ 64

≈ 54 2958 K

(Os) 2600

≈ 31.5 (W)

σ

(Os)

1500

78

2200 1000

0 Ir

10

20

30

40

Temperature (°C) 0 10 20 30 40 50 3500

50

60

3033°C

60

70

70

80 90 100 Os (wt %) Os

80

90

Rh (at. %) 100

~19

~31

12

(Os)

~12 1500 °C

1000

0 Os

10

20

~35 1500°C 30

40

50

1963 °C

(Rh)

60

70

80 90 100 Rh (wt %) Rh

Fig. 3.1-340 Phase diagram of Os−Rh [1.217, p. 90] Temperature (°C) 0 10 20 30 3500

40

50

60

70

10

µw

50

70 80

90 W W (at. %)

Fe –Ir

µw

400 200

6

0

4

–200

α γ α or γ

α γ α

α γ α γ α or γ

µw

α

γ α

α

γ α

0

Platinum (at. %) 80 90 100

10 20 Os (at. %)

Fe–Rh

12

Fe–Ru

µw

Os

10 20 Ir (at. %) Ir

20 10 Ru (at. %) Ru

800

α or γ

L

3000

60

α or γ

8

14

3033°C

40

Fe– Os

600

2000 1500

30

Fig. 3.1-342 Phase diagram of Os−W [1.245]

Magnetic moment 1000 in Weiß magnetons 800

2600 °C 2500

20

Temperature (°C)

L

3000

1800 1400 Os 10

α or γ

600

γ α

µw

2500

10

400

8

200

α 1955⫾15 °C

2000 (Os)

75 1769.0°C (Pt)

1500 1000

0 Os

10

20

30

40

50

60

70 80 90 100 Platinum (wt %) Pt

Fig. 3.1-341 Phase diagram of Os−Pt [1.217, p. 90]

6

0

10

20

30

40

403

Part 3 1.10

Temperature (°C) 0 10 20 3500

1.10 Noble Metals and Noble Metal Alloys

50 60 Rh (at. %)

Fig. 3.1-343 Temperature dependence of atomic moments, γ –α transition and magnetic transition of iron alloys [1.220, p. 259]

404

Part 3

Classes of Materials

Part 3 1.10

Table 3.1-267 Thermodynamic data of Os [1.217, p. 110] T (K)

c p (J/K mol)

S (J/K mol)

H (J/mol)

G (J/mol)

p (at)

298.15 400 800 1400

24.707 25.094 26.618 28.903

32.635 39.95 57.811 73.287

0 2.536 12.879 29.535

− 9.73 − 13.444 − 33.371 − 73.067

2.95 × 10−95 6.31 × 10−44 5.81 × 10−22

T = Temperature, cp = specific heat capacity, S = Entropy, H = Enthalpy, G = free Enthalpy, p = partial pressure of the pure elements

Table 3.1-268 Structure and lattice parameter of selected Os alloy phases [1.217, p. 118] Phase

Pearson symbol

a (nm)

c (nm)

Remarks

Os Os−Ir Os−Ir Os−Pt Os−Pt Os−Ru Os3 W7

hP2 hP2 cF4 hP2 cF4 hP2 tP30

0.27353 0.27361 0.38358 0.27361 0.39094 0.27193 0.9650

0.43191 0.43417

293 K

0.4394 0.4990

tle. The hardness is, as in the case of Ru, strongly anisotropic. Characterisitic properties for hardness of the element at different temperatures, as well as work hardening and hardness of Os−Pt alloys are given in Tables 3.1-269 and 3.1-270 [1.216, 217] and Fig. 3.1-262. Osmium exhibits a Young’s modulus of 570 GPa, a modulus of rigidity of 220 GPa, and the Poisson’s ratio is 0.25. Electrical Properties. The residual electrical resistivity ratio (273.2 K/4.2 K) is 400 [1.216] (Table 3.1-203). Table 3.1-269 Hardness of Os at different tempera-

tures [1.216] T (◦ C)

HV

20 200 600 1200

300–680 a 260–580 a 200–410 a 130–400 a

a

all values depending on crystal orientation

0.35 0.8 0.1 0.8 0.5 0.78

0.43247

Mechanical Properties. Osmium is very hard and brit-

Concentration x A(1 − x) B(x)

Table 3.1-271 Specific electrical resistivity ρi (T ) (µΩ cm) of Os at temperature T [ρ(T ) = ρ0 + ρi (T )]; (ρ0 = 0.09 µΩ cm a ) [1.216] T (K)

ρi (µ
cm)

25 100 273 900 1300

0.012 1.90 8.30 26.0 38.0

At T < 273 K; ρ0 = 0.8 µΩ cm at T > 273 K

Table 3.1-271 [1.216] gives the specific electric resistivity of Os at different temperatures. The increase of atomic resistivity is shown in Table 3.1-263. Osmium coatings on W-based dispenser cathodes lower its work function (source Ba−Ca aluminate). It enhances the secondary electron emission (Fig. 3.1-344) and enables the operation at higher current densities in high power klystron and magnetron valves. Osmium shows superconductivity below 0.71 K and Table 3.1-272 gives some examples of superconducting Os alloys [1.218].

Table 3.1-270 Hardness of Os−Pt alloys [1.217] Pt content (wt%)

HV

0 20 40

560 578 555

Thermoelectric Properties. Figure 3.1-269 shows a comparison of the thermoelectric power of the different noble metals of the platinum group as a function of temperature.

Metals

1.10 Noble Metals and Noble Metal Alloys

Os

Os 10 L 1

0.1 700

800

1000

900

1100

1200 T(°C)

Fig. 3.1-344 Current density as a function of cathodic temperature for a normal cathode (dashed curve) and a cathode with a 5 µm thick Os coating [1.298]

Magnetic Properties. Figures 3.1-271 and 3.1-345–

3.1-347 [1.216] give a survey and present selected data of the magnetic mass susceptibility for the element and for Os−Cr alloys. This alloy system exhibits antiferromagnetism in compositions from 0.3 to 2.2 at.% Os in the temperature range on the left-hand side of the bold vertical bars in Fig. 3.1-347. In Fe−Os alloys the temperature of the magnetic transitionand the atomic

Compound

Tc (K)

Ce3Os4Ge13 Pr3Os4Ge13 Nd3Os4Ge13 Eu3Os4Ge13 Tb3Os4Ge13 Dy3Os4Ge13 Er3Os4Ge13 ZrOsAs HfOsAs Y3Os4Ge13 Lu3Os4Ge13 Y5Os4Ge10 TiOsP ZrOsP HfOsP

6.1 16 1.9 10.1 14.1 2.1 1.9 8 3.2 3.9–3.7 3.6–3.1 8.68–8.41 99.94

3.2–4.5

5.5

12–13

30

3.2

Refined pure (r)

3.8

12.1

53

3.2

Chemical (c)

5.2

Chemical (r)

5.5

11.3

Undesilverized (e) Undesilverized (r)

4.7

8.6

17.9

20.0

47

17.2

50 17.9

1.2

45

19.3 16.5

Creep strength (0.2%/yr) (MPa)

51

6.9 5.0

15.8

(r) - rolled; (c) - cast; (e) - extruded

ing, flashings and weather stripping, water-proofing, and radiation shielding. The mechanical properties of pure grades of lead are listed in Table 3.1-274 [1.299–301]. The near ambient temperatures at which lead and its alloys are used correspond to high homologous temperatures (T/TM ∼ 0.5 or higher) for lead and therefore significant diffusion can occur. Consequently, the mechanical properties are affected by dynamic and static recovery, recrystallization effects, and creep deformation. Therefore, caution is advised in the use of short-term mechanical properties. The recrystallization temperatures of different lead grades are shown as a function cold work and grain size in Fig. 3.1-349 [1.303]. The lowest reported value of recrystallization temperature for 99.9999 wt% purity lead is ∼ −59 ◦ C; for lead of not very high purity it is ∼ −33 ◦ C. The fatigue behavior of 99.99 wt% pure lead in a Haigh push–pull test at a test cycle fre-

quency of 33.67 Hz is presented in the form of S–N (stress to failure versus number of cycles) curves in Fig. 3.1-350 [1.303]. Coefficients of internal friction of relevance to acoustic damping are given in Table 3.1-275 [1.299, 302]. As lead is used in sound attentuation applications, acoustic transmission data of selected single-skin and double-skin partitions with and without lead are given in Table 3.1-276 [1.299]. The sound reduction versus frequency is given in [1.299, 304]. Corrosion rates of lead in H2 SO4 and HF acids are presented in Figs. 3.1-351 and 3.1-352 [1.301]. Corrosion behavior of chemical lead in some common environments is presented in Table 3.1-277 [1.301]. Corrosion rates of the different lead grades normally fall in the same category. As lead is extensively used in radiation shielding, the gamma-ray mass-absorption data for lead are presented in Fig. 3.1-353 [1.299, 305].

Table 3.1-275 Experimental values of coefficient of internal friction Q −1 . Values in single crystal and polycrystalline

lead [1.299, 302] (RT = room temperature)

Material

Frequency (kHz)

Q −1

Pure polycrystalline lead

0.016–2 17–28 4–64 30 30 30 4

0.35 × 10−2 –4 × 10−2 0.2 × 10−2 –0.8 × 10−2 0.2 × 10−2 –0.7 × 10−2 0.11 × 10−2 (max. deformation of 10−7 , RT) 0.22 × 10−3 (max. deformation of 10−7 , RT) 0.9 × 10−3 (max. deformation of 10−7 , RT) 2 × 10−3 (max. deformation of 10−7 )

Single-crystal line lead Single-crystal Pb–0.033 wt% Sn Single-crystal Pb–0.035 wt% Bi Single-crystal Pb–0.0092 wt% Cd Single-crystal Pb–0.0022 wt% In

2

0

0

0 200 Annealing 100 temperature

50

0

0

0 20 40 60 80 100 Reduction through rolling at 18 °C (%)

Grain diameter (mm) 10

b)

8

6 T(°C) 300

4

2 200 Annealing 100 temperature

20 40 60 80 100 Reduction through rolling at 18 °C (%) 50 18

c)

Grain diameter (mm) 10

8

6 T(°C) 300

4

2

200 Annealing 100 temperature

50

20 40 60 80 100 Reduction through rolling at 18 °C (%) 5.65 17.16 7.94 19.04 52.20

0.5 1.52 2.17 117.76 121.88

40.2 51.8

22.7 31.8 27.4

Average SRI (dB)

SRI: sound reduction index; RW: weighted sound reduction; STC: sound transmission classification

Single skin – code 1 lead sheet Single skin – code 3 lead sheet Single skin – 0.5 mm lead equivalent lead impregnated PVC sheet Double skin – 12.4 mm Gyproc plasterboard – no infill Double skin – code 3 lead sheet bonded to 12.4 mm Gyproc plasterboard – no infill

Surface weight (kg/m2 )

42 52

25 35 30

RW (dB)

41 52

25 35 30

STC (dB)

4

Thickness (mm)

10 Grain diameter (mm)

8

T(°C) 300 1.11 Lead and Lead Alloys

Fig. 3.1-349a–c Recrystallization diagrams: (a) Electrolytic Pb. (b) Parkes Pb. (c) Pattinson Pb [1.303]

Part 3 1.11

6

Description of test partition

a)

Table 3.1-276 Acoustic transmission data of selected single skin and double skin partitions with and without lead [1.299,304]

Metals 409

410

Part 3

Classes of Materials

Part 3 1.11

σo , σu (× 981 Pa) 80 In vacuum

70

Test with rest intervals in air

60 50

In air

40

Blank in air-filled vacuum chamber

30 25 104

2

6 8 105

4

2

6 8 106

4

2

4

6

8 107

2

4

6 8 108 1.5 Cycles

Fig. 3.1-350 S–N (stress vs. number of cycles) curves for Pb in air and vacuum [1.303]

600

T (° F)

T (°F) > 5.1 mm /yr

500 400 300 200 175 125 75 50

urve 1.27 – 5.1 mm / yr int c 0.51–1.27 mm / yr

po iling

Bo

225 5.1

1.27 0.51 0.127

0.127– 0.51 mm / yr

Corrosion rates less than 0.51 mm / yr

150

Less than 0.127 mm / yr below 50% concentration 70

200 175

0 –0.127 mm / yr

60

Boiling point

250

80

90 100 Sulfuric acid (wt %)

Fig. 3.1-351 Corrosion rates of lead in H2 SO4 [1.301]

Corrosion rates more than 0.51 mm / yr

125 100 75

10

20

30

40

50 60 70 80 Concentration HF (%)

Fig. 3.1-352 Corrosion rates of lead in HF [1.301]

Metals

1.11 Lead and Lead Alloys

Chemical

Temperature (◦ C)

Concentration (wt%)

Corrosion class

Acetic acid

24

Glacial

B

Acetone

24–100

Acetylene, dry

24

Ammonia

24–100

Ammonium azide

24

Ammonium carbonate

24–100

Ammonium chloride

24

0–10

B

Ammonium hydroxide

27

3.5–40

A

Ammonium nitrate

20–52

Ammonium phosphate

66

−

A

Ammonium sulfate

24

−

B

Arsenic acid

24

Benzene

24

Boric acid

24–149

Bromine

24

−

B

Butane

24

−

A

Carbon tetrachloride (dry)

BP

100

A

Chlorine

38

−

B

Citric acid

24–79

DDT

24

−

Fluorine

24–100

−

Hydrochloric acid

24

Hydrogen chloride (anh HCl)

24

100

A

Mercury

24

100

D

Methanol

30

−

B

Methyl ethyl ketone

24–100

Phosphoric acid

24–93

Sodium carbonate

24

Sodium chloride

25

0.5–24

A

Sodium hydroxide

26

0–30

B

Sodium nitrate

24

Sodium sulfate

24

Sulfur dioxide

24–204

Natural outdoor atmospheres

24

−A

Industrial, natural and domestic waters

24

−A

Soils

24

−A

10–90 −

A A

10–30 −

B B

10

10–30

10 −

B

D

B B

10–100

10–30

B

B B A

0–10

10–100 −

C

B B

10

10 2–20 90

Data mostly correspond to chemical lead. The four corrosion performance categories: A < 0.051 mm/yr: Negligible corrosion – lead recommended for use; B < 0.51 mm/yr: Practically resistant – lead recommended for use; C = 0.51–1.27 mm/yr: Lead may be used where this effect on service life can be tolerated; D > 1.27 mm/yr: Corrosion rate too high to merit any consideration of lead

B

D A B

Part 3 1.11

Table 3.1-277 Classifying corrosion behavior of Pb in selected environments [1.301]

411

412

Part 3

Classes of Materials

Part 3 1.11

Attenuation coefficient 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Total

0.1 0.09 0.08 0.07 0.06 0.05 0.04 Photoelectric

0.03

Compton

Pair production

0.02

0.01 0.2

0.4

0.6

0.8

1

2

4

6 8 10 Gamma energy (MeV)

Fig. 3.1-353 Gamma-ray mass-absorption coefficients for lead [1.299, 305]

3.1.11.2 Pb–Sb Alloys Pb–Sb Binary Alloys Lead–antimony alloys are widely used for pipe, cable sheathing, collapsible tubes, storage battery grids, anodes, sulfuric acid fittings, and X-ray and gamma ray shielding (in the absence of neutron irradiation). The addition of 1 to 13 wt% Sb to Pb increases tensile strength, fatigue strength, and hardness compared to pure lead (99.99). Lead and Sb form a eutectic system as shown in Fig. 3.1-354 [1.303]. The maximum solubility of Sb in Pb is 3.45 wt% at the eutectic temperature and decreases to 0.3 wt% at 50 ◦ C. Thus considerable age-hardening

can be obtained in these alloys. Small additions of As (0.05–0.1 wt%) dramatically increase the rate of aging and final strength. The microstructure at higher Sb contents consists of proeutectic lead-rich phase surrounded by a network of eutectic phase that contributes to enhanced as-cast and high temperature strength. Shrinkage on solidification varies from 3.85% for Pb to 2.06% for a Pb–16 wt% Sb alloy. These alloys have high corrosion resistance in most environments. They form a protective and impermeable film faster than pure lead and, in some cases, even faster than chemical lead. Table 3.1-278 lists the physical properties of selected Pb−Sb alloys [1.300]. Table 3.1-279 lists the mechanical properties of cast

Table 3.1-278 Physical properties of Pb−Sb alloys [1.300] Alloy composition (wt%)

Solidification range (◦ C)

Coefficient of thermal expansion (10−6 K−1 )

Specific heat (J kg−1 K−1 )

Thermal conductivity (W m−1 K−1 )

Pb–1 Sb

322–317

28.8

131

33

Pb–3 Sb

310–269

28.1

Pb–6 Sb

285–252

27.2

135 (solid)

29

253

10.88

− 3.11

Pb–9 Sb

265–252

26.4

137 (solid)

27

271

10.60

− 2.76

a

Negative values show contraction

Resistivity

Density

(n
m)

(g cm−3 )

Volume change on freezinga (%)

11.27

− 3.75

11.19

Metals

10

20

30

40

°C 300

50

60

70

80

90

Antimony (at. %) 100

Liquid Liquid +α

600

α

630 ° C

3.45 Liquid

200 α+β

500 100 400

0

1

2

3

327 °C

4 5 (% Sb)

? Liquid + β

β

Liquid +α

300 α

252 °C 3.45

95.5 ?

11.1

200 α+β 100 0.3 (50°C) 0 0 10 Pb

20

30

40

50

60

70

80

90

100 Sb Antimony (wt %)

Yield strength Rp0.125 (MPa)

Fatigue strength for 2 × 107 cycles (MPa)

Creep strength

Young’s modulus (GPa)

19.3 − 55.2

7.6 7.6 −

190 h at 20.7 MPa

− − − −

Fig. 3.1-354 Pb−Sb phase diagram [1.303] Table 3.1-279 Mechanical properties of Pb−Sb alloys [1.299–301, 306] Sb content (wt%)

Tensile strength (MPa)

Elongation at fracture (%)

1 1 3 3 6 6 6

37.9 20 65.5 32.43 73.8 47 29.6

20 50 10 15 8 24 42

(a) (c) (a) (c) (a) (c) (r)

Hardness HB 7.0

630 h at 27.6 MPa

9.1 71.0 13 8.7

15.2

1000 h at 27.6 MPa 17.2 10.3

−

24.15 −

(c) cast; (a) cast and stored 30 days at room temperature; (r) rolled

alloys [1.299–301, 306]. Data for one of the rolled alloys are also given to indicate that they exhibit poorer properties. Pb–Sb-Based Lead Acid Battery Grid Alloys Lead–acid batteries are the most widely used secondary battery type in current automotive and industrial applications due to the relatively low cost and high availability of the raw materials, room temperature operation, ease of manufacture, long life cycle, versatility, and the ex-

cellent reversibility of the electrochemical system. Lead alloys are used as electrode grids, connectors, and grid posts. The two classes of alloys that are in extensive use are (i) Pb−Sb based ternary and multi-component alloys with As, Sn, Ag, Se, Cu, S, and Cd and (ii) Pb−Ca based ternary alloys and multi-component alloys with Sn, Ag, and Al. In the Pb−Sb based alloys, Sb addition to Pb enhances castability, tensile strength, creep strength, corrosion resistance under battery operating conditions, and resistance to structural changes during deep charge–

413

Part 3 1.11

T (°C) 0 700

1.11 Lead and Lead Alloys

414

Part 3

Classes of Materials

Part 3 1.11

discharge cycling. However, Sb migration from Pb−Sb based positive grid alloys to negative electrode results in the reduction of hydrogen over-voltage and consequent decrease in cell voltage. This led to increased degassing and water loss. To minimize this poisoning of negative plates, lower Sb contents (1–3 wt% Sb) are now used in battery grids. The posts and straps use about 3 wt% Sb. Low Sb content promotes the formation of solidification shrinkage porosity and cracking but the cracking tendency is overcome by the use of grain-refining additions of S, Cu, and Se. Arsenic additions to Pb−Sb alloys increase the rate of age-hardening and reduce the time of grid storage required after casting. Arsenic addition also increases the creep resistance which is very beneficial in deep cycling conditions. The addition of tin is used to act synergistically with As and Sb to improve fluidity and castability. It also increases cycle life of deep cycling batteries containing thin plates. Silver additions increases both the corrosion and creep resistance in Pb−Sb alloy grids. Cast Pb−Sb based alloys are typically used in grid alloys as the Pb−Sb based wrought alloys have lower yield strength, tensile strength, and creep strength. The corrosion behavior of wrought alloys is inferior due to the nature of distribution of the PbSb eutectic phase and lower creep resistance. Corrosion of cast Pb−Sb occurs by the attack of Pb−Sb eutectic. It solubilizes some Sb and stresses of corrosion product are accommodated. In rolled alloys the eutectic phase is isolated, which leads to stresses in the grid. The current choice of alloy composition is Pb−1.6Sb−0.2As−0.2Sn−0.2Se. Table 3.1-280 Table 3.1-280 Alloying components of common lead–

antimony battery grid alloys [1.300, 307] Alloy concentration (wt%) Sb Sn As

Cu

Se

2.75 2.75 2.9 2.9 1.6

0.075 0.075 0.04 0.05 −

− − − − 0.2

0.2 0.3 0.3 0.3 0.2

0.18 0.3 0.15 0.15 0.2

lists the compositions of common lead–antimony battery grid alloys [1.300, 307]. Lead–antimony alloys containing 0.2 to 1 wt% Sb are used to form barrier sheaths in high voltage cables. Properties of Pb−0.85Sb cable sheathing alloy are presented in the section on cable sheathing alloys. Lead alloys with 6–8 wt% Sb are used to fabricate a wide variety of equipment such as tank linings, pipe and one type of anode used in chromium plating. Alloys with 13 wt% Sb are used to make castings when hardness is of key importance. About 6% of the Pb produced in the world was used in the production of sports and military ammunition due to its high density and low cost. Lead containing up to 8 wt% Sb and 2 wt% As is used. Pb–Sb–Sn Alloys These alloys have low melting points, high hardness, and excellent high temperature strength and fluidity. These characteristics together with its applicability for the replication of detail make them suitable as printing types. Table 3.1-281 lists the characteristics of selected type-metal alloys [1.300]. The Pb-rich ternary Pb−Sb−Sn white metal alloys are also used in journal bearings due to the excellent anti-friction (and anti-seizure) characteristics and hardness. These Pb-rich white metal alloys, also referred to as Babbit alloys, contain 9–15 wt% Sb, 1–20 wt% Sn, and small amounts of Cu and As. Table 3.1-282 lists the physical properties of different bearing alloys [1.299, 300]. The mechanical property data for some of these alloys are presented in Table 3.1-283 [1.299, 308]. Most of the alloys lie in the primary crystallization field of Sb or SbSn of the ternary system. They contain primary crystals of Sb (or SbSn) in a binary (or ternary) eutectic matrix apart from the high-melting Cu-rich phases. Copper contents above 1.5 wt% also increase the hardness. Arsenic addition leads to a fine and uniform structure, improves fatigue strength, and minimizes softening. Arsenic is present in solid solution in Pb, Sb, and Sb-containing phases such as SbSn. The lead–alkali alloys, e.g., Bahnmetall, or the Pb−Sn−alkali alloys, also have a limited significance as bearing metals.

Table 3.1-281 Typical compositions and properties of selected type metals [1.299, 300] Alloy

Composition (wt%) Pb Sn Sb

Hardness HB

Liquidus temperature (◦ C)

Solidus temperature (◦ C)

Electrotype – General Linotype – Special Stereotype – Flat Monotype – Ordinary

94 84 80 78

14 22 23 24

299 246 256 262

245 239 239 239

3 5 6 7

3 11 14 15

Metals

1.11 Lead and Lead Alloys

Alloy composition (wt%)

Freezing range

Density

Sb

Sn

(◦ C)

9.5–10.5 14–16 14–16 14.5–17.5

5.5–6.5 4.5–5.5 9.3–9.7 0.8–1.2

256–240 272–240 268–240 353–247

a

(g cm−3 )

Volume change on freezinga (%)

Coefficient of thermal expansion (10−6 K−1 )

10.50 9.96 9.70 10.10

−2 −2 −2.3 −2.5

24 19.6

Specific heat (J kg−1 K−1 ) 150 150 160

Latent heat of fusion (kJ kg−1 )

Electrical resistivity

Thermal conductivity

(n
m)

(W m−1 K−1 )

0.9 0.1

287 282 286

24

Negative values show contraction

Table 3.1-283 Composition and mechanical properties of ASTM B23 Pb-based white metal bearing alloys [1.299, 308] Alloy Nominal alloy content (wt%) no.

7 8 15

Yield stress (MPa)

Sb

Sn

Cu

As

20 ◦ C

100 ◦ C

15 15 16

10.0 5.0 1.0

8)

–

–

–

–

–

–

–

–

57

–

–

780 – 1050

124

–

–

480

–

–

–

–

Forms white or grayish ceramics. It is readily absorbs CO2 and water from air to form calcium carbonate and slaked lime. It reacts readily with water to give Ca(OH)2 . Volumetric expansion coefficient 0.225 × 10−9 K−1 . It exhibits outstanding corrosion resistance in the following liquid metals: Li and Na. Pale yellow cubic crystals. Abrasive for polishing glass; used in interference filters and antireflection coatings. Insoluble in water, soluble in H2 SO4 and HNO3 , but insoluble in dilute acids.

IUPAC name (synonyms and common trade names)

Aluminium sesquioxide (alumina, corundum, sapphire)

Beryllium monoxide (beryllia)

Calcium monoxide (calcia, lime)

Cerium dioxide (ceria, Cerianite) Chromium oxide (eskolaite)

Dysprosium oxide (dysprosia) Europium oxide (europia) Hafnium dioxide (hafnia)

Gadolinium oxide (gadolinia) Insoluble in water, soluble in dilute strong mineral acids.

Lanthanum dioxide (lanthana)

Part 3 2.4

365 – 393

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α,MPa) HV (Mohs hardness HM)

440

Part 3

Classes of Materials

Table 3.2-9 Physical properties of oxides and oxide-based high-temperature refractories [2.4], cont. IUPAC name (synonyms and common trade names)

Part 3 2.4

Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000) MgO [1309-48-4] 40.304

Crystal system, Density lattice parameters, (, kg m−3 ) Strukturbericht symbol, Pearson symbol, space group, structure type, Z Cubic 3581 a = 420 pm B1, cF8, Fm3m, rock salt type (Z = 4)

Niobium pentoxide (columbite, niobia) Samarium oxide (samaria) Silicon dioxide (silica, α-quartz)

Nb2 O5 [1313-96-8] 265.810

Numerous polytypes

Sm2 O3 [12060-58-1] 348.72 α-SiO2 [7631-86-9] [14808-60-7] 60.085

Cubic 7620 D53 , c180, Ia3, Mn2 O3 type (Z =16) Trigonal 2202 – 2650 (rhombohedral) a = 491.27 pm c = 540.46 pm C8, h P9, R3c, α-quartz type (Z = 3)

Tantalum pentoxide (tantalite, tantala)

Ta2 O5 [1314-61-0] 441.893

Trigonal (rhombohedral) columbite type

Thorium dioxide (thoria, thorianite) Titanium dioxide (anatase)

ThO2 [1314-20-1] 264.037

Titanium dioxide (brookite)

TiO2 [13463-67-7] 79.866

Cubic a = 559 pm Cl, cF12, Fm3m, fluorite type (Z = 4) Tetragonal a = 378.5 pm c = 951.4 pm C5, tI12, I41 amd, anatase type (Z = 4) Orthorhombic a = 916.6 pm b = 543.6 pm c = 513.5 pm C21, oP24, Pbca, brookite type (Z = 8)

Magnesium monoxide (magnesia, periclase)

TiO2 [13463-67-7] [1317-70-0] 79.866

Electrical Melting resistivity point (◦ C) (ρ, µ
cm)

Thermal Specific heat Coefficient conductivity capacity of linear −1 −1 −1 −1 (κ, W m K ) (c p , J kg K ) thermal expansion (α, 10−6 K−1 )

1.3 × 1015

2852

50 – 75

962.3

11.52

5.5 × 1012

1520

–

502.41

–

–

2350

2.07

331

10.3

1020

1710

1.38

787

0.55

1012

1882

–

301.5

–

9860

4 × 1019

3390

14.19

272.14

9.54

3900

–

700 ◦ C (rutile)

–

–

–

4140

–

1750

–

–

–

4470

8200

Ceramics

2.4 Oxide Ceramics

441

Table 3.2-9 Physical properties of oxides and oxide-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural strength (τ, MPa)

Compressive Vickers strength hardness (α, MPa) HV (Mohs hardness HM)

441

1300 – 1379

750 Forms ceramics with a high reflection coefficient in the visible and (HM 5.5−6) near-UV region. Used in linings for steelmaking furnaces and in crucibles for fluoride melts. Very slowly soluble in pure water; but soluble in dilute strong mineral acids. It exhibits outstanding corrosion resistance in the following liquid metals: Mg, Li, and Na. It is readily attacked by molten metals such as Be, Si, Ti, Zr, Nb, and Ta. MgO reacts with water, CO2 , and dilute acids. Maximum service temperature 2400 ◦ C. Transmittance of 80 % and refractive index of 1.75 in the IR region from 7 to 300 µm. 1500 Dielectric used in film supercapacitors. Insoluble in water; soluble in HF and in hot concentrated H2 SO4 .

–

–

–

183

–

–

72.95

310

680 – 1380

–

–

–

144.8

–

1475

–

–

–

(HM 5.5–6)

–

–

–

(HM 5.5–6)

438

550 – 1000 Colorless amorphous (fused silica) or crystalline (quartz) material (HM 7) having a low thermal expansion coefficient and excellent optical transmittance in the far UV. Silica is insoluble in strong mineral acids and alkalis except HF, concentrated H3 PO4 , NH4 HF2 and concentrated alkali metal hydroxides. Owing to its good corrosion resistance to liquid metals such as Si, Ge, Sn, Pb, Ga, In, TI, Rb, Bi, and Cd, it is used in crucibles for melting these metals. Silica is readily attacked under an inert atmosphere by molten metals such as Li, Na, K, Mg, and Al. Quartz crystals are piezoelectric and pyroelectric. Maximum service temperature 1090 ◦ C. – Dielectric used in film supercapacitors. Tantalum oxide is a high-refractive index, low-absorption material usable for making optical coatings from the near-UV (350 nm) to the IR (8 µm). Insoluble in most chemicals except HF, HF−HNO3 mixtures, oleum, fused alkali metal hydroxides (e.g. NaOH and KOH) and molten pyrosulfates. 945 Corrosion-resistant container material for the following molten (HM 6.5) metals: Na, Hf, Ir, Ni, Mo, Mn, Th, U. Corroded by the following liquid metals: Be, Si, Ti, Zr, Nb, Bi. Radioactive.

IUPAC name (synonyms and common trade names)

Magnesium monoxide (magnesia, periclase)

Niobium pentoxide (columbite, niobia)

Samarium oxide (samaria) Silicon dioxide (silica, α-quartz)

Tantalum pentoxide (tantalite, tantala)

Thorium dioxide (thoria, thorianite) Titanium dioxide (anatase)

Titanium dioxide (brookite)

Part 3 2.4

303.4

Other physicochemical properties, corrosion resistance, a and uses

442

Part 3

Classes of Materials

Table 3.2-9 Physical properties of oxides and oxide-based high-temperature refractories [2.4], cont.

Part 3 2.4

IUPAC name (synonyms and common trade names)

Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Density Electrical Melting Crystal system, lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht, (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z

Titanium dioxide (rutile, titania)

TiO2 [13463-67-7] [1317-80-2] 79.866

Tetragonal a = 459.37 pm c = 296.18 pm C4, tP6, P4/mnm, rutile type (Z = 2)

4240

Uranium dioxide (uraninite)

UO2 [1344-57-6] 270.028

Cubic a = 546.82 pm Cl, cF12, Fm3m, fluorite type (Z = 4)

10 960

Yttrium oxide (yttria)

Y2 O3 [1314-36-9] 225.81

Trigonal (hexagonal) D52 , h P5, P3m1, lanthana type (Z =1)

Zirconium ZrO2 dioxide [1314-23-4] (baddeleyite) [12036-23-6] 123.223

Monoclinic a = 514.54 pm b = 520.75 pm c = 531.07 pm α = 99.23◦ C43, m P12, P21 c, baddeleyite type (Z = 4)

Zirconium dioxide PSZ (stabilized with MgO) (zirconia > 2300 ◦ C)

ZrO2 [1314-23-4] [64417-98-7] 123.223

Zirconium dioxide TTZ (stabilized with Y2 O3 ) (zirconia > 2300 ◦ C)

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α, 10−6 K−1 )

1019

1855

10.4 (|| c) 7.4 (⊥ c)

711

7.14

3.8 × 1010

2880

10.04

234.31

11.2

5030

–

2439

–

439.62

8.10

5850

–

2710

–

711

7.56

Cubic 5800 – 6045 Cl, cF12, Fm3m, fluorite type (Z = 4)

–

2710

1.8

400

10.1

ZrO2 [1314-23-4] [64417-98-7] 123.223

Cubic Cl, cF12, Fm3m, fluorite type (Z = 4)

–

2710

–

–

–

Zirconium dioxide TZP (zirconia > 1170 ◦ C)

ZrO2 [1314-23-4] 123.223

Tetragonal 5680 – 6050 C4, tP6, P42 /mnm, rutile type (Z = 2)

7.7 × 107

2710

–

–

10 – 11

Zirconium dioxide (stabilized with 10–15% Y2 O3 ) (zirconia > 2300 ◦ C)

ZrO2 [1314-23-4] [64417-98-7] 123.223

Cubic Cl, cF12, Fm3m, fluorite type (Z = 4)

–

2710

–

–

–

a

Corrosion data in molten salts from [2.9].

6045

6045

Ceramics

2.4 Oxide Ceramics

443

Table 3.2-9 Physical properties of oxides and oxide-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α,MPa) HV (Mohs hardness HM)

Other physicochemical properties, corrosion resistance,a and uses

248 – 282

340

800 – 940

145

–

–

114.5

–

393

241

–

2068

200

690

1850

1600

Zirconium dioxide PSZ (stabilized with MgO) (zirconia > 2300 ◦ C)

–

–

–

–

Zirconium dioxide TTZ (stabilized with Y2 O3 ) (zirconia > 2300 ◦ C)

200 – 210

> 800

> 2900

–

Zirconium dioxide TZP (zirconia > 1170 ◦ C)

–

–

–

–

Zirconium dioxide (stabilized 10–15% Y2 O3 ) (zirconia > 2300 ◦ C)

600 Used in nuclear power reactors in sintered nuclear-fuel elements (HM 6−7) containing either natural or enriched uranium.

700

Titanium dioxide (rutile, titania)

Uranium dioxide (uraninite)

Yttria is a medium-refractive-index, low-absorption material usable Yttrium for optical coating, in the near-UV (300 nm) to the IR (12 µm) oxide regions. Hence used to protect Al and Ag mirrors. Used for (yttria) crucibles containing molten lithium.

(HM 6.5) Zirconia is highly corrosion-resistant to molten metals such as Bi, Zirconium 1200 Hf, Ir, Pt, Fe, Ni, Mo, Pu, and V, while is strongly attacked by the dioxide following liquid metals: Be, Li, Na, K, Si, Ti, Zr, and Nb. Insoluble (baddeleyite) in water, but slowly soluble in HCl and HNO3 ; soluble in boiling concentrated H2 SO4 and alkali hydroxides and readily attacked by HF. Monoclinic (baddeleyite) below 1100 ◦ C, tetragonal between 1100 and 2300 ◦ C, cubic (fluorite type) above 2300 ◦ C. Maximum service temperature 2400 ◦ C.

Part 3 2.4

(HM 7−7.5) White, translucent, hard ceramic material. Readily soluble in HF and in concentrated H2 SO4 , and reacts rapidly with molten alkali hydroxides and fused alkali carbonates. Owing to its good corrosion resistance to liquid metals such as Ni and Mo, it is used in crucibles for melting these metals. Titania is readily attacked under an inert atmosphere by molten metals such as Be, Si, Ti, Zr, Nb, and Ta.

IUPAC name (synonyms and common trade names)

444

Part 3

Classes of Materials

3.2.4.1 Magnesium Oxide

Part 3 2.4

Table 3.2-10 lists the properties of the magnesium oxide rich raw material used in the production of oxide ceramics. MgO occurs rarely, as the mineral periclase, but is abundant as magnesite (MgCO3 ) and dolomite ((Mg,Ca)CO3 ). Magnesium oxide is mainly processed into a highpurity single-phase ceramic material, in either porous

or gas-tight form. Some properties of porous MgO are listed in Table 3.2-11. The properties of MgO ceramics that are of particular benefit in applications are their high electrical insulation capability and their high thermal conductivity. Typical examples of their application are for insulation in sheathed thermocouples and in resistive heating elements.

Table 3.2-10 Physical properties of MgO-rich raw materials used in the production of refractory ceramics [2.3]

Composition (wt%)

Sintered MgO clinker

Sintered doloma clinker

Fused MgO

MgO

96 – 99

39 – 40

97 – 98

Al2 O3

0.05 – 0.25

0.3 – 0.8

0.1 – 0.2

Fe2 O3

0.05 – 0.2

0.6 – 1.0

0.1 – 0.5

CaO

0.6 – 2.4

57.5 – 58.5

0.9 – 2.5

SiO2

0.1 – 0.5

0.6 – 1.1

B2 O3

0.005 – 0.6

Bulk density (g/cm3 )

3.4 – 3.45

3.15 – 3.25

3.5

2–3

5.5 – 7

0.5 – 2

Grain porosity (vol.%)

0.3 – 0.9 0.004 – 0.01

Table 3.2-11 Properties of MgO according to DIN EN 60672 [2.6] Designation C 820 Mechanical properties

Symbol

Open porosity

Units

Porous

vol. %

30

Density, minimum



Mg/m3

Bending strength

σB

MPa

50

Young’s modulus

E

GPa

90

2.5

Electrical properties Permittivity at 48–62 Hz

εr

10

Thermal properties Average coefficient of thermal expansion at 30–600 ◦ C

α30−600

10−6 K−1

11 – 13

Specific heat capacity at 30–100 ◦ C

c p,30−600

J kg−1 K−1

850 – 1050

Thermal conductivity

λ30−100

W m−1 K−1

6 – 10

(Rated)

Good

Thermal fatigue resistance

Ceramics

2.4 Oxide Ceramics

445

3.2.4.2 Alumina Alumina is widely applied both as an electronic ceramic material and in cases where its nonelectronic properties, such as fracture toughness, wear and high-temperature resistance, are required. Some typical applications are in insulators in electrotechnical equipment; substrates for electronic components; wear-resistant machine parts; refractory materials in the chemical industry, where resistance against vapors, melts, and slags is important; insulating materials in sheathed thermocouples and heating elements; medical implants; and high-temperature parts such as burner nozzles.

Table 3.2-12 Typical properties of high-density alumina [2.3] Al2 O3 content (wt%) > 99.9 (g/cm3 )

Density Hardness (GPa), HV 500 g Fracture toughness K IC at room temperature (MPa m1/2 ) Young’s modulus (GPa) Bending strength (MPa) at room temperature Thermal expansion coefficient (10−6 /K) at 200–1200 ◦ C Thermal conductivity at room temperature (W/m K) Firing temperature range (◦ C) a b

> 99.7 a

> 99.7 b

99 – 99.7

3.97 – 3.99 19.3 2.8 – 4.5 366 – 410 550 – 600 6.5 – 8.9

3.6 – 3.85 16.3 – 300 – 380 160 – 300 5.4 – 8.4

3.65 – 3.85 15 – 16 – 300 – 380 245 – 412 5.4 – 8.4

3.89 – 3.96 15 – 16 5.6 – 6 330 – 400 550 6.4 – 8.2

38.9 1600 – 2000

28 – 30 1750 – 1900

30 1750 – 1900

30.4 1700 – 1750

“Recrystallized” without MgO. With MgO.

Table 3.2-13 Properties of Al2 O3 according to DIN EN 60672 [2.6] Designation C 780 C 786 Mechanical properties Open porosity Density, min. Bending strength Young’s modulus Vickers hardness Fracture toughness

Al2 O3

Al2 O3

Al2 O3

Al2 O3

vol. % Mg/m3 MPa

Alumina 80–86% 0.0 3.2 200

Alumina Alumina Alumina 86–95% 95–99% >99% 0.0 0.0 0.0 3.4 3.5 3.7 250 280 300

Alumina 3.2 > 200

Alumina 92–96% 0 3.4 – 3.8 230 – 400

Alumina 99% 0 3.5 – 3.9 280 – 400

Alumina >99% 0 3.75 – 3.98 300 – 580

E

GPa

200

220

280

300

> 200

220 – 340

220 – 350

300 – 380

HV

100

−

−

−

−

12 – 15

12 – 15

12 – 20

17 – 23

K IC

MPa

−

−

−

−

3.5 – 4.5

4 – 4.2

4 – 4.2

4 – 5.5

Symbol

Units

σB

√ m

C 795

C 799

Part 3 2.4

The properties of commercial grades of alumina (corundum) are closely related to the microstructure. Pure α-Al2 O3 is denser, harder, stiffer, and more refractory than most silicate ceramics so that increasing the proportion of the second phase in an alumina ceramic tends to decrease the density, Young’s modulus, strength, hardness, and refractoriness. Sintered alumina is produced from high-purity powders, which densify to give singlephase ceramics with a uniform grain size. Table 3.2-12 gives typical examples of properties of high-density alumina, and Table 3.2-13 lists further properties of various alumina ceramics.

446

Part 3

Classes of Materials

Table 3.2-13 Properties of Al2 O3 according to DIN EN 60672 [2.6], cont. Designation

Thermal

Symbol

Units

properties

C 780

C 786

C 795

C 799

Al2 O3

Al2 O3

Al2 O3

Al2 O3

Alumina

Alumina

Alumina

Alumina

Alumina

Alumina

Alumina

Alumina

80–86%

86–95%

95–99%

>99%

99%

Part 3 2.4

Electrical properties Breakdown

Ed

kV/mm

10

15

15

17

10

15 – 25

15

17

U

kV

15

18

18

20

15

18

18

20

εr

−

8

9

9

9

9

9

9

tan δpf

10−3

1.0

0.5

0.5

0.2

tan δ1M

10−3

1.5

1

1

1

ρ20

Ωm

1012

1012

1012

1012

1012 – 1013

1012 – 1014

1012 – 1015

1012 – 1015

ρ600

Ωm

105

106

106

106

106

106

106

106

α30−600

10−6 K−1

6–8

6–8

6–8

7–8

6–8

6–8

6–8

7–8

850 – 1050

850 – 1050

850 – 1050

strength Withstand voltage Permittivity at

9 – 10

48–62 Hz Loss factor at

0.5 – 1.0

0.3 – 0.5

0.2 – 0.5

0.2 – 0.5

20 ◦ C,

1 kHz Loss factor

1

1

1

1

at 20 ◦ C, 1 MHz Resistivity at

20 ◦ C

Resistivity at

600 ◦ C

Ave. coeff. of thermal expansion at 30–600 ◦ C Specific heat at

c p,30−600 J kg−1 K−1 850 – 1050 850 – 1050 850 – 1050 850 – 1050 850 – 1050

30–100 ◦ C

Thermal

λ30−100

W m−1 K−1 10 – 16

14 – 24

16 – 28

19 – 30

10 – 16

14 – 25

16 – 28

19 – 30

(Rated)

Good

Good

Good

Good

Good

Good

Good

Good

◦C

−

−

−

−

1400 – 1500 1400 – 1500 1400 – 1500 1400 – 1700

conductivity Thermal fatigue resistance Typ. max. application temperature

T

Ceramics

2.4 Oxide Ceramics

447

3.2.4.3 Al–O–N Ceramics A class of variants of the ceramics related to alumina is based on the ternary Al–O–N system, which forms 13 different compounds, some of which are polytypes of aluminium nitride based on the wurtzite structure.

Table 3.2-14 lists some typical properties compiled from various publications. Al–O–N ceramics have optical and dielectric properties which make them suitable, for use, for example, in windows for elctromagnetic radiation.

Property

Value

Refractive index at λ = 0.55 µm

1.77 – 1.88

IR cutoff

5.12 µm

UV cutoff

0.27 µm

Dielectric constant at 20 ◦ C, 100 Hz Dielectric constant at

500 ◦ C,

8.5

100 Hz

14.0

Loss tangent at 20 ◦ C, 100 Hz

0.002

Loss tangent at 500 ◦ C, 100 Hz

1.0

Thermal conductivity at 20 ◦ C

10.89 W m−1 K−1

Thermal expansion coefficient at 25–1000 ◦ C

7.6 × 106 K−1

Flexural strength at 20 ◦ C Flexural strength at

306 MPa

1000 ◦ C

267 MPa 2.0–2.9 MPa m1/2

Fracture toughness

3.2.4.4 Beryllium Oxide Beryllium oxide (BeO, beryllia) is the only material apart from diamond which combines high thermal-shock resistance, high electrical resistivity, and high thermal conductivity at a similar level. Hence its major application is in heat sinks for electronic components. BeO is highly soluble in water, but dissolves slowly

in concentrated acids and alkalis. It is highly toxic. It is highly corrosion-resistant in several liquid metals, such as Li, Na, Al, Ga, Pb, Ni, and Ir. Its maximum service temperature is 2400 ◦ C. Some properties are listed in Table 3.2-15.

Table 3.2-15 Properties of BeO according to DIN EN 60672 [2.6] Designation C 810 Mechanical properties

Symbol

Open porosity

Units

Beryllium oxide, dense

vol. %

0.0 2.8

Density, minimum



Mg/m3

Bending strength

σB

MPa

150

Young’s modulus

E

GPa

300

Part 3 2.4

Table 3.2-14 Selected properties of Al−O−N ceramics [2.3]

448

Part 3

Classes of Materials

Table 3.2-15 Properties of BeO according to DIN EN 60672 [2.6], cont. Designation C 810

Part 3 2.4

Electrical properties Breakdown strength Withstand voltage Permittivity at 48–62 Hz Loss factor at 20 ◦ C, 1 kHz Loss factor at 20 ◦ C, 1 MHz Resistivity at 20 ◦ C Resistivity at 600 ◦ C Thermal properties Average coefficient of thermal expansion at 30–600 ◦ C Specific heat capacity at 30–100 ◦ C Thermal conductivity Thermal fatigue resistance

Symbol Ed U εr tan δpf tan δ1M ρ20 ρ600

Units kV/mm kV 10−3 10−3 Ωm Ωm

Beryllium oxide, dense 13 20 7 1 1 1012 107

α30−600

10−6 K−1

7 – 8.5

c p,30−100 λ30−100

J kg−1 K−1 W m−1 K−1 (Rated)

1000 – 1250 150 – 220 Good

3.2.4.5 Zirconium Dioxide Zirconium dioxide (ZrO2 ), commonly called zirconium oxide, forms three phases, with a monoclinic, a tetragonal, and a cubic crystal structure. Dense parts may be obtained by sintering of the cubic or tetragonal phase only. In order to stabilize the cubic phase, “stabilizers” such as MgO, CaO, Y2 O3 , and CeO2 are added. An important class of zirconium dioxide ceramics is known as partially stabilized zirconia (PSZ),

and Table 3.2-16 gives typical property data for several different grades. Further properties of PSZ are listed in Table 3.2-17. It should be noted that, as with most ceramic materials, the K 1C data depend on the test method applied, and all the other mechanical properties are strongly affected by the microstructure (grain size, stabilizer content, etc.) and further variables such as temperature and atmospheric conditions.

Table 3.2-16 Physical properties reported for commercial grades of partially stabilized zirconia (PSZ) [2.3] Mg-PSZ

Ca-PSZ

Y-PSZ

wt% stabilizer

2.5 – 3.5

3 – 4.5

5 – 12.5

3

Hardness (GPa)

14.4 a

17.1 b

13.6 c

15

Fracture toughness K IC at room temperature (MPa m1/2 )

7 – 15

6–9

6

4.6

Young’s modulus (GPa)

200 a

200 – 217

210 – 238

−

430 – 720

400 – 690

650 – 1400

350

Thermal expansion coefficient (10−6 /K) at 1000 ◦ C

9.2 a

9.2 b

10.2 c

−

Thermal conductivity at room temperature (W m−1 K−1 )

1–2

1–2

1–2

1–2

Bending strength (MPa) at room temperature

a b c

2.8% MgO. 4% CaO. 5% Y2 O3 .

Ca/Mg-PSZ

Ceramics

2.4 Oxide Ceramics

449

Table 3.2-17 Properties of PSZ according to DIN EN 60672 [2.6] Designation PSZ Mechanical properties

Symbol

Open porosity

Units

Partially stabilized ZrO2 0 5–6

Density, minimum



Mg/m3

Bending strength

σB

MPa

500 – 1000

Young’s modulus

E

GPa

200 – 210

Vickers hardness

HV

100

11 – 12.5

Fracture toughness

K IC

√ MPa m

5.8 – 10.5

Electrical properties Permittivity at 48–62 Hz

εr

Resistivity at 20 ◦ C

ρ20

Ωm

108 – 1013

Resistivity at 600 ◦ C

ρ600

Ωm

103 – 106

Thermal properties

Symbol

Units

Partially stabilized ZrO2

Average coefficient of thermal expansion at 30–600 ◦ C

α30−1000

10−6 K−1

10 – 12.5

c p,30−1000

J kg−1 K−1

400 – 550

λ30−100

W m−1 K−1

1.5 – 3

(Rated)

Good

◦C

900 – 1600

Specific heat capacity at

30–100 ◦ C

Thermal conductivity Thermal fatigue resistance Typical maximum application temperature

T

22

Part 3 2.4

vol. %

450

Part 3

Classes of Materials

3.2.4.6 Titanium Dioxide, Titanates, etc. feature that their permittivity and its temperature coefficient can be adjusted over a wide range. Furthermore, they have a low loss factor. Some properties are listed in Table 3.2-18.

Titanium dioxide (TiO2 ) is widely used in powder form as a pigment and filler material and in optical and catalytic applications. Technical ceramics made from titanium dioxide or titanates have the characteristic

Part 3 2.4

Table 3.2-18 Properties of titanium dioxide, titanates etc. according to DIN EN 60672 [2.6] Designation

Mechanical properties

C 310

C 320

Titanium dioxide

C 331

C 340

C 350

Magnesium Titanium

Titanium

Bismuth

Perovskites,

titanate

dioxide

dioxide

titanate,

middle εr

with other

with other

basic

oxides

oxides

0.0

0.0

chief Symbol

Open porosity

Units vol. %

Density, minimum



Mg/m3

Bending

σB

MPa

Breakdown strength

Ed

kV/mm

Withstand voltage

U

kV

Permittivity at

εr

constituent 0.0 3.5 70

0.0 3.1

C 330

4.0

4.5

0.0 3.0

0.0 4.0

70

80

80

70

50

strength 8

8

10

10

6

2

15

15

15

15

8

2

40 – 100

12 – 40

25 – 50

30 – 70

100 – 700

350 – 3000 −

48–62 Hz Loss factor

tan δ1k

10−3

6.5

2

tan δ1M

10−3

2

1.5

ρ20

Ωm

1010

109

α30−600

10−6 K−1

6–8

J kg−1 K−1

700 – 800

20.0

7

−

0.8

1

5

35.0

109

109

109

108

6 – 10

−

−

−

−

900 – 1000

−

−

−

−

3.5 – 4

−

−

−

−

at 20 ◦ C, 1 kHz Loss factor at

20 ◦ C,

1 MHz

Resistivity at 20 ◦ C Thermal properties Average coefficient of thermal expansion at 30–600 ◦ C

Specific heat capacity c p,30−100 at

30–100 ◦ C

Thermal conductivity

λ30−100

W m−1 K−1 3 – 4

Ceramics

2.5 Non-Oxide Ceramics

451

3.2.5 Non-Oxide Ceramics gives a survey. It is obvious that borides and carbides are superior to most oxide ceramics. Depending upon the microstructure, SiC has a higher hardness than that of β-Si3 N4 , but it decreases somewhat more rapidly, with increasing temperature. Both Si3 N4 and SiC ceramics possess a high thermal conductivity and thus excellent thermal-shock resistance.

3.2.5.1 Non-Oxide High-Temperature Ceramics

3.2.5.2 Borides

The two dominating design variables to be considered for high-temperature materials are hardness and thermal conductivity as a function of temperature. Figure 3.2-2

Borides and boride-based high-temperature refractories are treated extensively in [2.2, 3, 10]. Some properties are listed in Table 3.2-19.

b) Thermal conductivity (W/m k) 200

a) Vickers hardness (kg /mm2) 8000

180

660 – 1350 Diamond

160

SiC pure

Diamond

AlN, 0 % O

140

6000

AlN, 4 % O 120 CBN 4000 Si3N4

100

ZrB2

Si3N4 – TiC or –Ta2Si B6O SiB 4

B4C TiB2 + W SiB6

2000

80

TiB2

SiC hot pressed

60

TiC

40 Cr–C

WC

SiC

IVA,VA–Me–C,IVA–Me–B

ZrO2 00

WC

Al2O3 400

20 SiB6

VA–Me–(C,N)

800

1200 T (°C)

ZrC NbC HfC

0

0

200

ZrO2

400

600

Al2O3

800 1000 1200

B4C

Si3N4 B6O SiB4 SiO2

T (°C)

Fig. 3.2-2a,b Temperature dependence of (a) the hardness and (b) the thermal conductivity of ceramic materials in

comparison with diamond and cubic boron nitride (CBN) [2.3]

Part 3 2.5

The non-oxide ceramics comprise essentially borides, carbides, nitrides, and silicides. Like oxide ceramics they have two kinds of uses, which frequently overlap: application of their physical properties and of their refractory high-temperature properties. Extensive accounts can be found in [2.1–3, 8, 10].

452

Part 3

Classes of Materials

Table 3.2-19 Physical properties of borides and boride-based high-temperature refractories [2.4]

Part 3 2.5

IUPAC name Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z

Aluminium diboride

Hexagonal a = 300.50 pm c = 325.30 pm C32, h P3, P/6mmm, AlB2 type (Z = 1)

3190

–

1654

–

897.87

–

Aluminium AlB12 dodecaboride [12041-54-2] 156.714

Tetragonal a = 1016 pm c = 1428 pm

2580

–

2421

–

954.48

–

Beryllium boride

Be4 B [12536-52-6] 46.589

–

–

–

1160

–

–

–

Beryllium diboride

BeB2 [12228-40-9] 30.634

Hexagonal a = 979 pm c = 955 pm

2420

10 000

1970

–

–

–

Beryllium hemiboride

Be2 B [12536-51-5]

Cubic a = 467.00 pm Cl, cF12, Fm3m, CaF2 type (Z = 4)

1890

1000

1520

–

–

–

Beryllium hexaboride

BeB6 [12429-94-6]

Tetragonal a = 1016 pm c = 1428 pm

2330

1013

2070

–

–

–

Beryllium monoboride

BeB [12228-40-9]

–

–

–

1970

–

–

–

Boron

β-B [7440-42-8] 10.811

Trigonal (rhombohedral) a = 1017 pm α = 65◦ 12 h R105, R3m, β-B type

2460

18 000

2190

–

–

–

Chromium boride

Cr5 B3 [12007-38-4] 292.414

Orthorhombic a = 302.6 pm b = 1811.5 pm c = 295.4 pm D81 , ti32, I4/mcm, Cr5 B3 type (Z = 4)

6100

–

1900

15.8

–

13.7

Chromium diboride

CrB2 [12007-16-8] 73.618

Hexagonal 5160 – 5200 a = 292.9 pm c = 306.6 pm C32, hP3, P6/mmm, AlB2 type (Z = 1)

21

1850 – 2100

20 – 32

712

6.2 – 7.5

Chromium monoboride

CrB [12006-79-0] 62.807

Tetragonal a = 294.00 pm c = 1572.00 pm Bf , oC8, Cmcm, CrB type (Z = 4)

64.0

2000

20.1

–

12.3

AlB2 [12041-50-8] 48.604

6200

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α, 10−6 K−1 )

Ceramics

2.5 Non-Oxide Ceramics

453

Table 3.2-19 Physical properties of borides and boride-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α,MPa) HV (Mohs hardness HM)

Other physicochemical properties, corrosion resistance,a and uses

IUPAC name

–

–

2500

–

–

–

–

–

–

–

–

Beryllium boride

–

–

–

–

Beryllium diboride

–

–

–

870

Beryllium hemiboride

–

–

–

–

Beryllium hexaboride

–

–

–

–

Beryllium monoboride

320

–

–

2055 (11)

–

–

–

–

211

607

1300

1800

–

–

–

–

Soluble in hot HNO3 , insoluble in other acids and alkalis. Neutron- Aluminium shielding material. dodecaboride

Brown or dark powder, unreactive to oxygen, water, acids and alkalis. Boron ∆Hvap = 480 kJ mol−1 .

Chromium boride

Strongly corroded by molten metals such as Mg, Al, Na, Si, V, Cr, Chromium Mn, Fe, and Ni. It is corrosion-resistant to the following liquid diboride metals: Cu, Zn, Sn, Rb, and Bi.

Chromium monoboride

Part 3 2.5

Phase transition to AlB12 at 920 ◦ C. Soluble in dilute HCl. Nuclear Aluminium shielding material. diboride

–

454

Part 3

Classes of Materials

Table 3.2-19 Physical properties of borides and boride-based high-temperature refractories [2.4], cont.

Part 3 2.5

IUPAC name Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z

Hafnium diboride

HfB2 [12007-23-7] 200.112

11 190

8.8 – 11

3250 – 3380

51.6

247.11

6.3 – 7.6

Lanthanum hexaboride

LaB6 [12008-21-8] 203.772

Hexagonal a = 314.20 pm c = 347.60 pm C32, h P3, P6/mmm, AlB2 type (Z = 1) Cubic a = 415.7 pm D21 , cP7, Pm3m, CaB6 type (Z = 1) Trigonal a = 301.2 pm c = 2093.7 pm D81 , h R7, R3¯ m, Mo2 B5 type (Z = 1) Hexagonal a = 305.00 pm c = 311.30 pm C32, h P3, P6/mmm, AlB2 type (Z = 1) Tetragonal a = 554.3 pm c = 473.5 pm C16, tI2, I4/mcm, CuAl2 type (Z = 4) Tetragonal a = 311.0 c = 169.5 Bg , t14, I41 /amd, MoB type (Z = 2) Hexagonal a = 308.90 pm c = 330.03 pm C32, hP3, P6/mmm, AlB2 type (Z = 1) Orthorhombic a = 329.8 pm b = 316.6 pm c = 87.23 pm Bf , oC8, Cmcm, CrB type (Z = 4) Trigonal (rhombohedral) –

4760

17.4

2715

47.7

–

6.4

7480

22 – 55

1600

50

–

8.6

7780

45

2100

–

527

7.7

9260

40

2280

–

377

5

8770 – –

α-MoB 45, β-MoB 24

2180

–

368

–

6970

26 – 65

2900

17 – 23.5

418

8.0 – 8.6

7570

40 – 64.5

2270 – 2917

15.6

–

12.9

2430

200 000

1950

–

–

–

2400

–

– (dec.)

–

–

–

Hexagonal a = 309.80 pm c = 324.10 pm C32 , h P3, P6/mmm, AlB2 type (Z = 1)

12 540

33

3037 – 3200

10.9 – 16.0

237.55

8.2 – 8.8

Molybdenum Mo2 B5 boride [12007-97-5] 245.935

Molybdenum MoB2 diboride 117.59

Molybdenum Mo2 B hemiboride [12006-99-4] 202.691

Molybdenum MoB monoboride 106.77

Niobium diboride

-NbB2 [12007-29-3] 114.528

Niobium monoboride

δ-NbB [12045-19-1] 103.717

Silicon hexaboride Silicon tetraboride

SiB6 [12008-29-6] SiB4 [12007-81-7] 71.330 TaB2 [12077-35-1] 202.570

Tantalum diboride

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α, 10−6 K−1 )

Ceramics

2.5 Non-Oxide Ceramics

455

Table 3.2-19 Physical properties of borides and boride-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM)

IUPAC name

Gray crystals, attacked by HF, otherwise highly resistant.

Hafnium diboride

500

350

–

2900

479

126

–

–

Wear-resistant, semiconducting, thermoionic-conductor films.

Lanthanum hexaboride

672

345

–

–

Corroded by the following molten metals: Al, Mg, V, Cr, Mn, Fe, Ni, Cu, Nb, Mo, and Ta. It is corrosion resistant to molten Cd, Sn, Bi, and Rb.

Molybdenum boride

–

–

–

1280

–

–

–

–

–

–

637

–

–

–

–

–

–

–

–

–

–

Silicon hexaboride

–

–

–

–

Silicon tetraboride

257

–

–

Molybdenum diboride

– Corrosion-resistant films. (HM 8 – 9)

1570

Molybdenum hemiboride

Molybdenum monoboride

3130 Corrosion-resistant to molten Ta; corroded by molten Re. (HM > 8)

Niobium diboride

Wear-resistant, semiconducting films; neutron-absorbing layers on Niobium nuclear fuel pellets. monoboride

(HM > 8) Gray metallic powder. Severe oxidation in air above 800 ◦ C. Corroded by the following molten metals: Nb, Mo, Ta, and Re.

Tantalum diboride

Part 3 2.5

Other physicochemical properties, corrosion resistance,a and uses

456

Part 3

Classes of Materials

Table 3.2-19 Physical properties of borides and boride-based high-temperature refractories [2.4], cont.

Part 3 2.5

IUPAC name Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z

Tantalum monoboride

TaB [12007-07-7] 191.759

14 190

100

2340 – 3090

–

246.85

–

Thorium hexaboride

ThB6 [12229-63-9] 296.904

6800

–

2149

44.8

–

7.8

Thorium tetraboride

ThB4 [12007-83-9] 275.53

8450

–

2500

25

510

7.9

Titanium diboride

TiB2 [12045-63-5] 69.489

Orthorhombic a = 327.6 pm b = 866.9 pm c = 315.7 pm Bf , oC8, Cmcm, CrB type (Z = 4) Cubic a = 411.2 pm D21 , cP7, Pm3m, CaB6 type (Z = 1) Tetragonal a = 725.6 pm c = 411.3 pm D1e , tP20, P4/mbm, ThB4 type (Z = 4) Hexagonal a = 302.8 pm c = 322.8 pm C32, h P3, P6/mmm, AlB2 type (Z = 1)

4520

16 – 28.4

2980 – 3225

64.4

637.22

7.6 – 8.6

Tungsten hemiboride

W2 B [12007-10-2] 378.491

16 720

–

2670

–

168

6.7

Tungsten monoboride

WB [12007-09-9] 194.651 UB2 [12007-36-2] 259.651

Tetragonal a = 556.4 pm c = 474.0 pm C16, tI12, I4/mcm, CuAl2 type (Z = 4) Tetragonal a = 311.5 pm c = 1692 pm Hexagonal a = 313.10 pm c = 398.70 pm C32, h P3, P6/mmm, AlB2 type Cubic a = 747.3 pm D2f , cF52, Fm3m, UB12 type (Z = 4) Tetragonal a = 707.5 pm c = 397.9 pm D1e , tP20, P4/mbm, ThB4 type (Z = 4) Hexagonal a = 299.8 pm c = 305.7 pm C32, h P3, P6/mmm, AlB2 type (Z = 1)

15 200 16 000

4.1

2660

–

–

6.9

12 710

–

2385

51.9

–

9

5820

–

1500

–

–

4.6

5350

–

2495

4.0

–

7.0

5070

23

2450 – 2747

42.3

647.43

7.6 – 8.3

Uranium diboride

Uranium UB12 dodecaboride 367.91

Uranium tetraboride

UB4 [12007-84-0] 281.273

Vanadium diboride

VB2 [12007-37-3] 72.564

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α, 10−6 K−1 )

Ceramics

2.5 Non-Oxide Ceramics

457

Table 3.2-19 Physical properties of borides and boride-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α,MPa) HV (Mohs hardness HM)

IUPAC name

Severe oxidation above 1100–1400 ◦ C in air.

Tantalum monoboride

–

–

–

2200 (HM > 8)

–

–

–

–

Thorium hexaboride

148

137

–

–

Thorium tetraboride

372 – 551

240

669

3370 (HM > 9)

–

–

–

2420 (HM 9)

–

–

–

(HM 9)

–

–

–

1390

–

–

–

–

440

413

–

2500

268

–

–

Gray crystals, superconducting at 1.26 K. High-temperature Titanium electrical conductor, used in the form of a cermet as a crucible diboride material for handling molten metals such as Al, Zn, Cd, Bi, Sn, and Rb. It is strongly corroded by liquid metals such as Tl, Zr, V, Nb, Ta, Cr, Mn, Fe, Co, Ni, and Cu. Begins to be oxidized in air above 1100–1400 ◦ C. Corrosion-resistant in hot concentrated brines. Maximum operating temperature 1000 ◦ C (reducing environment) and 800 ◦ C (oxidizing environment). Black powder. Tungsten hemiboride

Black powder.

(HM 8 – 9) Wear-resistant, semiconducting films.

Tungsten monoboride Uranium diboride

Uranium dodecaboride

Uranium tetraboride

Vanadium diboride

Part 3 2.5

Other physicochemical properties, corrosion resistance,a and uses

458

Part 3

Classes of Materials

Table 3.2-19 Physical properties of borides and boride-based high-temperature refractories [2.4], cont.

Part 3 2.5

IUPAC name Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z

Zirconium diboride

Hexagonal a = 316.9 pm c = 353.0 pm C32, h P3, P6/mmm, AlB2 type (Z = 1)

6085

9.2

3060 – 3245

57.9

392.54

5.5 – 8.3

Cubic a = 740.8 pm D2f , cF52, Fm3m, UB12 type (Z = 4)

3630

60 – 80

2680

–

523

–

ZrB2 [12045-64-6] 112.846

Zirconium ZrB12 dodecaboride 283.217

Thermal Specific heat Coefficient conductivity capacity of linear −1 −1 −1 −1 (κ, W m K ) (c p , J kg K ) thermal expansion (α, 10−6 K−1 )

3.2.5.3 Carbides Carbides are treated extensively in [2.1–3].Some properties of carbides and carbide-based high-temperature refractories are listed in Table 3.2-20 and Table 3.2-21.

It should be noted that carbides also play a major role as hardening constituents in all carbon-containing steels (Sect. 3.1.5).

Table 3.2-20 Physical properties of carbides and carbide-based high-temperature refractories [2.4] IUPAC name (synonyms and common trade names)

Aluminium carbides Beryllium carbide

Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000) Al4 C3 [1299-86-1] 143.959 Be2 C [506-66-1] 30.035

Boron carbide B4 C r (Norbide
) [12069-32-8] 55.255

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z Numerous 2360 – 2798 polytypes Cubic a = 433 pm Cl, cF12, Fm3m, CaF2 type (Z = 4) Hexagonal a = 560 pm c = 1212 pm DIg , hR15, R3¯ m, B4 C type

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α, 10−6 K−1 )

n.a

n.a

n.a

1900

–

2100

21.0

1397

10.5

2512

4500

2350 – 2427

27

1854

2.63 – 5.6

Ceramics

2.5 Non-Oxide Ceramics

459

Table 3.2-19 Physical properties of borides and boride-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

343 – 506

305

–

–

–

–

Other physicochemical properties, corrosion resistance,a and uses

IUPAC name

1900 – 3400 Gray metallic crystals, excellent thermal-shock resistance, greatest Zirconium (HM 8) oxidation inertness of all refractory hard metals. Hot-pressed diboride material is used in crucibles for handling molten metals such as Zn, Mg, Fe, Cu, Zn, Cd, Sn, Pb, Rb, Bi, Cr, brass, carbon steel, and cast iron, and also molten cryolite, yttria, zirconia, and alumina. It is readily corroded by liquid metals such as Si, Cr, Mn, Co, Ni, Nb, Mo, and Ta, and attacked by molten salts such as Na2 O, alkali carbonates, and NaOH. Severe oxidation in air occurs above 1100–1400 ◦ C. Stable above 2000 ◦ C under inert or reducing atmosphere. – Zirconium dodecaboride

Corrosion data in molten salts from [2.9].

Table 3.2-20 Physical properties of carbides and carbide-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM)

n.a

n.a

n.a

n.a

314.4

–

723

2410 HK

440 – 470

–

2900

Other physicochemical properties, corrosion resistance,a and uses

IUPAC name (synonyms and common trade names)

Decomposed in water with evolution of CH4 .

Aluminium carbides

Brick-red or yellowish-red octahedra. Used in nuclear-reactor cores. Beryllium carbide

3200–3500 Hard, black, shiny crystals, the fourth hardest material known after Boron carbide r HK diamond, cubic boron nitride, and boron oxide. It does not burn in (Norbide
) (HM 9) an O2 flame if the temperature is maintained below 983 ◦ C. Maximum operating temperature 2000 ◦ C (inert or reducing environment) or 600 ◦ C (oxidizing environment). It is not attacked by hot HF or chromic acid. Used as abrasive, and in crucibles for molten salts, except molten alkalimetal hydroxides. In the form of molded shapes, it is used for pressure blast nozzles, wire-drawing dies, and bearing surfaces for gauges. For grinding and lapping applications, the available mesh sizes cover the range 240 to 800.

Part 3 2.5

a

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM)

460

Part 3

Classes of Materials

Table 3.2-20 Physical properties of carbides and carbide-based high-temperature refractories [2.4], cont. IUPAC name (synonyms and common trade names)

Part 3 2.5

Chromium carbide

Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000) Cr7 C3 400.005

Chromium carbide

Cr3 C2 [12012-35-0] 180.010

Diamond

C [7782-40-3] 12.011

Graphite

C [7782-42-5] 12.011

Hafnium monocarbide

HfC [12069-85-1] 190.501

Lanthanum dicarbide

LaC2 [12071-15-7] 162.928

Molybdenum hemicarbide

β-Mo2 C [12069-89-5] 203.891

Molybdenum monocarbide

MoC [12011-97-1] 107.951

Niobium hemicarbide

Nb2 C [12011-99-3] 197.824

Niobium monocarbide

NbC [12069-94-2] 104.917

Density Crystal system, lattice parameters, (, kg m−3 ) Strukturbericht symbol, Pearson symbol, space group, structure type, Z Hexagonal 6992 a = 1389.02 pm c = 453.20 pm Orthorhombic 6680 a = 282 pm b = 553 pm c = 1147 pm D510 , oP20, Pbnm, Cr3 C2 type (Z = 4) Cubic 3515.24 a = 356.683 pm A4, cF8, Fd3m, diamond type (Z = 8) Hexagonal a = 246 pm b = 428 pm c = 671 pm A9, hP4, P63 /mmc, graphite type (Z = 4) Cubic a = 446.0 pm B1, cF8, Fm3m, rock salt type (Z = 4) Tetragonal a = 394.00 pm c = 657.20 pm C11a, tI6, I4/mmm, CaC2 type (Z = 2) Hexagonal a = 300.20 pm c = 427.40 pm L 3, hP3,P63 /mmc, Fe2 N type (Z = 1) Hexagonal a = 290 pm c = 281 pm Bk , P63 /mmc, BN type (Z = 4) Hexagonal a = 312.70 pm c = 497.20 pm L 3, h P3, P63 /mmc, Fe2 N type (Z = 1) Cubic a = 447.71 pm B1, cF8, Fm3m, rock salt type (Z = 4)

Electrical Melting resistivity point (◦ C) (ρ, µ
cm)

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α,10−6 K−1 )

109.0

1665

–

–

11.7

75.0

1895

19.2

–

10.3

3550

900 (type I) 2400 (type IIa)

–

2.16

2250

>1016 (types I and IIa) >103 (type IIb) 1385

3650

–

–

0.6 – 4.3

12 670

45.0

3890 – 3950

22.15

–

6.3

5290

68.0

2360 – 2438

–

–

12.1

9180

71.0

2687

–

29.4

7.8

9159

50.0

2577

–

–

5.76

7800

–

3090

–

–

–

7820

51.1 – 74.0

3760

14.2

–

6.84

Ceramics

2.5 Non-Oxide Ceramics

461

Table 3.2-20 Physical properties of carbides and carbide-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM)

Other physicochemical properties, corrosion resistance,a and uses

IUAPC name (synonyms and common trade names)

–

–

1336

Resists oxidation in the range 800–1000 ◦ C. Corroded by the following molten metals: Ni and Zn.

Chromium carbide

386

–

1041

2650

Corroded by the following molten metals: Ni, Zn, Cu, Cd, Al, Mn, and Fe. Corrosion-resistant in molten Sn and Bi.

Chromium carbide

930

–

7000

8000 HK (HM 10)

Type I contains 0.1–0.2% N, type IIa is N-free, and type IIb is very pure, Diamond generally blue in color. Electrical insulator (E g = 7 eV). Burns in oxygen.

6.9

–

–

(HM 2)

High-temperature lubricant, used in crucibles for handling molten metals Graphite such as Mg, Al, Zn, Ga, Sb, and Bi.

424

–

–

–

–

–

221

–

n.a

1499 (HM > 7)

Gray powder. Wear-resistant film. Oxidized in air at 700–800 ◦ C. Molybdenum Corroded in the following molten metals: Al, Mg, V, Cr, Mn, Fe, Ni, Cu, hemicarbide Zn, and Nb. Corrosion-resistant in molten Cd, Sn, and Ta.

197

n.a.

n.a.

1800 (HM>9)

Oxidized in air at 700–800 ◦ C.

n.a.

n.a.

n.a.

2123

340

n.a.

n.a.

2470 (HM>9)

1870 – 2900 Dark, gray, brittle solid, the most refractory binary material known. Used Hafnium in control rods in nuclear reactors and in crucibles for melting HfO2 and monocarbide other oxides. Corrosion-resistant to liquid metals such as Nb, Ta, Mo, and W. Severe oxidation in air above 1100–1400 ◦ C, but stable up to 2000 ◦ C in helium. – Decomposed by H2 O. Lanthanum dicarbide

Molybdenum monocarbide

Niobium hemicarbide

Lavender-gray powder, soluble in HF-HNO3 mixture. Wear-resistant film, used for coating graphite in nuclear reactors. Oxidation in air becomes severe only above 1000 ◦ C.

Niobium monocarbide

Part 3 2.5

–

462

Part 3

Classes of Materials

Table 3.2-20 Physical properties of carbides and carbide-based high-temperature refractories [2.4], cont. IUPAC name (synonyms, and common trade names)

Part 3 2.5

Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type (Z)

Silicon α-SiC monocarbide [409-21-2] (moissanite, 40.097 r Carbolon
, r
Crystolon , r Carborundum
)

Hexagonal a = 308.10 pm c = 503.94 pm B4, h P4, P63 /mmc, wurtzite type (Z = 2)

3160

4.1 × 105

Silicon β-SiC monocarbide [409-21-2] r
(Carbolon , 40.097 r Crystolon
, r Carborundum
)

Cubic a = 435.90 pm B3, cF8, F43m, ZnS type (Z = 4)

3160

107 – 200 ∼ 2700, subl.

Tantalum hemicarbide

Ta2 C [12070-07-4] 373.907

Hexagonal a = 310.60 pm c = 493.00 pm L 3, h P3, P63 /mmc, Fe2 N type (Z = 2)

15 100

80.0

Tantalum monocarbide

TaC [12070-06-3] 194.955

Cubic a = 445.55 pm B1, cF8, Fm3m, rock salt type (Z = 4)

14 800

Thorium dicarbide

α-ThC2 [12071-31-7] 256.060

Thorium monocarbide

2093 transformation temperature

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α, 10−6 K−1 )

42.5

690

4.3 – 4.6

135

1205

4.5

3327

–

–

–

30 – 42.1

3880

22.2

190

6.64 – 8.4

Tetragonal 8960 – 9600 a = 585 pm c = 528 pm C11a, tI6, I4mmm, CaC2 type (Z = 2)

30.0

2655

23.9

–

8.46

ThC [12012-16-7] 244.089

Cubic a=534.60 pm B1, cF8, Fm3m, rock salt type (Z=4)

10 670

25.0

2621

28.9

–

6.48

Titanium monocarbide

TiC [12070-08-5] 59.878

Cubic a = 432.8 pm B1, cF8, Fm3m, rock salt type (Z = 4)

4938

52.5

3140 ± 90

17 – 21

–

7.5 – 7.7

Tungsten hemicarbide

W2 C [12070-13-2] 379.691

Hexagonal a = 299.82 pm c = 472.20 pm L 3, h P3, P63 /mmc, Fe2 N type (Z = 1)

17 340

81.0

2730

–

–

3.84

Tungsten monocarbide r (Widia
)

WC [12070-12-1] 195.851

Hexagonal a = 290.63 pm c = 283.86 pm L 3, h P3, P63 /mmc, Fe2 N type (Z = 1)

15 630

19.2

2870

121

–

6.9

Ceramics

2.5 Non-Oxide Ceramics

463

Table 3.2-20 Physical properties of carbides and carbide-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM)

Other physicochemical properties, corrosion resistance,a and uses

IUPAC name (synonyms and common trade names)

–

500

2400 – 2500 Semiconductor (E g = 3.03 eV). Soluble in fused alkalimetal hydrox- Silicon (HM 9.2) ides. monocarbide (moissanite, r Carbolon
, r Crystolon
, r Carborundum
)

262 – 468

–

1000

2700 – 3350 Green to bluish-black, iridescent crystals. Soluble in fused (HM 9.5) alkalimetal hydroxides. Abrasives made from this material are best suited to the grinding of low-tensile-strength materials such as cast iron, brass, bronze, marble, concrete, stone, glass, optical, structural, and wear-resistant components. Corroded by molten metals such as Na, Mg, Al, Zn, Fe, Sn, Rb, and Bi. Resistant to oxidation in air up to 1650 ◦ C. Maximum operating temperature of 2000 ◦ C in reducing or inert atmosphere.

Silicon monocarbide r (Carbolon
, r Crystolon
, r Carborundum
)

–

–

–

1714 – 2000

Tantalum hemicarbide

364

–

–

1599 – 1800 Golden-brown crystals, soluble in HF-HNO3 mixture. Used in Tantalum (HM 9 – 10) crucibles for melting ZrO2 and similar oxides with high melting monocarbide points. Corrosion-resistant to molten metals such as Ta, and Re. Readily corroded by liquid metals such as Nb, Mo, and Sn. Burning occurs in pure oxygen above 800 ◦ C. Severe oxidation in air above 1100–1400 ◦ C. Maximum operating temperature of 3760 ◦ C under helium.

–

–

–

600

α – β transition at 1427 ◦ C and β – γ transition at 1497 ◦ C. Decomposed by H2 O with evolution of C2 H6 .

Thorium dicarbide

–

–

–

1000

Readily hydrolyzed in water, evolving C2 H6 .

Thorium monocarbide

310 – 462

–

1310

421

–

–

3000

710

–

530

2700 (HM>9)

2620 – 3200 Gray crystals. Superconducting at 1.1 K. Soluble in HNO3 and Titanium (HM 9 – 10) aqua regia. Resistant to oxidation in air up to 450 ◦ C. Maximum monocarbide ◦ operating temperature 3000 C under helium. Used in crucibles for handling molten metals such as Na, Bi, Zn, Pb, Sn, Rb, and Cd. Corroded by the following liquid metals: Mg, Al, Si, Ti, Zr, V, Nb, Ta, Cr, Mo, Mn, Fe, Co, and Ni. Attacked by molten NaOH. Black. Resistant to oxidation in air up to 700 ◦ C. Corrosion-resistant to Mo.

Tungsten hemicarbide

Gray powder, dissolved by HF-HNO3 mixture. Cutting tools, wear-resistant semiconductor films. Corroded by the following molten metals: Mg, Al, V, Cr, Mn, Ni, Cu, Zn, Nb, and Mo. Corrosion-resistant to molten Sn.

Tungsten monocarbide r (Widia
)

Part 3 2.5

386 – 414

464

Part 3

Classes of Materials

Table 3.2-20 Physical properties of carbides and carbide-based high-temperature refractories [2.4], cont.

Part 3 2.5

IUPAC name (synonyms, and common trade names)

Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type (Z)

Uranium carbide

U2 C3 [12076-62-9] 512.091

Cubic a = 808.89 pm D5c, cI40, I 4¯ 3d, Pu2 C3 type (Z = 8)

12 880

–

1777

–

–

11.4

Uranium dicarbide

UC2 [12071-33-9] 262.051

Tetragonal a = 352.24 pm c = 599.62 pm C11a, ti6, I4/mmm, CaC2 type (Z = 2)

11 280

–

2350 – 2398

32.7

147

14.6

Uranium monocarbide

UC [12070-09-6] 250.040

Cubic a = 496.05 pm B1, cF8, Fm3m, rock salt type (Z = 4)

13 630

50.0

2370 – 2790

23.0

–

11.4

Vanadium hemicarbide

V2 C [2012-17-8] 113.89

Hexagonal a = 286 pm c = 454 pm L 3, h P3, P63 mmc, Fe2 N type (Z = 2)

5750

–

2166

–

–

–

Vanadium monocarbide

VC [12070-10-9] 62.953

Cubic a = 413.55 pm B1, cF8, Fm3m, rock salt type (Z = 4)

5770

65.0 – 98.0

2810

24.8

–

4.9

Zirconium monocarbide

ZrC [12020-14-3] 103.235

Cubic a = 469.83 pm B1, cF8, Fm3m, rock salt type (Z = 4)

6730

68.0

3540 – 3560

20.61

205

6.82

a

Corrosion data in molten salts from [2.9].

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α,10−6 K−1 )

Ceramics

2.5 Non-Oxide Ceramics

465

Table 3.2-20 Physical properties of carbides and carbide-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM) –

434

–

–

–

–

600

172.4

–

351.6

750 – 935 (HM>7)

–

–

–

614

–

613

345

–

1641

IUPAC name (synonyms and common trade names)

Uranium carbide

Transition from tetragonal to cubic at 1765 ◦ C. Decomposed in H2 O, slightly soluble in alcohol. Used in microsphere pellets to fuel nuclear reactors.

Uranium dicarbide

Gray crystals with metallic appearance, reacts with oxygen. Corroded by the following molten metals: Be, Si, Ni, and Zr.

Uranium monocarbide

3000

Corroded by molten Nb, Mo, and Ta.

Vanadium hemicarbide

2090

Black crystals, soluble in HNO3 with decomposition. Used in wear-resistant films and cutting tools. Resistant to oxidation in air up to 300 ◦ C.

Vanadium monocarbide

1830 – 2930 Dark gray, brittle solid, soluble in HF solutions containing nitrates Zirconium (HM>8) or peroxide ions. Used in nuclear power reactors and in crucibles monocarbide for handling molten metals such as Bi, Cd, Pb, Sn, and Rb, and molten zirconia (ZrO2 ). Corroded by the following liquid metals: Mg, Al, Si, V, Nb, Ta, Cr, Mo, Mn, Fe, Co, Ni, and Zn. In air, oxidized rapidly above 500 ◦ C. Maximum operating temperature of 2350 ◦ C under helium.

Part 3 2.5

179 – 221

Other physicochemical properties, corrosion resistance,a and uses

466

Part 3

Classes of Materials

Table 3.2-21 Properties of carbides according to DIN EN 60672 [2.6] Designation SSIC

SISIC

RSIC

NSIC

BC

Silicon carbide, Silicon carbide, Silicon carbide, Silicon carbide, Boron carbide sintered

Mechanical

Part 3 2.5

properties

Symbol

Open porosity

Units

silicon-

recrystallized

nitride-bonded

infiltrated

vol. %

0

0

0 – 15

−

0

Density, minimum



Mg/m3

3.08 – 3.15

3.08 – 3.12

2.6 – 2.8

2.82

2.50

Bending

σB

MPa

300 – 600

180 – 450

80 – 120

200

400

E

GPa

370 – 450

270 – 350

230 – 280

150 – 240

390 – 440

Hardness

HV

100

25 – 26

14 – 25

25

−

30 – 40

Fracture

K IC

√ MPa m

3.0 – 4.8

3.0 – 5.0

3.0

−

3.2 – 3.6

ρ20

Ωm

103 – 104

2 × 101 – 103

−

−

−

ρ600

Ωm

10

5

−

−

−

α30−1000

10−6 K−1

4 – 4.8

4.3 – 4.8

4.8

4.5

6

c p,30−1000

J kg−1 K−1

600 – 1000

650 – 1000

600 – 900

800 – 900

−

λ30−100

W m−1 K−1

40 – 120

110 – 160

20

14 – 15

28

(Rated)

Very good

Very good

Very good

Very good

−

◦C

1400 – 1750

1380

1600

1450

700 – 1000

strength Young’s modulus

toughness Electrical properties Resistivity at 20 ◦ C Resistivity at 600 ◦ C Thermal properties Average coefficient of thermal expansion at 30–600 ◦ C Specific heat capacity at 30–100 ◦ C Thermal conductivity Thermal fatigue resistance Typical maximum application temperature

T

Ceramics

2.5 Non-Oxide Ceramics

467

3.2.5.4 Nitrides Nitrides are treated extensively in [2.1–3]. Some properties are listed in Tables 3.2-22 and 3.2-23.

Table 3.2-22 Properties of nitrides according to DIN EN 60672 [2.6] Designation SSN

Mechanical properties Open porosity Density, minimum Bending strength Young’s modulus Hardness Fracture toughness Electrical properties Resistivity at 20 ◦ C Resistivity at 600 ◦ C Thermal properties Average coefficient of thermal expansion at 30–600 ◦ C Specific heat capacity at 30–100 ◦ C Thermal conductivity Thermal fatigue resistance Typical maximum application temperature

Silicon nitride, sintered

RBSN

HPSN

SRBSN

AlN

Silicon nitride, hot-pressed

Aluminium nitride

0 3.2 – 3.4 600 – 800 600 – 800 15 – 16 6.0 – 8.5

Silicon nitride, reactionbonded − 3.1 – 3.3 700 – 1200 150 – 240 − 3.0 – 6?

σB E HV K IC

Units vol. % Mg/m3 MPa GPa 100 √ MPa m

− 3 – 3.3 700 – 1000 250 – 330 4 – 18 5 – 8.5

Silicon nitride, reactionbonded − 1.9 – 2.5 200 – 330 80 – 180 8 – 10 1.8 – 4.0

ρ20

Ωm

1011

1013

1013

−

1013

ρ600

Ωm

102

1010

109

−

1012

α30−1000

10−6 K−1

2.5 – 3.5

2.1 – 3

3.1 – 3.3

3.0 – 3.4

4.5 – 5

c p,30−1000

J kg−1 K−1

700 – 850

700 – 850

700 – 850

700 – 850

−

λ30−100

W m−1 K−1

15 – 45

4 – 15

15 – 40

14 – 15

> 100

(Rated)

Very good

Very good

Very good

Very good

Very good

◦C

1250

1100

1400

1250

−

Symbol

T

0 3.0 200 320 11 3.0

Part 3 2.5

Silicon Nitride Si3 N4 is the dominant nitride ceramic material because of its favorable combination of properties. The preparation of powders for the formation of dense silicon nitride

materials requires the use of precursors. Four routes for the production of Si3 N4 powders are used in practice: nitridation of silicon, chemical vapor deposition from SiCl4 + NH3 , carbothermal reaction of SiO2 , and precipitation of silicon diimide Si(NH)2 followed by decomposition. Table 3.2-24 gives examples of the properties of the resulting powders.

468

Part 3

Classes of Materials

Table 3.2-23 Physical properties of nitrides and nitride-based high-temperature refractories [2.4]

Part 3 2.5

IUPAC name (synonyms and common trade names)

Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z

Aluminium mononitride

AIN [24304-00-5] 40.989

3050

1017

2230

29.96

820

5.3

Beryllium nitride

α-Be3 N2 [1304-54-7] 55.050

2710

–

2200

–

1221

–

Boron mononitride

BN [10043-11-5] 24.818

Hexagonal a = 311.0 pm c = 497.5 pm B4, h P4, P63 mc, wurtzite type (Z = 2) Cubic a = 814 pm D53 , cI80, Ia3, Mn2 O3 type (Z = 16) Hexagonal a = 250.4 pm c = 666.1 pm Bk , h P8, P63 /mmc, BN type (Z = 4)

2250

1019

2730 (dec.)

15.41

711

7.54

Boron mononitride r (Borazon
, CBN) Chromium heminitride

BN 24.818

Cubic a = 361.5 pm

3430

1900 (200◦ C)

1540

–

–

–

Cr2 N [12053-27-9] 117.999

Hexagonal a = 274 pm c = 445 pm L 3, h P3, P63 /mmc, Fe2 N type (Z = 1) Cubic a = 415.0 pm B1, cF8, Fm3m, rock salt type (Z = 4) Cubic a = 451.8 pm B1, cF8, Fm3m, rock salt type (Z = 4) Cubic a = 416 pm L 1, cP5, Pm3m, Fe4 N type (Z = 2) Hexagonal a = 572.5 pm c = 560.8 pm Bh , h P2, P6/mmm, WC type (Z = 1) Cubic a = 438.8 pm B1, cF8, Fm3m, rock salt type (Z = 4) Hexagonal a = 760.8 pm c = 291.1 pm P6/3m

6800

76

1661

22.5

630

9.36

6140

640

1499 (dec.)

12.1

795

2.34

13 840

33

3310

21.6

210

6.5

9460

19.8

760 – 899

17.9

293

6.12

9180

–

1749

–

–

–

8470

78

2575

3.63

–

10.1

3170

106

1850

28

713

2.25

Chromium mononitride

CrN [24094-93-7] 66.003

Hafnium mononitride

HfN [25817-87-2] 192.497

Molybdenum Mo2 N heminitride [12033-31-7] 205.887 Molybdenum MoN mononitride [12033-19-1] 109.947

Niobium mononitride

NbN [24621-21-4] 106.913

Silicon nitride

β-Si3 N4 [12033-89-5] 140.284

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α,10−6 K−1 )

Ceramics

2.5 Non-Oxide Ceramics

469

Table 3.2-23 Physical properties of nitrides and nitride-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM) –

2068

–

–

–

85.5

–

310

–

–

7000

–

–

–

IUPAC name (synonyms and common trade names)

1200 Insulator (E g = 4.26 eV). Decomposed by water, acids, and alkalis Aluminium (HM 9 – 10) to Al(OH)3 and NH3 . Used in crucibles for GaAs crystal growth. mononitride

–

Hard white or grayish crystals. Oxidized in air above 600 ◦ C. Slowly decomposed in water, quickly in acids and alkalis, with evolution of NH3 .

Beryllium nitride

Insulator (E g = 7.5 eV). Used in crucibles for molten metals such as Na, B, Fe, Ni, Al, Si, Cu, Mg, Zn, In, Bi, Rb, Cd, Ge, and Sn. Corroded by these molten metals: U, Pt, V, Ce, Be, Mo, Mn, Cr, V, and Al. Attacked by the following molten salts: PbO2 , Sb2 O3 , Bi2 O3 , KOH, and K2 CO3 . Used in furnace insulation, diffusion masks, and passivation layers. 4700 – 5000 Tiny reddish to black grains. Used as an abrasive for grinding tool (HM 10) and die steels and high-alloy steels when chemical reactivity of diamond is a problem.

Boron mononitride

–

1200 – 1571

Chromium heminitride

–

–

1090

Chromium mononitride

–

–

–

–

–

–

1700

–

–

–

650

–

–

–

1400 (HM> 8)

55

–

–

(HM>9)

230 (HM 2.0)

1640 Most refractory of all nitrides. (HM> 8−9)

Phase transition at 5.0 K.

Boron mononitride r (Borazon
, CBN)

Hafnium mononitride

Molybdenum heminitride

Molybdenum mononitride

Dark gray crystals. Transition temperature 15.2 K. Insoluble in HCl, HNO3 , and H2 SO4 , but attacked by hot caustic solutions, lime, or strong alkalis, evolving NH3 .

Niobium mononitride

Silicon nitride

Part 3 2.5

346

Other physicochemical properties, corrosion resistance,a and uses

470

Part 3

Classes of Materials

Table 3.2-23 Physical properties of nitrides and nitride-based high-temperature refractories [2.4], cont. IUPAC name (synonyms and common trade names)

Part 3 2.5

Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000)

Silicon nitride α-Si3 N4 r (Nitrasil
) [12033-89-5] 140.284 Tantalum heminitride

Ta2 N 375.901

Tantalum mononitride ()

TaN [12033-62-4] 194.955

Thorium mononitride

ThN [12033-65-7] 246.045

Thorium nitride

Th2 N3 [12033-90-8]

Titanium mononitride

TiN [25583-20-4] 61.874

Tungsten dinitride

WN2 [60922-26-1] 211.853 W2 N [12033-72-6] 381.687

Tungsten heminitride

Tungsten mononitride Uranium nitride

WN [12058-38-7] U2 N3 [12033-83-9] 518.259

Uranium mononitride

UN [25658-43-9] 252.096

Vanadium mononitride

VN [24646-85-3] 64.949

Zirconium mononitride

ZrN [25658-42-8] 105.231

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z

Thermal Specific heat Coefficient conductivity capacity of linear −1 −1 −1 −1 (κ, W m K ) (c p , J kg K ) thermal expansion (α,10−6 K−1 )

3184

1019

1900 (sub.)

17

700

2.5 – 3.3

15 600

263

2980

10.04

126

5.2

13 800

128 – 135

3093

8.31

210

3.2

Cubic a = 515.9 B1, cF8, Fm3m, rock salt type (Z = 4) Hexagonal a = 388 pm c = 618 pm D52 , h P5, 3¯ ml, La2 O3 type (Z = 1) Cubic a = 424.6 pm B1, cF8, Fm3m, rock salt type (Z = 4) Hexagonal a = 289.3 pm c = 282.6 pm Cubic a = 412 pm L 1, cP5, Pm3m, Fe4 N type (Z = 2) Hexagonal

11 560

20

2820

–

–

7.38

10 400

–

1750

–

–

–

5430

21.7

2930 (dec.)

29.1

586

9.35

7700

–

600 (dec.)

–

–

–

17 700

–

982

–

–

–

15 940

–

593

–

–

–

Cubic a = 1070 pm D53 , c180, Ia3, Mn2 O3 type (Z =16)

11 240

–

–

–

–

–

Cubic a = 489.0 pm B1, cF8, Fm3m, rock salt type (Z = 4) Cubic a = 414.0 pm B1, cF8, Fm3m, rock salt type (Z = 4) Cubic a = 457.7 pm B1, cF8, Fm3m, rock salt type (Z = 4)

14 320

208

2900

12.5

188

9.72

6102

86

2360

11.25

586

8.1

7349

13.6

2980

20.90

377

7.24

Hexagonal a = 775.88 pm c = 561.30 pm P31c Hexagonal a = 306 pm c = 496 pm L 3, h P3, P63 /mmc, Fe2 N type (Z = 1) Hexagonal a = 519.1 pm c = 290.6 pm

Ceramics

2.5 Non-Oxide Ceramics

471

Table 3.2-23 Physical properties of nitrides and nitride-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Other physicochemical properties, corrosion resistance,a and uses

IUAPC name (synonyms and common trade names)

304

–

–

(HM>9)

Gray amorphous powder or crystals. Corrosion-resistant to molten metals Silicon nitride r such as Al, Pb, Zn, Cd, Bi, Rb, and Sn, and molten salts NaCl-KCl, NaF, (Nitrasil
) and silicate glasses. Corroded by molten Mg, Ti, V, Cr, Fe, Co, cryolite, KOH, and Na2 O. Decomposed by KOH with evolution of NH3 . Tantalum heminitride

–

–

–

3200

–

–

–

1110 (HM>8)

–

–

–

600

–

–

–

–

248

–

972

–

–

–

–

–

–

–

Gray crystals.

Tungsten heminitride

–

–

–

–

Gray solid. Slowly hydrolyzed by water.

–

–

–

–

Tungsten mononitride Uranium nitride

149

–

–

455

–

–

–

–

–

979

Bronze-colored or black crystals. Transition temperature 1.8 K. Insoluble Tantalum in water, slowly attacked by aqua regia, HF, and HNO3 . mononitride () Gray solid. Slowly hydrolyzed by water. Thorium mononitride

Thorium nitride

1900 Bronze-colored powder. Transition temperature 4.2 K. Corrosion-resistant Titanium (HM 8 – 9) to molten metals such as Al, Pb, Mg, Zn, Cd, and Bi. Corroded by molten mononitride Na, Rb, Ti, V, Cr, Mn, Sn, Ni, Cu, Fe, and Co. Dissolved by boiling aqua regia; decomposed by boiling alkalis, evolving NH3 . – Brown crystals. Tungsten dinitride

Uranium mononitride

1520 Black powder. Transition temperature 7.5 K. Soluble in aqua regia. (HM 9 – 10)

1480 (HM>8)

Corrosion data in molten salts from [2.9].

Vanadium mononitride

Yellow solid. Transition temperature 9 K. Corrosion-resistant to steel, Zirconium basic slag, and cryolite, and molten metals such as Al, Pb, Mg, Zn, Cd, and mononitride Bi. Corroded by molten Be, Na, Rb, Ti, V, Cr, Mn, Sn, Ni, Cu, Fe, and Co. Soluble in concentrated HF, slowly soluble in hot H2 SO4 .

Part 3 2.5

a

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM)

472

Part 3

Classes of Materials

Table 3.2-24 Characteristics of Si3 N4 powders processed by different preparation techniques [2.3] Technique Nitridation of Si

Part 3 2.5

Sample no. Specific surface area (m2 /g) O (wt%) C (wt%) Fe, Al, Ca (wt%)

1 23 1.4 0.2 0.07

2 11 1.0 0.25 0.4

Other impurities (wt%) Crystallinity (%) α/(α + β) (%) Morphologya a

100 95 E

100 92 E

Chemical vapor deposition

Carbothermal reduction

1 2 4 10 1.0 3.0 − − 0.005 0.005  Cl 0.04 Mo + Ti 0.02 60 95 E+R

0 − E+R

10 2.0 0.9 0.22

100 98 E+R

Diimide precipitation 1 11 1.4 0.1 0.01

2 13 1.5 0.1 0.015

Cl 0.1

Cl 0.005

98 86 E

− 95 E

E, equiaxed; R, rod-like.

Table 3.2-25 Physical properties of silicides and silicide-based high-temperature refractories [2.4] IUPAC name Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000) Chromium CrSi2 disilicide [12018-09-6] 108.167

Chromium silicide

Cr3 Si [12018-36-9] 184.074

Hafnium disilicide

HfSi2 [12401-56-8] 234.66

Molybdenum MoSi2 disilicide [12136-78-6] 152.11

Niobium disilicide

NbSi2 [12034-80-9] 149.77

Tantalum disilicide

TaSi2 [12039-79-1] 237.119

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z Hexagonal 4910 1400 1490 a = 442 pm c = 635 pm C40, h P9, P62 22, CrSi2 type (Z = 3) Cubic 6430 45.5 1770 a = 456 pm A15, cP8, Pm3n, Cr3 Si type (Z = 2) Orthorhombic 8030 – 1699 a = 369 pm b = 1446 pm c = 346 pm C49, oC12, Cmcm, ZrSi2 type (Z = 4) Tetragonal 6260 21.5 1870 a = 319 pm c = 783 pm C11b, tI6, I4/mmm, MoSi2 type (Z = 2) Hexagonal 5290 50.4 2160 a = 479 pm c = 658 pm C40, h P9, P62 22, CrSi2 type (Z = 3) Hexagonal 9140 8.5 2299 a = 477 pm c = 655 pm C40, h P9, P62 22, CrSi2 type (Z = 3)

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α,10−6 K−1 )

106

–

13.0

–

–

10.5

–

–

–

58.9

–

8.12

–

–

–

–

–

8.8 – 9.54

Ceramics

2.5 Non-Oxide Ceramics

473

3.2.5.5 Silicides water and oxidizing media. Silicides of transition metals are highly oxidation-resistant. Silicides are used as ceramic materials mainly in high-temperature applications. MoSi2 is used in resistive heating elements. Some properties are listed in Table 3.2-25.

Table 3.2-25 Physical properties of silicides and silicide-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM)

Other physicochemical properties, corrosion resistance and uses

IUPAC name

–

–

–

1000 – 1130

Chromium disilicide

–

–

–

1005

Chromium silicide

–

–

–

865 – 930

407

–

2068 – 2415

1260

–

–

–

1050

–

–

–

Hafnium disilicide

The compound is thermally stable in air up to 1000 ◦ C. Molybdenum Corrosion-resistant to molten metals such as Zn, Pd, Ag, Bi, and disilicide Rb. It is corroded by the following liquid metals: Mg, Al, Si, V, Cr, Mn, Fe, Ni, Cu, Mo, and Ce.

1200 – 1600 Corroded by molten Ni.

Niobium disilicide

Tantalum disilicide

Part 3 2.5

Silicides, being compounds of silicon with metals, mostly show a metallic luster. Like intermetallic phases the silicides of a metal may occur in different stoichiometric variants, e.g. Ca2 Si, Ca5 Si3 , and CaSi. Silicides of the non-noble metals are unstable in contact with

474

Part 3

Classes of Materials

Table 3.2-25 Physical properties of silicides and silicide-based high-temperature refractories [2.4], cont.

Part 3 2.5

IUPAC name Theoretical chemical formula, [CASRN], relative molecular mass (12 C = 12.000) Tantalum Ta5 Si3 silicide [12067-56-0] 988.992 Thorium ThSi2 disilicide [12067-54-8] 288.209

Titanium disilicide

TiSi2 [12039-83-7] 104.051

Titanium trisilicide

Ti5 Si3 [12067-57-1] 323.657

Tungsten disilicide

WSi2 [12039-88-2] 240.01

Tungsten silicide Uranium disilicide

W5 Si3 [12039-95-1] 1003.46 USi2 294.200

Uranium silicide

β-U3 Si2 770.258

Vanadium disilicide

VSi2 [12039-87-1] 107.112

Vanadium silicide

V3 Si [12039-76-8] 147.9085

Zirconium disilicide

ZrSi2 [12039-90-6] 147.395

Crystal system, Density Electrical Melting lattice parameters, (, kg m−3 ) resistivity point (◦ C) Strukturbericht (ρ, µ
cm) symbol, Pearson symbol, space group, structure type, Z Hexagonal 13 060 – 2499

Tetragonal a = 413 pm c = 1435 pm Cc, tI12, I4amd, ThSi2 type (Z = 4) Orthorhombic a = 360 pm b = 1376 pm c = 360 pm C49, oC12, Cmcm, ZrSi2 type (Z = 4) Hexagonal a = 747 pm c = 516 pm D88 , hP16, P63 mcm, Mn5 Si3 type (Z = 2) Tetragonal a = 320 pm c = 781 pm C11b, tI6, I4/mmm, MoSi2 type (Z = 2)

Tetragonal a = 397 pm c = 1371 pm Cc, tI12, I4/amd, ThSi2 type (Z = 4) Tetragonal a = 733 pm c = 390 pm D5a, tP10, P4/mbm, U3 Si2 type (Z = 2) Hexagonal a = 456 pm c = 636 pm C40, h P9, P62 22, CrSi2 type (Z = 3) Cubic a = 471 pm A15, cP8, Pm3n, Cr3 Si type (Z = 2) Orthorhombic a = 372 pm b = 1469 pm c = 366 pm C49, oC12, Cmcm, ZrSi2 type (Z = 4)

Thermal Specific heat Coefficient conductivity capacity of linear (κ, W m−1 K−1 ) (c p , J kg−1 K−1 ) thermal expansion (α, 10−6 K−1 )

–

–

–

7790

–

1850

–

–

–

4150

123

1499

–

–

10.4

4320

55

2120

–

–

110

9870

33.4

2165

–

–

8.28

12 210

–

2320

–

–

–

9250

–

1700

–

–

–

12 200

150

1666

14.7

–

14.8

5100

9.5

1699

–

–

11.2

5740

203

1732

–

–

8.0

4880

161

1604

–

–

8.6

Ceramics

2.5 Non-Oxide Ceramics

475

Table 3.2-25 Physical properties of silicides and silicide-based high-temperature refractories [2.4], cont. Young’s modulus (E, GPa)

Flexural Compressive Vickers strength strength hardness (τ, MPa) (α, MPa) HV (Mohs hardness HM)

Other physicochemical properties, corrosion resistance, and uses

–

–

–

–

–

–

1120

–

–

–

890 – 1039

Titanium disilicide

–

–

–

986

Titanium trisilicide

–

–

–

1090

Tungsten disilicide

–

–

–

770

–

–

–

700

Uranium disilicide

77.9

–

–

796

Uranium silicide

–

–

–

1400

Vanadium disilicide

–

–

–

1500

Vanadium silicide

–

–

–

1030 – 1060

Zirconium disilicide

Corrosion-resistant to molten Cu, while corroded by molten Ni.

Corroded by molten Ni.

Tantalum silicide Thorium disilicide

Tungsten silicide

Part 3 2.5

1200 – 1500 The compound is thermally stable in air up to 400 ◦ C.

IUPAC name

476

Part 3

Classes of Materials

References 2.1 2.2

Part 3 2

2.3

2.4 2.5

L. E. Toth: Transition Metals, Carbides and Nitrides (Academic Press, New York 1971) R. Freer: The Physics and Chemistry of Carbides, Nitrides and Borides (Kluwer, Boston 1989) M. V. Swain (Ed.): Structure and properties of ceramics. In: Materials Science and Technology, Vol. 11 (Verlag Chemie, Weinheim 1994) F. Cardarelli: Materials Handbook (Springer, London 2000) J. R. Davis (Ed.): Heat-Resistant Materials, ASM Specialty Handbook (ASM International, Materials Park 1997)

2.6

2.7

2.8 2.9

2.10

Verband der keramischen Industrie: Brevier Technische Keramik (Fahner Verlag, Lauf 1999) (in German) P. Otschick (Ed.): Langzeitverhalten von Funktionskeramiken (Werkstoff-Informationsgesellschaft, Frankfurt 1997) (in German) G. V. Samsonov: The Oxides Handbook (Plenum, New York 1974) G. Geirnaert: Cé ramiques et mè taux liquides: Compatibilitié s et angles de mouillages, Bull. Soc. Fr. Ceram 106, 7 (1970) V. I. Matkovich (Ed.): Boron and Refractory Borides (Springer, Berlin, Heidelberg 1977)

477

Polymers

3.3. Polymers

The tables and figures include the physical and physicochemical properties of the most important polymers, copolymers, and polymer blends. “Most important” here means that these materials are widely used for scientific applications and in industry. The values in the

3.3.1 Structural Units of Polymers ................ 480 3.3.2 Abbreviations..................................... 482 3.3.3 Tables and Figures.............................. 3.3.3.1 Polyolefines............................ 3.3.3.2 Vinyl Polymers ........................ 3.3.3.3 Fluoropolymers ....................... 3.3.3.4 Polyacrylics and Polyacetals...... 3.3.3.5 Polyamides ............................ 3.3.3.6 Polyesters............................... 3.3.3.7 Polysulfones and Polysulfides ... 3.3.3.8 Polyimides and Polyether Ketones ............. 3.3.3.9 Cellulose ................................ 3.3.3.10 Polyurethanes ........................ 3.3.3.11 Thermosets............................. 3.3.3.12 Polymer Blends .......................

483 483 489 492 497 501 503 506 508 509 511 512 515

References .................................................. 522

shear rate, and creep modulus versus time. However, other physical properties are also included. Additionally, the most relevant applications of the materials are given.

main tables are given for room temperature, that is, ≈25 ◦ C; otherwise, the temperature is given in parentheses. The tables and figures include the following physical properties:

Melting temperature Tm : heating rate 10 K/min (ISO 11357). Enthalpy of fusion ∆Hu : the amount of enthalpy (given per monomer unit of the polymer) needed for the transition of the polymer from the solid state to the molten state. Entropy of fusion ∆Su : amount of entropy (given per monomer unit of the polymer) which is needed for the transition of a polymer from the solid state to the molten state. Heat capacity cp = (∂H/∂T ) p ≈ ∆H/∆T ; ∆H = quantity of heat per mass unit, ∆T = temperature increase. Enthalpy of combustion ∆Hc : amount of enthalpy released in flaming combustion per unit mass of the polymer. Glass transition temperature Tg : heating rate 10 K/min (ISO 11357). Vicat softening temperature : TV 10/50, force 10 N, heating rate 50 K/h; TV 50/50, force 50 N, heating rate 50 K/h (ISO 306).

Part 3 3

The physical properties of polymers depend not only on the kind of material but also on the molar mass, the molar-mass distribution, the kind of branching, the degree of branching, the crystallinity (amorphous or crystalline), the tacticity, the end groups, any superstructure, and any other kind of molecular architecture. In the case of copolymers, the physical properties are additionally influenced by the type of arrangement of the monomers (statistical, random, alternating, periodic, block, or graft). Furthermore, the properties of polymers are influenced if they are mixed with other polymers (polymer blends), with fibers (glass fibers, carbon fibers, or metal fibers), or with other fillers (cellulose, inorganic materials, or organic materials). The tables and figures include the physical and physicochemical properties of those polymers, copolymers, and polymer blends which are widely used for scientific applications and in industry. The figures include mainly the following physical properties: stress versus strain, viscosity versus

478

Part 3

Classes of Materials

Part 3 3

Thermal conductivity λ: dq/ dt = Aλ dT/ dx; dq/ dt = heat flux, A = area, dT/ dx = temperature gradient. Density = m/V (ISO 1183). Coefficient of expansion α = (1/V0 )(∂V/∂T ) p : T = 23–55 ◦ C (ISO 11359). Compressibility κ = −(1/V)(∂V/∂ p)T . Elastic modulus E = σ/ε (σ = stress, ε = strain (elongation)); elongation rate 1 mm/min (ISO 527). Shear modulus G = τ/γ (τ = shear stress, γ = shear angle). Poisson’s ratio µ = 0.5[1 − (E/σ)(∆V/V)]; ∆V/V = relative volume change. Stress at yield σy , strain (elongation) at yield εy : see Fig. 3.3-1; elongation rate 50 mm/min (ISO 527). Stress at 50% strain (elongation) σ50 : see Fig. 3.3-1; elongation rate 50 mm/min (ISO 527). Stress at fracture σb , strain (elongation) at fracture εb : see Fig. 3.3-1; elongation rate 5 mm/min (ISO 527). Impact strength, and notched impact strength (Charpy) (ISO 179). Sound velocity vs , longitudinal (long) and transverse (trans). Shore hardness A, D (ISO 868). Volume resistivity ρe , surface resistivity σe : contact electrodes, voltage 500 V (DIN 0303 T30, ISO 93, IEC 60093). Electric strength E B : specimen of thickness 1.0 ± 0.1 mm (ISO 10350, IEC 60243). Relative permittivity εr , dielectric loss (dissipation factor) tan δ (IEC 60250). Refractive index n D , temperature coefficient of refractive index dn D / dT . Steam permeation: 20–25 ◦ C, 85% relative humidity gradient (DIN 53122, ISO 15106). Gas permeation: 20–25 ◦ C, reduced to 23 ◦ C, 1 bar (ISO 2556, DIN 53380, ISO 15105). Melt-viscosity–molar-mass relation. Viscosity–molar-mass relation: [η] = K M a means [η]/[η0 ] = K(M/M0 )a , where [η0 ] = 1 cm3 /g, M0 = 1 g/mol, and [η] = intrinsic viscosity number at concentration C = 0 g/cm3 [3.1] (DIN 53726, DIN 53727). Stress σ(ε, T ); ε = strain (elongation), T = temperature (ISO 527). Viscosity η( dγ/ dt, T ); dγ/ dt = shear rate, T = temperature (ISO 11443). Creep modulus E tc (t, p, T ); t = time, p = pressure, T = temperature; E tc = σtc /ε(t) (σtc = creep stress, ε(t) = creep strain (creep elongation)); strain ≤ 0.5% (ISO 899). For selected polymers, the temperature dependence of some physical properties is given. Additionally, the most relevant applications of the materials are given. The tables and figures include the physical properties given in the table below (see [3.1–3]). As the physical and physicochemical properties of each polymer vary with its molecular architecture, the tables show the ranges of the physical and physicochemical properties, whereas the diagrams show the functional relationships for a typical species of the polymer, copolymer, or polymer blend. The table on page 479 shows the selected 77 polymers, copolymers and polymer blends.

Stress σ σb σy σ50

εb

εy

50% Strain ε

Fig. 3.3-1 Stress σ as a function of the strain ε for different

kinds of polymers (see page 478)

Polymers

Part 3 3

3.3.3.1 Polyolefines Polyolefines I Polyethylene: high density HDPE, medium density MDPE, low density LDPE, linear low density LLDPE, ultra high molecular weight UHMWPE Polyolefines II Poly(ethylene-co-vinylacetate) EVA, Polyethylene ionomer EIM, Cycloolefine copolymer COC [Poly(ethylene-conorbornene)], Poly(ethylene-co-acrylic acid) EAA Polyolefines III Polypropylene PP, Polybutene-1 PB, Polyisobutylene PIB, Poly(4-methylpentene-1) PMP 3.3.3.2 Vinylpolymers Vinylpolymers I Polystyrene PS, Poly(styrene-co-butadiene) SB, Poly(styrene-co-acrylonitrile) SAN Vinylpolymers II Poly(vinyl carbazole) PVK, Poly(acrylonitrile-co-butadiene-co-styrene) ABS, Poly(acrylonitrile-co-styrene-co-acrylester) ASA Vinylpolymers III Poly(vinyl chloride): unplastisized PVC-U, plastisized (75/25) PVC-P1, plastisized (60/40) PVC-P2 3.3.3.3 Fluoropolymers Polytetrafluoroethylene PTFE, Polychlorotrifluoroethylene PCTFE, Poly(tetrafluoroethylene-co-hexafluoropro- pylene) FEP, Poly(ethylene-co-tetrafluoroethylene) ETFE, Poly(ethylene-co-chlorotrifluoroethylene), ECTFE 3.3.3.4 Polyacrylics, Polyacetals Poly(methyl methacrylate) PMMA; Poly(oxymethylene) POM-H, Poly(oxymethylene-co-ethylene) POM-R 3.3.3.5 Polyamides Polyamide 6 PA6, Polyamide 66 PA66, Polyamide 11 PA11, Polyamide 12 PA12, Polyamide 610 PA610 3.3.3.6 Polyesters Polycarbonate PC, Poly(ethylene terephthalate) PET, Poly(butylene terephthalate) PBT, Poly(phenylene ether) PPE 3.3.3.7 Polysulfones, Polysulfides Polysulfon PSU, Poly(phenylene sulfide) PPS, Poly(ether sulfone) PES 3.3.3.8 Polyimides, Polyether ketones Poly(amide imide), PAI; Poly(ether imide), PEI; Polyimide, PI; Poly(ether ether ketone), PEEK 3.3.3.9 Cellulose Cellulose acetate CA, Cellulose propionate CP, Cellulose acetobutyrate CAB, Ethyl cellulose EC, Vulcanized fiber VF 3.3.3.10 Polyurethanes Polyurethane PUR, Thermoplastic polyurethane elastomer TPU 3.3.3.11 Thermosets Thermosets I Phenol formaldehyde PF, Urea formaldehyde UF, Melamine formaldehyde MF Thermosets II Unsaturated polyester UP, Diallylphthalat DAP, Silicone resin SI, Epoxy resin EP 3.3.3.12 Polymer Blends Polymer Blends I Polypropylene + Ethylene/propylene/diene-rubber PP + EPDM, Poly(acrylonitrile-co-butadiene-co-styrene) + Polycarbonate ABS + PC, Poly(acrylonitrile-co-butadiene-co-styrene) + Polyamide ABS + PA, Poly(acrylonitrileco-butadiene-co-acrylester) + Polycarbonate ASA + PC

479

480

Part 3

Classes of Materials

Polymer Blends II Poly(vinyl chloride) + Poly(vinylchloride-co-acrylate) PVC + VC/A, Poly(vinyl chloride) + chlorinated Polyethylene PVC + PE-C, Poly(vinyl chloride) + Poly(acrylonitrile-co-butadiene-co-acrylester) PVC + ASA Polymer Blends III Polycarbonate + Poly(ethylene terephthalate) PC + PET, Polycarbonate + Liquid crystall polymer PC + LCP, Polycarbonate + Poly(butylene terephthalate) PC + PBT, Poly(ethylene terephthalate) + Polystyrene PET + PS, Poly(butylene terephthalate) + Polystyrene PBT + PS Polymer Blends IV Poly(butylene terephthalate) + Poly(acrylonitrile-co-butadiene-co-acrylester) PBT + ASA, Polysulfon + Poly(acrylonitrile-co-butadiene-co-styrene) PSU + ABS, Poly(phenylene ether) + Poly(styrene-co-butadiene) PPE + SB, Poly(phenylene ether) + Polyamide 66 PPE + PA66, Poly(phenylene ether) + Polystyrene PPE + PS

Part 3 3.1

3.3.1 Structural Units of Polymers The polymers given in this chapter are divided into polyolefines, vinyl polymers, fluoropolymers, polyacrylics, polyacetals, polyamides, polyesters, polysulfones, polysulfides, polyimides, polyether ketones, cellulose, polyurethanes, and thermosets. The structural units of the polymers are as follows:

Poly(acrylonitrile), PAN:

CH2 CH CN

Poly(vinyl acetate), PVAC:

CH2 CH O CO CH3

Polyolefines Polyethylene, PE:

Poly(vinyl chloride), PVC:

CH2 CH Cl

CH2 CH2

Polypropylene, PP:

CH2 CH CH3

Poly(butene-1), PB:

CH2 CH CH2 CH3

Poly(isobutylene), PIB:

Poly(4-methylpentene-1), PMP:

CH3 CH2 C CH3 CH2 CH CH2 H3C CH CH3

Poly(vinyl carbazole), PVK:

Fluoropolymers Poly(tetrafluoroethylene), PTFE:

Poly(1,4-butadiene), BR: Vinyl Polymers Polystyrene, PS:

Poly(hexafluoropropylene):

Poly(acrylic acid), PAA:

Poly(oxymethylene), POM: Polyamides Polyamide 6, PA6:

CFCl CF2 CF2 CF CF3

Polyacrylics and Polyacetals Poly(methyl methacrylate), PMMA:

CH2 CH CH CH2

CH2 CH

CF2 CF2

Poly(chlorotrifluoroethylene), PCTFE:

Polynorbornene:

CH CH

CH2 CH N

CH3 CH2 C COOCH3 H CH2 C COOCH2 O

CO (CH2)5 NH

3.1 Structural Units of Polymers

Polymers

Polyamide 66, PA66:

Poly(ether imide), PEI:

NH (CH2)6 NH CO (CH2)4 CO Polyamide 11, PA11:

CO (CH2)10 NH

Polyamide 12, PA12:

CO (CH2)11 NH

O C N

C O

NH (CH2)6 NH CO (CH2)8 CO Polyimide, PI:

Polyamide 612, PA612:

CH3 C CH3

O

Polyamide 610, PA610:

NH (CH2)6 NH CO (CH2)10 CO

O C N C O

O C N C O

O

C O

C O

O C O

OR ROH2C

Poly(butylene terephthalate), PBT:

C O CH2 4O O CH3

Poly(phenylene ether), PPE:

O

O

Cellulose acetate, CA:

R = −COCH3

Cellulose propionate, CP:

R = −COCH2 CH3

Cellulose acetobutyrate, CAB: R = −COCH3 and

O CH3 Polysulfones and Polysulfides Polysulfone, PSU:

CH3 C CH3

O

OR

C O CH2 CH2 O O

C O

O

Cellulose

Poly(ethylene terephthalate), PET:

O

O S O

Poly(phenylene sulfide), PPS: Poly(ether sulfone), PES:

Ethyl cellulose, EC:

O H H O C N R N C

R = −CH2 CH3

Polyurethanes Polyurethane, PUR, TPU:

O

S O S O

R = −COCH2 CH2 CH3

CO NH (CH2)6 NH CO O (CH2)4 O Thermosets Phenol formaldehyde, PF:

OH

OH CH2

O Urea formaldehyde, UF:

CH2 N C O N CH2

Melamine formaldehyde, MF:

H2C N CH2 C N N N C C N N

Polyimides and Polyether Ketones Poly(amide imide), PAI:

C O

O

Part 3 3.1

CH3 C CH3

O

N

O C N C O

Poly(ether ether ketone), PEEK:

Polyesters Polycarbonate, PC:

O C

481

O C N R C O

482

Part 3

Classes of Materials

3.3.2 Abbreviations The following abbreviations are used in this chapter. The abbreviations are in accordance with international rules.

THF trans

tetrahydrofuran transverse

am

amorphous

C

chlorinated

DSC

differential scanning calorimetry

co

copolymer

DTA

differential thermal analysis

cr

crystalline

DOP

dioctyl phthalate

HI

high impact (modifier)

Part 3 3.2

iso

isotactic

long

longitudinal

LCP

liquid crystal polymer

mu

monomer unit

pcr

partially crystalline

syn

syndiotactic

str

strained

Abbreviated notations for polymer names ABS Poly(acrylonitrile-co-butadiene-co-styrene) ASA Poly(acrylonitrile-co-styrene-co-acrylester) CA Cellulose acetate CAB Cellulose acetobutyrate COC Cycloolefine copolymer CP Cellulosepropionate DAP Diallylphthalat EAA Poly(ethylene-co-acrylic acid) EC Ethylcellulose ECTFE Poly(ethylene-co-chlorotrifluoroethylene) EPDM Ethylene/propylene/diene-rubber EIM Polyethylene ionomer EP Epoxide; epoxy ETFE Poly(ethylene-co-tetrafluoroethylene) EVA Poly(ethylene-co-vinylacetate) FEP Poly(tetrafluoroethylene-co-hexafluoropropylene) HDPE High density polyethylene LDPE Low density polyethylene LLDPE Linear low density polyethylene MDPE Medium density polyethylene MF Melamine formaldehyde

CFa

carbon fiber content = a mass%, e.g. PS-CF20 means polystyrene with 20% carbon fiber

GBa

content of glass beads, spheres, or balls = a mass%, e.g. PS-GB20 means polystyrene with 20% glass beads

GFa

glass fiber content = a mass%, e.g. PS-GF20 means polystyrene with 20% glass fiber

MeFa

metal fiber content = a mass%

PEI PES PET PF PI PIB PMMA PMP POM PP PPE PPS PTFE PVC-P PVC-U PVK PS PSU PUR SAN SB

Poly(ether imide) Poly(ether sulfone) Poly(ethylene terephthalate) Phenol formaldehyde Polyimide Poly(isobutylene) Poly(methyl methacrylate) Poly(4-methylpenten-1) Poly(oxymethylene) Polypropylene Poly(phenylene ether) Poly(phenylene sulfide) Poly(tetrafluoro ethylene) Poly(vinyl chloride), plastisized with DOP Poly(vinyl chloride), unplastisized Poly(vinyl carbazole) Polystyrene Polysulfone Polyurethane Poly(styrene-co-acrylonitrile) Poly(styrene-co-butadiene)

Polymers

PA PAI PB PBT PC PCTFE PE PEEK

Polyamide Poly(amide imide) Polybutene-1 Poly(butylene terephthalate) Polycarbonate Poly(trifluorochloroethylene) Polyethylene Poly(ether ether ketone)

SI TPU UF UHMWPE UP VC/A VF

3.3 Tables and Figures

483

Silicone resin Thermoplastic polyurethane elastomer Urea formaldehyde Ultra high molecular weight polyethylene Unsaturated polyester Poly(vinyl chloride-co-acrylate) Vulcanized fiber

Part 3 3.3

3.3.3 Tables and Figures The following tables and diagrams contain physical and physicochemical properties of common polymers, copolymers, and polymer blends. The materials are arranged according to increasing number of functional groups, i. e. polyolefines, vinyl polymers, fluoropolymers, polyacrylics, polyacetals, polyamides, polyesters, and polymers with special functional groups [3.2–16]. Stress σ (MPa) 30

3.3.3.1 Polyolefines Polyethylene, HDPE, MDPE. Applications: injection molding for domestic parts and industrial parts; blow molding for containers and sports goods; extrusion for pressure pipes, pipes, electrical insulating material, bags, envelopes, and tissue. Viscosity η (Pa s)

B = fracture (break) point

23 ˚C 40 ˚C 60 ˚C

B

200 ˚C 240 ˚C 280 ˚C

103

20 B B

10

0

102

0

2

4

6

8

10 12 Strain ε (%)

Fig. 3.3-2 Polyethylene, HDPE: stress versus strain

100

101

102

103 104 Shear rate dγ/dt (s –1)

Fig. 3.3-3 Polyethylene, HDPE: viscosity versus shear rate

484

Part 3

Classes of Materials

Table 3.3-1 Polyethylene: high-density, HDPE; medium-density, MDPE; low-density, LDPE; linear low-density, LLDPE; ultrahigh-molecular-weight, UHMWPE

Part 3 3.3

HDPE

MDPE

LDPE

LLDPE

UHMWPE

Melting temperature Tm (◦ C)

126–135

120–125

105–118

126

130–135

Enthalpy of fusion ∆Hu (kJ/mol) (mu)

3.9–4.1

3.9–4.1

Entropy of fusion ∆Su (J/(K mol)) (mu)

9.6–9.9

9.6–9.9

Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 ))

2.1–2.7

2.1–2.5

Enthalpy of combustion ∆Hc (kJ/g)

−46.4

−46.5

Glass transition temperature Tg (◦ C)

−110

−110

Vicat softening temperature TV 50/50 (◦ C)

60–80

45–60

74

Thermal conductivity λ (W/(m K))

0.38–0.51

0.32–0.40

0.41

Density

0.94–0.96

0.925–0.935

0.915–0.92

≈ 0.935

0.93–0.94

14–18

18–23

23–25

18–20

15–20

Elastic modulus E (GPa)

0.6–1.4

0.4–0.8

0.2–0.4

0.3–0.7

0.7–0.8

Shear modulus G (GPa)

0.85

0.66

0.16–0.25

18–30

11–18

8 –10

20–30

≈ 22

Strain at yield εy (%)

8–12

10–15

≈ 20

≈ 15

≈ 15

Stress at fracture σb (MPa)

18–35

8 –23

Strain at fracture εb (%)

100–1000

300–1000

62

(g/cm3 )

Coefficient of thermal expansion α (10−5 /K) (linear) (296–328 K) Compressibility κ (10−4 /MPa) (cubic)

1.7–1.8

−46.5 −110

−110

2.2

Poisson’s ratio µ Stress at yield σy (MPa) Stress at 50% strain σ50 (MPa)

Impact strength (Charpy)

(kJ/m2 )

13–25

Notched impact strength (Charpy) (kJ/m2 )

3 –5

Sound velocity vs (m/s) (longitudinal)

2430

Sound velocity vs (m/s) (transverse)

950

Shore hardness D

58–63

45–60

45–51

38–60

> 1015

> 1015

> 1015

> 1015

Surface resistivity σe (Ω)

> 1014

> 1014

> 1014

> 1014

> 1014

Electric strength E B (kV/mm)

30–40

30–40

30–40

30–40

30–40

Relative permittivity εr (100 Hz)

2.4

2.3

2.3

2.3

2–2.4

Dielectric loss tan δ (10−4 ) (100 Hz)

1–2

2

2 –2.4

2

2

Refractive index n D (589 nm) Temperature coefficient dn D / dT (10−4 /K)

1.53

1.51–1.42

Steam permeation (g/(m2 d))

0.9 (40 µm)

1 (100 µm)

Gas permeation (cm3 /(m2 d bar)), 23 ◦ C, 100 µm

700 (N2 ) 1800 (O2 ) 10 000 (CO2 ) 1100 (air)

700 (N2 ) 2000 (O2 ) 10 000 (CO2 ) 1100 (air)

Volume resistivity ρe (Ω m)

> 1015

2400 1150

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

[η] = 62 × 10−3 M 0.70 (decalin, 135 ◦ C) [η] = 51 × 10−3 M 0.725 (tetralin, 130 ◦ C)

3.3 Tables and Figures

Polymers

485

Table 3.3-2 Polyethylene, HDPE: heat capacity, thermal conductivity, and coefficient of thermal expansion Temperature T (◦ C)

−200

Heat capacity c p (kJ/(kg K))

−150

0.55

Thermal conductivity λ (W/(m K)) Coefficient of thermal expansion

4.5

−100

−50

0

20

50

100

150

0.84

1.10

1.34

1.64

2.05

2.86

0.62

0.56

0.50

0.44

0.38

0.32

6.8

9.5

12.4

16.9

33.0

0.25

69.0

α (10−5 /K) (linear)

Table 3.3-3 Polyethylene, LDPE: heat capacity and thermal conductivity Temperature T (◦ C)

−200

Heat capacity c p (kJ/(kg K))

−150

0.55

−50

0

20

50

0.84

1.10

1.43

1.90

2.73

0.36

0.38

0.38

0.35

0.31

Creep modulus Etc (MPa)

100

0.24

150

0.25

Shear modulus G (MPa) 0.5 MPa 1.0 MPa 1.5 MPa 2.0 MPa 2.5 MPa 3.0 MPa 4.0 MPa 5.0 MPa

800

600

10 3

10 2 400

200 10 0

10 1

10 2

10 3

10 4 Time t (h)

Fig. 3.3-4 Polyethylene, HDPE: creep modulus versus time, at 23 ◦ C

30

– 50

0

50

100 150 Temperature T (˚C)

Fig. 3.3-5 Polyethylene, HDPE: shear modulus versus

temperature Viscosity η (Pa s) 10 4

Stress σ (MPa) – 40 ˚C – 20 ˚C 0 ˚C 23 ˚C 40 ˚C

20

10 1 –100

150 ˚C 210 ˚C 270 ˚C

10 3

10 2 10 10 1

0

0

1

2

3

4 Strain ε (%)

Fig. 3.3-6 Polyethylene, LDPE: stress versus strain

10 0 –1 10

10 0

10 1

10 2

10 3 10 4 10 5 Shear rate dγ /dt (s–1)

Fig. 3.3-7 Polyethylene, LDPE: viscosity versus shear rate

Part 3 3.3

Thermal conductivity λ (W/(m K))

−100

486

Part 3

Classes of Materials

Creep stress σ tc (MPa) 6

Creep modulus Etc (MPa) 300

0.6 MPa 1.2 MPa 1.8 MPa 2.4 MPa 3.0 MPa 3.6 MPa 4.8 MPa 6.0 MPa

5 250 4 200

3 2

10 h, 23 ˚C 100 h, 23 ˚C 1 000 h, 23 ˚C 10 000 h, 23 ˚C 100 000 h, 23 ˚C

1

Part 3 3.3

0

0

1

2

3

4

5 6 Creep strain ε (%)

150

100 1 10

10 2

10 3

10 4

10 5 Time t (h)

Fig. 3.3-8 Polyethylene, UHMWPE: isochronous stress

Fig. 3.3-9 Polyethylene, UHMWPE: creep modulus ver-

versus strain

sus time

Polyethylene, LDPE. Applications: all kinds of sheeting, bags, insulating material, hollow bodies, bottles, injection-molded parts. Polyethylene, LLDPE. Applications: foils, bags, waste bags, injection-molded parts, rotatory-molded parts. Polyethylene UHMWPE, Applications: mechanical engineering parts, food wrapping, commercial packaging, textile industry parts, electrical engineering parts, paper industry parts, low temperature materials, medical parts, chemical engineering parts, electroplating. Poly(ethylene-co-vinyl acetate), EVA. Applications: films, deep-freeze packaging, laminates, fancy leather,

food packaging, closures, ice trays, bags, gloves, fittings, pads, gaskets, plugs, toys. Polyethylene ionomer, EIM. Applications: transparent tubes for water and liquid foods, transparent films, bottles, transparent coatings, adhesion promoters. Cycloolefine copolymer, COC. Applications: precision optics, optical storage media, lenses, medical and labware applications. Poly(ethylene-co-acrylic acid), EAA. Applications: packaging foils, sealing layers, tubing. Polypropylene, PP. Applications: injection molding for domestic parts, car parts, electric appliances, packing materials, and pharmaceutical parts; blow

Table 3.3-4 Poly(ethylene-co-vinyl acetate), EVA; polyethylene ionomer, EIM; cycloolefine copolymer, COC (poly-

(ethylene-co-norbornene)); poly(ethylene-co-acrylic acid), EAA

Melting temperature Tm (◦ C)

EVA

EIM

90–110

95–110

COC

EAA 92–103

Enthalpy of fusion ∆Hu (kJ/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K))

2.2

Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg (◦ C)

66

Vicat softening temperature TV 50/50 (◦ C)

63–96 VST/A50

Thermal conductivity λ (W/(m K))

0.28–0.35

0.24

0.16

Density (g/cm3 )

0.93–0.94

0.94–0.95

1.02

0.925–0.935

≈ 25

10–15

6–7

≈ 20

Coefficient of thermal expansion α

(10−5 /K)

(linear)

80–180

Polymers

3.3 Tables and Figures

487

Table 3.3-4 Poly(ethylene-co-vinyl acetate), EVA; polyethylene ionomer, EIM; . . . , cont. EVA

EIM

COC

EAA

Elastic modulus E (GPa)

0.03–0.1

0.15–0.2

2.6–3.2

0.04–0.13

Shear modulus G (GPa)

0.04–0.14 7–8

66

4–7

> 20

3.5–10

> 20

Compressibility κ (10−4 /MPa) (cubic)

Poisson’s ratio µ Stress at yield σy (MPa)

5 –8

Strain at yield εy (%) 4 –9

Stress at fracture σb (MPa)

16–23

21–35

66

Strain at fracture εb (%)

700

250–500

3–10

Impact strength (Charpy)

(kJ/m2 )

Part 3 3.3

Stress at 50% strain σ50 (MPa)

13–20

Notched impact strength (Charpy) (kJ/m2 )

1.7–2.6

Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D

34–44

Volume resistivity ρe (Ω m)

> 1014

> 1015

> 1013

> 1014

Surface resistivity σe (Ω)

> 1013

> 1013

1014

> 1013

Electric strength E B (kV/mm)

30–35

40

Relative permittivity εr (100 Hz)

2.5–3

≈ 2.4

2.35

2.5–3

Dielectric loss tan δ (10−4 ) (100 Hz)

20–40

≈ 30

0.2

30–130

Refractive index n D (589 nm) Temperature coefficient dn D / dT (10−4 /K)

1.51

1.53

Steam permeation (g/(m2 d)) (25 µm)

25

1–1.8

Gas permeation (cm3 /(m2 d bar)) (25 µm)

9300 (O2 )

30–40

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

6

Viscosity η (Pa s)

Stress σ (MPa)

170 ˚C 200 ˚C 230 ˚C

5 10 3 4 3 2

10 2

1 23 ˚C 0

0

10

20

30

40 50 Strain ε (%)

Fig. 3.3-10 Poly(ethylene-co-vinylacetate), EVA: stress

versus strain

10 2

10 3

10 4 Shear rate dγ /dt (s–1)

Fig. 3.3-11 Poly(ethylene-co-vinylacetate), EVA: viscosity versus shear rate

488

Part 3

Classes of Materials

Table 3.3-5 Polypropylene, PP; polybutene-1, PB; polyisobutylene, PIB; poly(4-methylpentene-1), PMP

Melting temperature Tm

(◦ C)

PP

PB

160–170

126

Enthalpy of fusion ∆Hu (kJ/mol) (mu)

7–10

Entropy of fusion ∆Su (J/(K mol)) (mu)

15–20

Heat capacity c p (kJ/(kg K))

1.68

PIB

PMP 230–240

Temperature coefficient dc p / dT (kJ/(kg K2 ))

Part 3 3.3

Enthalpy of combustion ∆Hc (kJ/g)

−44

Glass transition temperature Tg (◦ C)

0 to −10

78

Vicat softening temperature TV 50/50 (◦ C)

60–102

108–113

Thermal conductivity λ (W/(m K))

0.22

0.22

0.12–0.20

0.17

Density (g/cm3 )

0.90–0.915

0.905–0.920

0.91–0.93

0.83

12–15

13

8–12

12

Coefficient of thermal expansion α

(10−5 /K)

(linear)

−45

Compressibility κ (10−4 /MPa) (cubic)

2.2

Elastic modulus E (GPa)

1.3–1.8

0.21–0.26

Stress at yield σy (MPa)

25–40

16–24

Strain at yield εy (%)

8–18

24

−70

1.1–2.0

Shear modulus G (GPa) Poisson’s ratio µ

Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa) Strain at fracture εb (%)

> 50

Impact strength (Charpy) (kJ/m2 )

60–140

Notched impact strength (Charpy) (kJ/m2 )

3–10

Sound velocity vs (m/s) (longitudinal)

2650

Sound velocity vs (m/s) (transverse)

1300

Shore hardness D

69–77

Volume resistivity ρe (Ω m)

> 1014

Surface resistivity σe (Ω)

> 1013

Electric strength E B (kV/mm)

30–38

2–6

25–28

300–380

> 1000

10–50

1950

2180 1080

> 1014

> 1013

30–70

18–40

23–25

Relative permittivity εr (100 Hz)

2.3

2.5

2.3

2.1

Dielectric loss tan δ (10−4 ) (100 Hz)

2.5

20–50

1014

1.46

3.3 Tables and Figures

Polymers

489

Table 3.3-6 Polypropylene, PP: heat capacity, thermal conductivity, and coefficient of thermal expansion Temperature T (◦ C)

−200

−150

−100

−50

0

20

50

100

Heat capacity c p (kJ/(kg K))

0.46

0.77

1.03

1.28

1.57

1.68

1.92

2.35

Thermal conductivity λ (W/(m K))

2.3

0.17

0.19

0.21

0.22

0.22

0.22

0.20

5.8

6.9

7.6

19.1

19.4

14.3

22.6

Coefficient of thermal expansion

150

29.4

α (10−5 /K) (linear)

30

Viscosity η (Pa s) 10 4

Stress σ (MPa) 23 ˚C 40 ˚C 60 ˚C 80 ˚C 100 ˚C 120 ˚C

25

Part 3 3.3

20

200 ˚C 240 ˚C 280 ˚C 10 3

15 10 2 10 5 10 1 0

0

1

2

3

4 Strain ε (%)

Fig. 3.3-12 Polypropylene, PP: stress versus strain Creep modulus Etc (MPa) 0.8 MPa 1.6 MPa 3.2 MPa 4.8 MPa 6.4 MPa 8.0 MPa

600 500 400 300 200

10 0

10 1

10 2 10 3 10 4 Shear rate dγ /d t (s–1)

Fig. 3.3-13 Polypropylene, PP: viscosity versus shear rate

Polybutene-1, PB. Applications: tubing, pipes, fittings, hollow bodies, cables, foils, packing. Polyisobutylene, PIB. Applications: adhesives, sealing compounds, electrical insulating oils, viscosity improvers. Poly(4-methylpentene-1), PMP. Applications: glasses, light fittings, molded parts, foils, packing, rings, tubes, fittings, cable insulation.

3.3.3.2 Vinyl Polymers

100 0 10 1

10 –1

10 2

10 3

10 4

10 5 Time t (h)

Fig. 3.3-14 Polypropylene, PP: creep modulus versus time,

at 23 ◦ C

molding for cases, boxes, and bags; pressure molding for blocks and boards; tissue coating; extrusion for pressure pipes, pipes, semiproducts, flexible tubing, textile fabrics, fibers, sheets; foamed polymers for sports goods, boxes, cases, handles, and domestic parts.

Polystyrene, PS. Applications: packaging, expanded films, toys, artificial wood, food holders, housings, plates, cases, boxes, glossy sheets, containers, medical articles, panels. Poly(styrene-co-butadiene), SB. Applications: flameretardant articles, housings. Poly(styrene-co-acrylnitrile), SAN. Applications: food holders, cases, shelves, covers, automotive and electrical parts, sheets, profiles, containers, plastic windows, doors, cosmetic items, medical items, pharmaceutical items, fittings, components, musical items, toys, displays, lighting, food compartments, cassettes, tableware, engineering parts, housings.

490

Part 3

Classes of Materials

Table 3.3-7 Polystyrene, PS; poly(styrene-co-butadiene), SB; poly(styrene-co-acrylonitrile), SAN PS

Part 3 3.3

SB

SAN

1.3

1.3

−36 to −38 90–95 80–110 0.18 1.05–1.06 8 –10

−36 to −38 110 105–120 0.18 1.07–1.08 7 –8

2.0–2.8 0.6

3.5–3.9 1.5

Melting temperature Tm (◦ C) Enthalpy of fusion ∆Hu (KJ/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg (◦ C) Vicat softening temperature TV 50/50 (◦ C) Thermal conductivity λ (W/(m K)) Density (g/cm3 ) Coefficient of thermal expansion α (10−5 /K) (linear)

> 243.2 (iso), > 287.5 (syn) 8.682 (iso), 8.577 (syn) 16.8 (iso), 15.3 (syn) 1.2–1.4 4.04 × 10−3 (323 K) −41.6 95–100 80–100 0.16 1.05 6–8

Compressibility κ (10−4 /MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ Stress at yield σy (MPa) Strain at yield εy (%) Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa) Strain at fracture εb (%) Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D

2.2 3.1–3.3 1.2 0.38 50

30–55 1.5–3 13–25 3–5 2400 1150 78

26–38 25–60 50–105 5 –10

65–85 2.5–5

Volume resistivity ρe (Ω m) Surface resistivity σe (Ω) Electric strength E B (kV/mm) Relative permittivity εr (100 Hz) Dielectric loss tan δ (10−4 ) (100 Hz)

> 1014 > 1014 30–70 2.4–2.5 (am); 2.61 (cr) 1–2

> 1014 > 1013 45–65 2.4–2.6 1 –3

1014 1014 30–60 2.8–3 40–50

Refractive index n D (589 nm) Temperature coefficient dn D / dT (10−4 /K) Steam permeation (g/(m2 d)) (100 µm) Gas permeation (cm3 /(m2 d bar)) (100 µm)

1.58–1.59 −1.42 12 2500 (N2 ) 1000 (O2 ) 5200 (CO2 ) η = 13.04M 3.4 (217 ◦ C) [η] = 11.3 × 10−3 M 0.73 (PS, toluene, 25 ◦ C)

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

25–45 1.1–2.5

2 –4

1.57

Table 3.3-8 Polystyrene, PS: heat capacity, thermal conductivity, and coefficient of thermal expansion Temperature T (◦ C) −200 −150 −100 −50 0 Heat capacity c p (kJ/(kg K)) 0.89 1.09 Thermal conductivity λ (W/(m K)) 0.13 0.14 0.14 0.16 Coefficient of thermal expansion 3.9 5.1 6.1 6.7 α (10−5 /K) (linear)

20 0.16 7.1

50 1.34 0.16 10.0

100 150 200 1.68 2.03 2.19 0.16 0.16 17.6 18.0 17.4

3.3 Tables and Figures

Polymers

80

491

Viscosity η (Pa s) 10 5

Stress σ (MPa)

Y = yield point, B = break point – 40 ˚C 0 ˚C 60 23 ˚C 40 ˚C 50 60 ˚C 80 ˚C 40

180 ˚C 230 ˚C 280 ˚C

Y

70

10 4

Y Y B

10 3

B

30

10 2

20 10 1

10 0.5

1.0

1.5

2.0 2.5 Strain ε (%)

Fig. 3.3-15 Polystyrene, PS: stress versus strain

10 0 –1 10

10 1

10 2

Creep modulus Etc (MPa)

60

Stress σ (MPa)

Y = yield point – 40 ˚C 50 0 ˚C 23 ˚C 40 ˚C 40 60 ˚C 80 ˚C 30

3000 2500 2000 1500

2 MPa 4 MPa 6 MPa 8 MPa 12 MPa 16 MPa 20 MPa

1000 500 0 1 10

10 2

10 3 10 4 10 5 Shear rate dγ /dt (s–1)

Fig. 3.3-16 Polystyrene, PS: viscosity versus shear rate

3500

Y

Y

Y Y

20

Y

Y

10 10 3

10 4

10 5

Time t (h)

Fig. 3.3-17 Polystyrene, PS: creep modulus versus time, at

23 ◦ C

0

0.0

0.5

1.0

1.5

2.0

2.5 3.0 Strain ε (%)

Fig. 3.3-18 Poly(styrene-co-butadiene), SB: stress versus

strain

Viscosity η (Pa s)

Creep modulus Etc (MPa) 190 ˚C 220 ˚C 250 ˚C

104

2000

1500

103 1000

102 500

101

10 0

100

101

102

103 104 Shear rate dγ /dt (s–1)

Fig. 3.3-19 Poly(styrene-co-butadiene), SB: viscosity versus shear rate

10 1

2.0 MPa 3.2 MPa 4.4 MPa 5.6 MPa 6.8 MPa 8.0 MPa 9.2 MPa 10.4 MPa 11.6 MPa 12.5 MPa 10 2

10 3

10 4

10 5

Time t (h)

Fig. 3.3-20 Poly(styrene-co-butadiene), SB: creep modulus versus time

Part 3 3.3

0 0.0

492

Part 3

Classes of Materials

Viscosity η (Pa s) 10 5

Stress σ (MPa) 120 Y = yield point, B = break point – 40 ˚C 100 – 20 ˚C 0 ˚C 23 ˚C 80 40 ˚C 60 ˚C 80 ˚C 60

B B

10 4

B Y

10 3

Y 40

Y

20

Part 3 3.3

0

190 ˚C 220 ˚C 250 ˚C

B

10 2 0

1

2

3

Fig. 3.3-21 Poly(styrene-co-acrylonitrile),

10 –1

4 Strain ε (%)

SAN: stress

versus strain

60

Stress σ (MPa) 0 ˚C 23 ˚C 40 ˚C 60 ˚C 80 ˚C 100 ˚C

50 40

0 10 1

10 2 10 3 10 4 Shear rate dγ /dt (s–1)

Fig. 3.3-22 Poly(styrene-co-acrylonitrile), SAN: viscosity

3000

1000

10 1

versus shear rate

Creep modulus Etc (MPa) 4000

2000

10 0

8.0 MPa 10.7 MPa 13.4 MPa 16.1 MPa 18.8 MPa 21.5 MPa 24.2 MPa 26.9 MPa 29.6 MPa 32.0 MPa 10 2

Y Y Y

30

Y

20

Y

10 Y 10 3

10 4

10 5 Time t (h)

Fig. 3.3-23 Poly(styrene-co-acrylonitrile), SAN: creep

0

0

1

2

Y = yield point 3

4 Strain ε (%)

modulus versus time

Fig. 3.3-24 Poly(acrylonitrile-co-butadiene-co-styrene), ABS: stress versus strain

Poly(vinyl carbazole), PVK. Applications: electrical insulating materials. Poly(acrylonitrile-co-butadiene-co-styrene), ABS. Applications: housings, boxes, cases, tools, office equipment, helmets, pipes, fittings, frames, toys, sports equipment, housewares, packaging, panels, covers, automotive interior parts, food packaging, furniture, automobile parts. Poly(acrylonitrile-co-styrene-co-acrylester), ASA. Applications: outdoor applications, housings, covers, sports equipment, fittings, garden equipment, antennas.

Poly(vinyl chloride), PVC-U. Applications: extruded profiles, sealing joints, jackets, furniture, claddings, roller shutters, fences, barriers, fittings, injection-molded articles, sheets, films, plates, bottles, coated fabrics, layers, toys, bumpers, buoys, car parts, cards, holders, sleeves, pipes, boxes, inks, lacquers, adhesives, foams. Poly(vinyl chloride), PVC-P1, PVC-P2. Applications: flexible tubes, technical items, compounds for insulation and jacketing, joints, seals, pipes, profiles, soling, tubes, floor coverings, wall coverings, car undersealing, mastics, foams, coatings, cap closures,

Polymers

3.3 Tables and Figures

493

Table 3.3-9 Poly(vinyl carbazole), PVK; poly(acrylonitrile-co-butadiene-co-styrene), ABS; poly(acrylonitrile-costyrene-co-acrylester), ASA PVK Melting temperature Tm

ABS

ASA

1.3

1.3

(◦ C)

Enthalpy of fusion ∆Hu (kJ/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg

(◦ C)

−35 173

100

95–105

90–102

0.18

0.18

1.03–1.07

1.07

1.19

8.5–10

9.5

3.5

2.2–3.0

2.3–2.9

0.7–0.9

0.7–0.9

Stress at yield σy (MPa)

45–65

40–55

Strain at yield εy (%)

2.5–3

3.1–4.3

Thermal conductivity λ (W/(m K))

0.29

Density (g/cm3 ) Coefficient of thermal expansion α (10−5 /K) (linear) Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ

Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa)

20–30

Strain at fracture εb (%) Impact strength (Charpy)

15–30 55–80

(kJ/m2 )

40–1000

105–118

Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal)

2040–2160

Sound velocity vs (m/s) (transverse)

830–930

Shore hardness D Volume resistivity ρe (Ω m)

> 1014

1012 – 1013

1012 – 1014

Surface resistivity σe (Ω)

1014

> 1013

1013

Electric strength E B (kV/mm)

30–40

Relative permittivity εr (100 Hz)

2.8–3.1

3.4–4

90–160

90–100

Dielectric loss tan δ

(10−4 )

(100 Hz)

Refractive index n D (589 nm)

6–10

1.52

Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) (100 µm)

27–33

30–35

Gas permeation (cm3 /(m2 d bar)) (100 µm)

100–200(N2 )

60–70 (N2 )

400– 900 (O2 )

150– 180 (O2 ) 6000– 8000 (CO2 )

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

Part 3 3.3

80–110

Vicat softening temperature TV 50/50 (◦ C)

494

Part 3

Classes of Materials

Creep modulus Etc (MPa) 2500

Viscosity η (Pa s) 10 4 230 ˚C 255 ˚C 280 ˚C

10 3

2000

1500

10 2

1000

10 1

Part 3 3.3

10 0 0 10

10 1

10 2

10 3

10 4 10 5 106 –1 Shear rate dγ /dt (s )

Fig. 3.3-25 Poly(acrylonitrile-co-butadiene-co-styrene),

500 1 10

1.6 MPa 3.2 MPa 4.8 MPa 6.4 MPa 8 MPa 9.6 MPa 11.2 MPa 12.8 MPa 14.4 MPa 16 MPa 10 2

10 3

10 4

10 5 Time t (h)

Fig. 3.3-26 Poly(acrylonitrile-co-butadiene-co-styrene), ABS: creep modulus versus time

ABS: viscosity versus shear rate Viscosity η (Pa s) 10 5

Stress σ (MPa) 100 – 40 ˚C 0 ˚C 80 23 ˚C 40 ˚C 60 ˚C 60 80 ˚C 100 ˚C 40

200 ˚C 240 ˚C 280 ˚C

Y 10 4 Y 10 3

Y Y Y

10 2

Y

20

Y = yield point 0

0

1

2

3

4 5 Strain ε (%)

10 1 –1 10

10 0

10 1

10 2

10 3 10 4 10 5 Shear rate dγ /dt (s–1)

Fig. 3.3-27 Poly(acrylonitrile-co-styrene-co-acrylester),

Fig. 3.3-28 Poly(acrylonitrile-co-styrene-co-acrylester),

ASA: stress versus strain

ASA: viscosity versus shear rate

Creep modulus Etc (MPa) 3000

60

Stress σ (MPa) 23 ˚C

2500

50

2000

40

1500

30

1000 500 10 1

4.0 MPa 6.2 MPa 8.4 MPa 10.6 MPa 12.8 MPa 10 2

15.0 MPa 17.2 MPa 19.4 MPa 21.6 MPa 24.0 MPa 10 3

20 10 10 4

10 5 Time t (h)

Fig. 3.3-29 Poly(acrylonitrile-co-styrene-co-acrylester), ASA: creep modulus versus time

0

0

1

2

3

4

5 6 Strain ε (%)

Fig. 3.3-30 Poly(vinyl chloride), PVC-U: stress versus

strain

Polymers

3.3 Tables and Figures

495

Table 3.3-10 Poly(vinyl chloride): unplasticized, PVC-U; plasticized (75/25), PVC-P1; plasticized (60/40), PVC-P2 PVC-U Melting temperature Tm

(◦ C)

PVC-P1

PVC-P2

0.9–1.8

0.9–1.8

≈ 80

175

Enthalpy of fusion ∆Hu (kJ/mol) (mu)

3.28

Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K))

0.85–0.9

Temperature coefficient dc p / dT (kJ/(kg K2 )) −18 to −19

Glass transition temperature Tg (◦ C)

85

≈ 80

Vicat softening temperature TV 50/50 (◦ C)

63–82

≈ 42

Thermal conductivity λ (W/(m K))

0.16

0.15

0.15

Density (g/cm3 )

1.38–1.4

1.24–1.28

1.15–1.20

7–8

18–22

23–25

Coefficient of thermal expansion α

(10−5 /K)

(linear)

Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa)

2.7–3.0

Shear modulus G (GPa)

0.12

2.9–37 0.07

Poisson’s ratio µ Stress at yield σy (MPa)

50–60

Strain at yield εy (%)

4–6

Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa)

40–80

10–25

10–25

Strain at fracture εb (%)

10–50

170–400

170–400

Impact strength (Charpy) (kJ/m2 )

13–25

Notched impact strength (Charpy) (kJ/m2 )

3–5

Sound velocity vs (m/s) (longitudinal)

2330

Sound velocity vs (m/s) (transverse)

1070

Shore hardness D

74–94

Volume resistivity ρe (Ω m)

> 1013

1012

1011

Surface resistivity σe (Ω)

1014

1011

1010

Electric strength E B (kV/mm)

20–40

30–35

≈ 25

Relative permittivity εr (100 Hz)

3.5

4–5

6–7

Dielectric loss tan δ (10−4 ) (100 Hz)

110–140

0.05–0.07

0.08–0.1

Refractive index n D (589 nm)

1.52–1.54 20

20

2126

Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) (100 µm) Gas permeation

(cm3 /(m2 d bar))

(100 µm)

2.5 2.7–3.8 (N2 )

350 (N2 )

350 (N2 )

33–45 (O2 )

1500 (O2 )

1500 (O2 )

120– 160 (CO2 )

8500 (CO2 )

8500 (CO2 )

550 (air)

550 (air)

28 (air) Melt viscosity–molar-mass relation Viscosity–molar-mass relation

[η] = 14.5 × 10−3 M 0.851 (PVC-U, THF, 25 ◦ C)

Part 3 3.3

Enthalpy of combustion ∆Hc (kJ/g)

496

Part 3

Classes of Materials

Table 3.3-11 Poly(vinyl chloride), PVC-U: heat capacity and thermal conductivity Temperature T (◦ C)

−150

−100

−50

0

20

Heat capacity c p (kJ/(kg K))

0.47

0.61

0.75

0.92

Thermal conductivity λ (W/(m K))

0.13

0.15

0.15

0.16

Viscosity η (Pa s) 180 ˚C 190 ˚C 200 ˚C 103

Part 3 3.3 102

102

103 Shear rate dγ /dt (s–1) 104

Fig. 3.3-31 Poly(vinyl chloride), PVC-U: viscosity versus

50

0.16

100

1.04

1.53

0.17

0.17

protective clothes, cable insulation, fittings, leads, films, artificial leathers.

3.3.3.3 Fluoropolymers Polytetrafluoroethylene, PTFE. Applications: molded articles, foils, flexible tubing, coatings, jackets, sealings, bellows, flasks, machine parts, semifinished goods, printed networks. Polychlorotrifluoroethylene, PCTFE. Applications: fittings, flexible tubing, membranes, printed networks, bobbins, insulating foils, packings. Poly(tetrafluoroethylene-co-hexafluoropropylene), FEP. Applications: cable insulation, coatings, coverings, printed networks, injection-molded parts, packaging foils, impregnations, heat-sealing adhesives.

shear rate Table 3.3-12 Polytetrafluoroethylene, PTFE; polychlorotrifluoroethylene, PCTFE; poly(tetrafluoroethylene-co-hexafluoro-propylene), FEP; poly(ethylene-co-tetrafluoroethylene), ETFE; poly(ethylene-co-chlorotrifluoroethylene), ECTFE

Melting temperature Tm

(◦ C)

PTFE

PCTFE

FEP

ETFE

ECTFE

325–335

210–215

255–285

265–270

240

1.2

24.3

0.9

1.12

Enthalpy of fusion ∆Hu (kJ/kg) Entropy of fusion ∆Su (J/(kg K)) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 ))

1.0

0.9

Enthalpy of combustion ∆Hc (kJ/g)

−5.1

Glass transition temperature Tg (◦ C)

127

Vicat softening temperature TV 50/50 (◦ C)

110

Thermal conductivity λ (W/(m K))

0.25

0.22

0.25

0.23

Density (g/cm3 )

2.13–2.23

2.07–2.12

2.12–2.18

1.67–1.75

1.68–1.70

Coefficient of thermal expansion α (10−5 /K) (linear)

11–18

6–7

8 –12

7–10

7–8

0.40–0.75

1.30–1.50

0.40–0.70

0.8–1.1

1.4–1.7

134

Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ Stress at yield σy (MPa) Strain at yield εy (%)

11.7

25–35 15–20

Polymers

3.3 Tables and Figures

497

Table 3.3-12 Polytetrafluoroethylene, PTFE; polychlorotrifluoroethylene, PCTFE; . . . , cont. PTFE

PCTFE

FEP

ETFE

ECTFE

Stress at fracture σb (MPa)

25–36

32–40

22–28

35–54

Strain at fracture εb (%)

350–550

120–175

250–330

400–500

Stress at 50% elongation σ50 (MPa)

Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy) (kJ/m2 ) 1410

Sound velocity vs (m/s) (transverse)

730

Shore hardness D

50–60

78

55–58

67–75

Volume resistivity ρe (Ω m)

> 1016

> 1016

> 1016

> 1014

> 1013

Surface resistivity σe (Ω)

> 1016

> 1016

> 1016

> 1014

1012

Electric strength E B (kV/mm)

48

55

55

40

Relative permittivity εr (100 Hz)

2.1

2.5–2.7

2.1

2.6

2.3–2.6 10–15

Dielectric loss tan δ

(10−4 )

0.5–0.7

90–140

0.5–0.7

5–6

Refractive index n D (589 nm) Temperature coefficient dn D / dT (10−5 /K)

1.35

1.43

1.344

1.403

Steam permeation (g/(m2 d))

0.03 (300 µm)

0.4–0.9 (25 µm)

0.6 (25 µm)

9 (25 µm)

60–80 (N2 ) 160– 250 (O2 ) 450– 700 (CO2 ) 80– 100 (air)

39 (N2 ) 110– 230 (O2 ) 250– 620 (CO2 )

470 (N2 ) 1560 (O2 ) 3800 (CO2 )

150 (N2 ) 39 (O2 ) 1700 (CO2 )

Gas permeation

(cm3 /(m2

(100 Hz)

d bar))

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

Table 3.3-13 Polytetrafluoroethylene, PTFE: heat capacity, thermal conductivity, and coefficient of thermal expansion Temperature T (◦ C)

−200

−150

−100

−50

Heat capacity c p (kJ/(kg K)) Thermal conductivity λ (W/(m K)) Coefficient of thermal expansion α (10−5 /K) (linear)

3.4

0

150

1.06

1.10

1.15

0.25

0.25

0.26

0.26

0.26

0.25

4.5

7.0

9.5

Poly(methyl methacrylate), PMMA. Applications: extruded articles, injection-molded parts, injection blow-

100

1.0

0.24

3.3.3.4 Polyacrylics and Polyacetals

50

0.96

0.23

Poly(ethylene-co-tetrafluoroethylene), ETFE. Applications: gear wheels, pump parts, packaging, laboratory articles, coverings, cable insulation, blown films. Poly(ethylene-co-chlorotrifluoroethylene), ECTFE. Applications: cable coverings, coverings, molded articles, packaging, printed networks, foils, fibers.

20

0.8

11.6

11.9

13.1

16.7

200

250

1.23

22.2

30.5

molded parts, houseware, medical devices, sanitary ware, automotive components, lighting, tubes, sheets, profiles, covers, panels, fiber optics, optical lenses, displays, disks, cards. Poly(oxymethylene), POM-H. Applications: molded parts, extruded parts, gears, bearings, snap-fits, fuel system components, cable ties, automotive components, seatbelt parts, pillar loops, tubes, panels. Poly(oxymethylene-co-ethylene), POM-R. Applications: extruded articles, injection-molded articles, gear wheels, bushes, bearings, rollers, guide rails, tubing, films, clips, zippers, boards, pipes.

Part 3 3.3

Sound velocity vs (m/s) (longitudinal)

498

Part 3

Classes of Materials

Table 3.3-14 Poly(methyl methacrylate), PMMA; poly(oxymethylene), POM-H; poly(oxymethylene-co-ethylene),

POM-R Melting temperature Tm (K)

PMMA

POM-H

POM-R

175

175

164–172

Enthalpy of fusion ∆Hu (kJ/kg)

222

211

Entropy of fusion ∆Su (J/(kg K))

1.49

1.44

Part 3 3.3

Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 ))

1.255

1.46

1.47

Enthalpy of combustion ∆Hc (kJ/g)

−26.2

−16.7

−17

Glass transition temperature Tg (◦ C)

104–105

25

Vicat softening temperature TV 50/50 (◦ C)

85–110

160–170

151–162

Thermal conductivity λ (W/(m K))

0.193

0.25–0.30

0.31

Density (g/cm3 )

1.17–1.19

1.40–1.42

1.39–1.41

Coefficient of thermal expansion α (10−5 /K) (linear)

7–8

11–12

10–11

Compressibility κ

(10−4 /MPa)

2.45

1.5

Elastic modulus E (GPa)

(cubic)

3.1–3.3

3.0–3.2

Shear modulus G (GPa)

1.7

0.7–1.0

50–77

60–75

65–73

8–25

8–12 59

2.8–3.2

Poisson’s ratio µ Stress at yield σy (MPa) Strain at yield εy (%) Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa)

60–75

62–70

Strain at fracture εb (%)

2–6

25–70

18–23

180

Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy)

(kJ/m2 )

2

9

Sound velocity vs (m/s) (longitudinal)

2690

2440

Sound velocity vs (m/s) (transverse)

1340

1000

Shore hardness D

85

80

Volume resistivity ρe (Ω m)

> 1013

> 1013

> 1013

Surface resistivity σe (Ω)

> 1013

> 1014

> 1013

Electric strength E B (kV/mm)

30

25–35

35

Relative permittivity εr (100 Hz)

3.5–3.8

3.5–3.8

3.6–4

Dielectric loss tan δ (10−4 ) (100 Hz)

500–600

30–50

30–50

Refractive index n D (589 nm) Temperature coefficient dn D / dT (10−4 /K)

1.492 − 1.2

1.49

Steam permeation (g/(m2 d)) (80 µm)

12

12

Gas permeation (cm3 /(m2 d bar))

2500 (N2 ) 1000 (O2 ) 5200 (CO2 )

5 (N2 ) 24 (O2 ) 470 (CO2 ) 8 (air)

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

[η] = 10.4 × 10−3 M 0.70 (PMMA, THF, 25 ◦ C) [η] = 11.3 × 10−3 M 0.76 (POM-H, Phenol, 90 ◦ C)

6.5

Polymers

3.3 Tables and Figures

499

Table 3.3-15 Poly(methyl methacrylate), PMMA: heat capacity, thermal conductivity, and coefficient of thermal expan-

sion Temperature T (◦ C) Heat capacity c p (kJ/(kg K)) Thermal conductivity λ (W/(m K)) Coefficient of thermal expansion α (10−5 /K) (linear)

100

−200

−150 0.67

−100 0.90

−50 1.06

0 1.26

20 1.26

50 1.42

100 1.85

0.16

0.18

0.19

0.19

0.19

0.19

0.20

3.0

3.7

4.5

5.7

6.9

7.5

Stress σ (MPa)

12.0

150

200

0.19

0.18

18.4

Viscosity η (Pa s) 10 B

200 ˚C 220 ˚C 240 ˚C

4

B B

10 3

40 10 2 20 0 0

1

2

3

4 Strain ε (%)

Fig. 3.3-32 Poly(methyl methacrylate), PMMA: stress ver-

sus strain

10 1

10 2

10 3 10 4 Shear rate dγ /dt (s–1)

Fig. 3.3-33 Poly(methyl methacrylate), PMMA: viscosity versus shear rate

80

2500

1500 0 10

10 0

Stress σ (MPa)

Creep modulus Etc (MPa)

2000

10 1 10 –1

60

40

2 MPa 4 MPa 8 MPa 12 MPa 16 MPa 20 MPa 24 MPa 10 1

– 20 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 120 ˚C

20

10 2

10 3

10 4 Time t (h)

Fig. 3.3-34 Poly(methyl methacrylate), PMMA: creep modulus versus time, at 23 ◦ C

0

0

5

10

15

20

25 Strain ε (%)

Fig. 3.3-35 Poly(oxymethylene), POM-H: stress versus

strain

Part 3 3.3

B = break point 0 ˚C –10 ˚C 80 23 ˚C 40 ˚C 60 ˚C 60

500

Part 3

Classes of Materials

Table 3.3-16 Poly(oxymethylene), POM-H: heat capacity, thermal conductivity, and coefficient of thermal expansion Temperature T (◦ C) Heat capacity c p (kJ/(kg K)) Thermal conductivity λ (W/(m K)) Coefficient of thermal expansion α (10−5 /K) (linear)

−200 0.47

−150 0.65

−100 0.82

−50 1.08

0 1.27

0.47

0.45

0.43

0.42

20

50 1.46

100 1.85

150

200

0.41

9.0

9.5

10.0

16.5

41.0

23.0

Stress σ (MPa) 100

Viscosity η (Pa s) 103 195 ˚C 215 ˚C 235 ˚C

8×102

Part 3 3.3

6×102

Y Y

80

Y

4×102

Y

60

Y

– 40 ˚C – 20 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 80 ˚C 100 ˚C

Y

40

Y Y

2×102 20

10 3

10 4 –1 Shear rate dγ /dt (s )

Fig. 3.3-36 Poly(oxymethylene), POM-H: viscosity versus shear rate Viscosity η (Pa s) 103

Y = yield point

0 0

2

4

6

8

10 12 Strain ε (%)

Fig. 3.3-37 Poly(oxymethylene-co-ethylene), POM-R:

stress versus strain 3000

Creep modulus Etc (MPa)

180 ˚C 200 ˚C 220 ˚C

18 MPa 21 MPa 24 MPa 27 MPa 30 MPa

3 MPa 6 MPa 9 MPa 12 MPa 15 MPa 2000

102 1000

102

103

104 Shear rate dγ /dt (s–1)

Fig. 3.3-38 Poly(oxymethylene-co-ethylene),

viscosity versus shear rate

POM-R:

10 0

10 1

10 2

10 3

10 4 Time t (h)

Fig. 3.3-39 Poly(oxymethylene-co-ethylene), POM-R: creep modulus versus time at 23 ◦ C

Polymers

3.3.3.5 Polyamides Polyamide 6, PA6; polyamide 66, PA66; polyamide 11, PA11; polyamide 12, PA12; polyamide 610, PA610. Ap-

3.3 Tables and Figures

501

plications: technical parts, bearings, gear wheels, rollers, screws, gaskets, fittings, coverings, housings, automotive parts,houseware,semifinishedgoods,sportsgoods,membranes, foils, packings, blow-molded parts, fibers, tanks.

Table 3.3-17 Polyamide 6, PA6; polyamide 66, PA66; polyamide 11, PA11; polyamide 12, PA12; polyamide 610, PA610 PA6

PA66

PA11

PA12

PA610

220–225

255–260

185

175–180

210–220

Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 ))

1.7

1.7

1.26

1.26

1.7

Enthalpy of combustion ∆Hc (kJ/g)

−31.4

−31.4

Glass transition temperature Tg (◦ C)

55

80

50

50

55–60

Vicat softening temperature TV 50/50 (◦ C)

180–220

195–220

180–190

140–160

205–215

Thermal conductivity λ (W/(m K))

0.29

0.23

0.23

0.23

0.23

Density (g/cm3 )

1.12–1.14

1.13–1.15

1.04

1.01–1.03

1.06–1.09

Coefficient of thermal expansion α (10−5 /K) (linear)

7–10

7–10

13

10–12

8–10

Elastic modulus E (GPa)

2.6–3.2

2.7–3.3

1.0

1.3–1.6

2.0–2.4

Shear modulus G (GPa)

1.1–1.5

1.3–1.7

0.4–0.5

0.5

0.8

Stress at yield σy (MPa)

70–90

75–100

45–60

60–70

Strain at yield εy (%)

4–5

4.5–5

4–5

4

Stress at fracture σb (MPa)

70–85

77–84

56

56–65

40

Strain at fracture εb (%)

200–300

150–300

500

300

500

Notched impact strength (Charpy) (kJ/m2 )

3–6

2–3

Sound velocity vs (m/s) (longitudinal)

2700

2710

Sound velocity vs (m/s) (transverse)

1120

1120

Shore hardness D

72

75

Volume resistivity ρe (Ω m)

> 1013

> 1012

1011

> 1013

> 1013

Surface resistivity σe (Ω)

> 1012

> 1010

1011

> 1013

> 1012

Electric strength E B (kV/mm)

30

25–35

42.5

27–29

Relative permittivity εr (100 Hz)

3.5–4.2

3.2–4

3.7

3.7–4

3.5

Dielectric loss tan δ tan δ (10−4 ) (100 Hz)

60–150

50–150

600

300–700

70–150

Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K)

1.52–1.53

1.52–1.53

1.52–1.53

1.52–1.53

1.53

Steam permeation (g/(m2 d)) (100 µm)

10–20

10–20

2.4–4

2.4–4

Gas permeation (cm3 /(m2 d bar)) (100 µm)

1–2 (N2 ) 2–8 (O2 ) 80– 120 (CO2 )

1–2 (N2 ) 2–8 (O2 ) 80– 120 (CO2 )

0.5–0.7 (N2 ) 2–3.5 (O2 ) 6–13 (CO)

0.5–0.7 (N2 ) 2–3.5 (O2 ) 6–13 (CO)

Melting temperature Tm (◦ C) Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu)

Poisson’s ratio µ

Stress at 50% elongation σ50 (MPa)

Impact strength (Charpy) (kJ/m2 )

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

4–10

Part 3 3.3

Compressibility κ (1/MPa) (cubic)

502

Part 3

Classes of Materials

Table 3.3-18 Polyamide 6, PA6; polyamide 66, PA66; polyamide 610, PA610: heat capacity, thermal conductivity, and coefficient of thermal expansion Temperature T (◦ C)

−200

Heat capacity c p (kJ/(kg K)), PA

−150

0.47

−100

−50

0

20

50

100

150

200

0.73

0.93

1.15

1.38

1.68

2.15

2.60

Thermal conductivity λ (W/(m K)), PA6

0.29

0.31

0.32

0.32

0.29

0.27

0.25

Thermal conductivity λ (W/(m K)), PA66

0.32

0.33

0.33

0.33

0.33

Thermal conductivity λ (W/(m K)), PA610

0.31

0.32

0.33

0.33

0.32

5.0

6.6

8.0

Part 3 3.3

Coefficient of thermal expansion α (10−5 /K) (linear), PA6

40

Stress σ (MPa)

30

800

20

600

10

400

0

1

2

3

4 5 Strain ε (%)

Fig. 3.3-40 Polyamide 6, PA6: stress versus strain Stress σ (MPa) 50 23 ˚C

200 0 10

15.1

14.0

34.6

6 MPa 7 MPa 8 MPa 9 MPa 11 MPa

1 MPa 2 MPa 3 MPa 4 MPa 5 MPa

10 1

10 2

10 3

10 4 Time t (h)

Fig. 3.3-41 Polyamide 6, PA6: creep modulus versus time Creep modulus Etc (MPa) 1200

40

1000

30

800

20

600

2 MPa 4 MPa 6 MPa 8 MPa 10 MPa

12 MPa 14 MPa 16 MPa 18 MPa 20 MPa

400

10

0 0

40.1

Creep modulus Etc (MPa) 1000

23 ˚C 40 ˚C 60 ˚C

0

9.1

0.31

200 0 10 1

2

3

4

5 6 Strain ε (%)

Fig. 3.3-42 Polyamide 66, PA66: stress versus strain

10 1

10 2

10 3 10 4 Time t (h)

Fig. 3.3-43 Polyamide 66, PA66: creep modulus versus

time

3.3 Tables and Figures

Polymers

3.3.3.6 Polyesters Polycarbonate, PC. Applications: injection-molded parts, extruded parts, disks, lamp housings, electronic articles, optical articles, houseware, foils. Poly(ethylene terephthalate), PET. Applications: bearings, gear wheels, shafts, couplings, foils, ribbons, flexible tubing, fibers.

Poly(butylene terephthalate), PBT. Applications: bearings, valve parts, screws, plugs, housings, wheels, houseware.

Viscosity η (Pa s) 10 3

Stress σ (MPa)

60 10 2 40

– 20 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 90 ˚C 120 ˚C

20

0

2

4

6

10 1 10 1

8 Strain ε (%)

10 2

10 3

10 4 10 5 Shear rate dγ /dt (s–1)

Fig. 3.3-45 Polycarbonate, PC: viscosity versus shear rate

Fig. 3.3-44 Polycarbonate, PC: stress versus strain 70

Creep modulus Etc (MPa)

Stress σ (MPa) 23 ˚C

60 2000 50 40

1500

30 1000

500 0 10

5 MPa 10 MPa 15 MPa 20 MPa 25 MPa 30 MPa 35 MPa 10 1

20 10 0 10 2

10 3

10 4 Time t (h)

0

1

2

3

4 Strain ε (%)

Fig. 3.3-47 Poly(ethylene terephthalate), PET: stress ver-

Fig. 3.3-46 Polycarbonate, PC: creep modulus versus time

sus strain

Table 3.3-19 Polycarbonate, PC: heat capacity and thermal conductivity Temperature T (◦ C) Heat capacity c p (kJ/(kg K)) Thermal conductivity λ (W/(m K))

−200 0.34

−150

−100

−50

0

0.50

0.70

0.90

1.10

0.17

0.19

0.21

0.23

20 1.17

50

100

150

1.30

1.50

1.70

0.24

0.24

0.24

Part 3 3.3

280 ˚C 300 ˚C 320 ˚C

80

0

503

504

Part 3

Classes of Materials

Table 3.3-20 Polycarbonate, PC; poly(ethylene terephthalate), PET; poly(butylene terephthalate), PBT; poly(phenylene

ether), PPE Melting temperature Tm

(◦ C)

PC

PET

PBT

PPE

Part 3 3.3

220–260

250– 260 (pcr)

220–225

Enthalpy of fusion ∆Hu (kJ/mol) (mu)

8.682 (iso), 8.577 (syn)

2.69

54 kJ/kg

Entropy of fusion ∆Su (J/(K mol)) (mu)

16.8 (iso), 15.3 (syn)

48.6

Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 ))

1.17 4.04 × 10−3

1.223

Enthalpy of combustion ∆Hc (kJ/g)

−30.7

−21.6

Glass transition temperature Tg (◦ C)

150

98

60

110–150

Vicat softening temperature TV 50/50 (◦ C)

83

79

165–180

105–132

Thermal conductivity λ (W/(m K))

0.21

0.11

0.21

0.17–0.22

Density (g/cm3 )

1.2 1.38–1.40 (pcr)

1.33–1.35 (am)

1.30–1.32

1.04–1.10

Coefficient of thermal expansion α (10−5 /K) (linear)

6.5–7

8 (am), 7(pcr)

8–10

8–9

Compressibility κ (1/MPa) (cubic)

2.2 × 10−4

6.99 × 10−6 (melt)

Elastic modulus E (GPa)

2.3–2.4

2.1–2.4 (am) 2.8–3.1 (pcr)

2.5–2.8

2.0–3.1

Shear modulus G (GPa)

0.72

1.2

1.0

Poisson’s ratio µ

1.35

0.38

Stress at yield σy (MPa)

55–65

55 (am), 60–80 (pcr)

50–60

45–70

Strain at yield εy (%)

6 –7

4 (am), 5–7 (pcr)

3.5–7

3–6

Stress at fracture σb (MPa)

69–72

30–55

52

35–55

Strain at fracture εb (%)

120–125

1.5–3

Stress at 50% elongation σ50 (MPa) 15–40

Impact strength (Charpy) (kJ/m2 )

13–25

Notched impact strength (Charpy) (kJ/m2 )

3–5

6–16 2220

Sound velocity vs (m/s) (longitudinal)

2220

2400

Sound velocity vs (m/s) (transverse)

909

1150

Shore hardness D

1000 80

Volume resistivity ρe (Ω m)

> 1014

> 1013

> 1013

1014 − 1015

Surface resistivity σe (Ω)

> 1014

> 1014

> 1014

1016 − 1017

Electric strength E B (kV/mm)

30–75

42

42

25–35

Relative permittivity εr (100 Hz)

2.8–3.2

3.4–3.6

3.3–4.0

2.6–2.9

Dielectric loss tan δ (10−4 ) (100 Hz)

7 –20

20

15–20

10–40

Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K)

1.58–1.59 −1.42 × 10−4

1.57–1.64

1.58

Steam permeation (g/(m2 d))

4

4.5–5.5, 0.6 (str)

Gas permeation (cm3 /(m2 d bar))

680 (N2 ), 4000 (O2 ) 14 500 (CO2 )

6.6 (N2 ), 30 (O2 ) 140 (CO2 ), 12 (air) 9–15 (str, N2 ) 80–110 (str, O2 ) 200–340 (str, CO2 )

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

[η] = 4.25 × 10−3 M 0.69 (PET)

Polymers

1.2 × 103

Viscosity η (Pa s)

3.3 Tables and Figures

Stress σ (MPa) 280 ˚C

10 3

80

8 × 102

60

6 × 102

40

10 0

10 1

10 2 10 3 Shear rate dγ /dt (s–1)

0

0

2

4

6 Strain ε (%)

Fig. 3.3-48 Poly(ethylene terephthalate), PET: viscosity

Fig. 3.3-49 Poly(butylene terephthalate), PBT: stress ver-

versus shear rate

sus strain Viscosity η (Pa s) Creep modulus Etc (MPa) 2500

250 ˚C 260 ˚C 270 ˚C

5 MPa 10 MPa 15 MPa 20 MPa 25 MPa

2000

10 2 1500 1000 500 10 1 1 10

10

2

10

3

4

10 10 Shear rate dγ /dt (s–1)

5

0

10 0

10 1

10 2

Fig. 3.3-50 Poly(butylene terephthalate), PBT: viscosity

10 3

10 4 Time t (h)

Fig. 3.3-51 Poly(butylene terephthalate), PBT: creep mod-

versus shear rate

ulus versus time Stress σ (MPa) 80

Viscosity η (Pa s) 280 ˚C 300 ˚C 320 ˚C

10 3 60

40

– 20 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 80 ˚C 100 ˚C 120 ˚C

20

0 0

1

2

3

4 5 Strain ε (%)

10 2

10 2

10 3

4 Shear rate dγ /dt (s–1)10

Fig. 3.3-52 Poly(phenylene ether), PPE: stress versus

Fig. 3.3-53 Poly(phenylene ether), PPE: viscosity versus

strain

shear rate

Part 3 3.3

– 20 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 80 ˚C

20 4 × 102 –1 10

505

506

Part 3

Classes of Materials

3.3.3.7 Polysulfones and Polysulfides

Creep modulus Etc (MPa) 2500

Polysulfone, PSU; Poly(ether sulfone), PES. Applications: injection-molded parts, coatings, electronic articles, printed circuits, houseware, medical devices, membranes, lenses, optical devices. Poly(phenylene sulfide), PPS. Applications: injection-molded parts, sintered parts, foils, fibers, housings, sockets, foams.

2000 1500 10.5 MPa 7 MPa 14 MPa 3.5 MPa 17.5 MPa 21 MPa 24.5 MPa 28 MPa

1000 500

Part 3 3.3

0 10 0

10 1

10 2

10 3

10 4 Time t (h)

Fig. 3.3-54 Poly(phenylene ether), PPE: creep modulus

versus time

Stress σ (MPa) Y

100

Stress σ (MPa) Y

Y Y

80

Y

60

Y

Y

60

Y Y

0 ˚C 23 ˚C 40 ˚C 60 ˚C 80 ˚C 100 ˚C 120 ˚C 140 ˚C 160 ˚C

20 Y = yield point 1

2

3

Y – 40 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 80 ˚C 100 ˚C 120 ˚C 140 ˚C 160 ˚C

Y

Y

0 0

Y

Y

Y 40

Y

Y

4

5 Strain ε (%)

Fig. 3.3-55 Polysulfone, PSU: stress versus strain

40

B

20 0 0

Y = yield point B = break point 1

2

3

4

5

6

7

8 9 Strain ε (%)

Fig. 3.3-57 Poly(ether sulfone), PES: stress versus strain Creep modulus Etc (MPa) 3000

Creep modulus Etc (MPa) 2500

2300 2200

2000 2100 2000 1900 1800 1700 1 10

1500 10 MPa 13.3 MPa 16.6 MPa 19.9 MPa 23.2 MPa 10 2

26.5 MPa 29.8 MPa 33.1 MPa 36.4 MPa 40 MPa 10 3

1000 10 1 10 4

10 5 Time t (h)

Fig. 3.3-56 Polysulfone, PSU: creep modulus versus time

10 MPa 14.4 MPa 18.8 MPa 23.2 MPa 27.6 MPa 10 2

32.0 MPa 36.4 MPa 40.8 MPa 45.2 MPa 50.0 MPa 10 3

10 4

10 5 Time t (h)

Fig. 3.3-58 Poly(ether sulfone), PES: creep modulus ver-

sus time

Polymers

3.3 Tables and Figures

507

Table 3.3-21 Polysulfone, PSU; poly(phenylene sulfide), PPS; poly(ether sulfone), PES PSU Melting temperature Tm

(◦ C)

PPS

PES

285

Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K))

1.30

1.10

Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g)

17

Glass transition temperature Tg (◦ C)

190

85

225

Vicat softening temperature TV 50/50 (◦ C)

175–210

200

215–225

Thermal conductivity λ (W/(m K))

0.28

0.25

0.18

Density (g/cm3 )

1.24–1.25

1.34

1.36–1.37

Coefficient of thermal expansion

5.5–6

5.5

5–5.5

2.5–2.7

3.4

2.6–2.8

36

Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ Stress at yield σy (MPa)

70–80

80–90

Strain at yield εy (%)

5.5–6

5.5–6.5

Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa)

50–100

75

85

Strain at fracture εb (%)

25–30

3

30–80

Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal)

2260

Sound velocity vs (m/s) (transverse)

920

2260

Shore hardness D Volume resistivity ρe (Ω m)

> 1013

Surface resistivity σe (Ω)

> 1015

Electric strength E B (kV/mm)

20–30

59.5

20–30

Relative permittivity εr (100 Hz)

3.2

3.1

3.5–3.7

8–10

4

10–20

Dielectric loss tan δ

(10−4 )

(100 Hz)

Refractive index n D (589 nm)

1.63

Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) (25 µm) Gas permeation (cm3 /(m2 d bar)) (25 µm)

6 630 (N2 ) 3600 (O2 ) 15 000 (CO2 )

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

> 1013

1013 > 1013

1.65

Part 3 3.3

α (10−5 /K) (linear)

508

Part 3

Classes of Materials

3.3.3.8 Polyimides and Polyether Ketones Poly(amide imide), PAI. Applications: constructional parts, wheels, rotors, bearings, housings, slip fittings, lacquers.

Poly(ether imide), PEI. Applications: electrical housings, sockets, microwave parts, bearings, gear wheels, automotive parts. Polyimide, PI. Applications: foils, semifinished goods, sintered parts.

Table 3.3-22 Poly(amide imide), PAI; poly(ether imide), PEI; polyimide, PI; poly(ether ether ketone), PEEK PAI

Part 3 3.3

Melting temperature Tm (◦ C) Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg (◦ C) Vicat softening temperature TV 50/50 (◦ C) Thermal conductivity λ (W/(m K)) Density (g/cm3 ) Coefficient of thermal expansion α (10−5 /K) (linear) Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ Stress at yield σy (MPa) Strain at yield εy (%) Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa) Strain at fracture εb (%) Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D Volume resistivity ρe (Ω m) Surface resistivity σe (Ω) Electric strength E B (kV/mm) Relative permittivity εr (100 Hz) Dielectric loss tan δ (10−4 ) (100 Hz) Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) (25 µm) Gas permeation (cm3 /(m2 d bar)) (25 µm)

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

PEI

PI

PEEK

335–345

1.1

240–275

250–270 260 0.29–0.35 1.43 5–6

145

0.26 1.38–1.40 3.0–3.5

215 220 0.22 1.27 5.5–6.0

4.5–4.7

2.9–3.0

3.0–3.2

4.7

0.25 1.32 4.7

0.41 5 150–160 7–8

105 60

75–100 88

100 50

1015 > 1016 25 3.5–4.2 10

1016 > 1016 25 3.2–3.5 10–15

> 1014 > 1015 200 3.4 52

1014

1.66 25 94 (N2 ) 390 (O2 ) 700 (CO2 )

3.2 30

3.3 Tables and Figures

Polymers

Viscosity η (Pa s)

509

Stress σ (MPa) 355 ˚C 375 ˚C 395 ˚C

10 3

140 120 100 80 60

10 2

20

10 2

10 3

10 4 Shear rate dγ /dt (s–1)

Fig. 3.3-59 Poly(ether imide), PEI: viscosity versus shear

0

0

2

4

6

8 Strain ε (%)

Fig. 3.3-60 Poly(ether imide), PEI: stress versus strain

rate

Poly(ether ether ketone), PEEK. Applications: injection-molded parts, automotive parts, aircraft parts, electronic parts, cable insulation, foils, fibers, tapes, plates.

Creep modulus Etc (MPa) 3000

3.3.3.9 Cellulose

2500

2000

33 MPa 38.5 MPa 44 MPa 49.5 MPa

5.5 MPa 11 MPa 16.5 MPa 22 MPa 27.5 MPa

10 0

10 1

10 2

10 3

10 4 Time t (h)

Fig. 3.3-61 Poly(ether imide), PEI: creep modulus versus

time

Cellulose acetate, CA. Applications: tool handles, pens, combs, buckles, buttons, electronic parts, spectacles, hollow fibers, fibers, foils, lacquers, resin adhesives, sheet molding compounds (SMCs), bulk molding compounds (BMCs). Cellulose propionate, CP. Applications: fibers, foils, lacquers, resin adhesives, sheet molding compounds, bulk molding compounds (BMC), spectacles, houseware goods, boxes.

Table 3.3-23 Cellulose acetate, CA; cellulose propionate, CP; cellulose acetobutyrate, CAB; ethylcellulose, EC; vulcan-

ized fiber, VF

Melting temperature Tm

CA

CP

CAB

1.6

1.7

1.6

77–110

70–100

65–100

(◦ C)

Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg (◦ C) Vicat softening temperature TV 50/50 (◦ C)

EC

VF

Part 3 3.3

– 40 ˚C 0 ˚C 23 ˚C 100 ˚C 120 ˚C 180 ˚C

40

510

Part 3

Classes of Materials

Table 3.3-23 Cellulose acetate, CA; cellulose propionate, CP; cellulose acetobutyrate, CAB; . . . , cont. CA

CP

CAB

EC

VF

Thermal conductivity λ (W/(m K))

0.22

0.21

0.21

Density (g/cm3 )

1.26–1.32

1.17–1.24

1.16–1.22

1.12–1.15

1.1–1.45

Coefficient of thermal expansion

10–12

11–15

10–15

10

1.0–3.0

1.0–2.4

0.8–2.3

1.2–1.3

0.75

0.85

α (10−5 /K) (linear) Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ

Part 3 3.3

Stress at yield σy (MPa)

25–55

20–50

20–55

Strain at yield εy (%)

2.5–4

3.5–4.5

3.5–5

Stress at fracture σb (MPa)

38

14–55

26

Strain at fracture εb (%)

3

30–100

4

Volume resistivity ρe (Ω m)

1010 – 1014

1010 –1014

1010 –1014

1011 – 1013

Surface resistivity σe (Ω)

1010 – 1014

1012 –1014

1012 –1014

1011 – 1013

Electric strength E B (kV/mm)

25–35

30–35

32–35

≈ 30

Relative permittivity εr (100 Hz)

5–6

4.0–4.2

3.7–4.2

≈4

Dielectric loss tan δ (10−4 ) (100 Hz)

70–100

50

50–70

100

Refractive index n D (589 nm)

1.47–1.50

1.47–1.48

1.48

35–40

Stress at 50% elongation σ50 (MPa) 85–100

Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D

Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) (25 µm) Gas permeation

(cm3 /(m2

d bar)) (25 µm)

150–600

460–600

470– 630 (N2 )

3800 (N2 )

13 000– 15 000 (O2 )

15 000 (O2 )

14 000 (CO2 )

94 000 (CO2 )

1800–2300 (air) Melt viscosity–molar-mass relation Viscosity–molar-mass relation

Cellulose acetobutyrate, CAB. Applications: fibers, foils, lacquers, resin adhesives, sheet molding compounds, bulk molding compounds, automotive parts, switches, light housings, spectacles.

Ethylcellulose, EC. Applications: foils, injectionmolded parts, lacquers, adhesives. Vulcanized fiber, VF. Applications: gear wheels, abrasive wheels, case plates.

Polymers

3.3.3.10 Polyurethanes Polyurethane, PUR; thermoplastic polyurethane elastomer, TPU. Applications: blocks, plates, formed pieces, cavity forming, composites, coatings, impregnations,

3.3 Tables and Figures

511

films, foils, fibers, molded foam plastics, insulation boards, sandwich boards, installation boards, reaction injection molding (RIM), automotive parts, houseware goods, sports goods.

Table 3.3-24 Polyurethane, PUR; thermoplastic polyurethane elastomer, TPU PUR

TPU

1.76

0.5

Glass transition temperature Tg (K)

15–90

−40

Vicat softening temperature TV 50/50 (◦ C)

100–180

Thermal conductivity λ (W/(m K))

0.58

1.70

Density

1.05

1.1–1.25

1.0–2.0

15

4.0

0.015–0.7

Melting temperature Tm (◦ C) Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu)

Enthalpy of combustion ∆Hc (kJ/mol) (mu)

(g/cm3 )

Coefficient of thermal expansion α (10−5 /K) (linear) Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa)

0.006–0.23

Poisson’s ratio µ Stress at yield σy (MPa) Strain at yield εy (%) Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa)

70–80

30–50

Strain at fracture εb (%)

3 –6

300–500

Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal)

1550–1750

Sound velocity vs (m/s) (transverse) Shore hardness D

60–90

30–70

Volume resistivity ρe (Ω m)

1014

1010

Surface resistivity σe (Ω)

1014

1011

Electric strength E B (kV/mm)

24

30–60

Relative permittivity εr (100 Hz)

3.6

6.5

500

300

Dielectric loss tan δ

(10−4 )

(100 Hz)

Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) (25 µm)

13–25

Gas permeation (cm3 /(m2 d bar)) (25 µm)

550–1600 (N2 ) 1000–4500 (O2 ) 6000–22 000 (CO2 )

Melt viscosity–molar-mass relation Viscosity–molar-mass relation

Part 3 3.3

Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 ))

512

Part 3

Classes of Materials

Table 3.3-25 Polyurethane, PUR: thermal conductivity and coefficient of thermal expansion Temperature T (◦ C) −200 −150 Thermal conductivity λ (W/(m K)) 0.20 Average coefficient of thermal 9.9 12.7 expansion α∗ (10−5 /K) (linear)a  a α∗ (T ) = (1/(T − 20)) T T in ◦ C T =20 α (T ) dT,

−100 0.21 16.0

Viscosity η (Pa s) 10 3

60

235 ˚C 240 ˚C 245 ˚C

−50 0.22 26.0

0 0.21 20.0

20

50 0.20

100 0.20

Stress σ (MPa) B

50

Part 3 3.3

40

B

10 2

B

30 20 10

1

10 1

23 ˚C 80 ˚C 120 ˚C B = break point

10 10 2

10 3 10 4 Shear rate dγ /dt (s–1)

Fig. 3.3-62 Thermoplastic polyurethane elastomer, TPU: viscosity versus shear rate

3.3.3.11 Thermosets Phenol formaldehyde, PF; urea formaldehyde, UF; melamine formaldehyde, MF. Applications: molded pieces, granulated molding compounds (GMCs), bulk molding compounds, dough molding compounds

0 0.0

0.2

0.4

0.6

Fig. 3.3-63 Phenol formaldehyde, PF: stress versus strain

(DMCs), sheet molding compounds, plates, gear wheels, abrasive wheels, lacquers, coatings, chipboards, adhesives, foams, fibers. Unsaturated polyester, UP; diallyl phthalate, DAP. Applications: molding compounds, cast resins, electronic parts, automotive parts, containers, tools, houseware goods, sports goods.

Table 3.3-26 Phenol formaldehyde, PF; urea formaldehyde, UF; melamine formaldehyde, MF PF

UF

MF

1.30

1.20

1.20

Thermal conductivity λ (W/(m K))

0.35

0.40

0.50

Density (g/cm3 )

1.4

1.5

1.5

3–5

5 –6

5–6

Melting temperature Tm

(◦ C)

Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg (◦ C) Vicat softening temperature TV 50/50 (◦ C)

Coefficient of thermal expansion α

(10−5 /K)

(linear)

0.8 Strain ε (%)

Polymers

3.3 Tables and Figures

513

Table 3.3-26 Phenol formaldehyde, PF; urea formaldehyde, UF; melamine formaldehyde, MF, cont. PF

UF

MF

5.6–12

7.0–10.5

4.9–9.1

Stress at fracture σb (MPa)

25

30

30

Strain at fracture εb (%)

0.4–0.8

0.5–1.0

0.6–0.9

Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ Stress at yield σy (MPa) Strain at yield εy (%) Stress at 50% elongation σ50 (MPa)

Part 3 3.3

Impact strength (Charpy)

(kJ/m2 )

4.5–10

Notched impact strength (Charpy) (kJ/m2 )

1.5–3

Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D

82

Volume resistivity ρe (Ω m)

109

109

90 109

Surface resistivity σe (Ω)

> 108

> 1010

> 108

Electric strength E B (kV/mm)

30–40

30–40

29–30

Relative permittivity εr (100 Hz)

6

8

9

Dielectric loss tan δ (10−4 ) (100 Hz)

1000

400

600

Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K)

1.63

Steam permeation (g/(m2 d)) (40 µm)

43

400

Gas permeation (cm3 /(m2 d bar)) Melt viscosity–molar-mass relation Viscosity–molar-mass relation

Stress σ (MPa) B

80

Stress σ (MPa) 50

60

B

B

40 B

40

B 23 ˚C 80 ˚C 120 ˚C B = break point

20

0 0.0

30

B

0.5

1.0

1.5 Strain ε (%)

Fig. 3.3-64 Melamine formaldehyde, MF: stress versus

strain

20 23 ˚C 80 ˚C 120 ˚C B = break point

10 0 0.0

0.2

0.4

0.6 Strain ε (%)

Fig. 3.3-65 Unsaturated polyester, UP: stress versus strain

514

Part 3

Classes of Materials

Table 3.3-27 Unsaturated polyester, UP; diallyl phthalate, DAP; silicone resin, SI; epoxy resin, EP UP

DAP

SI

EP

0.8–0.9

0.8–1.0

Melting temperature Tm (◦ C) Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 ))

1.20

Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg (◦ C)

70–120

Vicat softening temperature TV 50/50 (◦ C)

Part 3 3.3

Thermal conductivity λ (W/(m K))

0.7

0.6

0.3–0.4

0.88

Density

2.0

1.51–1.78

1.8–1.9

1.9

2–4

1–3.5

2–5

1.1–3.5

14–20

9.8–15.5

6–12

21.5

Stress at fracture σb (MPa)

30

40–75

28–46

30–40

Strain at fracture εb (%)

0.6–1.2

(g/cm3 )

Coefficient of thermal expansion α (10−5 /K) (linear) Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ Stress at yield σy (MPa) Strain at yield εy (%) Stress at 50% elongation σ50 (MPa)

Impact strength (Charpy)

4

(kJ/m2 )

Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D

82

Volume resistivity ρe (Ω m)

> 1010

1011 –1014

1012

> 1012

Surface resistivity σe (Ω)

> 1010

1013

1012

> 1012

Electric strength E B (kV/mm)

25–53

40

20–40

30–40

Relative permittivity εr (100 Hz)

6

5.2

4

3.5–5

Dielectric loss tan δ (10−4 ) (100 Hz)

400

400

300

10

Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K)

1.54–1.58

1.47

Steam permeation (g/(m2 d)) Gas permeation (cm3 /(m2 d bar)) Melt viscosity–molar-mass relation Viscosity–molar-mass relation

Table 3.3-28 Unsaturated polyester, UP: coefficient of thermal expansion Temperature T (◦ C) Coefficient of thermal expansion α (10−5 /K) (linear)

−200 3.0

−150 4.1

−100 4.9

−50 5.8

0 7.3

20 8.4

50 10.7

100 15.0

Polymers

3.3 Tables and Figures

515

Table 3.3-29 Epoxy resin, EP: thermal conductivity and coefficient of thermal expansion Temperature T (◦ C)

−200

−150

−100

−50

Thermal conductivity λ (W/(m K)) Coefficient of thermal expansion α (10−5 /K) (linear)

1.8

2.8

3.8

4.9

0

20

50

100

150

0.20

0.20

0.20

0.20

6.1

6.2

6.3

7.5

13.0

Viscosity η (Pa s)

Stress σ (MPa) 80

B

260 ˚C 280 ˚C 300 ˚C

10 3

70 60

Part 3 3.3

B

50

10 2 40 30

B

20

23 ˚C 80 ˚C 120 ˚C B = break point

10 0 0.0

0.2

0.4

0.6

0.8 Strain ε (%)

Fig. 3.3-66 Epoxy resin, EP: stress versus strain

Silicone resin, SI. Applications: molding compounds, laminates. Epoxy resin EP, Applications: moulding compounds.

10 1 10 1

10 2

10 3

10 4 10 5 Shear rate dγ /dt (s–1)

Fig. 3.3-67 Poly(acrylonitrile-co-butadiene-co-styrene) +

polycarbonate, ABS + PC: viscosity versus shear rate Stress σ (MPa) 60

B B

3.3.3.12 Polymer Blends

B B

40

Polypropylene + ethylene/propylene/diene rubber, PP + EPDM. Applications: automotive parts, flexible tubes, sports goods, toys. Poly(acrylonitrile-co-butadiene-co-styrene) + polycarbonate, ABS + PC; Poly(acrylonitrile-co-butadieneco-acrylester) + polycarbonate ASA + PC; poly(acrylonitrile-co-butadiene-co-styrene) + polyamide, ABS + PA. Applications: semifinished goods, automotive parts, electronic parts, optical parts, houseware goods. Poly(vinyl chloride) + poly(vinyl chloride-coacrylate), PVC + VC/A; poly(vinyl chloride) + chlorinated polyethylene, PVC + PE-C, poly(vinyl chloride) + poly(acrylonitrile-co-butadiene-co-acrylester), PVC + ASA. Applications: semifinished goods, foils, plates, profiles, pipes, fittings, gutters, window frames, door frames, panels, housings, bottles, blow molding, disks, blocking layers, fibers, fleeces, nets. Polycarbonate + poly(ethylene terephthalate), PC + PET; polycarbonate + liquid crystal polymer, PC +

B B 20

B = break point 0

0

2

4

– 20 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 90 ˚C Strain ε (%) 6

Fig. 3.3-68 Poly(acrylonitrile-co-butadiene-co-styrene) + polycarbonate, ABS + PC: stress versus strain

LCP; polycarbonate + poly(butylene terephthalate), PC + PBT. Applications: optical devices, covering devices, panes, safety glasses, semifinished goods, houseware goods, compact discs, bottles. Poly(ethylene terephthalate) + polystyrene, PET + PS; poly(butylene terephthalate) + polystyrene, PBT + PS. Applications: same as for PET, PBT, and PS.

516

Part 3

Classes of Materials

Table 3.3-30 Polypropylene + ethylene/propylene/diene rubber, PP + EPDM; poly(acrylonitrile-co-butadiene-costyrene) + polycarbonate, ABS + PC; poly(acrylonitrile-co-butadiene-co-styrene) + polyamide, ABS + PA; poly(acrylonitrile-co-butadiene-co-acrylester) + polycarbonate, ASA + PC PP + EPDM

ABS + PC

ABS + PA

ASA + PC

0.89–0.92

1.08–1.17

1.07–1.09

1.15

15–18

7–8.5

9

7–9

0.5–1.2

2.0–2.6

1.2–1.3

2.3–2.6

Stress at yield σy (MPa)

10–25

40–60

30–32

53–63

Strain at yield εy (%)

10–35

3–3.5

> 50

> 50

> 50

> 50

Volume resistivity ρe (Ω m)

> 1014

> 1014

2 × 1012

1011 –1013

Surface resistivity σe (Ω)

> 1013

1014

3 × 1014

1013 –1014

Electric strength E B (kV/mm)

35–40

24

30

Relative permittivity εr (100 Hz)

2.3

3

3–3.5

2.5

30–60

20–160

Melting temperature Tm (◦ C)

160–168

Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g)

Part 3 3.3

Glass transition temperature Tg (◦ C) Vicat softening temperature TV 50/50 (◦ C) Thermal conductivity λ (W/(m K)) Density (g/cm3 ) Coefficient of thermal expansion α

(10−5 /K)

(linear)

Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ 4.6–5

Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa) Strain at fracture εb (%) Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D

Dielectric loss tan δ

(10−4 )

(100 Hz)

Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) Gas permeation (cm3 /(m2 d bar)) Melt viscosity–molar-mass relation Viscosity–molar-mass relation

3.3 Tables and Figures

Polymers

Creep modulus Etc (MPa) 1200

60

Stress σ (MPa)

1000

Y Y

600 400

– 20 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 90 ˚C Y = yield point

Y

40

800

2 MPa 4 MPa 6 MPa 8 MPa 10 MPa

20

12 MPa 14 MPa 16 MPa 18 MPa

10 1

10 2

10 3Time t (h) 10 4

0 0

2

4

6 Strain ε (%)

Fig. 3.3-69 Poly(acrylonitrile-co-butadiene-co-styrene) +

polycarbonate, ABS + PC: creep modulus versus time Viscosity η (Pa s) 10 5 200 ˚C 250 ˚C 300 ˚C

10 4

Fig. 3.3-70 Poly(acrylonitrile-co-butadiene-co-styrene) + polyamide, ABS + PA: stress versus strain Stress σ (MPa) Y

80 Y

10 3

Y

60

Y Y

10 2

– 40 ˚C – 20 ˚C 0 ˚C 23 ˚C 40 ˚C 60 ˚C 80 ˚C 100 ˚C

Y

40 Y

10 1 Y 20 10

0

10 –2

10 –1

10 0

10 1

10 2

10 3 10 4 10 5 Shear rate dγ /dt (s–1)

Fig. 3.3-71 Poly(acrylonitrile-co-butadiene-co-acrylester)

+ polycarbonate, ASA + PC: viscosity versus shear rate

Y = yield point 0 0

1

2

3

4

5

6

7 8 Strain ε (%)

Fig. 3.3-72 Poly(acrylonitrile-co-butadiene-co-acrylester)

+ polycarbonate, ASA + PC: stress versus strain

Creep modulus Etc (MPa) 2000

Poly(butylene terephthalate) + poly(acrylonitrileco-butadiene-co-acrylester), PBT + ASA. Applications: same as for PBT and ASA. Polysulfone + poly(acrylonitrile-co-butadiene-costyrene), PSU + ABS. Applications: same as for PSU. Poly(styrene-co-butadiene), PPE + SB. Applications: same as for PPE. Poly(phenylene ether) + polyamide 66, PPE + PA66. Applications: automotive parts, semifinished goods.

1500

1000

500 1 10

6 MPa 8.7 MPa 11.4 MPa 14.1 MPa 16.8 MPa 10 2

19.5 MPa 22.2 MPa 24.9 MPa 27.6 MPa 30.0 MPa 10 3

10 4

10 5 Time t (h)

Fig. 3.3-73 Poly(acrylonitrile-co-butadiene-co-acrylester)

+ polycarbonate, ASA + PC: creep modulus versus time

Part 3 3.3

200 10 0

517

518

Part 3

Classes of Materials

Table 3.3-31 Poly(vinyl chloride) + poly(vinyl chloride-co-acrylate), PVC + VC/A; poly(vinyl chloride) + chlorinated polyethylene, PVC + PE-C; poly(vinyl chloride) + poly(acrylonitrile-co-butadiene-co-acrylester), PVC + ASA PVC + VC/A

PVC + PE-C

PVC + ASA

1.42–1.44

1.36–1.43

1.28–1.33

7–7.5

8

7.5–10

2.5–2.7

2.6

2.6–2.8

Stress at yield σy (MPa)

45

40–50

45–55

Strain at yield εy (%)

4–5

3

3–3.5

> 50

10 to >50

≈8

Volume resistivity ρe (Ω m)

1013

1012 to >1013

1012 to >1014

Surface resistivity σe (Ω)

> 1013

> 1013

1012 – 1014

Relative permittivity εr (100 Hz)

3.5

3.1

3.7–4.3

Dielectric loss tan δ (10−4 ) (100 Hz)

120

140

100–120

Melting temperature Tm

(◦ C)

Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg (◦ C)

Part 3 3.3

Vicat softening temperature TV 50/50 (◦ C) Thermal conductivity λ (W/(m K)) Density (g/cm3 ) Coefficient of thermal expansion α

(10−5 /K)

(linear)

Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ

Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa) Strain at fracture εb (%) Impact strength (Charpy)

(kJ/m2 )

Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D

Electric strength E B (kV/mm)

Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) Gas permeation (cm3 /(m2 d bar)) Melt viscosity–molar-mass relation Viscosity–molar-mass relation

Polymers

Viscosity η (Pa s) 10 3

Stress σ (MPa) 80 240 ˚C 268 ˚C 297 ˚C

3.3 Tables and Figures

Y

– 40 ˚C – 20 ˚C 23 ˚C 40 ˚C 60 ˚C 80 ˚C

Y 60 Y

10 2

Y

20

10 2

0

10 3 10 4 Shear rate dγ /dt (s–1)

Fig. 3.3-74 Polycarbonate + poly(butylene terephthalate),

PC + PBT: viscosity versus shear rate

0

2

4

6

8

10

12 Strain ε (%)

Fig. 3.3-75 Polycarbonate + poly(butylene terephthalate), PC + PBT: stress versus strain

Table 3.3-32 Polycarbonate + poly(ethylene terephthalate), PC + PET; polycarbonate + liquid crystall polymer, PC +

LCP; polycarbonate + poly(butylene terephthalate), PC + PBT; poly(ethylene terephthalate) + polystyrene, PET + PS; poly(butylene terephthalate) + polystyrene, PBT + PS PC + PET Melting temperature Tm

PC + LCP

PC + PBT

PET + PS

PBT + PS

1.05

1.30

(◦ C)

Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K)) Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Glass transition temperature Tg (◦ C) Vicat softening temperature TV 50/50 (◦ C) Thermal conductivity λ (W/(m K))

0.24

0.21

Density (g/cm3 )

1.22

1.2–1.26

1.37

1.31

Coefficient of thermal expansion α (10−5 /K) (linear)

9–10

8–9

7

6.0

Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa)

2.1–2.3

2.6–4.0

2.3

3.1

2.0

Stress at yield σy (MPa)

50–55

66

50–60

47

40

Strain at yield εy (%)

5

5.6–6.9

4–5

Shear modulus G (GPa) Poisson’s ratio µ

Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa) Strain at fracture εb (%) Impact strength (Charpy) (kJ/m2 ) Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal)

74–82 > 50

15 25 to > 50

50

Part 3 3.3

10 1

Y = yield point

Y

40

519

520

Part 3

Classes of Materials

Table 3.3-32 Polycarbonate + poly(ethylene terephthalate), PC + PET; polycarbonate + liquid crystall polymer, PC +

LCP; polycarbonate + poly(butylene terephthalate), PC + PBT; poly(ethylene terephthalate) + polystyrene, PET + PS; poly(butylene terephthalate) + polystyrene, PBT + PS, cont. PC + PET

Part 3 3.3

Sound velocity vs (m/s) (transverse) Shore hardness D Volume resistivity ρe (Ω m) Surface resistivity σe (Ω) Electric strength E B (kV/mm) Relative permittivity εr (100 Hz) Dielectric loss tan δ (10−4 ) (100 Hz) Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) Gas permeation (cm3 /(m2 d bar)) Melt viscosity–molar-mass relation Viscosity–molar-mass relation

PC + LCP

> 1013 > 1015 30 3.3 200

Viscosity η (Pa s)

PC + PBT

PET + PS

1014 1014 35 3.3 20–40

> 1012 > 1012

PBT + PS

Stress σ (MPa) 240 ˚C 270 ˚C 300 ˚C

10 4

80

60

10 3

40

10 2

Y = yield point – 40 ˚C Y 0 ˚C 23 ˚C 60 ˚C 100 ˚C

20 10 1

10

0

10

1

10

2

3

10 4 –1

10 Shear rate dγ /dt (s )

Fig. 3.3-76 Poly(phenylene ether) + poly(styrene-co-

butadiene), PPE + SB: viscosity versus shear rate

0

0

1

2

3

4 Strain ε (%)

Fig. 3.3-77 Poly(phenylene ether) + poly(styrene-cobutadiene), PPE + SB: stress versus strain

Creep modulus Etc (MPa)

Poly(phenylene ether) + polystyrene, PPE + PS. Applications: automotive parts, foams, office goods, electrical parts, houseware goods.

2000

1500

1000 10 1

8 MPa 9.8 MPa 11.6 MPa 13.4 MPa 15.2 MPa 10 2

17.0 MPa 18.8 MPa 20.6 MPa 22.4 MPa 24.0 MPa 10 3

10 4

10 5 Time t (h)

Fig. 3.3-78 Poly(phenylene ether) + poly(styrene-co-

butadiene), PPE + SB: creep modulus versus time

Polymers

3.3 Tables and Figures

521

Table 3.3-33 Poly(butylene terephthalate) + poly(acrylonitrile-co-butadiene-co-acrylester), PBT + ASA; polysulfon +

poly(acrylonitrile-co-butadiene-co-styrene), PSU + ABS; poly(phenylene ether) + poly(styrene-co-butadiene), PPE + SB; poly(phenylene ether) + polyamide 66, PPE + PA66; poly(phenylene ether) + polystyrene PPE + PS PBT + ASA Melting temperature Tm (◦ C)

PSU + ABS

PPE + SB

PPE + PA66

PPE + PS

225

Enthalpy of fusion ∆Hu (J/mol) (mu) Entropy of fusion ∆Su (J/(K mol)) (mu) Heat capacity c p (kJ/(kg K))

1.40

Temperature coefficient dc p / dT (kJ/(kg K2 )) Enthalpy of combustion ∆Hc (kJ/g) Vicat softening temperature TV 50/50 (◦ C) Thermal conductivity λ (W/(m K))

0.23

Density (g/cm3 )

1.21–1.22

1.13

1.04–1.06

1.09–1.10

1.06

Coefficient of thermal

10

6.5

6.0–7.5

8–11

6.0

2.5

2.1

1.9–2.7

2.0–2.2

2.5

Stress at yield σy (MPa)

53

50

45–65

50–60

55

Strain at yield εy (%)

3.6

4

3–7

5

20 to >50

> 50

> 50

> 50

Volume resistivity ρe (Ω m)

> 1014

> 1013

> 1014

> 1011

1012

Surface resistivity σe (Ω)

> 1015

> 1014

> 1014

> 1012

1012

Electric strength E B (kV/mm)

30

20–30

35–40

95

Relative permittivity εr (100 Hz)

3.3

3.1–3.3

2.6–2.8

3.1–3.4

200

40–50

5–15

450

expansion α (10−5 /K) (linear) Compressibility κ (1/MPa) (cubic) Elastic modulus E (GPa) Shear modulus G (GPa) Poisson’s ratio µ

Stress at 50% elongation σ50 (MPa) Stress at fracture σb (MPa) Strain at fracture εb (%) Impact strength (Charpy)

50

(kJ/m2 )

Notched impact strength (Charpy) (kJ/m2 ) Sound velocity vs (m/s) (longitudinal) Sound velocity vs (m/s) (transverse) Shore hardness D

Dielectric loss tan δ

(10−4 )

(100 Hz)

Refractive index n D (589 nm) Temperature coefficient dn D / dT (1/K) Steam permeation (g/(m2 d)) Gas permeation (cm3 /(m2 d bar)) Melt viscosity–molar-mass relation Viscosity–molar-mass relation

Part 3 3.3

Glass transition temperature Tg (◦ C)

522

Part 3

Classes of Materials

References 3.1 3.2 3.3 3.4 3.5 3.6

Part 3 3

3.7 3.8 3.9

M. D. Lechner, K. Gehrke, E. H. Nordmeier: Makromolekulare Chemie (Birkhäuser, Basel 2003) G. W. Becker, D. Braun (Eds.): Kunststoff Handbuch (Hanser, Munich 1969 – 1990) Kunststoffdatenbank CAMPUS, M-Base, Aachen (www.m-base.de) J. Brandrup, E. H. Immergut, E. A. Grulke (Eds.): Polymer Handbook (Wiley, New York 1999) J. E. Mark (Ed.): Physical Properties of Polymers Handbook (AIP, Woodbury 1996) C. C. Ku, R. Liepins: Electrical Properties of Polymers (Hanser, Munich 1987) H. Saechtling: Kunststoff Taschenbuch (Hanser, Munich 1998) W. Hellerich, G. Harsch, S. Haenle: Werkstoff-Führer Kunststoffe (Hanser, Munich 1996) B. Carlowitz: Kunststoff Tabellen (Hanser, Munich 1995)

3.10 3.11 3.12

3.13

3.14

3.15 3.16

G. Allen, J. C. Bevington (Eds.): Comprehensive Polymer Science (Pergamon, Oxford 1989) H. Domininghaus: Die Kunststoffe und ihre Eigenschaften (VDI, Dü sseldorf 1992) H. J. Arpe (Ed.): Ullmann’s Encyclopedia of Industrial Chemistry, 5th edn. (VCH, Weinheim 1985 – 1996) R. E. Kirk, D. F. Othmer (Eds.): Encyclopedia of Chemical Technology, 4th edn. (Wiley, New York 1978 – 1984) H. F. Mark, N. Bikales, C. G. Overberger, G. Menges, J. I. Kroschwitz: Encyclopedia of Polymer Science and Engineering (Wiley, New York 1985 – 1990) Werkstoff-Datenbank POLYMAT, Deutsches Kunststoff-Institut, Darmstadt M. Neubronner: Stoffwerte von Kunststoffen. In: VDI-Wärmeatlas, 8th edn. (VDI, Dü sseldorf 1997)

523

Glasses

3.4.1 Properties of Glasses – General Comments ............................. 526 3.4.2 Composition and Properties of Glasses . 527 3.4.3 Flat Glass and Hollowware .................. 528 3.4.3.1 Flat Glass ............................... 528 3.4.3.2 Container Glass ....................... 529 3.4.4 Technical Specialty Glasses .................. 3.4.4.1 Chemical Stability of Glasses ..... 3.4.4.2 Mechanical and Thermal Properties............ 3.4.4.3 Electrical Properties ................. 3.4.4.4 Optical Properties ....................

530 530 533 537 539

3.4.5 Optical Glasses ................................... 3.4.5.1 Optical Properties .................... 3.4.5.2 Chemical Properties ................. 3.4.5.3 Mechanical Properties.............. 3.4.5.4 Thermal Properties ..................

543 543 549 550 556

3.4.6 Vitreous Silica..................................... 556 3.4.6.1 Properties of Synthetic Silica..... 556 3.4.6.2 Gas Solubility and Molecular Diffusion ........... 557 3.4.7 Glass-Ceramics ................................... 558 3.4.8 Glasses for Miscellaneous Applications . 3.4.8.1 Sealing Glasses ....................... 3.4.8.2 Solder and Passivation Glasses.. 3.4.8.3 Colored Glasses ....................... 3.4.8.4 Infrared-Transmitting Glasses...

559 559 562 565 568

References .................................................. 572

Glasses are very special materials that are formed only under suitable thermodynamic conditions; these conditions may be natural or man-made. Most glass products manufactured on a commercial scale are made by quenching a mixture of oxides from the melt (Fig. 3.4-1). For some particular applications, glasses are also made by other technologies, for example by chemical vapor deposition to achieve extreme purity, as required in optical fibers for communication, or by roller chilling in the case of amorphous metals, which need extremely high quenching rates. The term “amorphous” is a more

general, generic expression in comparison with the term “glass”. Many different technological routes are described in [4.1]. Glasses are also very universal engineering materials. Variation of the composition results in a huge variety of glass types, families, or groups, and a corresponding variety of properties. In large compositional areas, the properties depend continuously on composition, thus allowing one to design a set of properties to fit a specific application. In narrow ranges, the properties depend linearly on composition; in wide ranges, nonlinearity and step-function behavior have to be con-

Part 3 4

This chapter has been conceived as a source of information for scientists, engineers, and technicians who need data and commercialproduct information to solve their technical task by using glasses as engineering materials. It is not intended to replace the comprehensive scientific literature. The fundamentals are merely sketched, to provide a feeling for the unique behavior of this widely used class of materials. The properties of glasses are as versatile as their composition. Therefore only a selection of data can be listed, but their are intended to cover the preferred glass types of practical importance. Wherever possible, formulas, for example for the optical and thermal properties, are given with their correct constants, which should enable the reader to calculate the data needed for a specific situation by him/herself. For selected applications, the suitable glass types and the main instructions for their processing are presented. Owing to the availability of the information, the products of Schott AG have a certain preponderance here. The properties of glass types from other manufacturers have been included whenever available.

3.4. Glasses

524

Part 3

Classes of Materials

Volume 1 Glass formation curve

Q[2]

2 [3]

Q[2]

Q[3/432] 3

Q[3]

Q[4/433]

Crystallization curve

4

Tg

Ts Temperature

Fig. 3.4-1 Schematic volume–temperature curves for glass

Part 3 4

formation along path 1–2–3 and crystallization along path 1–4. Ts , melting temperature; Tg , transformation temperature. 1, liquid; 2, supercooled liquid; 3, glass; 4, crystal

sidered. The most important engineering glasses are mixtures of oxide compounds. For some special requirements, for example a particular optical transmission window or coloration, fluorides, chalcogenides, and colloidal (metal or semiconductor) components are also used. A very special glass is single-component silica, SiO2 ,which is a technological material with extraordinary properties and many important applications. On a quasi-macroscopic scale (> 100 nm), glasses seem to be homogeneous and isotropic; this means that all structural effects are, by definition, seen only as average properties. This is a consequence of the manufacturing process. If a melt is rapidly cooled down, there is not sufficient time for it to solidify into an ideal, crystalline structure. A structure with a well-defined short-range order (on a scale of less than 0.5 nm, to fulfill the energy-driven bonding requirements of structural elements made up of specific atoms) [4.2] and a highly disturbed long-range order (on a scale of more than 2 nm, disturbed by misconnecting lattice defects and a mixture of different structural elements) (Fig. 3.4-2). Crystallization is bypassed. We speak of a frozen-in, supercooled, liquid-like structure. This type of quasistatic solid structure is thermodynamically controlled but not in thermal equilibrium and thus is not absolutely stable; it tends to relax and slowly approach an “equilibrium” structure (whatever this may be in a complex multicomponent composition, it represents a minimum of the Gibbs free enthalpy). This also means that all

[3/432]

Q[3]

Q[4/4333] [4]

Q[3]

Q[4] Q[4]

Fig. 3.4-2 Fragment of a sodium silicate glass structure. The SiO2 tetrahedra are interconnected by the bridging oxygen atoms, thus forming a three-dimensional network. Na2 O units form nonbridging oxygen atoms and act as network modifiers which break the network. The Q [i/klmn] nomenclature describes the connectivity of different atom shells around a selected central atom (after [4.2])

properties change with time and temperature, but in most cases at an extremely low rate which cannot be observed under the conditions of classical applications (in the range of ppm, ppb, or ppt per year at room temperature). However, if the material is exposed to a higher temperature during processing or in the final application, the resulting relaxation may result in unacceptable deformation or internal stresses that then limit its use. If a glass is reheated, the quasi-solid material softens and transforms into a liquid of medium viscosity in a continuous way. No well-defined melting point exists. The temperature range of softening is called the “transition range”. By use of standardized measurement techniques, this imprecise characterization can be replaced by a quasi-materials constant, the “transformation temperature” or “glass temperature” Tg , which depends on the specification of the procedure (Fig. 3.4-3). As illustrated in Fig. 3.4-4, the continuous variation of viscosity with temperature allows various technologies for hot forming to be applied, for example casting, floating, rolling, blowing, drawing, and pressing, all of which have a specific working point.

Glasses

Relative contraction ∆l/l

525

Nucleation rate (N) or crystal growth rate (C) Cmax

A

B

C C Tg

Nmax

N 0

200

400

600

800 1000 Temperature (K)

Fig. 3.4-3 Definition of the glass transition temperature Tg

Fig. 3.4-5 Nucleation rate (N) and crystal growth rate (C) of glass as a function of temperature Temperature (°C) 1800 1600

lg (η /dPa s) 15

a

1400 10

Transforma13 tion range

Part 3 4

by a diagram of length versus temperature during a measurement, as the intersection of the tangents to the elastic region B and to the liquid region to the right of C. In the transformation range C, the glass softens

Temperature

14.5

dPa s

Strain point Annealing point

1013 dPa s

1200 800 600

11

d

b

1000 c e

400 200

9 7

107.6 dPa s

Sintering, sagging

0 Softening point

Blowing 5 Pressing, 3 drawing Melting, casting 1 0 200

104 dPa s Working point

600

1000

1400 1800 Temperature (°C)

Fig. 3.4-4 Typical viscosity–temperature curve: viscosity

ranges for the important processing technologies, and definitions of fixed viscosity points

The liquid-like situation results in thermodynamically induced density and concentration fluctuations, with a tendency toward phase separation and crystallization, which starts via a nucleation step. This can also be used as a technological route to produce unconventional, i. e. inhomogeneous, glasses. Some examples are

Time

Fig. 3.4-6 Temperature–time schedule for glass-ceramic

production: a, melting; b, working; c, nucleation; d, crystallization; e, cooling to room temperature

colored glasses with colloidal inclusions, porous glasses, and glass-ceramics, to name just a few. The commercially important glass-ceramics consist of a mixture of 30–90% crystallites (< 50 nm in diameter) and a residual glass phase, without any voids. The material is melted and hot-formed as a glass, cooled down, then annealed for nucleation, and finally tempered to allow crystal growth to a percentage that depends on the desired properties [4.3, 4]. Some characteristic features of the manufacturing process are shown in Figs. 3.4-5 and 3.4-6. As the melt is cooled, a region of high velocity of crystal growth has to be passed through, but no nuclei exist in that region. The nuclei are formed at a much lower temperature, where the crystallization is slow again. Thus the material solidifies as a glass in the

526

Part 3

Classes of Materials

first process step. In a second process step, the glass is reheated, annealed in the range of maximum nucleation rate Nmax , and then annealed at a higher temperature in the range of maximum crystal growth rate Cmax . The

overall bulk properties are the averages of the properties of the components. One of the major properties of commercially important glass-ceramics is a near-zero coefficient of thermal expansion.

3.4.1 Properties of Glasses – General Comments

Part 3 4.1

As for all materials, there are many properties for every type of glass described in the literature. In this section only a limited selection can be given. We also restrict the presentation to commercially important glasses and glass-ceramics. For the huge variety of glasses that have been manufactured for scientific purposes only, the original literature must be consulted. Extensive compilations of data of all kind may be found in books, e.g. [4.5–7], and in software packages [4.8, 9], which are based upon these books and/or additional original data from literature, patents, and information from manufacturers worldwide. Almost all commercially important glasses are silicate-based. For practical reasons, these glasses are subdivided into five major groups which focus on special properties. These groups are: 1. Mass-production glasses, such as window and container glasses, which are soda–lime–silicate glasses. Besides the application-dependant properties such as transparency, chemical resistance, and mechanical strength, the main concern is cost. 2. Technical specialty glasses, such as display or television glasses, glasses for tubes for pharmaceutical packaging, glasses for industrial ware and labware, glasses for metal-to-glass sealing and soldering, and glasses for glassware for consumers. The dominant properties are chemical inertness and corrosion resistance, electrical insulation, mechanical strength, shielding of X-ray or UV radiation, and others. To fulfill these specifications, the glass composition may be complex and even contain rare components. 3. Optical glasses have the greatest variety of chemical components and do not exclude even the most exotic materials, such as rare earth and non-oxide compounds. The dominant properties are of optical origin: refraction and dispersion with extremely high homogeneity, combined with low absorption and light scattering within an extended transmission range, including the infrared and ultraviolet parts of the electromagnetic spectrum. They are produced in comparably small volumes but with raw materials of high purity, and are thus quite expensive.

4. Vitreous silica, as a single-component material, has some extraordinary properties: high transparency from 160 nm to 1800 nm wavelength, high electrical insulation if it is of low hydrogen content, high chemical and corrosion resistance, and quite low thermal expansion with high thermal-shock resistance. A technological handicap is the high glass temperature Tg ≈ 1250 ◦ C, depending on the water content. 5. Glass-ceramics are glassy in the first production step. An important property is the final (after ceramization) coefficient of thermal expansion, often in combination with a high elastic modulus and low specific weight. High thermal stability and thermalshock resistance are a prerequisite for the major applications. This group has the potential for many other applications which require different property combinations [4.3]. This separation into groups seems to be somewhat artificial, in view of the material properties alone, and is justified only by the very different technological conditions used for manufacturing and processing. It corresponds to the specialization of the industry and to a traditional structuring in the literature. For all these groups, various classes of product defects exist, and these defects may occur in varying concentration. Among these defects may be bubbles, striations, crystalline inclusions, and metal particles, which are relics of a nonideal manufacturing process. There may also be inclusions of foreign components which were introduced with the raw materials as impurities or contamination. If a three-dimensional volume of glass is cooled down, the finite heat conductivity causes the volume elements to have nonidentical histories in time and temperature. As a consequence, the time- and temperature-dependent relaxation processes produce internal mechanical stress, which results in optical birefringence. These “technical” properties are often very important for the suitability of a piece of glass for a specific application, but they are not “intrinsic” properties of the material, and are not considered in this section.

Glasses

4.2 Composition and Properties of Glasses

527

3.4.2 Composition and Properties of Glasses A very common method for describing the composition of a glass is to quote the content of each component (oxide) by weight fraction (wi in wt%) or mole fraction (m i in mol%). If Mi is the molar mass of the component i, the relationship between the two quantities is given by 100wi
n mi = , 1≤i ≤n, (4.1) Mi j=1 w j /M j

If components other than oxides are used, it is advantageous to define fictitious components, for example the component F2 −O ( = fluorine–oxygen, with M = 2 × 19 − 16 = 22); this can be used to replace a fluoride with an oxide and this hypothetical oxide component, for example CaF2 = CaO + F2 −O. This reduces the amount of data required

and

ities [4.10]

100m i Mi , wi =
n j=1 m j M j

1≤i ≤n,

(4.2)

with the side conditions n n   m i = 1 and wi = 1 . i=1

Table 3.4-1 Factors wi for the calculation of glass dens-

(4.3)

i=1

8

wi (g/cm3 )

Na2 O

3.47

MgO

3.38

CaO

5.0

Al2 O3

2.75

SiO2

2.20

1b 2b 3a 4a 5a 6a 7a 0

H

b) 1a 2a 3b 4b 5b 6b 7b

He

8

1b 2b 3a 4a 5a 6a 7a 0

H

He

Li Be

B C N O F Ne

Li Be

B C N O F Ne

Na Mg

Al Si P

Na Mg

Al Si P

S Cl Ar

S Cl Ar

K Ca Sc Ti V Cr Mn Fe Co N Cu Zn Ga Ge As Se Br Kr

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe

Rb Rb Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Te Pb Bi Po At Rn

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Te Pb Bi Po At Rn

Fig. 3.4-7 (a) Elements whose oxides act as glass-formers (gray) and conditional glass-formers (brown) in oxide systems (after [4.11]). (b) Elements whose fluorides act as glass-formers (gray) and conditional glass-formers (brown) in fluoride glass

systems (after [4.12]) Table 3.4-2 Composition of selected technical glasses Glass type

Code a

Main components (wt%) SiO2

B2 O3

Al2 O3

Minor components Na2 O

PbO

< 10%

28

Al2 O3 , Na2 O, K2 O

Lead glass

S 8095

57

Low dielectric loss glass

S 8248

70

27

Al2 O3 , Li2 O, Na2 O, K2 O, BaO

Sealing glass

S 8250

69

19

Al2 O3 , Li2 O, Na2 O, K2 O, ZnO

Duran®

S 8330

80

13

Supremax®

S 8409

52

Sealing glass

S 8465

Sealing glass

S 8487

75

VycorTM

C 7900

96

a

Al2 O3 , Na2 O, K2 O 22

11 16.5

Code prefix: S = Schott AG, Mainz; C = Corning, New York.

11

B2 O3 , CaO, MgO, BaO, P2 O5 75

SiO2 Al2 O3 , Na2 O, K2 O Al2 O3 , B2 O3 , Na2 O

Part 3 4.2

a) 1a 2a 3b 4b 5b 6b 7b

Component i

528

Part 3

Classes of Materials

to handle the different cation–anion combinations (Fig. 3.4-7). With given weight or mole fractions, a property P can be calculated (or approximated) via a linear relation of the type 1  pwi wi 100 n

P=

1  pm i m i . 100 n

or

P=

i=1

i=1

(4.4)

The component-specific factors pi were first systematically determined by Winckelmann and Schott [4.13], and are listed in detail in the standard literature, e.g. [4.14]. As an example, the density can be calculated via (4.4) from: P = 1/ , pwi = 1/ wi , and the data in Table 3.4-1. The composition of selected technical glasses is given in Table 3.4-2.

3.4.3 Flat Glass and Hollowware

Part 3 4.3

By far the highest glass volume produced is for windows and containers. The base glass is a soda–lime composition, which may be modified for special applications. Owing to the Fe content of the natural raw materials, a green tint is observed for thicknesses that are not too small. If the product is designed to have a brown or green color (obtained by the use of reducing or oxidizing melting conditions), up to 80% waste glass can be used as a raw material.

3.4.3.1 Flat Glass Plate glass for windows is mainly produced by floating the melt on a bath of molten tin. All manufacturers worldwide use a soda–lime-type glass, with the average composition given in Table 3.4-3. For some other applications, this base glass may be modified by added coloring agents, for example Cr and Fe oxides. For architectural applications, the surface(s) may be modified by coatings or grinding to achieve specific

Table 3.4-3 Average composition in wt% and viscosity data, for soda–lime glass, container glass, and Borofloat glass Soda–lime glass

Container glass

Borofloat® 33

71–73

71–75

81

Composition (wt%) SiO2 CaO + MgO Na2 O + K2 O

9.5–13.5 13–16

B2 O3

0–1.5

Al2 O3

0.5–3.5

Other

0–3

10–15 12–16

4 13 2

0–3

Temperature (◦ C) at viscosity of 1014.5 dPa s

518

at viscosity of 1013 dPa s

525–545

at viscosity of 107.6 dPa s

717–735

820

at viscosity of 104 dPa s

1015–1045

1270

Density (g/cm3 ) Young’s modulus (GPa)

2.5 72

Poisson’s ratio

Thermal expansion coefficient α, 20–300 ◦ C (10−6 /K) Specific heat capacity c p , 20–100 ◦ C (kJ/kg K)

2.2 64 0.2

Knoop hardness Bending strength (MPa)

560

480 30 9.0

25 3.25 0.83

Glasses

4.3 Flat Glass and Hollowware

529

Table 3.4-3 Average composition in wt% and viscosity data for soda–lime glass, cont. Soda–lime glass

Container glass

Borofloat® 33

Heat conductivity λ at 90 ◦ C (W/m kg)

1.2

Chemical resistance Water

HGB1/HGA1

Acid

1

Alkali

A2

Refractive index n d Abbe value νe

1.47140 65.41

Stress-optical constant K (10−6 mm2 /N)

4.0

Dielectric constant εr

4.6

Dielectric loss tan δ at 25 ◦ C, 1 MHz

37 × 10−4

at 250 ◦ C (Ω cm)

108

at 350 ◦ C (Ω cm)

106.5

optical effects, such as decorative effects, a higher reflectivity in certain spectral regions (e.g. the IR), or an opaque but translucent appearance. Some other applications require antireflection coatings. If steel wires are embedded as a web into rolled glass, the resulting product can be used as a window glass for areas where improved break-in protection is required. Fire-protecting glasses are designed to withstand open fire and smoke for well-defined temperature– time programs, for example from 30 min to 180 min with a maximum temperature of more than 1000 ◦ C (test according to DIN 4102, Part 13). The main goal is to avoid the glass breaking under thermal load. There are various ways to achieve this, such as mechanical wire reinforcement, prestressing the plate by thermal or surface-chemical means, or reducing the thermal expansion by using other glass compositions, for example the floated borosilicate glass Pyran® (Schott). In automotive applications, flat glass is used for windows and mirrors. Single-pane safety glass is produced by generating a compressive stress near to the surface by a special tempering program: a stress of 80–120 MPa is usual. In the case of a breakage the window breaks into small pieces, which greatly reduces the danger of injuries.

Windshields are preferably made of laminated compound glass. Here, two (or more) layers are joined under pressure with a tough plastic foil. The compound technique is also used for armorplate glass: here, at least four laminated glass layers with a total thickness of at least 60 mm are used. For plasma and LCD displays and photovoltaic substrates, extremely smooth, planar, and thin sheets of glass are needed which fit the thermal expansion of the electronic materials in direct contact with them. These panes must remain stable in geometry (no shrinkage) when they are processed to obtain the final product.

3.4.3.2 Container Glass For packaging, transportation, storage of liquids, chemicals, pharmaceuticals, etc., a high variety of hollowware is produced in the shape of bottles and tubes. Most of the products are made from soda–lime glass (Table 3.4-3) directly from the glass melt. Vials and ampoules are manufactured from tubes; for pharmaceuticals these are made from chemically resistant borosilicate glass. Clear glass products have to be made from relatively pure raw materials. To protect the contents from light, especially UV radiation, the glass may be colored brown or green by the addition of Fe or Cr compounds. For other colors, see Sect. 3.4.8.3.

Part 3 4.3

Volume resistivity ρ

530

Part 3

Classes of Materials

3.4.4 Technical Specialty Glasses Technical glasses are special glasses manufactured in the form of tubes, rods, hollow vessels, and a variety of special shapes, as well as flat glass and granular form. Their main uses are in chemistry, pharmaceutical packaging, electronics, and household appliances. A list of typical applications of different glass types is given in Table 3.4-10, and a list of their properties is given in Table 3.4-11. The multitude of technical glasses can be roughly arranged in the following four groups, according to their oxide composition (in weight percent). However, certain glass types fall between these groups or even completely outside. Borosilicate Glasses. The network formers are substantial amounts of silica (SiO2 ) and boric oxide (B2 O3 > 8%). The following subtypes can be differentiated:

Part 3 4.4

• •

•

Non-alkaline-earth borosilicate glass: with SiO2 > 80% and B2 O3 at 12–13%, these glasses show high chemical durability and low thermal expansion (about 3.3 × 10−6 K−1 ). Alkaline-earth-containing glasses: with SiO2 ≈ 75%, B2 O3 at 8–12%, and alumina (Al2 O3 ) and alkaline earths up to 5%, these glasses are softer in terms of viscosity, and have high chemical durability and a thermal expansion in the range of 4.0–5.0 × 10−6 K−1 . High-borate glasses: with 65–70% SiO2 , 15–25% B2 O3 , and smaller amounts of Al2 O3 and alkalis, these glasses have a low softening point and a thermal expansion which is suitable for glass-to-metal seals.

Alkaline-Earth Aluminosilicate Glasses. These glasses

are free from alkali oxides, and contain 52–60% SiO2 , 15–25% Al2 O3 , and about 15% alkaline earths. A typical feature is a very high transformation temperature. Alkali–Lead Silicate Glasses. These glasses contain

over 10% lead oxide (PbO). Glasses with 20–30% PbO, 54–58% SiO2 , and about 14% alkalis are highly insulating and provide good X-ray shielding. They are used in cathode-ray tube components. Alkali–Alkaline-Earth Silicate Glasses (Soda–Lime Glasses). This is the oldest glass type, which is pro-

duced in large batches for windows and containers (see Sect. 3.4.3). Such glasses contain about 71% SiO2 ,

13–16% alkaline earths CaO + MgO, about 15% alkali (usually Na2 O), and 0–2% Al2 O3 . Variants of the basic composition can contain significant amounts of BaO with reduced alkali and alkaline-earth oxides: these are used for X-ray shielding of cathode-ray tube screens.

3.4.4.1 Chemical Stability of Glasses Characteristically, glasses are highly resistant to water, salt solutions, acids, and organic substances. In this respect, they are superior to most metals and plastics. Glasses are attacked to a significant degree only by hydrofluoric acid, strongly alkaline solutions, and concentrated phosphoric acid; this occurs particularly at higher temperatures. Chemical reactions with glass surfaces, induced by exchange, erosion, or adsorption processes, can cause the most diverse effects, ranging from virtually invisible surface modifications to opacity, staining, thin films with interference colors, crystallization, holes, and rough or smooth ablation, to name but a few such effects. These changes are often limited to the glass surface, but in extreme cases they can completely destroy or dissolve the glass. The glass composition, stress medium, and operating conditions will decide to what extent such chemical attacks are technically significant. Chemical Reaction Mechanisms with Water, Acid, and Alkaline Solutions Chemical stability is understood as the resistance of a glass surface to chemical attack by defined agents; here, temperature, exposure time, and the condition of the glass surface play important roles. Every chemical attack on glass involves water or one of its dissociation products, i. e. H+ or OH− ions. For this reason, we differentiate between hydrolytic (water), acid, and alkali resistance. In water or acid attack, small amounts of (mostly monovalent or divalent) cations are leached out. In resistant glasses, a very thin layer of silica gel then forms on the surface, which normally inhibits further attack (Fig. 3.4-8a,b). Hydrofluoric acid, alkaline solutions, and in some cases phosphoric acid, however, gradually destroy the silica framework and thus ablate the glass surface in total (Fig. 3.4-8c). In contrast, waterfree (i. e. organic) solutions do not react with glass. Chemical reactions are often increased or decreased by the presence of other components. Alkali attack on glass is thus hindered by certain ions, particularly those

4.4 Technical Specialty Glasses

Glasses

a) Release (mg Na2O/g) from glass grains

531

Attacked layer thickness (µm) 1

0.04

c (HCl) = 6 mol/l Exposure time: 16 h

0.03 0.02 0.1

0.01 0

2

4

6

b) Weight loss (mg per 100 cm ) 2

Na2O

8 Time (h)

Si2O

0.01

0.60 0.40

0.001

0.20 0.00

0

2

4

6

2

c) Weight loss (mg per 100 cm )

8 Time (h)

50

100 150 Temperature (°C)

Fig. 3.4-9 Acid attack on Duran® 8330 as a function of

temperature, determined from leached amounts of Na2 O and SiO2

160

Attacked layer thickness (µm) 1.5 c (NaOH) = 1 mol/l Exposure time: 1h

80

0

2

4

6

8 Time (h)

Fig. 3.4-8a–c Attack by (a) water, (b) acid, and (c) alkaline solution on chemically resistant glass as a function of time

of aluminium. On the other hand, complex-forming compounds such as EDTA, tartaric acid, and citric acid can increase the solubility. In general terms, the glass surface reacts with solutions which induce small-scale exchange reactions and/or adsorption. Such phenomena are observed, for example, in high-vacuum technology when residual gases are removed, and in certain inorganic-chemical operations, when small amounts of adsorbed chromium, resulting from treatment with chromic acid, are removed. Because acid and alkali attacks on glass are fundamentally different, silica-gel layers produced by acid attack obviously are not necessarily effective against alkali solutions and may be destroyed. Conversely, the presence of ions that inhibit alkali attack does not necessarily represent protection against acids and water. The most severe chemical exposure is therefore an alternating treatment with acids and alkaline solutions. As in all chemical reactions, the intensity of the interaction in-

1.0

0.5

0

20

40

60

80 100 Temperature (°C)

Fig. 3.4-10 Alkali attack on Duran® 8330 as a function of temperature, determined from weight loss

creases rapidly with increasing temperature (Figs. 3.4-9 and 3.4-10). In the case of truly ablative solutions such as hydrofluoric acid, alkaline solutions, and hot concentrated phosphoric acid, the rate of attack increases rapidly with increasing concentration (Fig. 3.4-11). As can be seen in Fig. 3.4-12, this is not true for the other frequently used acids. Determination of the Chemical Stability In most cases, either is the glass surface is analyzed in its “as delivered” condition (with the original fire-polished surface), or the basic material is analyzed with its fire-

Part 3 4.4

240

0

532

Part 3

Classes of Materials

in [4.2, 15] and summarized in Tables 3.4-4–3.4-6. The DIN classes of hydrolytic, acid, and alkali resistance of technical glasses are also listed Table 3.4-11, second page, last three colums.

Weight loss after 3 h (mg/100 cm2) 50

40

Significance of the Chemical Stability Release of Glass Constituents. In various processes in

30

20

10

0

8

10

12

14 pH

Fig. 3.4-11 Alkali attack on Duran® 8330 at 100 ◦ C as a function of pH value

Part 3 4.4

Attacked layer thickness (µm) 0.03 Temperature: 100 °C Time: 1 h

HCl 0.02

chemical technology, pharmaceutical manufacture, and laboratory work, the glass material used is expected to release no constituents (or a very minimal amnount) into reacting solutions or stored specimens. Because even highly resistant materials such as nonalkaline-earth and alkaline-earth borosilicate glasses do react to a very small degree with the surrounding media, the fulfillment of this requirement is a question of quantity and of detection limits. Concentrations of 10−6 –10−9 (i. e. trace amounts), which are measurable today with highly sophisticated analytical instruments, can be released even from borosilicate glasses in the form of SiO2 , B2 O3 , and Na2 O, depending on the conditions. However, solutions in contact with high-grade colorless Duran® laboratory glass will not be contaminated by Fe, Cr, Mn, Zn, Pb, or other heavy-metal ions. Undesirable Glass Surface Modifications. When an ap-

0.01

H2SO4

HNO3

0.00 CH3COOH

0

5

10 15 20 Acid concentration (molarity)

Fig. 3.4-12 Acid attack on Duran® 8330 as a function of

concentration

polished surface removed by mechanical or chemical ablation, or after crushing. The standardized DIN (Deutsches Institut für Normung, German Institute for Standardization) test methods, which are universally and easily applicable, are the most reliable analysis methods. They include the determination of hydrolytic resistance (by two graintitration methods and one surface method), of acid resistance to hydrochloric acid, and of alkali resistance to a mixture of alkaline solutions. Details are described

preciable interaction between a glass surface and an aqueous solution occurs, there is an ion exchange in which the easily soluble glass components are replaced by H+ or OH− ions. This depletion of certain glass components in the surface leads to a corresponding enrichment in silica, which is poorly soluble, and thus to the formation of a silica-gel layer. This layer proves, in most cases, to be more resistant than the base glass. When its thickness exceeds about 0.1–0.2 µm, interference colors caused by the different refractive indices of the layer and the base glass make this silica-gel layer visible to the unaided eye. With increasing layer thickness it becomes opaque and finally peels off, destroying the glass. Between these stages there is a wide range of possible surface modifications, some of which, although optically visible, are of no practical significance, whereas others must be considered. In the case of less resistant glasses, small amounts of water (from air humidity and condensation) in the presence of other agents such as carbon dioxide or sulfur oxides can lead to surface damage. In the case of sensitive glasses, hand perspiration or impurities left by detergents can sometimes induce strongly adhering surface defects, mostly recognizable as stains. If a contaminated glass surface is reheated (> 350–400 ◦ C), the

4.4 Technical Specialty Glasses

Glasses

533

Table 3.4-4 Hydrolytic classes according to DIN 12111 (ISO 719)

Hydrolytic class

Acid consumption of 0.01 mol/l hydrolytic acid per g glass grains (ml/g)

Base equivalent as Na2 O per g glass grains (µg/g)

Possible designation

1 2 3 4 5

Up to 0.10 Above 0.10, up to 0.20 Above 0.20, up to 0.85 Above 0.85, up to 2.0 Above 2.0, up to 3.5

Up to 31 Above 31, up to 62 Above 62, up to 264 Above 264, up to 620 Above 620, up to 1085

Very high resistance High resistance Medium resistance Low resistance Very low resistance

Table 3.4-5 Acid classes according to DIN 12116

Acid class

High acid resistance Good acid resistance Medium acid attack High acid attack

Half loss in weight after 6 h (mg/100 cm2 )

Alkali class

Up to 0.7 Above 0.7, up to 1.5 Above 1.5, up to 15 Above 15

1 2 3

Designation

Low alkali attack Medium alkali attack High alkali attack

Loss in weight after 3 h (mg/100 cm2 ) Up to 75 Above 75, up to 175 Above 175

3.4.4.2 Mechanical and Thermal Properties contaminants or some of their components may burn in. Normal cleaning processes will then be ineffective and the whole surface layer has to be removed (e.g. by etching). Desirable Chemical Reactions with the Glass Surface (Cleaning and Etching). Very strong reactions between

aqueous agents and glass can be used for the thorough cleaning of glass. The complete ablation of a glass layer leads to the formation of a new surface. Hydrofluoric acid reacts most strongly with glass. Because it forms poorly soluble fluorides with a great number of glass constituents, it is mostly used only in diluted form. The best etching effect is usually achieved when another acid (e.g. hydrochloric or nitric acid) is added. A mixture of seven parts by volume of water, two parts of concentrated hydrochloric acid (c = 38%) and one part of hydrofluoric acid (c = 40%) is recommended for a moderate surface ablation of highly resistant borosilicate glasses. When chemically less resistant glasses (e.g. Schott 8245 and 8250) are exposed for 5 min to a stirred solution at room temperature, a surface layer with a thickness of 1–10 µm is ablated, and a transparent, smooth, completely new surface is produced. Glasses can also be ablated with alkaline solutions, but the alkaline etching process is much less effective.

Viscosity As described earlier, the viscosity of glasses increases by 15–20 orders of magnitude during cooling. Within this viscosity range, glasses are subject to three different thermodynamic states:

• • •

the melting range, above the liquidus temperature Ts ; the range of the supercooled melt, between the liquidus temperature Ts and the transformation temperature Tg , which is defined by ISO 7884-8; the frozen-in, quasi-solid melt range (“glass range”), below the transformation temperature Tg .

The absence of any significant crystallization in the range of the supercooled melt (see Fig. 3.4-1, line segment 2) is of the utmost importance for glass formation. Hence a basically steady, smooth variation in the viscosity in all temperature regions is a fundamental characteristic of glasses (Fig. 3.4-4) and a crucial property for glass production. Figure 3.4-13 shows the strongly differing temperature dependences of the viscosity for some glasses. The best mathematical expression for practical purposes is the VFT (Vogel, Fulcher, and Tammann) equation, log η(T ) = A + B/(T − T0 ) ,

(4.5)

Part 3 4.4

1 2 3 4

Designation

Table 3.4-6 Alkali classes according to DIN ISO 695

534

Part 3

Classes of Materials

log η (dPa s) 14 3

12

2

1

4 10 8 7

6

6 5

4 2 0

200

400

600

800

1000

1200 1400 1600 Temperature (°C)

Fig. 3.4-13 Viscosity–temperature curves for some impor-

Part 3 4.4

tant technical glasses. 1, fused silica; 2, 8405; 3, 8330; 4, 8248; 5, 8350; 6, 8095; 7, 8465. Glasses with steep gradients (such as 7) are called “short” glasses, and those with relatively shallow gradients (such as 4) are called “long” glasses

where A, B, and T0 are glass-specific constants (Table 3.4-7). Somewhat above 1010 dPa s, the viscosity becomes increasingly time-dependent. With increasing viscosity (i. e. with decreasing temperature), the delay in establishing structural equilibrium finally becomes so large that, under normal cooling conditions, the glass structure at 1013 dPa s can be described as solidified or “frozen-in”. This temperature (for which a method of measurement is specified by ISO 7884-4) is called the “annealing point”. At this viscosity, internal stresses in the glass are released after ≈15 min annealing time, while the dimensional stability of the glass is sufficient

for many purposes, and its brittleness (susceptibility to cracking) is almost fully developed. The lower limit of the annealing range is indicated by the “strain point”, at which the glass has a viscosity of 1014.5 dPa s (determined by extrapolation from the viscosity–temperature curve). For most glasses, the strain point lies about 30–40 K below the annealing point. Relaxation of internal stresses here takes 3–5 h. The strain point marks the maximum value for short-term heat load. Thermally prestressed glasses, in contrast, show significant stress relaxation even at 200–300 K below Tg . For glass objects with precisely defined dimensions (e.g. etalons and gauge blocks) and in the case of extreme demands on the stability of certain properties of the glass, application temperatures of 100–200 ◦ C can be the upper limit. Strength The high structural (theoretical) strength of glasses and glass-ceramics (> 104 N/mm2 = 10 GPa) is without practical significance, because the strength of glass articles is determined by surface defects induced by wear, such as tiny chips and cracks (Griffith flaws), at whose tips critical stress concentrations may be induced by a mechanical load, especially if the load is applied perpendicular to the plane of the flaw (fracture mode I). Glasses and glass-ceramics, in contrast to ductile materials such as metals, show no plastic flow and behave under a tensile stress σ in as brittle a manner as ceramics. A flaw will result in a fracture if the “stress intensity factor” √ K I = 2σ a > K Ic , (4.6)

where a is the depth of the flaw and K Ic is the “critical stress intensity factor”, a material constant which is temperature- and humidity-dependent: see Table 3.4-8. √ For K Ic = 1 MPa m and a stress σ = 50 MPa, the critical flaw depth ac is 100 µm. Thus very small flaws

Table 3.4-7 Parameters of the VFT equation (4.5) for the glasses in Fig. 3.4-13

Glass

A

B (◦ C)

T0 (◦ C)

8095 8248 8330 8350 8405 8465 Fused silica Soda–lime glass

− 1.5384 − 0.2453 − 1.8500 − 1.5401 − 2.3000 − 1.6250 − 7.9250 − 1.97

4920.68 4810.78 6756.75 4523.85 5890.50 1873.73 31 282.9 4912.5

96.54 126.79 105.00 218.10 65.00 256.88 − 415.00 475.4

Glasses

can cause cracking at a comparatively low stress level, and the practical strength of a glass is not a materials constant! Surface Condition. As a result of wear-induced surface

defects, glass and glass-ceramic articles have practical tensile strengths of 20–200 N/mm2 = 20–200 MPa, depending on the surface condition and the atmospheric-exposure condition. To characterize the strength, a Weibull distribution for the cumulative failure probability F is assumed:

 F(σ) = 1 − exp −(σ/σc )m , (4.7)

value. In contrast to the rapid stress increase occurring in an impact, for example, a slowly increasing tensile stress or continuous stress above a certain critical limit may – as a result of stress corrosion cracking – cause the propagation of critical surface flaws and cracks and thus enhance their effect. Hence the tensile strength is time- and stress-rate-dependent (this is mainly important for test loads), as shown in Fig. 3.4-15. Independent of surface damage or the initial tensile strength, increasing F (%) Nominal strength values for

dσ /dt = 0.01

0.1 1 10 100

2

1000 N/(mm s)

99 Chem.- Normal 95 techn. glass large- consruc80 scale tions units 60 50 40 20 10 6 4 2 3

5

7

1 10

20

30

50 70 100

Stress Rate. The rate of increase of the stress and the

size of the glass area exposed to the maximum stress have to be considered for the specification of a strength F (%) Without Grain size 200 220 300 600 deliberate damage

Nominal strength values for

99 Chem.- Normal 95 techn. glass large- construc- 80 scale tions 60 units 50 40

(100 mm2 ; grain size 600) for various rates of increase of stress dσ/ dt. A, range of nominal strength for large-scale units in chemical technology; B, range of nominal strength for normal glass structures σ D (N/mm2)

80

Lifetime 102 s (1.7 min)

20

60 105 s (1.2 d) 40

1

3

5

7

10

200 300 σ E (N/mm2)

Fig. 3.4-15 Failure probability F of a predamaged surface

100

10 6 4 2

20

30

50 70 100

200 300 σ E (N/mm2)

Fig. 3.4-14 Failure probability F for samples abraded by

variously sized grains. Predamaged surface area 100 mm2 , rate of stress increase dσ/ dt = 10 MPa s−1 . A, range of nominal strength for large-scale units in chemical technology; B, range of nominal strength for normal glass structures

535

Part 3 4.4

where 0 ≤ F(σ) ≤ 1 is the probability of a fracture if the applied stress is less than σ; σc denotes the characteristic value (approximately the mean value of the distribution), and m is the Weibull modulus of the distribution (which determines the standard deviation). To obtain reproducible measurements, the surface is predamaged by grinding with a narrow grain-size distribution (Fig. 3.4-14). Only a slight – as a rule with neglible – dependence on the chemical composition is found for silicate glasses (Table 3.4-8).

4.4 Technical Specialty Glasses

108 s (3.17 y) 1011 s (3170 y)

20

0

20

40

60

80

100

120 160 σ E (N/mm2)

Fig. 3.4-16 Time-related strength σD (strength under constant loading) of soda–lime glass compared with the experimental strength σE at dσ/ dt = 10 N/mm2 s for various lifetimes, in a normal humid atmosphere

536

Part 3

Classes of Materials

the rate of increase of the stress by a factor of 10 results in an increase in the strength level of about 15%. Constant Loading. Fracture analysis of the effect and

behavior of cracks in glasses and glass-ceramics yield further information about the relationship between the experimentally determined tensile strength σE (usually measured for a rapidly increasing load) and the tensile strength σD expected under constant loading (= fatigue strength), as shown in Fig. 3.4-16. Such analyses show that, depending on the glass type, the tensile strength under constant loading σD (for years of loading) may amount to only about 1/2 to 1/3 of the experimental tensile strength σE .

F (%) Nominal strength values for

S = 10 000

1000 100 10 mm2

99 Chem.- Normal 95 techn. glass large- consruc80 scale tions units 60 50 40 20 10 6 4 2 3

5

7

1 10

20

30

50 70 100

Area Dependence. The larger the stressed area, the

Part 3 4.4

higher is the probability of large defects (large crack depths) within this area. This relationship is important for the transfer of experimental tensile strengths, which are mostly determined with relatively small test samples, to practical glass applications such as pipelines, where many square meters of glass can be uniformly stressed (Fig. 3.4-17).

Fig. 3.4-17 Failure probability F for differently sized stressed areas S. All samples abraded with 600 mesh grit, stress rate dσ/ dt = 10 N/mm2 s. A, range of nominal strength for large-scale units in chemical technology; B, range of nominal strength for normal glass structures

700

Elasticity The ideal brittleness of glasses and glass-ceramics is matched by an equally ideal elastic behavior up to breaking point. The elastic moduli for most technical glasses lie within a range of 50–90 kN/mm2 . The mean value of 70 kN/mm2 is about equal to the Young’s modulus of aluminium (see Table 3.4-11, first page, column 7). Coefficient of Linear Thermal Expansion With few exceptions, the length and the volume of glasses increase with increasing temperature (positive coefficient). The typical curve begins with a zero gradient at absolute zero (Fig. 3.4-3) and increases slowly. At about room temperature (section A in Fig. 3.4-3), the curve shows a distinct bend and then gradually increases (section B, the quasi-linear region) up to the beginning of the experimentally detectable plastic behavior. Another distinct bend in the expansion curve characterizes the transition from a predominantly elastic to a more plastic behavior of the glass (section C, the transformation range). As a result of increasing structural mobility, the temperature dependence of almost all glass properties changes distinctly in this range. Figure 3.4-18 shows the linear thermal expansion curves of five glasses; 8330 and 4210 roughly define the normal range of technical glasses, with expansion coefficients

200 300 σ E (N/mm2)

∆l/l × 103 4210

600 500

8095

400 8250

300

8330

200 100

Fused silica 0

100

200

300

400

500 600 700 Temperature (°C)

Fig. 3.4-18 Linear thermal expansion coefficients of various technical glasses and of fused silica

α(20 ◦ C/300 ◦ C) = 3.3–12.0 × 10−6 /K (see Table 3.4-11, first page, third column). The linear thermal expansion is an essential variable in determining the sealability of glasses to other materials and in determining thermally induced stress formation, and is therefore of prime importance for applications of glasses. Thermal Stresses. Owing to the low thermal conduc-

tivity of glasses (typically 0.9–1.2 W/m K at 90 ◦ C, and a minimum of 0.6 W/m K for high-lead-content glasses), temperature changes produce relatively high temperature differences ∆T between the surface and

Glasses

3.4.4.3 Electrical Properties Glasses are used as electrically highly insulating materials in electrical engineering and electronics, in the production of high-vacuum tubes, lamps, electrode seals, hermetically encapsulated components, highvoltage insulators, etc. Moreover, glasses may be used as insulating substrates for electrically conducting surface layers (in surface heating elements and data displays). Volume Resistivity Electrical conductivity in technical silicate glasses is, in general, a result of the migration of ions – mostly alkali ions. At room temperature, the mobility of these ions is usually so small that the volume resistivity, with values above 1015 Ω cm, is beyond the range of measurement. The ion mobility increases with increasing temperature. Besides the number and nature of the charge carriers, the structural effects of other components also influence the volume resistivity and its relationship to temperature. The Rasch and Hinrichsen law applies to this relationship at temperatures below the transformation range:

log ρ = A − B/T ,

(4.10)

where ρ is the electrical volume resistivity in Ω cm, A, B are constants specific to the particular glass, and T is the absolute temperature in K.

log ρ (Ω cm) 200

Temperature (°C) 400 500 700

300

13

537

12 8409

11 8250

10 9

8095

8 7

Fused silica

N16B

6 5 4 3

2.5 T –1/ (103 K–1)

2.0

1.5

1.0

Fig. 3.4-19 Electrical volume resistivity of various tech-

nical glasses and fused silica as a function of reciprocal absolute temperature

A plot of log ρ = f(1/T ) thus yields straight lines (Fig. 3.4-19). Because of the relatively small differences in slope for most glasses, the electrical insulation of glasses is often defined only by the temperature at which the resistivity is 108 Ω cm. According to DIN 52326, this temperature is denoted by Tk100 . The international convention is to quote volume resistivities at 250 ◦ C and 350 ◦ C (Table 3.4-11, second page, second column), from which the constants A and B Table 3.4-8 Fracture toughness of some glasses

Glass

√ K Ic (MPa m)

BK7 F5 SF6 K50 Duran®

1.08 0.86 0.74 0.77 0.85

Table 3.4-9 Parameters of the volume resistivity (4.10) of

the glasses in Fig. 3.4-19

Glass

A

B (K)

8095 8250 8409 N16B Fused silica

− 2.863 − 0.594 − 0.463 − 1.457 − 0.394

− 6520.0 − 5542.0 − 6520.0 − 3832.4 − 6222.4

Part 3 4.4

the interior, which, depending on the elastic properties E (Young’s modulus) and µ (Poisson’s ratio) and on the coefficient of linear thermal expansion α, can result in stresses ∆T αE σ= (4.8) N/mm2 . (1 − µ) In addition to the geometric factors (shape and wall thickness), the material properties α, E, and µ decisively influence the thermal strength of glasses subjected to temperature variations and/or thermal shock. Thermal loads in similar articles made from different glasses are easily compared by means of the characteristic material value σ αE ϕ= (4.9) = N/(mm2 K) , ∆T (1 − µ) which indicates the maximum thermally induced stress to be expected in a flexure-resistant piece of glass for a local temperature difference of 1 K. Because cracking originates almost exclusively from the glass surface and is caused there by tensile stress alone, cooling processes are usually much more critical than the continuous rapid heating of glass articles.

4.4 Technical Specialty Glasses

538

Part 3

Classes of Materials

(Table 3.4-9) and various other values below Tg can be calculated. Surface Resistivity The generally very high volume resistivity of glasses at room temperature has superimposed on it in a normal atmosphere a surface resistivity which is several orders of magnitude lower. The all-important factor is the adsorption of water on the glass surface. Depending on the glass composition, surface resistivities of 1013 –1015 Ω occur at low relative humidities, and 108 –1010 Ω at high relative humidities. Above 100 ◦ C, the effect of this hydrated layer disappears almost completely. (Treatment with silicones also considerably reduces this effect.)

Part 3 4.4

Dielectric Properties With dielectric constants generally between 4.5 and 8, technical glasses behave like other electrically insulating materials. The highest values are obtained for lead glasses such as 8531 (εr = 9.5) and for ultra-high-leadcontent solder glasses (εr ∼ 20). The dependence of the dielectric constants εr on frequency and temperature is relatively small (Fig. 3.4-20). For a frequency range of 50–109 Hz, εr values generally do not vary by more than 10%. The dielectric dissipation factor tan δ is frequencyand temperature-dependent. Owing to the diverse mechanisms which cause dielectric losses in glasses, there is a minimum of tan δ in the region of 106 –108 Hz, and increasing values at lower and higher frequencies (Fig. 3.4-21).

7

tan δ

3 2

4

1 0

2

4

6

10

12 14 log f (Hz)

Fig. 3.4-21 Schematic representation of the frequency spectrum of dielectric losses in glasses at room temperature. The solid curve gives the total losses, made up of (1) conduction loss, (2) relaxation loss, (3) vibration loss, and (4) deformation loss

At 106 Hz, the dissipation factors tan δ for most glasses lie between 10−2 and 10−3 ; fused silica, with a value of 10−5 , has the lowest dissipation factor of all glasses. The special glass 8248 has relatively low losses, and in this cases tan δ increases only slightly up to 5.5 GHz (where tan δ = 3 × 10−3 ). The steep increase in dielectric losses with increasing temperature (Fig. 3.4-22) can lead to instability, i. e. overheating of the glass due to dielectric loss energy in the case of restricted heat dissipation and corresponding electrical power.

Dielectric constant ε r

Dissipation factor tan δ 8095

8

10–3

N16B 8245

8412 8330 8486 8487

8245

6

10–2 8486

8330

4 –100

8095

8487

5

10–1

–100 0

100

200 Temperature (°C)

Fig. 3.4-20 Dielectric constant εr of electrotechnical

glasses as a function of temperature, measured at 1 MHz

0

100 200 Temperature (°C)

Fig. 3.4-22 Dissipation factor tan δ as a function of temperature in the range −100 ◦ C < T < +200 ◦ C, measured at 1 MHz

Glasses

Dielectric Strength Some approximate values for the dielectric strength of glasses are a field strength of 20–40 kV/mm for a glass thickness of 1 mm at 50 Hz at 20 ◦ C, and 10–20 kV/mm for greater thicknesses. At higher temperatures and frequencies, decreasing values can be expected.

3.4.4.4 Optical Properties

Stress Birefringence Owing to its structure, glass is an isotropic material. Mechanical stress causes anisotropy, which manifests itself as stress-induced birefringence. A light beam, after passing through a plate of thickness d which is subjected to a principal-stress difference ∆σ, shows an optical path difference ∆s between the two relevant polarization directions. This path difference can either be estimated by means of the birefrigence colors or be measured with a compensator, and is given by

∆s = Kd∆σ nm ,

539

of up to 4 × 10−6 mm2 /N. High-lead-content glasses can have values down to nil or even negative (Table 3.4-11, second page, fifth column). Light Transmittance The transmittance due to the refractive index can be further reduced by coloring agents (oxides of transition elements or colloids) or by fine particles in the glass which have a different refractive index (in this case light scattering occurs, giving opal glasses). Absorption caused by impurities such as Fe2 O3 and by some major glass components such as PbO strongly reduces transparency in the UV range. Particularly good UV-transmitting multicomponent glasses have a cutoff Transmission (%) 100 80

Part 3 4.4

Refraction of Light The refractive indices n d of technical glasses at a wavelength of λd = 587.6 nm generally lie within the range 1.47–1.57. The exceptions to this rule are lead glasses with PbO contents of over 35% (e.g. glass 8531, which has n d = 1.7; see Table 3.4-11, second page, fourth column). The principal dispersion n F − n C (λF = 486.1 nm, λC = 656.3 nm) of technical glasses lies between 0.007 and 0.013. At perpendicular incidence, the reflectance Rd of a glass–air interface is 3.6% to 4.9%. The transmittance τd and the reflectance ρd of a nonabsorbing, planar, parallel-sided glass plate with two glass–air interfaces, with multiple reflections taken into account, can be calculated from the refractive index as 2n d τd = 2 (4.11) nd + 1 and (n d − 1)2 ρd = (4.12) . nd + 1 The transmittance τd at perpendicular incidence has values between 90.6% and 93.1%.

4.4 Technical Specialty Glasses

8337B

60 40

8405

20 210

230

250

270

300 340 Wavelength (nm)

Fig. 3.4-23 UV transmission of highly UV-transparent glasses 8337B and 8405 for 1 mm glass thickness Transmission (%) 100 90

1mm

80 70

8 mm

60 50 40 30

(4.13)

20

where K is the stress-optical coefficient of the glass (determined according to DIN 52314), ∆s 1 (4.14) K= mm2 /N . d ∆σ Many glasses have stress-optical coefficients of about 3 × 10−6 mm2 /N, and borosilicate glasses have values

10 0 200

2 mm

500

1000

2000

5000 10 000 Wavelength (nm)

Fig. 3.4-24 Transmission of Duran® 8330 for thicknesses

of 1, 2, and 8 mm

540

Part 3

Classes of Materials

(50% value) at a wavelength of 220 nm (Fig. 3.4-23); normal technical glasses already absorb considerably at 300 nm.

In the IR range, absorption caused by impurities such as H2 O and by lattice vibrations limits the transmittance (Fig. 3.4-24).

Table 3.4-10 Schott technical specialty glasses and their typical applications

8095 8245 8248 8250 8252 8253 8321 8326 8330 8337B

Part 3 4.4

8350 8405 8409 8412 a 8414 8415 8421 8422 8436 8486 8487 8488 8490 8512 8516 8531 8532 8533 8625 8650 8651 8652 8656 a

Lead glass (28% PbO), electrically highly insulating, for general electrotechnical applications Sealing glass for Fe–Ni–Co alloys and molybdenum, minimum X-ray absorption, chemically highly resistant Borosilicate glass (of high B2 O3 content), minimum dielectric losses up to the GHz range, electrically highly insulating Sealing glass for Ni–Fe–Co alloys and molybdenum, electrically highly insulating Alkaline-earth aluminosilicate glass for high-temperature applications, for sealing to molybdenum Alkaline-earth aluminosilicate glass for high-temperature applications, for sealing to molybdenum Alumino-borosilicate glass for TFT displays SBW glass, chemically highly resistant Duran® , borosilicate glass, general-purpose glass for apparatus for the chemical industry, pipelines, and laboratory glassware Borosilicate glass, highly UV-transmitting, for sealing to glasses and to metals of the Kovar and Vacon-10 ranges and tungsten AR glass® , soda–lime silicate glass tubing Highly UV-transmitting soft glass Supremax® (black identification line), alkali-free, for high application temperatures in thermometry, apparatus construction, and electrical engineering Fiolax® , clear (blue identification line), neutral, glass tubing (chemically highly resistant) for pharmaceutical packaging Fiolax® , amber (blue identification line), neutral, glass tubing (chemically highly resistant) for pharmaceutical packaging Illax® , amber tubing glass for pharmaceutical packaging Sealing glass for seals to NiFe45 (DIN 17745) and compression seals Sealing glass for seals to NiFe47 or 49 (DIN 17745) and compression seals Particularly resistant to sodium vapor and alkaline solutions, suitable for sealing to sapphire Suprax® , borosilicate glass, chemically and thermally resistant, suitable for sealing to tungsten Sealing glass for tungsten, softer than 8486 Borosilicate glass, chemically and thermally resistant Black glass, light-transmitting in the UV region, highly absorbing in the visible region IR-absorbing sealing glass for Fe–Ni, lead-free (reed switches) IR-absorbing sealing glass for NiFe, lead-free, slow-evaporating (reed switches) Soft glass, Na-free, high lead-content, for low temperature encapsulation of semiconductor components (diodes) Soft glass, Na-free, high lead-content, for low-temperature encapsulation of semiconductor components (diodes) IR-absorbing sealing glass for Ni–Fe, lead- and potassium-free, slow-evaporating (reed switches) IR-absorbing biocompatible glass for (implantable) transponders Alkali-free sealing glass for molybdenum, especially for implosion diodes; high lead content Tungsten sealing glass for power diodes Tungsten sealing glass, low-melting, for power diodes Borofloat® 40, borosilicate float glass adapted for prestressing

Also known as 8258, Estax® , low-potassium glass tubing for the manufacture of counting vials.

Glasses

4.4 Technical Specialty Glasses

541

Table 3.4-11 Characteristic data of technical specialty glasses Glass

Shapes

Thermal

Trans-

Temperature

Density

Young’s

Poisson’s

Heat con-

No.

produceda

expansion

formation

at viscosity

at 25 ◦ C

modulus

ratio µ

ductivity

coefficient

tempera-

1013 dPa s

107.6 dPa s

104 dPa s

α(20/300)

ture Tg

(10−6 /K)

(◦ C)

(◦ C)

(◦ C)

(◦ C)

λ at 90 ◦ C (g/cm3 )

(103 N/mm2 )

(W/m K)

8095

TP

9.2

435

435

635

985

3.01

60

0.22

0.9

8245

MTRP

5.1

505

515

720

1040

2.31

68

0.22

1.2

8248

BP

3.1

445

490

740

1260

2.12

44

0.22

1.0

8250

MTBPC

5.0

490

500

720

1055

2.28

64

0.21

1.2

8252

TP

4.6

725

725

935

1250

2.63

81

0.24

1.1

8253

TP

4.7

785

790

1000

1315

2.65

83

0.23

1.1

8261

SP

3.7

720

725

950

1255

2.57

79

0.24

1.1

8326

MTP

6.6

560

565

770

1135

2.46

75

0.20

1.2

8330

MSTRPC

525

560

820

1260

2.23

63

0.20

1.12

4.1

430

465

715

1090

2.21

51

0.22

1.0

8350

TRP

9.1

525

530

715

1040

2.50

73

0.22

1.1

8405

MTP

9.8

460

450

660

1000

2.51

65

0.21

1.0

8409

MTRP

4.1

745

740

950

1230

2.57

85

0.24

1.2

8412

TP

4.9

565

565

780

1165

2.34

73

0.20

1.2

8414

TP

5.4

560

560

770

1155

2.42

71

0.19

1.2

8415

TP

7.8

535

530

720

1050

2.50

74

0.21

1.1

8421

P

9.7

525

535

705

1000

2.59

74

0.22

1.0

8422

P

8.7

540

535

715

1010

2.46

76

0.21

1.1

8436

TRP

6.7

630

630

830

1110

2.76

85

0.22

1.1

8486

MP

4.1

555

580

820

1220

2.32

66

0.20

1.1

8487

TRP

3.9

525

560

775

1135

2.25

66

0.20

1.2

8488

M

4.3

545

560

800

1250

2.30

67

0.20

1.2

8490

MP

9.6

475

480

660

1000

2.61

70

0.22

1.0

8512

TP

9.0

445

460

665

980

2.53

68

0.22

1.0

8516

TP

8.9

440

445

650

990

2.56

72

0.21

1.1

8531

TP

9.0

440

430

590

830

4.34

52

0.24

0.57

8532

TP

8.8

430

425

565

760

4.47

56

0.24

0.7

8533

TP

8.7

475

480

645

915

2.57

79

0.21

1.1

8625

TP

9.0

510

520

710

1030

2.53

73

0.22

1.1

8650

TP

5.2

475

475

620

880

3.57

62

0.23

0.5

8651

TP

4.5

540

540

735

1040

2.87

59

0.24

0.9

8652

TP

4.5

495

490

640

915

3.18

58

0.25

0.9

8656

SP

4.1

590

600

850

1270

2.35

−

−

−

a

Shapes produced: B = block glass; C = capillaries; M = molded glass (blown or pressed); P = powder, spray granulates, or sintered parts;

R = rods; S = sheet glass; T = tubing

Part 3 4.4

3.3

8337B TP

542

Part 3

Classes of Materials

Table 3.4-11 Characteristic data of technical specialty glasses, cont. Tk100

Logarithm of

Dielectric properties

Refractive

Stress-

Classes of chemical

electrical volume

at 1 MHz

index nd

optical

stability against

resistivity

and 25 ◦ C

(λd = 587.6 nm)

coefficient K

(
cm) at

εr

tan δ

(◦ C)

250 ◦ C

350 ◦ C

330

9.6

7.6

6.6

11

215

7.4

5.9

5.7

Alkaline

(10−4 )

(10−6 mm2 /N)

Water

Acid

solution

1.556

3.1

3

2

3

80

1.488

3.8

3

4

3

4.3

10

1.466

5.2

3

3

3

4.9

22

1.487

3.6

3

4

3

−

12

375

10

660

−

12

6.1

11

1.538

3.3

1

3

2

630

−

11

6.6

15

1.547

2.7

1

2

2

585

−

−

5.8

14

1.534

3.1

1

4

2

10 8.3

Part 3 4.4

210

7.3

6.0

6.4

65

1.506

2.8

1

1

2

250

8.0

6.5

4.6

37

1.473

4.0

1

1

2

315

9.2

7.5

4.7

22

1.476

4.1

3

4

3

200

7.1

5.7

7.2

70

1.514

2.7

3

1

2

6.9

6.5

45

1.505

2.8

5

3

2

6.1

23

1.543

2.9

1

4

3

280 530

8.5 12

10

215

7.4

6.0

5.7

80

1.492

3.4

1

1

2

200

7.1

5.6

6.3

107

1.523

2.2

1

2

2

180

6.7

5.3

7.1

113

1.521

3.2

2

2

2

255

8.1

6.4

7.4

43

1.526

2.7

3

3

2

205

7.3

5.8

7.3

60

1.509

2.9

2

3

3

245

7.9

6.5

7.9

75

1.564

2.9

1–2

1–2

1

230

7.5

6.1

5.1

40

1.487

3.8

1

1

2

300

8.3

6.9

4.9

36

1.479

3.6

4

3

3

200

7.1

5.8

5.4

96

1.484

3.2

1

1

2

235

7.7

6.1

6.7

32

1.52

−

3

2

2

320

9.5

7.5

6.5

21

1.510

3.0

3

1–2

2

8.1

250

6.4

6.5

25

1.516

3.0

3

1

2

450

11

9.8

9.5

9

1.700

2.2

1

4

3

440

11

9.4

10.2

9

1.724

1.7

1

4

3

5.5

6.9

55

1.527

3.0

1

2

2

5.8

200

7.0

7.1

68

1.525

−

3

1

2

−

−

−

7.6

33

1.618

2.8

1

4

3

−

11.2

10.0

6.0

31

1.552

3.6

1

4

3

−

−

−

6.9

35

1.589

3.4

1

4

3

5.5

51

1.493

3.6

1

1

1

210

265

7.2

8.3

6.8

Glasses

4.5 Optical Glasses

543

3.4.5 Optical Glasses Historically, optical glasses were developed to optimize imaging refractive optics in the visible part of the spectrum. With new mathematical tools, new light sources, and new detectors, the resulting lens systems, which used a combination of different glasses (or even sometimes crystalline materials), changed the requirement from high versatility in terms of material properties to homogeneity, precision, and reproducibility, and an extended spectral range in the ultraviolet and infrared regions; environmental aspects also became important. Consequently, the high number of glass types has been reduced.

3.4.5.1 Optical Properties

Table 3.4-12 Wavelengths of a selection for frequently used spectral lines Wavelength (nm) 2325.42 1970.09 1529.582 1060.0 1013.98 852.11 706.5188 656.2725 643.8469 632.8 589.2938 587.5618 546.0740 486.1327 479.9914 435.8343 404.6561 365.0146 334.1478 312.5663 296.7278 280.43 248.00 248.35 194.23 193.00

Designation

t s r C C D d e F F g h i

Spectral line used

Element

Infrared mercury line Infrared mercury line Infrared mercury line Neodymium glass laser Infrared mercury line Infrared cesium line Red helium line Red hydrogen line Red cadmium line Helium–neon gas laser Yellow sodium line (center of the double line) Yellow helium line Green mercury line Blue hydrogen line Blue cadmium line Blue mercury line Violet mercury line Ultraviolet mercury line Ultraviolet mercury line Ultraviolet mercury line Ultraviolet mercury line Ultraviolet mercury line Excimer laser Ultraviolet mercury line

Hg Hg Hg Nd Hg Cs He H Cd He–Ne Na D He Hg H Cd Hg Hg Hg Hg Hg Hg Hg KrF Hg

Excimer laser

ArF

Part 3 4.5

Refractive Index, Abbe Value, Dispersion, and Glass Designation The most common identifying features used for characterizing an optical glass are the refractive index n d

in the middle range of the visible spectrum, and the Abbe value νd = (n d − 1)/(n F − n C ) as a measure of the dispersion. The difference n F − n C is called the principal dispersion. The symbols have subscripts that identify spectral lines that are generally used to determine refractive indices; these spectral lines are listed in Table 3.4-12. The quantities n e and νe = (n e − 1)/(n F − n C ) based on the e-line are usually used for specifying optical components. For the comparison of glass types from different manufacturers, an abbreviated glass code is defined in the following way: the first three digits correspond to n d − 1, the second three digits represent the Abbe value νd , and, after a dot, three more digits characterize the density (see Table 3.4-13). Glasses can be grouped into families in an n d /νd Abbe diagram (Fig. 3.4-25). These glass families differ in chemical composition as shown in Fig. 3.4-26.

544

Part 3

Classes of Materials

vd nd 2.00

90

85

80

75

70

65

60

55

55

45

40

35

30

25

20

2.00

Description of symbols Circles All glasses except short flint glasses (KZFS)

1.95

1.95

KZFS Only N-type (lead-free and arsenic-free type) N-type and conventional type Conventional type

1.90

66

1.90

46 31

LASF

1.85

9 41

32

21

33

34 35 34

LAK

64

5

Part 3 4.5

53

16 14 5

1.60 PSK

10 4

1.55

BAK

3

1.50

BALF 1 4

11 2

PK

7

52 A

10

7

BK ZK7

52

2

SK

K

LF

2 5

LLF

KF9

5

3

4

1.70

5 19 2

1.65

2

4 4

8

64 15

11

BAF

2

8

2

5

51

SSK

15

12

BASF

10

22

7

1.75

1

3

9 12

21

14 4

7

2

14

1.65

1.80

10

10

8

1.70

6 11

56

LAF

33 A

1.75

SF

45

43 36

1.85

57

40

44

1.80

51

nd

5

4

1.60

F

5

1.55

1

10

1.50

5

51

FK 1.45

1.45 vd

90

85

80

75

70

65

60

55

55

45

40

35

30

25

20

Fig. 3.4-25 Abbe diagram of glass families Table 3.4-13 Examples of glass codes

Refractive index nd 2.00 1.95 1.90 1.85 1.80

SiO2PbOM2O

(B2O3,SiO2)La2O3-MO

1.70

SiO2-B2O3BaO

1.65 1.60 1.50

B2O3-La2O3 -MmOn

MmOn: ZrO2, Ta2O5, Nb2O5, ... MO: MgO, CaO, SrO, BaO, ZnO M2O: Li2O, Na2O, K2O, Cs2O

1.75

1.55

Glass nd type

KzF glasses: SiO2-Sb2O3-B2O3 KzFS glasses: B2O3-PbO-Al2O2

P2O5Al2O3MO(F2-O)

Density Glass code  (g cm−3 )

Remarks

N-SF6 1.80518 25.36 3.37

805 254.337 Lead- and arsenic-free glass

SF6

805 254.518 Classical lead silicate glass

1.80518 25.43 5.18

(SiO2, B2O3) -BaO-PbO

SiO2P2O5M2OAl2O3SiO2TiO 2SiO MO2 BaO-M2O -PbO B2O3 (F2-O) -M2O SO2- SiO2,B2O3B2O3- M2O-MO M2O

1.45 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 Abbe number Ψ d

Fig. 3.4-26 Abbe diagram showing the chemical composition of

the glass families

νd

The designation of each glass type here is composed of an abbreviated family designation and a number. The glass families are arranged by decreasing Abbe value in the data tables (Table 3.4-14). Table 3.4-14 gives an overview of the preferred optical glasses from Schott, Hoya, and Ohara. The glass types are listed in order of increasing refractive index n d .

Glasses

4.5 Optical Glasses

545

Table 3.4-14 Comparison of the preferred optical glasses from different manufacturers Schott Code

Hoya Glass type

Code

Schott

Ohara Glass type

Code

Glass type

Code

Hoya Glass type

Code

Ohara Glass type

439950 S-FPL53

580537 N-BALF4

456903 S-FPL52

581409 N-LF5

581407 E-FL5

487704 FC5

487702 S-FSL5

581409 LF5

581409 FL5

497816 FCD1

497816 S-FPL51

583465 N-BAF3

487845 N-FK51 497816 N-PK52 498670 N-BK10

589613 N-SK5

501564 K10

592683 N-PSK57

583464 BAM3 583594 S-BAL42

589613 BaCD5

589612 S-BAL35 593353 S-FTM16

594355 FF5

511604 K7

596392 E-F8

517522 CF6 517524 S-NSL36

517642 BSC7

516641 S-BSL7

603380 E-F5

517696 S-APL1

603380 F5

518590 S-NSL3

603606 N-SK14

603606 BaCD14

607567 N-SK2

606437 S-BAM4 607568 BaCD2

607568 S-BSM2

613370 F3

613370 PBM3

613443 ADF10

613443 BPM51

613587 BaCD4

613587 S-BSM4

609464 N-BAF52

523515 N-KF9 529517 SSL2

613443 KZFSN4

529770 N-PK51

613445 N-KZFS4

532488 FEL6 532489 E-FEL6

540597 N-BAK2

532489 S-TIL6

613586 N-SK4

614550 BSM9

540595 S-BAL12 541472 E-FEL2

541472 S-TIL2

617366 F4 617628 S-PHM51

541472 FEL2 618498 N-SSK8

547536 N-BALF5 548458 LLF1

548458 FEL1

548458 N-LLF1

548458 E-FEL1

548458 S-TIL1

551496 SbF1 552635 N-PSK3

618634 S-PHM52

620364 N-F2

620363 E-F2

620363 S-TIM2

620364 F2

620364 F2

620603 N-SK16

620603 BaCD16

620603 S-BSM16

620622 ADC1 560612 S-BAL50

569561 N-BAK4

618498 S-BSM28 618634 PCD4

558542 N-KZFS2 564608 N-SK11

603607 S-BSM14 603655 S-PHM53

606439 N-BAF4 522598 S-NSL5

603380 S-TIM5 603380 F5

521526 SSL5 522595 N-K5

596392 S-TIM8

596392 F8

620635 N-PSK53 621359 TIM11

564607 EBaCD11 564607 S-BAL41 567428 FL6

567428 PBL26

621603 SK51

569563 BaC4

569563 S-BAL14

622532 N-SSK2

571508 S-BAL2

623569 N-SK10

623570 EBaCD10 623570 S-BSM10

571530 S-BAL3

623580 N-SK15

623582 BaCD15

622532 BSM22

569713 N-PSK58

573576 N-BAK1

573578 S-BAL11

624470 BaF8

623582 S-BSM15

Part 3 4.5

517524 E-CF6

518590 E-C3

532488 N-LLF6

581407 S-TIL25

583594 BaCD12

508612 N-ZK7

517642 N-BK7

Glass type

575415 S-TIL27

434950 N-FK56

487704 N-FK5

Code

546

Part 3

Classes of Materials

Table 3.4-14 Comparison of the preferred optical glasses from different manufacturers, cont. Schott Code

639421

Hoya Glass type

N-SK18

640601

N-LAK21

Part 3 4.5

651559

Glass type

626357

F1

626357

E-F1

Code

Glass type

626357

S-TIM1

639449

S-BAM12

Code

Hoya Glass type

Code

Ohara Glass type

699301 N-SF15

699301 E-FD15

699301 SF15

699301 FD15

SF2

699301 S-TIM35

702412 S-BAH27

713539 S-LAL8

639554

BaCD18

639554

S-BSM18

704394 NBASF64

640345

E-FD7

640345

S-TIM27

706303 N-SF64

640601

LaCL60

640601

S-BSM81

713538 N-LAK8

713539 LaC8

641569

S-BSM93

717295 N-SF1

717295 E-FD1

643584

S-BSM36

717295 SF1

717295 FD1

717295 PBH1

717480 N-LAF3

717480 LaF3

717479 S-LAM3

648339

FD2

648338

E-FD2

648338

S-TIM22

720347 BPH8

649530

E-BaCED20 649530

S-BSM71

720420 LAM58 720437 S-LAM52

N-LAK22 651562

LaCL2

651562

S-LAL54

720460 LAM61 720506 N-LAK10 720504 LaC10

N-BAF51

652585

N-LAK7

652585

LaC7

652585

S-LAL7

654396

KZFSN5

654396

ADF50

654397

BPH5

724381 NBASF51

658509

N-SSK5

658509

BaCED5

658509

S-BSM25

724381 BASF51

724381 BaFD8

658573

S-LAL11

664360

N-BASF2

728284 SF10

728284 FD10 728285 E-FD10

667484 N-BAF10

Glass type

702412 BaFD7

652449

670471

Code

700481 S-LAM51

N-KZFS11

639554

648339

Schott

Ohara

Code

670473

BaF11 BaF10

673322

N-SF5

673321

E-FD5

673322

SF5

673322

FD5

678507

LaCL9

720502 S-LAL10 722292 S-TIH18 723380 S-BAH28 726536 S-LAL60

667330

S-TIM39

728285 N-SF10

667483

S-BAH11

729547 N-LAK34 729547 TaC8

728285 S-TIH10 729547 S-LAL18

670393

BAH32

734515 TaC4

734515 S-LAL59

670473

S-BAH10

740283 PBH3W 741276 FD13

740283 PBH3

670573

S-LAL52

741278 E-FD13

741278 S-TIH13

673321

S-TIM25

741527 TaC2

741527 S-LAL61

743492 N-LAF35 743493 NbF1

743493 S-LAM60

744447 N-LAF2

744447 LaF2

744448 S-LAM2

750350 LaFN7

750353 LaF7

750353 LAM7

678507

S-LAL56

678549

LAKL12

678552

N-LAK12

678553

LaC12

678553

S-LAL12

750350 N-LAF7

689312

N-SF8

689311

E-FD8

689311

S-TIM28

754524 N-LAK33 755523 TaC6

755523 S-YGH51

689312

FD8

755276 N-SF4

755275 E-FD4

755275 S-TIH4

691547

N-LAK9

691548

LaC9

691548

S-LAL9

755276 SF4

755276 FD4

694508

LaCL5

694508

LAL58

694533

LAKN13

694532

LaC13

694532

S-LAL13

695422

S-BAH54

697554

N-LAK14

697485

LaFL2

697485

LAM59

697555

LaC14

697555

S-LAL14

697565

S-LAL64

756251 TPH55 757478 NbF2

757478 S-LAM54

762265 N-SF14

762265 FD140

762265 S-TIH14

762265 SF14

762266 FD14 762401 S-LAM55

772496 N-LAF34 772496 TaF1

772496 S-LAH66

Glasses

Table 3.4-14 Comparison of preferred optical glasses, cont. Schott Code

Hoya

Ohara

Glass type

Code

Glass type

785258

SF11

785258 FD11

785261

SF56A

785261

N-SF56

785261 FDS30

786441

N-LAF33

786439 NBFD11 786442

S-LAH51

787500

S-YGH52

788475

N-LAF21

788475 TAF4

788474

S-LAH64

794454

N-LAF32

795453

S-LAH67

800423

N-LAF36

800423 NBFD12 800422

S-LAH52

801350

N-LASF45

801350

S-LAM66

804396

S-LAH63

785258 FD110

Code

785257 785263

Glass type S-TIH11 S-TIH23

N-LASF44 804465 TAF3

804466

S-LAH65

805254

N-SF6

805254 FD60

805254

S-TIH6

805254

SF6

805254 FD6 805396 NBFD3 806333 NBFD15

806407

N-LASF43 806407 NBFD13 806409 808228

S-LAH53 S-NPH1

816445 TAFD10 816444

S-LAH54

816466 TAF5

816466

S-LAH59

834374

N-LASF40 834373 NBFD10 834372

S-LAH60

835430

N-LASF41 835430 TAFD5

835427

S-LAH55

847238

N-SF57

847238

S-TIH53

847236

SFL57

847238

SF57

850322

LASFN9

881410

N-LASF31

901315

N-LASF46

923209

SF66

847238 FDS90 847238 FDS9

847238

TIH53

874353

S-LAH75

883408 TAFD30 883408

S-LAH58

901315

LAH78

923213

PBH71

923209 E-FDS1 1003283 S-LAH79

1022291 N-LASF35

Formulas for Optical Characterization The characterization of optical glasses through the refractive index and Abbe value alone is insufficient for high-quality optical systems. A more accurate description of the properties of a glass can be achieved with the aid of the relative partial dispersion.

547

Relative Partial Dispersion. The relative partial disper-

sion Px,y for the wavelengths x and y based on the blue F hydrogen line and red C hydrogen line is given by Px,y = (n x − n y )/(n F − n C ) .

(4.15)

The corresponding value based on the blue F cadmium line and red C cadmium line is given by  = (n x − n y )/(n F − n C ) . Px,y

(4.16)

Relationship Between the Abbe Value and the Relative Partial Dispersion. A linear relationship exists

between the Abbe value and the relative partial dispersion for what are known as “normal glasses”: Px,y ≈ axy + bxy νd .

(4.17)

Deviation from the “Normal Line”. All other glasses

deviate from the “normal line” defined by ∆Px,y . For the selected wavelength pairs the ∆P-value are calculated from the following equations: Px,y = axy + bxy νd + ∆Px,y , ∆PC,t = (n C − n t )/(n F − n C ) − (0.5450 + 0.004743νd ) , ∆PC,s = (n C − n s )/(n F − n C ) − (0.4029 + 0.002331νd ) , ∆PF,e = (n F − n e )/(n F − n C ) − (0.4884 − 0.000526νd ) , ∆Pg,F = (n g − n F )/(n F − n C ) − (0.6438 − 0.001682νd ) , ∆Pi,g = (n i − n g )/(n F − n C ) − (1.7241 − 0.008382νd ) .

(4.18)

(4.19)

(4.20)

(4.21)

(4.22)

(4.23)

The “normal line” has been determined based on value pairs of glasses types K7 and F2. The term ∆Px,y quantitatively describes the deviation of the behavior of the dispersion from that of “normal glasses”. The Sellmeier dispersion formula for the refractive index, n 2 (λ) − 1 = B1 λ2 /(λ2 − C1 ) + B2 λ2 /(λ2 − C2 ) + B3 λ2 /(λ2 − C3 ) ,

(4.24)

can be derived from classical dispersion theory with the assumption of three resonance wavelengths. It is valid only for interpolation within a spectral region in which the refractive index has been measured. The vacuum wavelength λ in µm has to be used. The precision of the calculation achievable is generally better than 1 × 10−5 .

Part 3 4.5

804466

4.5 Optical Glasses

548

Part 3

Classes of Materials

Temperature Dependence of the Refractive Index. The refractive index is also dependent on temperature. This temperature dependence is represented by ∆n rel /∆T for an air pressure of 1013.3 hPa and ∆n abs /∆T in vacuum. The following equation is derived from the Sellmeier formula and is valid with the given coefficients in the temperature range −40 ◦ C < T < +80 ◦ C and within the wavelength range 435.8 nm < λ < 643.8 nm:

dn abs (λ, T ) n 2 (λ, T0 ) − 1 = dT 2n(λ, T0 ) 

E 0 + 2E 1 ∆T × D0 + 2D1 ∆T + 3D2 ∆T 2 + λ2 − λ2TK

 ,

Transmission. The transmittance of glasses is limited

by electronic excitiations and light scattering in the UV, by vibronic excitations in the IR, and by reflections and impurity absorptions within the transmission window (in the visible part of the spectrum): Fig. 3.4-27. The UV absorption edge is temperature dependent. An example is shown in Fig. 3.4-28. Spectral Internal Transmittance. The spectral internal transmittance is given by (4.30) τiλ = Φeλ /Φiλ , where Φiλ is the incident light intensity and Φeλ is the intensity at the exit.

(4.25) ◦C

where ∆T is the temperature difference in from 20 ◦ C, and λTK is an effective resonance wavelength. The changes in the refractive index and Abbe value caused by a change in the annealing rate are given by

Part 3 4.5

n d (h x ) = n d (h 0 ) + m nd log(h x /h 0 ) , (4.26) νd (h x ) = νd (h 0 ) + m νd log(h x /h 0 ) , (4.27) m nd − νd (h 0 )m nF−nC m νd = , (n F − n C ) + 2m nF−nC log(h x /h 0 ) (4.28)

where h 0 is the original annealing rate in ◦ C/h, h x is the new annealing rate in ◦ C/h, m nd is the annealing coefficient for the refractive index (Table 3.4-15), m νd is the annealing coefficient for the Abbe value and m nF−nC is the annealing coefficient for the principal dispersion. The last three quantities depend on the glass type. The measurement accuracy of the Abbe value can be calculated using σ(νd ) ≈ σ(n F − n C )νd /(n F − n C ) .

(4.29)

The accuracy of precision measurements of the refractive indices is better than ±1 × 10−5 , and the accuracy of the dispersion is ±3 × 10−6 . In the infrared wavelength range above 2 µm, the corresponding accuracies are ±2 × 10−5 and ±5 × 10−6 .

Spectral Transmission. The spectral transmission is given by τλ = τiλ Pλ , (4.31) where Pλ is the reflection factor.

Transmission (%) 100 90 80 70 60 50 40 30 20 10 0 200 500

of 5 mm: Brown line FK5; dashed line SF2; gray line SF11 Transmission (%) 100 80 60

types

40 mnd

mnF−nC

mνd

N-BK7

−0.00087

−0.000005

−0.0682

N-FK51

−0.00054

−0.000002

−0.0644

SF6

−0.00058

+0.000035

−0.0464

N-SF6

−0.0025

−0.000212

+0.0904

5000 Wavelength (nm)

Fig. 3.4-27 Transmission of three glasses for a thickness

Table 3.4-15 Annealing coefficients for selected glass Glass type

1000

20 °C 100 °C 200 °C 300 °C 400 °C 500 °C

20 0

300

400

500

600

700 800 Wavelength (µm)

Fig. 3.4-28 Influence of temperature on the UV transmission of glass F2 for a thickness of 10 mm

Glasses

Fresnel Reflectivity. For a light beam striking the surface

perpendicularly, the Fresnel reflectivity is, independent of polarization, R = (n − 1)2 /(n + 1)2 .

(4.32)

Reflection Factor. The reflection factor, taking account of multiple reflection, is given by

P = (1 − R)2 /(1 − R2 ) = 2n/(n 2 + 1) ,

(4.33)

where n is the refractive index for the wavelength λ. Conversion of Internal Transmittance to Another Layer Thickness. The conversion of data for internal

transmittance to another sample thickness is accomplished by the use of the equation log τi1 / log τi2 = d1 /d2

(4.34)

,

(4.35)

where τi1 and τi2 are the internal transmittances for the thicknesses d1 and d2 , respectively. Stress Birefringence. The change in optical path length for existing stress birefringence can be calculated from

∆s = (n − n ⊥ )d = (K − K ⊥ )dσ = Kdσ , (4.36) where K is the stress optical coefficient, dependent on the glass type, d is the length of the light path in the sample, and σ is the mechanical stress (positive for tensile stress). If K is given in 10−6 mm2 /N, d is given in mm, and σ is measured in MPa = N/mm2 , ∆s comes out in mm. For the Pockels glass SF57, the stress optical coefficient K is close to 0 in the visible wavelength range. Homogeneity. The homogeneity of the refractive index of a sample can be measured from the interferometrically measured wavefront deformation using the equation

∆n = ∆W/2d = ∆W(λ) × 633 × 10−6 /(2d[mm]) ,

(4.37)

where the wavefront deformation is in units of the wavelength and is measured using a test wavelength of 633 nm (He–Ne laser); ∆W is the wavefront deformation for double beam passage; and d is the thickness of the test piece. With special effort during melting and careful annealing, it is possible to produce pieces of glass having high homogeneity. The refractive-index homogeneity achievable for a given

549

glass type depends on the volume and the form of the individual glass piece. Values of ±5 × 10−7 (class H5) cannot be achieved for all dimensions and glass types. The properties of a selection of optical glasses are collected together in Table 3.4-16. Internal Transmittance and Color Code The internal transmittance, i. e. the light transmission excluding reflection losses, is closely related to the optical position of the glass type, according to general dispersion theory. This can be achieved, however, only by using purest raw materials and costly melting technology. The internal transmittance of lead- and arsenicfree glasses, in which lead has been replaced by other elements, is markedly less than in the lead-containing predecessor glasses. The limit of the transmission range of optical glasses towards the UV area is of special interest and is characterized by the position and slope of the UV absorption curve, which is described by a color code. The color code gives the wavelengths λ80 and λ5 , at which the transmission (including reflection losses) is 0.80 and 0.05, respectively, at 10 mm thickness. The color code 33/30 means, for example, λ80 = 330 nm and λ5 = 300 nm.

3.4.5.2 Chemical Properties The composition of optical glasses includes elements that reduce chemical resistance. For these glasses, five test methods are used to assess the chemical behavior of polished glass surfaces in typical applications. The test methods and classification numbers take the place of those described for technical glasses in Sect. 3.4.4. Data for optical properties are found in Table 3.4-16c. Climatic Resistance (ISO/WD 13384): Division into Climatic Resistance Classes CR 1–4 Climatic resistance describes the behavior of optical glasses at high relative humidity and high temperatures. In the case of sensitive glasses, a cloudy film can appear that generally cannot be wiped off. The classifications are based on the increase in transmission haze ∆H after a 30 h test period. The glasses in class CR 1 display no visible attack after being subjected to 30 h of climatic change. Under normal humidity conditions, no surface attack should be expected during the fabrication and storage of

Part 3 4.5

or

(d /d ) τi2 = τi1 2 1

4.5 Optical Glasses

550

Part 3

Classes of Materials

optical glasses in class CR 1. On the other hand, the fabrication and storage of optical glasses in class CR 4 should be done with caution because these glasses are very sensitive to climatic influences.

Part 3 4.5

Stain Resistance: Division into Stain Resistance Classes FR 0–5 The test procedure gives information about possible changes in the glass surface (stain formation) under the influence of lightly acidic water (for example perspiration and acidic condensates) without vaporization. Two test solutions are used. Test solution I is a standard acetate solution with pH = 4.6, for classes FR 0 to 3. Test solution II is a sodium acetate buffer solution with pH = 5.6, for classes FR 4 and FR 5. Interference color stains develop as a result of decomposition of the surface of the glass by the test solution. The measure used for classifying the glasses is the time that elapses before the first brown–blue stain occurs at a temperature of 25 ◦ C. Stain resistance class FR 0 contains all glasses that exhibit virtually no interference colors even after 100 h of exposure to test solution I. Glasses in classification FR 5 must be handled with particular care during processing. Acid Resistance (ISO 8424: 1987): Division into Acid Resistance Classes SR 1–4, 5, and 51–53 Acid resistance classifies the behavior of optical glasses that come into contact with large quantities of acidic solutions (from a practical standpoint, these may be perspiration, laminating substances, carbonated water, etc.). The time t required to dissolve a layer with a thickness of 0.1 µm serves as a measure of acid resistance. Two aggressive solutions are used in determining acid resistance. A strong acid (nitric acid, c = 0.5 mol/l, pH = 0.3) at 25 ◦ C is used for the more resistant glass types. For glasses with less acid resistance, a weakly acidic solution with a pH value of 4.6 (standard acetate) is used, also at 25 ◦ C. Alkali Resistance (ISO 10629) and Phosphate Resistance (ISO 9689): Division into Alkali Resistance Classes AR 1–4 and Phosphate Resistance Classes PR 1–4 These two test methods indicate the resistance to aqueous alkaline solutions in excess and use the same classification scheme. The alkali resistance indicates the sensitivity of optical glasses when they are in contact with warm, alkaline liquids, such as cooling liquids used

in grinding and polishing processes. The phosphate resistance describes the behavior of optical glasses during cleaning with phosphate-containing washing solutions (detergents). The alkali resistance class AR is based on the time required to remove a layer of glass of thickness 0.1 µm in an alkaline solution (sodium hydroxide, c = 0.01 mol/l, pH = 12) at a temperature of 50 ◦ C. The phosphate resistance class PR is based on the time required to remove a layer of glass of thickness 0.1 mm in an alkaline phosphate-containing solution (pentasodium triphosphate, Na5 P3 O10 , c = 0.01 mol/l, pH = 10) at a temperature of 50 ◦ C. The thickness is calculated from the weight loss per unit surface area and the density of the glass.

3.4.5.3 Mechanical Properties Young’s Modulus and Poisson’s Ratio The adiabatic Young’s modulus E (in units of 103 N/mm2 ) and Poisson’s ratio µ have been determined at room temperature and at a frequency of 1 kHz using carefully annealed test samples. Data are listed in Table 3.4-16c. In most cases, the values decrease slightly with temperature. The torsional modulus can be calculated from

G = E/[2(1 + µ)] .

(4.38)

The longitudinal sound velocity is  vlong =

E(1 − µ) , (1 + µ)(1 − 2µ)

(4.39)

where is the density. Knoop Hardness The Knoop hardness (HK) of a material is a measure of the residual surface changes after the application of pressure with a test diamond. The standard ISO 9385 describes the measurement procedure for glasses. In accordance with this standard, values for Knoop hardness HK are listed in the data sheets for a test force of 0.9807 N (corresponds to 0.1 kp) and an effective test period of 20 s. The test was performed on polished glass surfaces at room temperature. The data for hardness values are rounded to 10 HK 0.1/20. The microhardness is a function of the magnitude of the test force and decreases with increasing test force.

Table 3.4-16a Properties of optical glasses. Refractive index and Sellmeier constants Glass type

Refractive index nd ne

Abbe value vd ve

Constants of the Sellmeier dispersion formula B1 B2 B3

C1

C2

C3

9.97743871 × 10−03

4.70450767 × 10−02

1.11886764 × 10+02

9.37357162 × 10−01

36.11

K10

1.50137 1.50349 56.41

56.15

1.15687082 × 10+00 6.42625444 × 10−02 8.72376139 × 10−01 8.09424251 × 10−03 3.86051284 × 10−02 1.04747730 × 10+02

LASF35

2.02204 2.03035 29.06

28.84

2.45505861 × 10+00 4.53006077 × 10−01 2.38513080 × 10+00 1.35670404 × 10−02 5.45803020 × 10−02 1.67904715 × 10+02

LF5

1.58144 1.58482 40.85

40.57

1.28035628 × 10+00 1.63505973 × 10−01 8.93930112 × 10−01 9.29854416 × 10−03 4.49135769 × 10−02 1.10493685 × 10+02

LLF1

1.54814 1.55098 45.89

45.60

1.23326922 × 10+00 1.16923839 × 10−01 8.62645379 × 10−01 8.85396812 × 10−03 4.36875155 × 10−02 1.04992168 × 10+02

N-BAF10

1.67003 1.67341 47.11

46.83

1.58514950 × 10+00 1.43559385 × 10−01 1.08521269 × 10+00 9.26681282 × 10−03 4.24489805 × 10−02 1.05613573 × 10+02

N-BAF52

1.60863 1.61173 46.60

46.30

1.43903433 × 10+00 9.67046052 × 10−02 1.09875818 × 10+00 9.07800128 × 10−03 5.08212080 × 10−02 1.05691856 × 10+02

N-BAK4

1.56883 1.57125 55.98

55.70

1.28834642 × 10+00 1.32817724 × 10−01 9.45395373 × 10−01 7.79980626 × 10−03 3.15631177 × 10−02 1.05965875 × 10+02

N-BALF4

1.57956 1.58212 53.87

53.59

1.31004128 × 10+00 1.42038259 × 10−01 9.64929351 × 10−01 7.96596450 × 10−03 3.30672072 × 10−02 1.09197320 × 10+02

N-BASF64

1.70400 1.70824 39.38

39.12

1.65554268 × 10+00 1.71319770 × 10−01 1.33664448 × 10+00 1.04485644 × 10−02 4.99394756 × 10−02 1.18961472 × 10+02

N-BK7

1.51680 1.51872 64.17

63.96

1.03961212 × 10+00 2.31792344 × 10−01 1.01046945 × 10+00 6.00069867 × 10−03 2.00179144 × 10−02 1.03560653 × 10+02

N-FK56

1.43425 1.43534 94.95

94.53

9.11957171 × 10−01 1.28580417 × 10−01 9.83146162 × 10−01 4.50933489 × 10−03 1.53515963 × 10−02 2.23961126 × 10+02

N-KF9

1.52346 1.52588 51.54

51.26

1.19286778 × 10+00 8.93346571 × 10−02 9.20819805 × 10−01 8.39154696 × 10−03 4.04010786 × 10−02 1.12572446 × 10+02

N-KZFS2

1.55836 1.56082 54.01

53.83

1.23697554 × 10+00 1.53569376 × 10−01 9.03976272 × 10−01 7.47170505 × 10−03 3.08053556 × 10−02 7.01731084 × 10+01

N-LAF2

1.74397 1.74791 44.85

44.57

1.80984227 × 10+00 1.57295550 × 10−01 1.09300370 × 10+00 1.01711622 × 10−02 4.42431765 × 10−02 1.00687748 × 10+02

N-LAK33

1.75398 1.75740 52.43

52.20

1.45796869 × 10+00 5.55403936 × 10−01 1.19938794 × 10+00 6.80545280 × 10−03 2.25253283 × 10−02 8.27543327 × 10+01

N-LASF31

1.88067 1.88577 41.01

40.76

1.71317198 × 10+00 7.18575109 × 10−01 1.72332470 × 10+00 8.19172228 × 10−03 2.97801704 × 10−02 1.38461313 × 10+02

N-PK51

1.52855 1.53019 76.98

76.58

1.15610775 × 10+00 1.53229344 × 10−01 7.85618966 × 10−01 5.85597402 × 10−03 1.94072416 × 10−02 1.40537046 × 10+02

N-PSK57

1.59240 1.59447 68.40

68.01

9.88511414 × 10−01 5.10855261 × 10−01 7.58837122 × 10−01 4.78397680 × 10−03 1.58020289 × 10−02 1.29709222 × 10+02

N-SF1

1.71736 1.72308 29.62

29.39

1.60865158 × 10+00 2.37725916 × 10−01 1.51530653 × 10+00 1.19654879 × 10−02 5.90589722 × 10−02 1.35521676 × 10+02

N-SF56

1.78470 1.79179 26.10

25.89

1.73562085 × 10+00 3.17487012 × 10−01 1.95398203 × 10+00 1.29624742 × 10−02 6.12884288 × 10−02 1.61559441 × 10+02

N-SK16

1.62041 1.62286 60.32

60.08

1.34317774 × 10+00 2.41144399 × 10−01 9.94317969 × 10−01 7.04687339 × 10−03 2.29005000 × 10−02 9.27508526 × 10+01

N-SSK2

1.62229 1.62508 53.27

52.99

1.43060270 × 10+00 1.53150554 × 10−01 1.01390904 × 10+00 8.23982975 × 10−03 3.33736841 × 10−02 1.06870822 × 10+02

SF1

1.71736 1.72310 29.51

29.29

1.55912923 × 10+00 2.84246288 × 10−01 9.68842926 × 10−01 1.21481001 × 10−02 5.34549042 × 10−02 1.12174809 × 10+02

SF11

1.78472 1.79190 25.76

25.55

1.73848403 × 10+00 3.11168974 × 10−01 1.17490871 × 10+00 1.36068604 × 10−02 6.15960463 × 10−02 1.21922711 × 10+02

SF2

1.64769 1.65222 33.85

33.60

1.40301821 × 10+00 2.31767504 × 10−01 9.39056586 × 10−01 1.05795466 × 10−02 4.93226978 × 10−02 1.12405955 × 10+02

SF66

1.92286 1.93325 20.88

20.73

2.07842233 × 10+00 4.07120032 × 10−01 1.76711292 × 10+00 1.80875134 × 10−02 6.79493572 × 10−02 2.15266127 × 10+02

SK51

1.62090 1.62335 60.31

60.02

1.44112715 × 10+00 1.43968387 × 10−01 8.81989862 × 10−01 7.58546975 × 10−03 2.87396017 × 10−02 9.46838154 × 10+01

K7

1.51112 1.51314 60.41

60.15

1.12735550 × 10+00 1.24412303 × 10−01 8.27100531 × 10−01 7.20341707 × 10−03 2.69835916 × 10−02 1.00384588 × 10+02

N-SF6

1.80518 1.81266 25.36

25.16

1.77931763 × 10+00 3.38149866 × 10−01 2.08734474 × 10+00 1.33714182 × 10−02 6.17533621 × 10−02 1.74017590 × 10+02

SF6

1.80518 1.81265 25.43

25.24

1.72448482 × 10+00 3.90104889 × 10−01 1.04572858 × 10+00 1.34871947 × 10−02 5.69318095 × 10−02 1.18557185 × 10+02

N-FK51

1.48656 1.48794 84.47

84.07

9.71247817 × 10−01 2.16901417 × 10−01 9.04651666 × 10−01 4.72301995 × 10−03 1.53575612 × 10−02 1.68681330 × 10+02

LithosilTM Q

1.45843 1.46004 67.87

67.67

6.69422575 × 10−01 4.34583937 × 10−01 8.71694723 × 10−01 4.48011239 × 10−03 1.32847049 × 10−02 9.53414824 × 10+01

4.5 Optical Glasses

1.62004 1.62408 36.37

551

Part 3 4.5

2.09073176 × 10−01

Glasses

F2

1.34533359 × 10+00

552

Part 3

Classes of Materials

Table 3.4-16b Data for dn/dT Glass type

Data for dn/dT 106 D0

108 D1

1011 D2

107 E0 9.34

1010 E1

λTK (µm)

10.4

0.250

F2

1.51

1.56

− 2.78

K10

4.86

1.72

− 3.02

LASF35

0.143

0.871

− 2.71

0.971

− 2.83

8.36

9.95

0.228

LF5

− 2.27

3.82 10.2

4.53 15.0

0.260 0.263

LLF1

0.325

1.74

− 6.12

6.53

2.58

0.233

N-BAF10

3.79

1.28

− 1.42

5.84

7.60

0.220

N-BAF52

1.15

1.27

− 0.508

5.64

6.38

0.238

N-BAK4

3.06

1.44

− 2.23

5.46

6.05

0.189

N-BALF4

5.33

1.47

− 1.58

5.75

6.58

0.195

N-BASF64

1.60

1.02

− 2.68

7.87

9.65

0.229

N-BK7

1.86

1.31

− 1.37

4.34

6.27

0.170

N-FK56

Part 3 4.5

N-KF9

− 20.4

− 1.03

− 1.66

N-KZFS2

6.77

4.37

0.138

− 1.01

0.243

6.10

6.96

0.217

1.31

− 1.23

3.84

5.51

0.196

0.920

− 0.600

6.43

6.11

0.220

N-LAK33

2.57

1.16

− 7.29

6.01

1.59

0.114

N-LASF31

2.29

0.893

− 1.59

6.52

8.09

0.236

N-LAF2

− 3.64

3.41

0.844

N-PK51

− 19.8

− 0.606

1.60

4.16

5.01

0.134

N-PSK57

− 22.3

− 0.560

0.997

4.47

5.63

−

N-SF1

− 3.72

0.805

− 1.71

8.98

13.4

0.276

N-SF56

− 4.13

0.765

− 1.12

9.90

15.7

0.287

N-SK16

− 0.0237

1.32

− 1.29

4.09

5.17

0.170

N-SSK2

5.21

1.34

− 1.01

5.21

5.87

0.199

4.84

1.70

− 4.52

13.8

12.6

0.259

1.81

− 5.03

14.6

15.8

0.282

1.75

− 1.29

10.8

10.3

0.249

−

−

−

SF1 SF11

11.2

SF2 SF66

1.10 −

−

SK51

− 5.63

0.738

− 6.20

3.91

K7

− 1.67

0.880

− 2.86

5.42

N-SF6

− 4.93

0.702

− 2.40

9.84

SF6 N-FK51 LithosilTM Q

6.69 − 18.3 20.6

−

2.64

0.230

7.81

0.172

15.4

0.290

17.0

0.272

1.78

− 3.36

− 0.789

− 0.163

3.74

3.46

0.150

2.51

− 2.47

3.12

4.22

0.160

17.7

Table 3.4-16c Chemical and physical data Stressoptical coefficient K

Chemical properties

Density Viscosity (dPa s) 1014.5 1013 107.6

CR FR SR

AR PR

(10−6 mm2 /N) 0 0 0 0 0 0 0 0 0 0 0 0 0 4 3 1 0 0 0 0 0 4 0 1 0 0 5 3 0 0 3 0 −

1 1 1.3 1 1 4.3 1 1.2 1 3.2 1 52.3 1 52.3 52.2 51.3 2 51.2 51.3 1 1 53.3 1.2 3.2 1 2 53.4 52.3 2 2 51.3 52.3 1

2.3 1 1 2.3 2 1.3 1.3 1 1 1.2 2 4.3 1 4.3 1 1 1 3.3 1.2 1 1.3 3.3 1 2.3 1.2 2.3 2.3 1.3 1 1 2.3 2.2 1

1.3 1.2 1.3 2 1 1 1 1 1 1 2.3 4.3 1 4.2 2.2 2.3 1 4.3 4.3 1 1 3.2 1 3 1 2 4.2 4.3 2.3 1 3.3 4.3 −

3.61 2.52 5.41 3.22 2.94 3.75 3.05 3.05 3.11 3.20 2.51 3.54 2.50 2.55 4.30 4.26 5.41 3.96 4.48 3.03 3.28 3.58 3.53 4.46 4.74 3.86 6.03 3.52 2.53 3.37 5.18 3.73 2.20

0.557 0.770 0.445 0.657 0.650 0.560 0.680 0.680 0.690 − 0.858 0.750 0.860 0.830 0.510 0.554 − − 0.490 0.750 0.700 0.578 0.580 − 0.431 0.498 0.340 − − 0.69 0.389 0.636 0.790

57 65 132 59 60 89 86 77 77 105 82 70 66 66 94 124 124 74 69 90 91 89 82 56 66 55 51 75 69 93 55 81 72

432 459 774 419 448 660 594 581 578 582 557 422 476 491 653 652 758 496 497 553 592 636 653 417 503 441 384 597 513 594 423 420 980

421 453 − 411 426 652 596 569 584 585 557 416 476 488 645 648 756 486 499 554 585 633 655 415 500 428 385 579 − 591 410 403 1080

593 691 − 585 628 790 723 725 661 712 719 − 640 600 742 − − − − 660 691 750 801 566 635 600 482 684 712 694 538 − 1600

0.780 1.120 0.920 0.866 − 0.780 0.960 0.880 0.850 − 1.114 0.840 1.040 0.810 0.670 0.900 0.910 − 0.560 1.000 0.940 0.818 0.810 − 0.737 0.735 0.530 − − 0.96 0.673 0.911 1.310

8.20 6.50 7.40 9.10 8.10 6.18 6.86 6.99 6.52 7.30 7.10 − 9.61 4.43 8.06 6.00 6.80 12.70 13.17 9.13 8.70 6.30 5.81 8.10 6.10 8.40 9.01 8.90 8.4 9.03 8.1 13.3 0.50

9.20 7.40 8.50 10.60 9.20 7.04 7.83 7.93 7.41 8.70 8.30 16.16 10.95 5.43 9.10 7.00 7.70 14.40 14.75 10.54 10.00 7.30 6.65 8.80 6.80 9.20 11.48 10.10 9.7 10.39 9 15.3 −

HK 0.220 0.190 0.303 0.223 0.208 0.271 0.237 0.240 0.245 0.264 0.206 0.293 0.225 0.266 0.288 0.291 0.299 0.295 0.298 0.250 0.255 0.264 0.261 0.232 0.235 0.227 0.258 0.291 0.214 0.262 0.244 0.293 0.170

420 470 810 450 450 620 600 550 540 650 610 350 480 490 530 780 770 400 370 540 560 600 570 390 450 410 310 450 520 550 370 430 580

4.5 Optical Glasses

1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 2 1 1 1 4 1 2 1 1 2 2 3 1 2 2 1

(103 N/mm2 )

Glasses

F2 2.81 K10 3.12 LASF35 0.73 LF5 2.83 LLF1 3.05 N-BAF10 2.37 N-BAF52 2.42 N-BAK4 2.90 N-BALF4 3.01 N-BASF64 2.38 N-BK7 2.77 N-FK56 0.68 N-KF9 2.74 N-KZFS2 4.02 N-LAF2 1.42 N-LAK33 1.49 N-LASF31 1.10 N-PK51 0.54 N-PSK57 0.13 N-SF1 2.72 N-SF56 2.87 N-SK16 1.90 N-SSK2 2.51 SF1 1.80 SF11 1.33 SF2 2.62 SF66 − 1.20 SK51 1.47 K7 2.95 N-SF6 2.82 SF6 0.65 N-FK51 0.70 LithosilTM Q 3.40

Mechanical properties Young’s Poisson’s Knoop modulus E ratio µ hardness

at temperature (g/cm3 ) (◦ C) (◦ C) (◦ C)

Thermal properties Heat Heat Thermal expansion capacity conductivity cp λ α(30/70) α(20/300) (J/g K) (W/m K) (10−6 /K) (10−6 /K)

553

Part 3 4.5

Glass type

554

Part 3

Classes of Materials

Table 3.4-16d Internal transmission and color code

Part 3 4.5

Glass

Color

Internal transmission measured for 25 mm sample thickness at wavelength λ (nm)

type

code

2500

2325

1970

1530

1060

700

660

620

580

546

500

460

436

F2

35/32

0.610

0.700

0.890

0.990

0.998

0.998

0.996

0.997

0.997

0.997

0.996

0.993

0.991

K10

33/30

0.520

0.630

0.850

0.983

0.996

0.997

0.994

0.993

0.993

0.992

0.991

0.990

0.988

LASF35

−/37

0.690

0.880

0.972

0.992

0.990

0.978

0.970

0.962

0.950

0.920

0.810

0.630

0.470

LF5

34/31

−

0.660

0.870

0.992

0.998

0.998

0.998

0.998

0.997

0.997

0.996

0.995

0.994

LLF1

33/31

0.500

0.610

0.840

0.990

0.996

0.997

0.996

0.996

0.997

0.997

0.996

0.996

0.996

N-BAF10

39/35

0.450

0.680

0.920

0.980

0.994

0.994

0.990

0.991

0.990

0.990

0.981

0.967

0.954

N-BAF52

39/35

0.390

0.630

0.890

0.975

0.994

0.993

0.990

0.989

0.990

0.989

0.980

0.967

0.954

N-BAK4

36/33

0.540

0.710

0.900

0.982

0.995

0.997

0.995

0.995

0.996

0.996

0.994

0.989

0.988

N-BALF4

37/33

0.580

0.740

0.920

0.984

0.993

0.997

0.995

0.995

0.996

0.995

0.993

0.986

0.983

N-BASF64

40/35

0.450

0.670

0.900

0.970

0.985

0.970

0.955

0.949

0.949

0.950

0.940

0.920

0.900

N-BK7

33/29

0.360

0.560

0.840

0.980

0.997

0.996

0.994

0.994

0.995

0.996

0.994

0.993

0.992

N-FK56

33/28

−

−

0.979

0.991

0.996

0.996

0.996

0.996

0.996

0.996

0.996

0.996

0.995

N-KF9

37/34

0.300

0.430

0.740

0.981

0.995

0.997

0.995

0.994

0.996

0.996

0.994

0.990

0.988

N-KZFS2

34/30

0.040

0.260

0.800

0.940

0.991

0.996

0.994

0.994

0.994

0.994

0.992

0.987

0.981

N-LAF2

40/34

0.400

0.690

0.930

0.990

0.997

0.996

0.993

0.992

0.993

0.994

0.983

0.962

0.940

N-LAK33

39/32

0.090

0.400

0.850

0.975

0.995

0.991

0.990

0.990

0.990

0.990

0.987

0.977

0.967

N-LASF31

45/32

0.540

0.810

0.960

0.992

0.993

0.994

0.994

0.993

0.993

0.990

0.973

0.940

0.910

N-PK51

35/29

0.890

0.920

0.965

0.985

0.992

0.991

0.991

0.992

0.994

0.995

0.993

0.989

0.987

N-PSK57

34/29

−

−

0.950

0.970

0.982

0.996

0.996

0.996

0.996

0.996

0.992

0.991

0.991

N-SF1

41/36

0.460

0.580

0.850

0.973

0.995

0.990

0.986

0.987

0.990

0.986

0.968

0.940

0.910

N-SF56

44/37

0.590

0.680

0.900

0.981

0.996

0.986

0.981

0.981

0.983

0.976

0.950

0.910

0.860

N-SK16

36/30

0.260

0.540

0.880

0.973

0.995

0.996

0.994

0.993

0.994

0.994

0.991

0.984

0.981

N-SSK2

37/33

0.500

0.720

0.930

0.981

0.992

0.996

0.994

0.993

0.995

0.995

0.992

0.985

0.980

SF1

39/34

0.650

0.730

0.900

0.985

0.996

0.996

0.995

0.995

0.996

0.996

0.993

0.984

0.976

SF11

44/39

0.610

0.700

0.930

0.982

0.997

0.993

0.991

0.991

0.991

0.989

0.976

0.940

0.860

SF2

37/33

0.620

0.710

0.880

0.985

0.996

0.996

0.994

0.995

0.995

0.995

0.993

0.988

0.982

SF66

48/38

0.700

0.740

0.920

0.990

0.995

0.990

0.989

0.989

0.988

0.985

0.965

0.890

0.770

SK51

36/31

0.270

0.520

0.830

0.959

0.993

0.993

0.993

0.993

0.993

0.993

0.990

0.981

0.975

K7

33/30

0.340

0.500

0.790

0.980

0.994

0.996

0.995

0.995

0.994

0.994

0.993

0.990

0.990

N-SF6

45/37

0.850

0.880

0.962

0.994

0.994

0.987

0.980

0.979

0.980

0.970

0.940

0.899

0.850

SF6

42/36

0.730

0.780

0.930

0.990

0.996

0.996

0.995

0.995

0.995

0.994

0.989

0.972

0.940

N-FK51

34/28

0.750

0.840

0.940

0.980

0.994

0.995

0.995

0.996

0.997

0.997

0.996

0.993

0.992

LithosilTM Q

17/16

0.780

−

−

−

−

−

−

−

−

−

−

−

−

Glasses

4.5 Optical Glasses

555

Internal transmission measured for 25 mm sample thickness at wavelength λ (nm) 405

400

390

380

370

365

350

334

320

310

300

290

248

200

193

0.990

0.986

0.984

0.977

0.963

0.940

0.920

0.780

0.210

−

−

−

−

−

−

−

0.988

0.987

0.986

0.982

0.973

0.966

0.958

0.910

0.720

0.310

0.130

0.020

−

−

−

−

0.320

0.170

0.120

0.050

0.010

−

−

−

−

−

−

−

−

−

−

−

0.993

0.992

0.992

0.984

0.973

0.961

0.954

0.880

0.570

0.040

−

−

−

−

−

−

0.995

0.994

0.993

0.992

0.988

0.984

0.981

0.955

0.810

0.300

0.010

−

−

−

−

−

0.940

0.900

0.880

0.800

0.660

0.440

0.310

0.010

−

−

−

−

−

−

−

−

0.938

0.900

0.880

0.800

0.650

0.370

0.210

−

−

−

−

−

−

−

−

−

0.987

0.983

0.980

0.967

0.940

0.890

0.840

0.550

0.070

−

−

−

−

−

−

−

0.981

0.970

0.964

0.940

0.900

0.820

0.750

0.380

−

−

−

−

−

−

−

−

0.880

0.840

0.820

0.750

0.610

0.370

0.220

−

−

−

−

−

−

−

−

−

0.993

0.993

0.992

0.989

0.983

0.977

0.971

0.920

0.780

0.520

0.250

0.050

−

−

−

−

0.994

0.996

0.996

0.995

0.992

0.985

0.975

0.920

0.760

0.460

0.210

0.060

0.010

−

−

−

0.985

0.975

0.965

0.940

0.880

0.770

0.680

0.210

−

−

−

−

−

−

−

−

0.975

0.967

0.963

0.950

0.930

0.910

0.890

0.800

0.590

0.240

0.030

−

−

−

−

−

0.915

0.865

0.840

0.760

0.630

0.430

0.310

0.025

−

−

−

−

−

−

−

−

0.954

0.928

0.910

0.860

0.790

0.690

0.630

0.400

0.140

0.020

−

−

−

−

−

−

0.880

0.840

0.820

0.750

0.650

0.530

0.460

0.210

0.040

0.020

−

−

−

−

−

−

0.986

0.985

0.984

0.977

0.965

0.940

0.910

0.750

0.430

0.120

0.030

−

−

−

−

−

0.991

0.991

0.992

0.992

0.989

0.975

0.965

0.880

0.680

0.380

0.130

0.020

−

−

−

−

0.870

0.760

0.700

0.520

0.250

0.030

−

−

−

−

−

−

−

−

−

−

0.780

0.640

0.570

0.370

0.130

−

−

−

−

−

−

−

−

−

−

−

0.979

0.974

0.970

0.956

0.930

0.890

0.860

0.700

0.400

0.110

0.020

−

−

−

−

−

0.975

0.963

0.954

0.920

0.860

0.750

0.670

0.250

−

−

−

−

−

−

−

−

0.961

0.930

0.920

0.870

0.790

0.640

0.500

0.030

−

−

−

−

−

−

−

−

0.700

0.340

0.200

0.010

−

−

−

−

−

−

−

−

−

−

−

−

0.975

0.962

0.954

0.920

0.870

0.790

0.720

0.370

−

−

−

−

−

−

−

−

0.610

0.340

0.240

0.050

−

−

−

−

−

−

−

−

−

−

−

−

0.971

0.963

0.958

0.940

0.910

0.850

0.800

0.600

0.300

0.100

0.030

−

−

−

−

−

0.990

0.990

0.990

0.988

0.983

0.976

0.971

0.940

0.780

0.420

0.100

−

−

−

−

0.780

0.640

0.570

0.370

0.140

−

−

−

−

−

−

−

−

−

−

−

0.900

0.810

0.760

0.620

0.370

0.100

0.020

−

−

−

−

−

−

−

−

−

0.992

0.993

0.993

0.992

0.988

0.976

0.963

0.875

0.630

0.300

0.120

0.035

0.010

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

0.995

0.990

0.980

Part 3 4.5

420

556

Part 3

Classes of Materials

Part 3 4.6

Viscosity As explained in the introduction, glasses pass through three viscosity ranges between the melting temperature and room temperature: the melting range, the supercooled melt range, and the solidification range. The viscosity increases during the cooling of the melt, starting from 100 –104 dPa s. A transition from a liquid to a plastic state is observed between 104 and 1013 dPa s. The softening point, i. e. the temperature where the viscosity is 107.6 dPa s, identifies the plastic range in which glass parts rapidly deform under their own weight. The glass structure can be described as solidified or “frozen” above 1013 dPa s. At this viscosity, the internal stresses in glass anneal out equalize in approximately 15 min. The temperature at which the viscosity is 1013 dPa s is called the upper annealing point, and is important for the annealing of glasses. In accordance with ISO 7884-8, the rate of change of the relative linear thermal expansion can be used to determine the transformation temperature Tg , which is close to the temperature at which the viscosity is 1013 dPa s. Precision optical surfaces may deform and refractive indices may change if a temperature of Tg − 200 K is exceeded during any thermal treatment. Coefficient of Linear Thermal Expansion The typical curve of the linear thermal expansion of a glass begins with an increase in slope from absolute zero to approximately room temperature. Then a nearly linear increase to the beginning of the plastic behavior follows. The transforma-

tion range is distinguished by a distinct bending of the expansion curve, which results from the increasing structural rearrangement in the glass. Above this range, the expansion again exhibits a nearly linear increase, but with a noticeably greater slope. Two averaged coefficients of linear thermal expansion α are usually given: α30/70 , averaged from −30 ◦ C to +70 ◦ C, which is the relevant value for room temperature; and α20/300 , averaged from +20 ◦ C to +300 ◦ C, which is the standard international value. These values are listed in Table 3.4-16.

3.4.5.4 Thermal Properties Thermal Conductivity The range of values for the thermal conductivity of glasses at room temperature extends from 1.38 W/m K (pure vitreous silica) to about 0.5 W/m K (high-leadcontent glasses). The most commonly used silicate glasses have values between 0.9 and 1.2 W/m K. All data in Table 3.4-16c are given for a temperature of 90 ◦ C, with an accuracy of ±5%. Specific Thermal Capacity The mean isobaric specific heat capacities c p (20 ◦ C; 100 ◦ C) listed in Table 3.4-16c were measured from the heat transfer from a hot glass sample at 100 ◦ C into a liquid calorimeter at 20 ◦ C. The values of c p (20 ◦ C; 100 ◦ C) and also of the true thermal capacity c p (20 ◦ C) for silicate glasses range from 0.42 to 0.84 J/g K.

3.4.6 Vitreous Silica Vitreous silica has a unique set of properties. It is produced either from natural quartz by fusion or, if extreme purity is required, by chemical vapor deposition or via a sol–gel routes. Depending on the manufacturing process, variable quantities impurities are incorporated in the ppm or ppb range, such as Fe, Mg, Al, Mn, Ti, Ce, OH, Cl, and F. These impurities and radiationinduced defects, as well as complexes of impurities and defects, and also overtones, control the UV and IR transmittance. In the visible part of the spectrum, Rayleigh scattering from thermodynamically caused density fluctuations dominates. Defects are also responsible for the damage threshold under radiation load, and for fluorescence. The refractive index n and the absorption

constant K as a function of wavelength are found in Fig. 3.4-29. The highest transmittance is required for applications in optical communication networks, in optics for lithography, and in high-power laser physics. For certain applications, for example to increase the refractive index in the IR in fiber optics, the silica is “doped” with GeO2 , P2 O5 , B2 O3 , etc. in the range of 5–10%. In such cases the scattering loss increases owing to concentration fluctuations. There are also many technical applications which make use of the chemical inertness, light weight, high temperature stability, thermal-shock resistance, and low thermal expansion of vitreous silica. A very low thermal

Glasses

Refractive index n(λ ) 3.5 n k 3.0

Absorption constant k( λ ) 101 100

2.5 2.0

10–1

1.5

10–2

Table 3.4-17 Electrical

4.6 Vitreous Silica

557

properties of vitreous silica

(LithosilTM )

Dielectric constant εr Dielectric loss angle ϕ tan δ (δ = 90◦ − ϕ) Electrical resistivity

3.8 ± 0.2 89.92◦ ± 0.03◦ at 25 ◦ C and 1 MHz 14 ± 5 × 10−4 1.15 × 1018 (Ω cm) at 20 ◦ C

1.0 10–3

0.5 0

10–1

100

101 Wavelength λ (µm)

10–4

Fig. 3.4-29 Measured optical constants n(λ) and k(λ) of vitreous silica according to [4.16]

The relatively open structure of vitreous silica provides space for the incorporation and diffusion of molecular species. The data in the literature are not very consistent; Table 3.4-18 should serve as an orientation. The pressure dependence of the solubility is small up to about 100 atm. The diffusion coefficient depends on temperature as

3.4.6.1 Properties of Synthetic Silica

D = D0 T exp (−Q/RT ) .

The precise data for materials from various suppliers differ slightly, depending on the thermal history and impurity concentration. The data listed in Table 3.4-16a–d and in Table 3.4-17, are for LithosilTM Q0 (Schott Lithotec). The various quantities are defined in the same way as for optical glasses, as described in Sect. 3.4.5.

(4.40)

Water can react with the silica network: H2 O + Si−O−Si = 2 Si−OH .

(4.41)

The reaction has a strong influence on the concentration and apparent diffusion of dissolved molecular water.

Table 3.4-18 Solubility and diffusion of molecular gases in vitreous silica (LithosilTM ) Gas

Helium

Molecular diameter (nm)

0.20

cglass /cgas at

Dissolved molecules S (cm−3 atm−1 )

Diffusion coefficient D0 (cm2 /s)

Activation energy Q (kJ/mole)

200–1000 ◦ C

at 200 ◦ C

25 ◦ C

0.025

3.9 × 10−17

2.4 × 10−8

5.5 × 10−5

20

5.0 × 10−12

2.5 × 10−6

37

1000 ◦ C

Neon

0.24

0.019

3.1 × 10−17

Hydrogen

0.25

0.03

4.7 × 10−17

2.2 × 10−11

7.3 × 10−6

36

Argon

0.32

0.01

1.5 × 10−17

−

1.4 × 10−9

111

Oxygen

0.32

0.01

1.5 × 10−17

−

6.6 × 10−9

105

Water

0.33

−

−

−

≈ 3.0 × 10−7

71

Nitrogen

0.34

−

−

−

−

110

Krypton

0.42

−

−

−

−

≈ 190

Xenon

0.49

−

−

−

−

≈ 300

Part 3 4.6

expansion is obtained in ULE glass (Corning “ultralow expansion” glass) by doping with ≈ 9% TiO2 .

3.4.6.2 Gas Solubility and Molecular Diffusion

558

Part 3

Classes of Materials

3.4.7 Glass-Ceramics

Part 3 4.7

Glass-ceramics are distinguished from glasses and from ceramics by the characteristics of their manufacturing processes (see introduction to this chapter 3.4) as well as by their physico-chemical properties. They are manufactured in two principal production steps. In the first step, a batch of exactly defined composition is melted (as for a conventional glass). The composition is determined by the desired properties of the endproduct and by the necessary working properties of the glass. After melting, the product is shaped by pressing, blowing, rolling, or casting, and then annealed. In this second step, “glassy” articles are partly crystallized by use of a specific temperature–time program between 800 and 1200 ◦ C (this program must be defined for each composition). Apart from the crystalline phase, with crystals 0.05–5 µm in size, this material contains a residual glass phase that amounts to 5–50% of the volume. In the temperature range between 600 and 700 ◦ C, small amounts of nucleating agents (e.g. TiO2 , ZrO2 , or F) induce precipitation of crystal nuclei. When the temperature is increased, crystals grow on these nuclei. Their type and properties, as well as their number and size, are predetermined by the glass composition and the annealing program. By selection of an appropriate program, either transparent, slightly opaque, or highly opaque, nontransparent glass-ceramics can be produced. Unlike conventional ceramics, these glass ceramics are fully dense and pore-free. Like the composition of glasses, the composition of glass-ceramics is highly variable. Some well-known compositions lie within the following systems: Li2 O−Al2 O3 −SiO2 , MgO−Al2 O3 −SiO2 , and CaO−P2 O5 −Al2 O3 −SiO2 . Glass-ceramics of the Li2 O−Al2 O3 −SiO2 system, which contain small amounts of alkali and alkalineearth oxides, as well as TiO2 and ZrO2 as nucleating agents, have achieved the greatest commercial importance. On the basis of this system, glass-ceramics with coefficients of linear thermal expansion near to zero can be produced (Fig. 3.4-30 and Table 3.4-19). This exceptional property results from the bonding of crystalline constituents (such as solid solutions of h-quartz, h-eucryptite, or h-spodumene) which have negative coefficients of thermal expansion with the residual glass phase of the system, which has a positive coefficient of thermal expansion. Such “α = 0 glass-ceramics” can be subjected to virtually any thermal shock or temperature variation below

700 ◦ C. Wall thickness, wall thickness differences, and complicated shapes are of no significance. Another technical advantage is the exceptionally high dimensional and shape stability of objects made from these materials, even when the objects are subjected to considerable temperature variations. The Zerodur® glass-ceramic, whose coefficient of linear thermal expansion at room temperature can be kept at ≤ 0.05 × 10−6 /K (Table 3.4-19), was especially developed for the production of large mirror blanks for astronomical telescopes. Zerodur® has further applications in optomechanical precision components such as length standards, and mirror spacers in lasers. With ∆l/l/10–4 20

Soda–lime glass

15 10

Duran® borosilicate glass

5 0

Glass-ceramics –5 –200

0

200

400

600 800 Temperature (°C)

Fig. 3.4-30 Thermal expansion of glass-ceramics com-

pared with borosilicate glass 3.3 and soda–lime glass Table 3.4-19 Coefficient of linear thermal expansion α,

density, and elastic properties of Zerodur® and Ceran® glass-ceramics Zerodur® α0/50

α20/300 α20/500 α20/600 α20/700 Density Young’s modulus E Poisson’s ratio µ

0 ± 0.05 0 ± 0.1 0 ± 0.15 + 0.1 − + 0.2 −

Ceran®

Units

Product class

− − −

10−6 /K 10−6 /K 10−6 /K

1 2 3

− 0.2 − 0.01 − + 0.15

10−6 /K 10−6 /K 10−6 /K 10−6 /K

2.53

2.56

g/cm3

91 × 103

92 × 103

N/mm2

0.24

0.24

Glasses

a length aging coefficient A (where L = L 0 (1 + A∆t), ∆t = time span) below 1 × 10−7 /y, Zerodur® has excellent longitudinal stability. The Ceran® glass-ceramic is colored and is designed for applications in cooker surface panels. As in glasses, the variability of the composition can be used to design very different sets of properties of glass-ceramics. Some examples are:

• • •

photosensitive, etchable glass-ceramics based on Ag doping: Foturan (Schott), and Fotoform and Fotoceram (Corning); machinable glass-ceramics based on mica crystals, for example for electronic packaging: Macor and Dicor (Corning), and Vitronit (Vitron and Jena); glass-ceramics used as substrates for magnetic disks, based on spinel or gahnite crystals, resulting in a very

• •

•

4.8 Glasses for Miscellaneous Applications

high elastic modulus and thus stiffness: Neoceram (NEG), and products from Corning and Ohara; glass-ceramics with extremely good weathering properties for architectural applications: Neoparies (NEG) and Cryston (Asahi Glass); biocompatible, bioactive glass-ceramics based on apatite and orthophosphate crystals for dental restoration or bone replacement in medicine: Cerabone (NEG), Bioverit (Vitron), Ceravital, IPS Empress, etc.; highly transparent glass-ceramics and glassceramics with specific dopings for temperatureresistant fiber optic components, high-temperature loaded color filters, and luminescent solar collectors.

An excellent overview and many details can be found in [4.4].

Glasses are very well suited for the production of mechanically reliable, vacuum-tight fusion seals with metals, ceramics, and mica. Some particularly favorable properties are the viscosity behavior of glass and the direct wettability of many crystalline materials by glasses. As a result, the production technology for such seals is characterized by uncomplicated procedures with few, easily manageable, well-controllable process steps. A necessary condition for the stability and mechanical strength of glass seals is the limitation of the mechanical stress in the glass component at temperatures encountered during production and use. To ensure “sealability” (which means that the thermal contractions of the two sealing components match each other below the transformation temperature of the glass), glasses of special compositions, called sealing glasses, have been developed. Apart from sealability, such glasses must very often fulfill other requirements such as high electrical insulation or special optical properties. The sealability can be tested and evaluated with sufficient accuracy and certainty by stress-optical measurements in the glass portion of a test seal (ISO 4790). Apart from characteristic material values such as the coefficient of linear thermal expansion, transformation temperature, and elastic properties, the cooling rate (Fig. 3.4-31) and the shape can also have a considerable

influence on the degree and distribution of seal stresses. The material combinations for sealing between metals and ceramics recommended for Schott glasses are shown in Fig. 3.4-32. Types of Sealing Glasses Sealing glasses may be classified by reference to the expansion coefficients of metals (e.g. tungsten and molybdenum) and alloys (Ni–Fe–Co, Ni–Fe–Cr, and other alloys) with which they are used. Hence sealing

1000

Optical path difference =^ Sealing stress (cm) Tension

800 600 400 200 0 –200 –400

Compression

100

200

300

400 500 Temperature (°C)

Fig. 3.4-31 Influence of the cooling rate on the sealing stress in an 8516–Ni/Fe combination. The lower curve corresponds to a low cooling rate; the upper curve corresponds to a high cooling rate

Part 3 4.8

3.4.8 Glasses for Miscellaneous Applications 3.4.8.1 Sealing Glasses

559

560

Part 3

Classes of Materials

Ceramics

Glasses

Metals

Solder glasses Application range

α (20 °C/300 °C) (10–6 K)

Devitrifying

Vitreous and composites

Fused silica 8228

2

2

8229

8230 3

3 8330

Hard porcelain KER 110/111

8337 B Tungsten

8449 8447

8412

5

8487

8486

8250

Vacon 10, Kovar Molybdenum

8245

5

8450 6

6 8454

8350

9

8512

8516 8531

Platinum

Vacovit 501 Cu-sheathed wire

Forsterite KER 225

8095

8405 8490

Intermediate sealing glasses

Tried-out, unrestricted seals with stresses ≤ 8 N/mm2 at room temperature Producible seals, limited with regard to size and geometry, with stresses between 8 N/mm2 and 20 N/mm2 at room temperature

Fig. 3.4-32 Recommended material combinations for “graded seals”

G 017–393 G 017–340

8470

51 Ni–1Cr–Fe Technical glasses

8

Vacovit 465–485

51–53 Ni–Fe

10

7

9 8467

N16 B

G 017–695

8596

8

8465

8456

Sapphire

8468

Al2O3 ceramic

G 017–508

Vacon 70 Steatite KER 220/221

8593

7

Vacon 20

8436

G 017–383

2954 8455

4

G 017–339

8409

8587

Part 3 4.8

4

G 017–002

8448

10

11

Glasses

4.8 Glasses for Miscellaneous Applications

561

Table 3.4-20 Special properties and principal applications of technically important sealing glasses, arranged according to their

respective sealing partners

Metal α20/300 (10−6 /K)

Glass number

Glass characteristics

Principal applications as sealing glass

Tungsten (4.4)

8486

Alkaline-earth borosilicate, high chemical resistance, high working temperature. Suprax® High boron content, low melting temperature Alkaline-earth borosilicate, high chemical resistance. Fiolax® clear Alkaline-earth aluminosilicate glass High boron content, low melting temperature, high electrical insulation, low dielectric losses High boron content, low melting temperature, low X-ray absorption Alkali–alkaline-earth silicate, sealable with steatite and Al2 O3 ceramics Alkali–alkaline-earth silicate, sealable with sapphire, resistant to Na vapor and alkalis Soda–lime silicate glass. AR glass

Lamp bulbs

8487 Molybdenum (5.2) Molybdenum and 28Ni/18Co/Fe (5.1)

8412 8253 8250

28Ni/23Co/Fe (7.7)

8454 8436

51Ni/1Cr/Fe (10.2) Cu-sheathed wire (α20/400 radial 99, α20/400 axial 72)

8350 8095

8531

52–53Ni/Fe (10.2–10.5)

8532 8512 8516

Alkali–lead silicate, high electrical insulation ⎫ Dense lead silicate, Na- and Li-free, ⎪ ⎬ low melting temperature ⎪ ⎭ High electrical insulation Contains FeO for hot forming by IR, leadfree Contains FeO for hot forming by IR, low volatilization, lead-free

glasses may be referred to as “tungsten sealing glasses”, “Kovar glasses”, etc. (see Table 3.4-20). Alkaline-earth borosilicate glasses (8486 and 8412) and aluminosilicate glasses (8252 and 8253) have the necessary sealability and thermal resistance to be particularly suitable for the tungsten and molybdenum seals frequently used in heavy-duty lamps. Ni–Fe–Co alloys, which often substitute for molybdenum, require that the transformation temperature be limited to 500 ◦ C maximum. Suitable glasses (8250 and

Lamp bulbs Lamp interior structures, lamp bulbs Transmitter tubes, image converters, TV receiver tubes X-ray tubes Intermediate sealing glass Special applications

Tubes Lead glass, stem glass for electric lamps and tubes Low-temperature encapsulation of diodes Reed switches Reed switches

8245) characteristically contain relatively high amounts of B2 O3 . These glasses have additional special properties, such as high electrical insulation, low dielectric loss, and low X-ray absorption, and meet the most stringent requirements for vacuum-tube technology and electronic applications. For Ni–Fe–(Cr) alloys, which are frequently used in technological applications, as well as for coppersheathed wire, glass groups belonging to the soft-glass category are recommended. Such glasses usually meet

Part 3 4.8

8245

Discharge lamps, surge diverters

562

Part 3

Classes of Materials

certain special requirements, such as high electrical insulation (e.g. alkali–lead silicate, 8095) or an exceptionally low working temperature (e.g. the dense-lead glasses 8531 and 8532). FeO-containing glasses (8512 and 8516) are frequently used for hermetic encapsulation of electrical switches and electronic components in an inert gas. Hot forming and sealing are easily achieved by the absorption of IR radiation with an intensity maximum at 1.1 µm wavelength (Fig. 3.4-33). The presence of a proportion of Fe2 O3 makes these glasses appear green. At appropriately high IR intensities, they require considerably shorter processing times than do flame-heated clear glasses.

Part 3 4.8

Compression Seals A common feature of all compression seals is that the coefficient of thermal expansion of the external metal part is considerably higher than the thermal expansion coefficients of the sealing glass and the metallic inner partner (conductor). As a result, the glass body is under overall radial pressure after sealing. This prestressing protects the glass body against dangerous mechanical loads. Because the compressive stress of the glass is compensated by a tensile stress in the jacket, the jacket wall must be sufficiently thick (at least 0.5 mm, even for small seals) to be able to permanently withstand such tension. If the thermal expansion of the metallic inner partner is lower than that of the sealing glass, an additional prestressing of the glass body results.

100

Transmission (%) Emission spectrum of a tungsten–halogen lamp

90 80 70 60

Thickness 0.5 mm

50 40 30

Thickness 1 mm

20 10 0 200

500

1000

2000

5000 10 000 Wavelength (nm)

Fig. 3.4-33 IR absorption of Fe-doped glasses compared with the emission of a tungsten–halogen lamp at 3000 K (in relative units). The transmission of reed glass 8516 with thicknesses 0.5 mm and 1 mm is shown

Glasses for Sealing to Ceramics Dielectrically superior, highly insulating ceramics such as hard porcelain, steatite, Al2 O3 ceramics, and forsterite exhaust almost the complete expansion range offered by technical glasses. Hard porcelain can generally be sealed with alkaline-earth borosilicate glasses (for example 8486), which are also compatible with tungsten. Glass seals to Al2 O3 ceramics and steatite are possible with special glasses such as 8454 and 8436, which will also seal to a 28Ni/18Co/Fe alloy. Soft glasses with thermal expansions around 9 × 10−6 /K are suitable for sealing to forsterite. Intermediate Sealing Glasses Glasses whose thermal expansion differs so widely from that of the partner component that direct sealing is impossible for reasons of stress must be sealed with intermediate sealing glasses. These glasses are designed in such a way that for the recommended combinations of glasses, the sealing stress does not exceed 20 N/mm2 at room temperature (Table 3.4-21).

3.4.8.2 Solder and Passivation Glasses Solder glasses are special glasses with a particularly low softening point. They are used to join glasses to other glasses, ceramics, or metals without thermally damaging the materials to be joined. Soldering is carried out in the viscosity range 104 –106 dPa s of the solder glass; this corresponds to a temperature range Tsolder = 350–700 ◦ C. One must distinguish between vitreous solder glasses and devitrifying solder glasses, according to their behavior during the soldering process. Vitreous solder glasses behave like traditional glasses. Their properties do not change during soldering; upon reheating of the solder joint, the temperature dependence of the softening is the same as in the preceding soldering process. Unlike vitreous solder glasses, devitrifying solder glasses have an increased tendency to crystallize. They change into a ceramic-like polycrystalline state during soldering. Their viscosity increases by several orders of magnitude during crystallization so that further flow is suppressed. An example of this timedependent viscosity behavior is shown in Fig. 3.4-34 for a devitrifying solder glass processed by a specific temperature–time program. Crystallization allows a stronger thermal reloading of the solder joint, up to the temperature range of the soldering process itself (e.g. glass 8596 has a soldering temperature of approx-

4.8 Glasses for Miscellaneous Applications

Glasses

563

Table 3.4-21 Intermediate sealing glasses and the combinations of sealing partners in which they are used Glass

Sealing

no.

partners a

α20/300

⎧ ⎪ ⎨ N16B KER 250 N16B Vacovit 501 − 8456 ⎪ ⎪ Platinum ⎫ ⎭ ⎩ (Red Line® ) ⎬ KER 220 ⎪ 2954 KER 221 − 2954 ⎪ Vacon 20 ⎭ ⎫ ⎪ ⎬

(10−6

/K)

Transform-

Temperature at

Density

ation

viscosity



Tk100

temperature Tg

1013 dPa s 107.6 dPa s

104 dPa s

(◦ C)

(◦ C)

(◦ C)

(◦ C)

(g/cm3 )

(◦ C)

8.8

540

540

720

1045

2.48

128

6.3

600

604

790

1130

2.42

145

12.7

450

455

615

880

2.66

−

Iron–4210

8228

Fused silica–8228–8229

1.3

∼ 700

726

1200

1705

2.15

355

8229

8228–8229–8230

2.0

630

637

930

1480

2.17

350

8230

8229–8230–8330

2.7

570

592

915

1520

2.19

257

8447

8412–8447–Vacon 10

4.8

480

505

720

1035

2.27

271

8448

8330–8448–8449, 8486, 8487   8486 − 8449 − 8447 8412 8487

3.7

510

560

800

1205

2.25

263

4.5

535

550

785

1150

2.29

348

5.4

570

575

778

1130

2.44

200

6.4

565

575

750

1070

2.49

210

6.7

565

−

740

1030

2.44

−

7.4

445

−

685

1145

2.49

−

8449 8450 8454

8455

8456 a

8412–8450 − KER 220 2954, 8436 KER 221 −8454 − Vacon 70 Al2 O3⎫ ⎬ 2954 ⎪ 8436 ⎪ –8455–8456 8454 ⎭  8455–8456 −

N16B 8350

Type designation of ceramics according to DIN 40685; manufacturer of Vacon alloys Vacuumschmelze Hanau (VAC).

imately 450 ◦ C and a maximum reload temperature of approximately 435 ◦ C). The development of solder glasses (Table 3.4-22) with very low soldering temperatures is limited by the fact that reducing the temperature generally means increasing the coefficient of thermal expansion. This effect is less pronounced in devitrifying solder glasses. It can be avoided even more effectively by adding inert (nonreacting) fillers with low or negative coefficients of thermal expansion (for example ZrSiO4 or β-eucryptite). The resulting glasses are called composite solder glasses. As a rule, the coefficient of thermal expansion of a solder glass should be smaller than the expansion coefficients of the sealing partners by ∆α = 0.5–1.0 × 10−6 /K. Up to their maximum service temperature, solder glasses are moisture- and gas-proof. Their good elec-

14

log η (dPa s)

Temperature (°C) 500 Temperature

12

450

10 log η

8

350

6 4 0

400

10

20

30

40

300 50 60 Time (min)

Fig. 3.4-34 Variation of the viscosity of a crystallizing

solder glass during processing

Part 3 4.8

4210

564

Part 3

Classes of Materials

Table 3.4-22 Schott solder glasses Glass number

α(20/300)

Tg

(10−6 /K)

(◦ C)

T at viscosity 107.6 dPa s (◦ C)

Firing conditions T thold (◦ C) (min)

Density  (g/cm3 )

Tk100 (◦ C)

εr

tan δ (10−4 )

Vitreous and composite solder glasses

Part 3 4.8

G017-002a

3.6

540

650

700

15

3.4

−

6.8

37

G017-339a

4.7b

325

370

450

30

4.0

320

11.5

19

G017-383a

5.7b

325

370

430

15

4.7

325

13.0

15

G017-393a

6.5b

320

370

425

15

4.8

305

11.6

15

G017-340a

7.0b

315

360

420

15

4.8

320

13.4

14

8465

8.2

385

460

520

60

5.4

375

14.9

27

8467

9.1

355

420

490

60

5.7

360

15.4

29

8468

9.6

340

405

450

60

6.0

335

16.3

31

8470

10.0

440

570

680

60

2.8

295

7.7

8471

10.6b

330

395

440

30

6.2

−

17.1

52

8472

12.0b

310

360

410

30

6.7

−

18.2

47

8474

19.0b

325

410

480

30

2.6

170

7.2

5

15.5

Devitrifying solder glasses G017-508

6.5

365

−

530c

60

5.7

340

15.6

206

8593

7.7

300

−

520c

30

5.8

230

21.3

260

8596

8.7

320

−

450c

60

6.4

280

17.4

58

G017-695

8.9

310

−

425c

45

5.7

275

15.4

54

315

−

435c

40

6.6

265

22.1

33

8587

10.0

a

b

Composite.

α20/250 .

c

Heating rate

7–10 ◦ C/min.

trical insulating properties are superior to those of many standard technical glasses. They are therefore also suitable as temperature-resistant insulators. The chemical resistance of solder glasses is generally lower than that of standard technical glasses. Therefore, solder glass seals can be exposed to chemically aggressive environments (e.g. acids or alkaline solutions) only for a limited time. Passivation glasses are used for chemical and mechanical protection of semiconductor surfaces. They are generally zinc–borosilicate or lead–alumina–silicate glasses. To avoid distortion and crack formation, the different coefficients of thermal expansion of the passivation glass and the semiconductor component must be taken into account. If the mismatch is too large, a network of cracks will originate in the glass layer during cooling or subsequent processing and destroy the hermetic protection of the semiconductor surface. There are three ways to overcome this problem:

• • •

A thinner passivation glass layer. Schott recommends a maximum thickness for this layer. Slow cooling in the transformation range. As a rough rule, a cooling rate of 5 K/min is suitable for passivation layers in the temperature range Tg ± 50 K. Use of composite glasses. Composites can be made with an inert filler such as a powdered ceramic with a very low or negative thermal expansion.

Properties of Passivation Glasses The electrical insulation, including the dielectric breakdown resistance, generally depends on the alkali content, particularly the Na+ content. Typical contents are below 100 ppm for Na2 O and K2 O, and below 20 ppm for Li2 O. Heavy metals which are incompatible with semiconductors are controlled as well. The CuO content, for example, is below 10 ppm. Because the mobility of charge carriers increases drastically with increasing temperature, a temperature

Glasses

limit, called the junction temperature Tj , is defined up to which glass-passivated components can be used in blocking operations. Various types of passivation glasses are listed in Table 3.4-23.

3.4.8.3 Colored Glasses In physics, color is a phenomenon of addition or subtraction of parts of the visible spectrum, due to selective absorption or scattering in a material. The light transmission through a sample of thickness d at a wavelength λ is described by Lambert’s law,    τi (λ) = exp − εn (λ, cn , cm )d , (4.42) where ε is the extinction coefficient, which depends on the wavelength and the concentration of the active agents. For low concentrations, ε is additive and pro-

4.8 Glasses for Miscellaneous Applications

portional to the concentration, and we obtain Beer’s law,    τi (λ) = exp − εn (λ)cn d , (4.43) where ε now depends only on the wavelength and the specific species or process n. In glasses, the extinction is caused by electronic and phononic processes in the UV and IR regions, respectively, and by absorption and scattering by ions, lattice defects, and colloids and microcrystals in the visible region. Different oxidation states of one atom, for example Fe2+ and Fe3+ , must be treated as different species. Charge transfer and ligand fields are examples of multiatom mechanisms that modify the absorption characteristics. The position of the maximum-extinction peak depends on the refractive index of the base glass; for example, for Ag metal colloids the position of the peak shifts from λmax = 403 nm in Duran® , with n d = 1.47, to λmax = 475 nm in SF 56, with n d = 1.79.

Type

Typical applications

α(20/300)

Tg

(10−6 /K)

(◦ C)

Pb content (wt%)

Sealing temp. (◦ C)

Sealing time (min)

Tj (◦ C)

Layer thickness (µm)

G017-057

Zn−B−Si

Sintered glass diodes

4.5

546

1–5

690

10

180

−

G017-388

Zn−B−Si composite

Thyristors, high-blocking 3.6 rectifiers

550

1–5

700

5

180

≤ 30

G017-953

Zn−B−Si composite

2.81

a

1–5

770

30

180

−

G017-058

Zn−B−Si

Sintered glass diodes

4.5

543

1–5

690

10

180

−

G017-002

Zn−B−Si composite

Sintered glass diodes

3.7

545

1–5

700

10

180

−

G017-984

Zn−B−Si

Stack diodes

4.6

538

5–10

720

10

180

−

G017-096R

Pb−B−Si

Sintered glass diodes, pla- 4.8 nar and mesa diodes

456

10–50

680

5

160

−

G017-004

Pb−B−Si

Mesa diodes

4.1

440

10–50

740

5

160

≤ 30

G017-230

Pb−B−Si composite

Power transistors

4.2

440

10–50

700

5

160

≤ 25

G017-725

Pb−B−Si

Sintered glass diodes

4.9

468

10–50

670

10

180

−

G017-997

Pb−B−Si composite

Wafers

4.4

485

10–50

760

20

180

−

G017-209

Pb−Zn−B

ICs, transistors

6.6

416

10–50

510

10

180

≤ 5

G017-980

Pb−Zn−B

Varistors

−

−

Vitreous

6.5

393

520

30

−

−

Devitrified

5.8

a

620

30

−

−

4.88

425

560

30

−

−

G018-088 a

Pb−Zn−B composite

Cannot be determined.

Varistors

10–50

10–50

Part 3 4.8

Table 3.4-23 Schott passivation glasses Glass number

565

566

Part 3

Classes of Materials

Colored glasses are thus technical or optical colorless glasses with the addition of coloring agents. A collection of data can be found in [4.17]. They are widely used as optical filters for various purposes, such as short-pass or long-pass edge filters, or in combinations of two or more elements as band-pass or blocking filters. Owing to the absorbed energy, inhomogeneous heating occurs (between the front and rear sides, and, especially, in the radial direction), which results in internal stress via the thermal expansion under intense illumination. Precautions have to be taken in the mechanical mounting to avoid breakage. The application temperature T should satisfy the conditions T ≤ Tg − 300 ◦ C in the long term and T ≤ Tg − 250 ◦ C for short periods. Prestressing may be necessary to improve the breaking strength in heavy-load applications. The Schott filter glasses are classified into groups listed in Table 3.4-24:

Part 3 4.8

Table 3.4-24 Groups of Schott Filter glasses

UG Black and blue glasses, ultraviolet-transmitting BG Blue, blue–green, and multiband glasses VG Green glasses OG Orange glasses, IR transmitting RG Red and black glasses, IR-transmitting NG Neutral glasses with uniform attenuation in the visible WG Colorless glasses with different cutoffs in the UV, which transmit in the visible and IR KG Virtually colorless glasses with high transmission in the visible and absorption in the IR (heat protection filters) FG Bluish and brownish color temperature conversion glasses DIN has defined a nomenclature to allow one to see the main optical properties for a reference thickness d from the identification symbol (see Table 3.4-25): Multiband filters and color conversion filters are not specified by DIN. Ionically Colored Glasses Ions of heavy metals or rare earths influence the color when in true solution. The nature, oxidation state, and quantity of the coloration substance, as well as the type of the base glass, determine the color (Figs. 3.4-35 – 3.4-38, and Table 3.4-26).

Table 3.4-25 DIN nomenclature for optical filter glasses

Band-pass filters BP λmax /∆λHW , where λmax = wavelength of maximum internal transmission, and ∆λHW = bandwidth at 50% internal transmission. Short-pass filters KP λ50% , where λ50% = cutoff wavelength at 50% internal transmission. Long-pass filters LP λ50% , where λ50% = cutoff wavelength at 50% internal transmission. Neutral-density filters

N τ, where τ = internal transmission at 546 nm.

Internal transmission (%) 100 90 80 70 60 50 40 30 20 10 0 300 400 500 600 Internal transmission (%) 100 90 80 70 60 50 40 30 20 10 0 300 400 500 600 Internal transmission (%) 100 90 80 70 60 50 40 30 20 10 0 300 400 500 600

V2O5 Cr2O5 Co2O3 700 800 900 Wavelength (nm)

MnO2 NiO2 700 800 900 Wavelength (nm)

CuO Fe2O3 700 800 900 Wavelength (nm)

Fig. 3.4-35 Spectral internal transmission of BK7, colored

with various oxides; sample thickness 100 mm

4.8 Glasses for Miscellaneous Applications

Glasses

Transmission (%)

567

Transmission (%)

100

100

80

WG280 (3 mm) NG4 (1 mm)

80

Cr3+

60

Cr(IV)

60 GG19 (1 mm) GG457 (3 mm)

Cr(IV)

40 20

Fe3+

40

2+ Co2+ Fe3+ Co

Fe2+

Fe3+ 20

0 200

300

400

500

600

700 800 Wavelength (nm)

Fig. 3.4-36 Transmission spectra of yellow glasses Transmission (%) 100

60 Cr3+ 40 Cu2+

Cr(VI) 20 0 200

300

400

500

600

700 800 Wavelength (nm)

Fig. 3.4-37 Transmission spectra of blue and green glasses Table 3.4-26 Colors of some ions in glasses Element Fe Fe Cu Cr Cr Ni Ni Co Co Mn Mn V Ti Pr Nd Er

Valency 2+ 3+ 2+ 3+ 6+ 2+ 2+ 2+ 3+ 2+ 3+ 3+ 3+ 3+ 3+ 3+

Color Green, sometimes blue Yellowish brown Light blue, turquoise Green Yellow Violet (tetrahedral coordination) Yellow (octahedral coord.) Intense blue Green Pale yellow Violet Green (silicate), brown (borate) Violet (reducing melt) Light green Reddish violet Pale red

Fig. 3.4-39 Transmission spectra of red glasses

300

400

500

600

700 800 Wavelength (nm)

Fig. 3.4-38 Transmission spectra of gray and white glasses

Colloidally Colored Glasses The colorants of these glasses are, in most cases, rendered effective by a secondary heat treatment (striking) of the initially nearly colorless glass. Particularly important glasses of this type are the yellow, orange, red, and black filter glasses, with their steep absorption edges. As with ionic coloration, the color depends on the type and concentration of the additives, on the type of the base glass, and on the thermal history, which determines the number and diameter of the precipitates (Fig. 3.4-39 and Table 3.4-27). Table 3.4-27 Colors of some metal colloids Element

Peak position (nm)

nd

Color

Ag Cu Au Se

410 530–560 550 500

1.5 ? 1.55 ?

Yellow Red Red Pink

Transmission (%) 100 80

RG6 (2 mm) RG610 (3 mm)

60 40

Au0

20 0 200

300

400

500

600

700 800 Wavelength (nm)

Part 3 4.8

BG39 (1 mm) VG14 (1 mm)

80

0 200

568

Part 3

Classes of Materials

Doping with semiconductors results in microcrystalline precipitates which have band gap energies in the range 1.5–3.7 eV, corresponding to wavelengths in the range 827–335 nm. The preferred materials are ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe, which also form solid solutions. By mixing these dopants, any cutoff wavelength between 350 nm and 850 nm can be achieved (Table 3.4-30).

Transmission (%) 100

Part 3 4.8

Oxide Glasses The transmission is determined by the vibrations of the common network formers [4.19] (Fig. 3.4-40). The vibrations of the network modifiers are found at longer wavelengths. The heavy-metal oxide (HMO) glasses are transparent up to approximately 7 µm for a 1 mm thickness. But often they show a strong tendency toward devitrification, which very much limits the glass-forming compositions. The transmission of some commercial glasses is shown in Fig. 3.4-41.

1.0

Absorbance

0.9 0.8 0.7 0.6 0.5

B

Si

Ge

Te Bi

0.4 0.3 0.2 0.1 0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 Wavelength (µm)

Fig. 3.4-40 Infrared absorbance of analogous oxide

glasses with different network-forming cations [4.18]; sample thickness 1.85 mm, except for Bi, where the thickness was 2.0 mm

h

70 50

a b c d e f g h

g

h

f

60

d c b

KzSF N2 BK1 BaSF2 LLF1 Ultran 20 IRG7 IRGN6 IRG2

e

30 20

The transmission in the infrared spectral region is limited by phonons and by local molecular vibrations and their overtones. The vibration frequencies decrease with increasing atomic mass. This intrinsic absorption has extrinsic absorption caused by impurities and lattice defects, such as hydroxyl ions, dissolved water, and microcrystals, superimposed on it. An overview can be found in [4.12].

e f

80

40

3.4.8.4 Infrared-Transmitting Glasses

e

90

a

10 0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Wavelength (µm)

Fig. 3.4-41 Infrared transmission spectra of some Schott

optical and special IR glasses; thickness 2.5 mm. The OH absorption of the glasses may vary owing to differences in the raw materials and the melting process

Halide Glasses These glasses use F, Cl, Br, and I (halogens) as anions instead of oxygen. The transmission range is extended up to approximately 15 µm [4.20]. The oldest halide glasses are BeF2 , ZnCl2 , and AlF3 , which, however, have limited application owing to their toxicity, tendency toward crystallization, and hygroscopic behavior. Some new glasses use ZrF4 , HfF4 , and ThF4 as glass formers, and BaF2 , LaF3 (heavy-metal flourides, HMFs) as modifiers. They are often named after their cation composition; for example, a glass with a cation composition Zr55 Ba18 La6 Al4 Na17 would be called a ZBLAN glass. Chalcogenide Glasses These glasses use S, Se, and Te (chalcogens) as anions instead of oxygen. The transmission range is extended up to approximately 30 µm. Stable glass-forming regions are found in the Ge−As−S, Ge−As−Se, and Ge−Sb−Se systems; an example of a commercial glass is Ge30 As15 Se55 . A combination of chalcogenides with halides is found in the TeX glasses, for example Te3 Cl2 S and Te2 BrSe. The main properties of infrared-transmitting glasses are compiled in Tables 3.4-29 and 3.4-30.

Table 3.4-28 Properties of Schott filter glasses Reference thickness dr (mm)

Density  (g/cm3 )

Refractive index nd

Chemical resistance Stain Acid FR SR

Alkali AR

Transformation temperature Tg (◦ C)

UG1 UG5 UG11

BP 351/78 BP 318/173 BP 324/112 + BP 720/57 BP 378/185 BP 378/165 BP 466/182 BP 409/140 BP 480/250 + KP 605 Multiband BP 459/232 + KP 575 BP 342/253 BP 401/156 − BP 436/156 + KP 514 Color conversion Multiband BP 487/334 + KP 654 BP 475/269 + KP 609 BP 482/318 + KP 641 BP 478/253 + KP 604 BP 523/160 BP 530/114 BP 52487 LP 385 LP 395 LP 400 LP 420

1 1

2.77 2.85

1.54 1.54

0 0

1.0 3.0

1.0 2.0

603 462

7.9 8.1

8.9 9.4

− −

1 1 1 1 1

2.92 2.56 2.66 2.61 2.58

1.56 1.51 1.53 1.52 1.52

0 0 0 0 0

3.0 1.0 1.0 1.0 1.0

2.0 1.0 1.0 1.0 1.0

545 478 536 468 480

7.8 8.8 7.7 8.5 8.6

9 10.2 9 19.9 10.1

− − − − −

1 −

2.68 2.86

1.54 1.55

0 0

2.0 1.0

2.0 1.0

459 561

7.4 8.3

8.8 9.3

− −

1 1 1 1

2.37 2.72 2.56 2.56

1.52 1.53 1.51 1.51

0 0 0 0

1.0 3.0 1.0 1.0

1.0 1.0 1.0 1.0

483 460 487 494

8.9 8.5 8.7 8.8

10.2 9.7 10.1 10.3

− − − −

1 2 −

2.60 3.23 3.62

1.52 1.59 1.69

0 0 1

1.0 1.0 52.2

1.0 1.0 1.2

474 441 660

8.7 9.9 6.1

10 10.7 7.2

− − −

1

2.62

1.53

0

2.0

2.0

466

7.5

8.9

−

1

2.73

1.54

0

5.1

3.0

321

11.6

13.1

−

1

2.67

1.53

0

5.1

3.0

305

11.9

13.7

−

1 1 1 1 3 3 3 3

2.69 2.90 2.87 2.89 3.22 3.61 2.75 2.76

1.54 1.55 1.55 1.56 1.58 1.62 1.54 1.54

0 0 0 0 0 0 3 3

2.0 1.0 1.0 1.0 2 1 4.4 4.4

2.0 1.0 1.0 1.0 2.3 2.3 1.0 1.0

477 470 470 470 459 438 595 586

7.3 9.1 9.2 9.2 7.7 7.7 9.6 9.6

8.7 10.6 10.6 10.6 8.8 8.6 10.5 10.5

− − − − 0.07 0.08 0.07 0.07

BG20 BG23 BG24A BG25 BG26 BG28 BG34 BG36 BG38 BG39 BG40 BG42 VG6 VG9 VG14 GG385 GG395 GG400 GG420

Temp. coeff. TK (nm/K)

569

Part 3 4.8

BG3 BG4 BG7 BG12 BG18

Thermal expansion α−30/+70 ◦ C α20/300 ◦ C (10−6 /K) (10−6 /K)

4.8 Glasses for Miscellaneous Applications

DIN identification

Glasses

Glass type

Part 3 4.8

570

RG610 RG630 RG645 RG665 RG695 RG715 RG780 RG830 RG850 RG1000 NG1 NG3 NG4 NG5 NG9 NG10 NG11 NG12 WG225 WG280 WG295 WG305 WG320 KG1 KG2 KG3 KG4 KG5 FG3 FG13

LP 435 LP 455 LP 475 LP 495 LP 515 LP 530 LP 550 LP 570 LP 590 BP 885307 + LP 731 LP 610 LP 630 LP 645 LP 665 LP 695 LP 715 LP 780 LP 830 LP 850 LP 1000 N 10-4 N 0.09 N 0.27 N 0.54 N 0.04 N 0.004 N 0.72 N 0.89 LP 225 LP 280 LP 295 LP 305 LP 320 KP 751 KP 814 KP 708 KP 868 KP 689 Color conversion Color conversion

3 3 3 3 3 3 3 3 3

2.75 2.75 2.75 2.75 2.76 2.75 2.75 2.75 2.75

1.54 1.54 1.54 1.54 1.54 1.54 1.54 1.54 1.54

3 3 3 3 3 3 3 3 3

4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4 4.4

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

605 600 594 600 597 595 597 596 599

9.5 9.7 9.8 9.6 9.7 9.7 9.6 9.7 9.8

10.5 10.5 10.6 10.6 10.6 10.6 10.7 10.7 10.6

0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15

3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2

2.76 2.75 2.76 2.76 2.75 2.76 2.75 2.9 2.94 2.93 2.75 2.49 2.44 2.43 2.43 2.44 2.47 2.42 2.34 2.17 2.51 2.51 2.59 3.22 2.53 2.52 2.52 2.53 2.53 2.37 2.78

1.54 1.54 1.54 1.54 1.54 1.54 1.54 1.56 1.56 1.56 1.55 1.52 1.51 1.51 1.5 1.51 1.52 1.5 1.49 1.47 1.52 1.52 1.52 1.58 1.52 1.51 1.51 1.51 1.51 1.5 1.56

3 3 3 3 3 3 3 5 5 5 0 1 1 1 1 1 1 1 4 3 0 0 0 0 0 0 0 0 0 0 1

4.4 4.4 4.4 4.4 4.4 3 3 52.4 53.4 53.4 1 2.2 2.2 3.2 3.2 3.2 3.2 3.4 51.4 51.3 1 1 1 1 2.0 2.0 2.0 2.0 3.0 1.0 3.4

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.2 1.0 1.0 2.0 2.0 2.0 2.0 2.0 2.0 3.3 2.0 2.0 1.0 2.3 3.0 3.0 4.0 3.0 4.0 1.0 1.0

581 595 597 597 592 599 589 571 569 571 478 466 462 483 474 487 468 473 460 437 563 557 546 413 599 605 581 613 565 564 556

9.8 9.8 9.6 9.6 9.8 9.6 9.8 9.7 9.5 9.5 9.2 6.6 6.5 6.7 6.6 6.4 6.4 6.9 5.9 3.8 7.0 7.1 8.2 9.1 5.3 5.4 5.3 5.4 5.4 5.4 9.6

10.7 10.7 10.7 10.7 10.8 10.6 10.7 10.7 10.5 10.5 9.9 7.2 7.3 7.2 7.3 7.3 7.2 7.5 6.4 4.1 8.3 8.3 9.6 10.6 6.1 6.3 6.1 6.2 6.2 6 10.5

0.07 0.16 0.17 0.17 0.17 0.18 0.18 0.22 0.23 0.24 0.38 − − − − − − − − 0.02 0.04 0.06 0.06 0.06 − − − − − − −

Classes of Materials

GG435 GG455 GG475 GG495 OG515 OG530 OG550 OG570 OG590 RG9

Part 3

Table 3.4-28 Properties of Schott filter glasses, cont.

Glasses

4.8 Glasses for Miscellaneous Applications

571

Table 3.4-29 Property ranges of various infrared-transmitting glass types Glass type

Transparency

Refractive

Abbe

Thermal

rangea

index nd

value

expansion α

νd

(10−6 /K)

(µm)

Microhardness

Transformation

Density

temperature



HV

Tg (◦ C)

(g/cm3 )

0.51

800

1075

2.2

330–700

300–700

2–8

−

400–500

3–4

Fused silica

0.17–3.7

1.46

67

Oxide glasses

0.25–6.0

1.45–2.4

20–100

3–15

Fluorophosphate

0.2–4.1

1.44–1.54

75–90

13–17

Fluoride glasses

0.3–8.0

1.44–1.60

30–105

7–21

225–360

200–490

2.5–6.5

Chalcogenide

0.7–25

2.3–3.1b

105–185c

8–30

100–270

115–370

3.0–5.5

glasses

glasses a

50% internal transmission for 5 mm path length.

b

Infrared refractive index at 10 µm.

c

Infrared Abbe value ν8−12 = (n 10 − 1)/(n 8 − n 12 ).

Table 3.4-30 Commercial infrared-transmitting glasses Glass

Transparency

Refractive Density

name

rangea

index n

 (g/cm3 )

(µm) Fused silica

SiO2

0.17–3.7

1.4585b

2.20

Thermal

Transformation

expansion

temperature

α (10−6 /K)

Tg (◦ C)

0.51

1075

Manufacturer

Corning, Heraeus, General Electric, Quartz et Silice, Schott Lithotec

0.32–3.8

1.5644b

3.06

9.6

413

Schott

IRG15

0.28–4.0

1.5343b

2.80

9.3

522

Schott

IRG3

0.40–4.3

1.8449b

4.47

8.1

787

Schott

Fluorophosphate

IRG9

0.36–4.2

1.4861b

3.63

16.1

421

Schott

Ca aluminate

9753c

0.40–4.3

1.597d

2.80

6.0

830

Corning

IRG N6c

0.35–4.4

1.5892b

2.81

6.3

713

Schott

WB37Ac

0.38–4.7

1.669b

2.9

8.3

800

Sasson

VIR6

0.35–5.0

1.601b

3.18

8.5

736

Corning France

IRG11

0.38–5.1

1.6809b

3.12

8.2

800

Schott

BS39B

0.40–5.1

1.676b

3.1

8.4

−

Sasson

9754

0.36–5.0

1.664b

3.58

6.2

735

Corning

VIR3

0.49–5.0

1.869b

5.5

7.7

490

Corning France

IRG2

0.38–5.2

1.8918b

5.00

8.8

700

Schott

EO

0.5–5.8

2.31d

8.2

11.1

320

Corning

Silicates

Germanate

Heavy-metal oxide

IRG7

Heavy-metal

ZBLA

0.30–7.0

1.5195b

4.54

16.8

320

Verre Fluor´e

fluoride

Zirtrex

0.25–7.1

1.50b

4.3

17.2

260

Galileo

HTF-1

0.22–8.1

1.517d

3.88

16.1

385

Ohara

Part 3 4.8

Glass type

572

Part 3

Classes of Materials

Table 3.4-30 Commercial infrared-transmitting glasses, cont. Glass type

Glass name

Transparency Refractive rangea index n (µm)

Chalcogenide

AMTIR1 IG1.1 AMTIR3 IG6 IG2 IG3 As2 S3 IG5 IG4 1173

0.8–12 0.8–12 1.0–13 0.9–14 0.9–15 1.4–16 1.0–16 1.0–16 0.9–16 0.9–16

a b c d

Part 3 4

e

2.5109e 2.4086e 2.6173e 2.7907e 2.5098e 2.7993e 2.653e 2.6187e 2.6183e 2.616e

Density  (g/cm3 )

Thermal Transformation Manufacturer expansion temperature α (10−6 /K) Tg (◦ C)

4.4 3.32 4.7 4.63 4.41 4.84 4.53 4.66 4.47 4.67

12 24.6 13.1 20.7 12.1 13.4 30 14.0 20.4 15

362 150 278 185 368 275 98 285 225 300

Amorph. Materials Vitron Amorph. Materials Vitron Vitron Vitron Corning France Vitron Vitron Texas Instruments

50% internal transmission for 5 mm path length. Refractive index at 0.587 µm. This glass contains SiO2 . Refractive index at 0.75 µm. Refractive index at 5 µm.

References 4.1 4.2

4.3 4.4 4.5 4.6

4.7

4.8 4.9 4.10

S. R. Elliott: Physics of Amorphous Materials (Longman, Harlow 1990) H. Bach, D. Krause (Eds.): Analysis of the Composition and Structure of Glass and Glass Ceramics (Springer, Berlin, Heidelberg 1999) 2nd printing H. Bach (Ed.): Low Thermal Expansion Glass Ceramics (Springer, Berlin, Heidelberg 1995) W. Höland, G. Beall: Glass Ceramic Technology (American Ceramic Society, Westerville 2002) N. P. Bansal, R. H. Doremus: Handbook of Glass Properties (Academic Press, Orlando 1986) O. V. Mazurin, M. V. Streltsina, T. P. ShvaikoShvaikovskaya: Handbook of Glass Data, Part A, Silica Glass and Binary Silicate Glasses; Part B, Single Component and Binary Non-silicate Oxide Glasses; Part C, Ternary Silicate Glasses, Physical Sciences Data Series, Vol. 15, (Elsevier, Amsterdam 1983–1987) R. Blachnik (Ed.): Taschenbuch für Chemiker und Physiker, D’Ans-Lax, Vol. 3, 4th edn. (Springer, Berlin, Heidelberg 1998) MDL SciGlass, Version 4.0 (Elsevier, Amsterdam) INTERGLAD (International Glass Database), Version 5, New Glass Forum S. English, W. E. S. Turner: Relationship between chemical composition and the thermal expansion of glasses, J. Am. Ceram. Soc. 10, 551 (1927); J. Am. Ceram. Soc. 12 (1929) 760

4.11 4.12

4.13

4.14 4.15 4.16

4.17 4.18 4.19

4.20

A. Paul: Chemistry of Glasses (Chapman and Hall, New York 1982) H. Bach, N. Neuroth (Eds.): The Properties of Optical Glass, Schott Series on Glass and Glass Ceramics, 2nd printing (Springer, Berlin, Heidelberg 1998) A. Winckelmann, F. O. Schott: Über thermische Widerstandskoeffizienten verschiedener Gläser in ihrer Abhängigkeit von der chemischen Zusammensetzung, Ann. Phys. (Leipzig) 51, 730– 746 (1894) H. Scholze: Glass (Vieweg, Braunschweig 1965) Schott: Schott Technical Glasses (Schott Glas, Mainz 2000) H. R. Philipp: Silicon dioxide (SiO2 ) (glass). In: Handbook of Optical Constants of Solids, ed. by E. D. Palik (Academic Press, New York 1985) pp. 749–763 C. R. Bamford: Colour Generation and Control in Glass (Elsevier, Amsterdam 1977) W. H. Dumbaugh: Infrared-transmitting oxide glasses, Proc. SPIE 618, 160–164 (1986) N. Neuroth: Zusammenstellung der Infrarotspektren von Glasbildnern und Gläsern, Glastechn. Ber. 41, 243–253 (1968) J. Lucas, J.-J. Adam: Halide glasses and their optical properties, Glastechn. Ber. 62, 422–440 (1989) W. Vogel: Glass Chemistry (Springer, Berlin, Heidelberg 1994)

573

Part 4

Functional Part 4 Functional Materials

3 Magnetic Materials 1 Semiconductors Hideki Harada, Higashikaya, Fukaya, Werner Martienssen, Frankfurt/Main, Germany Saitama, Japan Manfred Müller, Dresden, Germany Hans Warlimont, Dresden, Germany 2 Superconductors 4 Dielectrics and Electrooptics Claus Fischer, Dresden, Germany Gagik G. Gurzadyan, Garching, Germany Günter Fuchs, Dresden, Germany Pancho Tzankov, Berlin, Germany Bernhard Holzapfel, Dresden, Germany Barbara Schüpp-Niewa, Dresden, Germany 5 Ferroelectrics and Antiferroelectrics Hans Warlimont, Dresden, Germany Toshio Mitsui, Takarazuka, Japan

574

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575

The organization of this section follows a two-step approach. The first step corresponds to searching for the substance of interest, that is, the relevant group of substances. The second step corresponds to the physical property of interest. This section has three subsections, characterized by the groups of the Periodic Table that the constituent elements belong to. The first subsection, Sect. 4.1.1, deals with the elements of Group IV of the Periodic Table and semiconducting binary compounds between elements of this group (IV–IV compounds). The second subsection, Sect. 4.1.2, treats the semiconducting binary compounds between the elements of Groups III and V (III–V compounds); Sect. 4.1.3 treats compounds between the elements of Groups II and VI (II–VI compounds). These two subsections are subdivided further according to the first element in the formula of the compound. The elements and compounds treated in Sect. 4.1.1 (Group IV and IV–IV compounds) are treated as one group; the data in the tables are given for the whole group in all cases. In Sects. 4.1.2 (III–V compounds) and 4.1.3 (II–VI compounds), data are given separately for each subdivision of those subsections. For each group of substances, the physical properties are organized into four classes. These are A. Crystal structure, mechanical and thermal properties. B. Electronic properties. C. Transport properties. D. Electromagnetic and optical properties. These property classes, finally, are subdivided into individual properties, which are described in the text, tables, and figures.

4.1.1 Group IV Semiconductors and IV–IV Compounds ......................... 578 4.1.2 III–V Compounds ................................ 4.1.2.1 Boron Compounds ................... 4.1.2.2 Aluminium Compounds............ 4.1.2.3 Gallium Compounds ................ 4.1.2.4 Indium Compounds .................

604 604 610 621 638

4.1.3 II–VI Compounds ................................ 4.1.3.1 Beryllium Compounds .............. 4.1.3.2 Magnesium Compounds ........... 4.1.3.3 Oxides of Ca, Sr, and Ba ........... 4.1.3.4 Zinc Compounds...................... 4.1.3.5 Cadmium Compounds .............. 4.1.3.6 Mercury Compounds ................

652 652 655 660 665 676 686

References .................................................. 691

Part 4 1

Semiconducto 4.1. Semiconductors

576

Part 4

Functional Materials

Part 4 1

This section deals with the physical properties of semiconductors. Semiconductors are substances which, like metals, are electronic conductors. In contrast to metals, however, the density of freely mobile charge carriers in semiconductors is, under normal conditions, smaller by orders of magnitude than it is in metals. Therefore, in semiconductors, a small change in the absolute value of the charge carrier density can induce a large relative change in this carrier density and in the electrical conductivity. In metals, on the other hand, the carrier density is so high from the beginning that it is practically impossible to produce a reasonable relative change by small changes of the absolute value of the carrier density. In conclusion, we can say that in semiconductors, and only in semiconductors, is it possible to manipulate the electronic conduction by small changes of the carrier density. Such changes can be effected by a number of techniques, for instance by chemical doping, by temperature changes, by the application of an electric field, or by light. The electronic conductivity of a semiconductor can be changed intentionally by these techniques by orders of magnitude; some techniques allow stationary changes, and some techniques also allow time-dependent changes on a very short timescale. Semiconducting materials are functional materials thanks to the above properties: they can be used as very small, robust, energy-efficient devices to control the current in electrical networks, either on the basis of external driving or on the basis of their internal, tailor-made device characteristics. During the last 50 years, a tremendous amount of knowledge and experience has been collected worldwide in research and development laboratories in the field of semiconductor physics, semiconductor engineering, and semiconductor chemistry. During this time, semiconductor technology laid the foundations for the development of data processing and of communication technology and, more generally, for the establishment of the information society. Today, semiconductor technology is a basic technology of our economy, business practice, and daily life with its modern comforts. We can give an account of only a very small part of the empirical knowledge about semiconductors in this Handbook. Thus, a very limited selection of semiconducting substances and of physical properties is treated here. Only three major groups of substances are considered. These are, first, the elements of the fourth group of the Periodic Table, C, Si, Ge, and Sn, and binary compounds between these (IV–IV compounds); second,

binary compounds between one element from the third group of the Periodic Table, namely B, Al, Ga, or In, and one element from the fifth group of the Periodic Table, N, P, As, or Sb, the so-called III–V semiconductors; and third, binary compounds between one element from the second group of the Periodic Table, namely Mg, Ca, Sr, Ba, Zn, Cd, or Hg, and one element from the sixth group of the Periodic Table O, S, Se, or Te, the so-called II–VI semiconductors. In fact, these three major groups form a kind of basic set for the physical understanding of semiconductor phenomena and for the wide field of semiconductor applications. It has to be kept in mind, however, that ternary and higher compounds play a very important role in many semiconductor applications and, furthermore, that a large number of semiconducting substances containing elements other than those mentioned above have been developed for special applications. The limited number of pages of this Handbook has forced us, furthermore, to be even more restrictive with regard to the properties of semiconductors, which are considered as being of first-order importance for this data collection. So, semiconductor chemistry is beyond the scope of this Handbook. The very broad and important field of semiconductor technology could not be included at all. Also, the wide field of the influence of chemical doping, impurities, and defects on the properties of semiconductors had to be left out. The Handbook’s emphasis is on the physical properties of a restricted number of most important pure semiconducting materials. All the data have been compiled from Landolt– Börnstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Group III, Vol. 41, Semiconductors, published in eight subvolumes between 1998 and 2003 [1.1]. The CD-ROM and the online version of the Landolt– Börnstein volume present a completely revised and supplemented version of the older Landolt–Börnstein volumes III/17 and III/22 on semiconductors. The printed edition of Vol. III/41 contains only a supplement to the earlier Volumes III/17 and III/22, but nevertheless the printed version of Vol. III/41 extends to more than 4000 pages in the eight subvolumes. If, in addition to the data in this Handbook, further or more detailed information is needed, the reader is recommended to consult [1.1]. Only a very restricted number of references is given in this chapter to the original publications in journals.

Semiconductors

• •

Phonon wavenumbers ν˜ , frequencies ν, energies E phon at symmetry points, given in cm−1 , THz, and eV, respectively. Phonon dispersion relations, i. e. wavenumber ν¯ versus wave vector q.

B. Electronic properties:

• • • • • • •

First Brillouin zone (figures). Band structure (text and figures). Energy gap, given in eV. Exciton binding energies, given in eV. Spin–orbit splitting energies, given in eV. Effective masses, in units of the electron mass m 0 . g-factor gc of conduction electrons.

C. Transport properties:

• • • •

Electronic transport, general description. Intrinsic carrier concentrations, n and p, given in cm−3 . Electrical conductivity σ, given in Ω−1 cm−1 . Electron and hole mobilities µn and µp , given in cm2 /V s. Thermal conductivity, given in W/cm K.

A. Crystal structure, mechanical and thermal properties:

•

•

D. Electromagnetic and optical properties:

• • • • • • • •

Crystal structure (space group, crystal system, and structure type) (tables and figures). Lattice parameters a and c, given in nm. Density , given in g/cm3 . Elastic constants cik , given in GPa. Melting point Tm , given in K. Temperature dependence of the lattice parameters, i. e. the functional relationships a(T ) and c(T ). Linear thermal expansion coefficient α, given in 10−6 K−1 . Heat capacity c p , given in J/mol K. Debye temperature ΘD , given in K.

• • •

Dielectric constant ε. Refractive index n. Spectral dependence of the optical constants (tables and figures).

The data given in this Handbook, if not stated otherwise, are numerical data valid at room temperature (RT) and at normal pressure (100 kPa). If the material crystallizes in different modifications, the data given, if not stated otherwise, concern the phase which is stable under normal conditions (i. e. RT and 100 kPa).

Part 4 1

A very large number of references to all the original papers are given, however, in the Landolt–Börnstein volume mentioned above [1.1] (see also [1.2]). The data are presented mainly in tables, which always cover data concerning one or a few related properties for a full group of substances. It is felt that this synoptic presentation will provide an immediate overview of the data for the group of substances. This might be especially helpful if one is interested in development or modeling of materials. In many cases, functional relationships, in particular temperature dependences, are of the utmost importance in condensed-matter physics and materials science. Therefore a large number of figures have been included, in addition to short sections of text and the numerical data in the tables. Figures in the form of graphs allow one to see the general features of a functional relationship at a glance; they also, of course, present information in a very condensed form. The physical properties of semiconductors treated in this section are the following:

577

578

Part 4

Functional Materials

Part 4 1.1

4.1.1 Group IV Semiconductors and IV–IV Compounds A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-1 – 4.1-10. Table 4.1-1 Crystal structures of Group IV semiconductors and IV–IV compounds Crystal Diamond Silicon Germanium Gray tina Silicon carbideb Silicon–germanium alloys d a b

c

d

Space group C Si Ge α-Sn 3C-SiC c 2H-SiC c

Oh7 Oh7 Oh7 Oh7 Td2 4 C6v Oh7

Fd3m Fd3m Fd3m Fd3m F43m P63 mc Fd3m

Crystal system

Structure type

Figure

fcc fcc fcc fcc fcc Hexagonal fcc

Diamond Diamond Diamond Diamond Zinc blende Wurtzite Diamond

Fig. 4.1-1 Fig. 4.1-1 Fig. 4.1-1 Fig. 4.1-1 Fig. 4.1-2 Fig. 4.1-3 Fig. 4.1-1

Below 290 K (17 ◦ C) and at ambient pressure. Silicon carbide is said to be polytypic because it crystallizes in more than one hundred different modifications. This is due to the small energy differences between the different structures. The labels “3C”, “2H”, etc. indicate the stacking order along the c axis in a hexagonal system; the cubic form can be considered as fitting into this system by taking the [111] direction as the “c axis”. Silicon and germanium form a continuous series of solid solutions with gradually varying properties.

a

Fig. 4.1-1 The diamond lattice. The elementary cubes of

Fig. 4.1-2 The zinc blende lattice (a is the lattice parame-

the two face-centered cubic lattices are shown. In the diamond lattice all the atoms in the two elementary cubes are identical, they are atoms from the same chemical element. Each atom in this lattice is surrounded tetrahedrally by four nearest neighbour atoms

ter). This is a diamond lattice in which the two elementary cubes are occupied by different atomic species, for example by Zn-ions and by S-ions of opposite charge. Each Zn-ion is surrounded tetrahedrally by four nearest neighbour S-atoms and vice versa

Semiconductors

1.1 Group IV Semiconductors and IV–IV Compounds

Crystal Diamond Silicon Germanium Gray tin Silicon carbide

Lattice parameters (nm) C Si Ge α-Sn 3C-SiC 2H-SiC

Silicon–germanium alloys

Temperature (K)

Remarks

a = 0.356685 298 a = 0.543102018 (34) 295.7 a = 0.56579060 298.15 a = 0.64892 (1) 293.15 a = 0.43596 297 a = 0.30763 (10) 300 c = 0.50480 (10) There is a small deviation from Vegard’s law (Fig. 4.1-4)

5.70

X-ray diffraction High-purity single crystal, vacuum Single crystal X-ray diffraction Debye–Scherrer method Laue and Weissenberg patterns

a (Å) SiXGe1–X

5.65 5.60 5.55

c

5.50 5.45 5.40 a

Fig. 4.1-3 The wurtzite lattice (a and c are the lattice

parameters)

0

0.2

0.4

0.6

0.8

Fig. 4.1-4 Six Ge1−x . Compositional dependence of the lattice parameter. Circles, experimental results from X-ray diffraction; dashed curve, calculated by Vegard’s law from the values for pure Ge and Si; solid curve, experimental results from [1.3]

Table 4.1-3 Densities of Group IV semiconductors and IV–IV compounds Crystal Diamond

C

Silicon Germanium Gray tin Silicon carbide

Si Ge α-Sn 3C-SiC 6H-SiC

1.0 x

Density (g/cm3 )

Temperature (K)

Remarks

3.51537 (5) 3.51506 (5) 2.329002 5.3234 7.285 3.166 3.211

298 298 298.15 298 291 293 300

Flotation, type Ia Flotation, type IIb High-purity crystal, hydrostatic weighing Hydrostatic weighing Polycrystalline sample

Part 4 1.1

Table 4.1-2 Lattice parameters of Group IV semiconductors and IV–IV compounds

579

580

Part 4

Functional Materials

Part 4 1.1

Table 4.1-4 Elastic constants cik of Group IV semiconductors and IV–IV compounds Crystal Diamond Silicon Germanium Gray tin Silicon carbide a b

C Si Ge α-Sn 3C-SiC 4H-SiC

c11 (GPa)

c12 (GPa)

1076.4 (2) 165.77 124.0 69.0 289 507 (6)

125.2 (2.3) 63.93 41.3 29.3 234 108 (8) 547 (6)

c33 (GPa)

c44 (GPa)

Temperature (K)

Remarks

577.4 (1.4) 79.62 68.3 36.2 55.4 159 (7)

296 298 298

Brillouin scattering Ultrasound measurement a Ultrasound measurement b

300 RT

Brillouin scattering

p-type sample, ρ = 410 Ω cm. Calculated from an 11-parameter shell model fitted to experimental data.

Table 4.1-5 Melting point Tm of Group IV semiconductors and IV–IV compounds Crystal

Melting point (K)

Remarks

Diamond

C

4100

Diamond–graphite–liquid eutectic at p = 12.5 GPa

Silicon

Si

1687

The coordination number changes from 4 in the diamond phase to 6.4 in the liquid phase with an increase in bond length from 0.235 to 0.25 nm. The liquid phase shows metallic conduction

Germanium

Ge

Gray tin

α-Sn

Silicon carbide

3C-SiC

1210.4 Transforms into metallic β-Sn slightly below RT 3103 (40)

Peritectic decomposition temperature at p = 35 bar

Table 4.1-6 Temperature dependence of the lattice parameters of Group IV semiconductors and IV–IV compounds Crystal

Temperature dependence of lattice parameter

Diamond

C

Fig. 4.1-5

Silicon

Si

Fig. 4.1-6 a

Germanium

Ge

Fig. 4.1-7

Gray tin

α-Sn

da/ dT = 3.1 × 10−6 nm/K; temperature range −130 to 25 ◦ C

Silicon carbide

3C-SiC

Fig. 4.1-8

6H-SiC

Fig. 4.1-9

a

The lattice parameter a of high-purity Si can be approximated in the range 20–800 ◦ C by a(T ) = 5.4304 +1.8138 × 10−5 (T −298.15 K)+1.542 × 10−9 (T −298.15 K)2.

Semiconductors

a (Å) 5.447

3.574

Si

Diamond 3.573

5.444

3.572

5.441

3.571 5.438 3.570 5.435 3.569 5.432

3.568

5.429

3.567 3.566

0

100

200

300

400

500

600

700 800 T (°C)

Fig. 4.1-6 Si. Lattice parameter vs. temperature in the 0

100

200

300

b) α (10 –6 K–1)

400

500

600 700 T (°C)

range 20–740 ◦ C, measurements on various samples [1.6] a (Å)

6

Ge

5

5.69

4 5.68

3 2

5.67

1 0

5.66 0

200

400

600

800

1000 1200 1400 1600 T (K)

Fig. 4.1-5a,b Diamond. (a) Lattice parameter vs. temperature [1.4]; (b) linear thermal expansion coefficient vs.

temperature [1.5]

5.65

0

581

Part 4 1.1

a) a (Å)

1.1 Group IV Semiconductors and IV–IV Compounds

100 200 300 400 500 600 700 800 900 T (°C)

Fig. 4.1-7 Ge. Lattice parameter vs. temperature [1.7]

582

Part 4

Functional Materials

Part 4 1.1

4.384

a (Å)

4.9085

c/a SiC

SiC 4.380

4.9070

4.376

4.9055 15.215 c (Å)

4.372

15.200 4.368

15.185 4.364

15.170 4.360

15.155 4.356

0

400

800

1200

1600 T (K)

15.140

Fig. 4.1-8 SiC (3C). Lattice parameter vs. tempera15.125

ture [1.8]

15.110 3.100 a (Å) 3.085 3.070

0

400

800

1200

1600 T (K)

Fig. 4.1-9 SiC (6H). Lattice parameters vs. tempera-

ture [1.8]

Table 4.1-7 Linear thermal expansion coefficient α of Group IV semiconductors and IV–IV compounds and its temperature dependence Crystal Diamond Silicon Germanium Gray tin Silicon carbide a

C Si Ge α-Sn 3C-SiC

Expansion coefficient α (K−1 )

Temperature (K)

Remarks

1.0 × 10−6 2.92 (6) × 10−6 5.90 × 10−6 4.7 × 10−6 2.77 (42) × 10−6

300 293 300 293 300

See Fig. 4.1-5 for temperature dependence See Fig. 4.1-10 for temperature dependencea See Fig. 4.1-11 for temperature dependence See Fig. 4.1-12 for temperature dependence See Fig. 4.1-13 for temperature dependence

The linear thermal expansion coefficient α of Si can be approximated in the temperature range 120–1500 K by  

α(T ) = 3.725 1 − exp[−5.88 × 10−3 (T − 124)] + 5.548 × 10−4 T × 10−6 (K−1 ) (T measured in K)

Semiconductors

α (10 –6 K–1)

α (10– 6K–1) Ge

6

Si 4.5 4.0

5 3.5 3.0

4

2.5 2.0

3

1.5

α (10–6 K–1)

1.0

0.2

2

0.5 0.1 0 – 0.5

1 0

200

400

600

800

1000 1200 1400 1600 T (K)

0 0 – 0.1

Fig. 4.1-10 Si. Linear thermal expansion coefficient vs.

temperature. Experimental data from [1.9] (filled circles) and [1.10] (open circles) 6

α

–1

0

50

100

0

150

50 T (K) 200

250

(10 –6 K–1)

300 T (K)

Fig. 4.1-11 Ge. Linear thermal expansion coefficient vs.

α-Sn

temperature. Experimental data from various authors (symbols) and theoretical results (solid line) [1.11]

4

8

2

α (10 –6 K–1) 3C-SiC

6 0

–2

4 2 0

40

80

120

160

200

240 T (K)

Fig. 4.1-12 α-Sn. Coefficient of linear thermal expansion

vs. temperature [1.12, 13]

0 –2

0

500

1000

1500

2000

2500

583

Part 4 1.1

5.0

1.1 Group IV Semiconductors and IV–IV Compounds

3000 T (K)

Fig. 4.1-13 3C-SiC. Recommended linear thermal expan-

sion coefficient vs. temperature according to an analysis of data from nine references [1.5]

584

Part 4

Functional Materials

Part 4 1.1

Table 4.1-8 Heat capacities and Debye temperatures of Group IV semiconductors and IV–IV compounds Crystal

Heat capacity c p (J/mol K)

Debye temperature ΘD

Temperature (K) Remarks

1860 (10)

300

Diamond

C

6.195

Silicon

Si

636

Germanium

Ge

45.358 45.882 51.88

374

77 298 298

Gray tin

α-Sn

19.09

220

100

Silicon carbide

3C-SiC

28.5

5.5

1270 (20)

See Fig. 4.1-14 for temperature dependence of c p , cV See Fig. 4.1-15 for temperature dependence of cV See Fig. 4.1-16 for temperature dependence of cV See Fig. 4.1-17 for temperature dependence of cV Polycrystalline sample

293

cp , cv (cal/mol K)

c V (J/mol K) 30

Diamond

Si

5.0 cp 4.5

20

cv

5.0

c V (J/mol K)

4.0 2.5

10

3.5

0

3.0 0 2.5

0

100

200

0

25

300

50 T (K)

400

500 T (K)

Fig. 4.1-15 Si. Heat capacity at constant volume vs. temperature. Figure from [1.11]

2.0 1.5

c V (J/mol K) 1.0

300 400

500

600

700

800

900

1000 1100 T (K)

30

Ge

Fig. 4.1-14 Diamond. Molar heat capacity vs. tempera-

ture [1.14]

c V (J/mol K)

20 5.0

0 20 5 cV (cal/K α-Sn g-atom) 4

40

60

T (K) 100

80

cV (cal/K g-atom) 1.0 0.8

3

10 0

0

0

0.6

100

200

300

0

50 T (K)

400

500 T (K)

2 0.4 1 0

0.2 0

3

6

9

12

15

18

0.0 21 T (K)

Fig. 4.1-16 Ge. Heat capacity at constant volume vs. tem-

perature Fig. 4.1-17 α-Sn. Heat capacity cv vs. temperature. Lower

curve, temperature range 0–20 K; upper curve, temperature range 0–105 K [1.15]

Semiconductors

1.1 Group IV Semiconductors and IV–IV Compounds

(Si) (ν in THz, 296 K, from inelastic neutron scattering); germanium (Ge) (ν in THz, 300 K, from coherent inelastic neutron scattering); gray tin (α-Sn) (ν in THz, 90 K, from inelastic thermal neutron scattering); silicon carbide (3C-SiC) (phonon wavenumbers ν˜ in cm−1 , RT, from Raman spectroscopy); silicon carbide (6H-SiC) (ν in THz, derived from photoluminescence data) Diamond (C) ν TO/LO (Γ25 ) ν TA (L3 ) νLA (L1 ) νLO (L2 ) ν TO (L3 ) ν TA (X3 ) νLA/LO (X1 ) ν TO (X4 )

Silicon (Si) νLTO (Γ25 ) ν TA (X3 ) νLAO (X1 ) ν TO (X4 ) ν TA (L3 ) νLA (L2 ) νLO (L1 ) ν TO (L3 )

39.9 16.9 30.2 37.5 36.2 24.2 35.5 32.0

15.53 (23) 4.49 (6) 12.32 (20) 13.90 (30) 3.43 (5) 11.35 (30) 12.60 (32) 14.68 (30)

Germanium (Ge)

Gray tin (Sn)

νLTO (Γ25 ) ν TA (X3 ) νLAO (X1 ) ν TO (X4 ) ν TA (L3 ) νLA (L2 ) ν TO (L3 ) ν TO (L1 )

ν TO/LO (Γ25 ) ν TA (L3 ) νLA (L1 ) νLO (L2 ) ν TO (L3 ) ν TA (X3 ) νLA/LO (X1 ) ν TO (X4 )

9.02 (2) 2.38 (2) 7.14 (2) 8.17 (3) 1.87 (2) 6.63 (4) 8.55 (3) 7.27 (2)

Table 4.1-9 Phonon frequencies at symmetry points, cont. 8.1 12.2 22.9 25.2

8.8 12.9 23.1 25.5

9.5 16.2 23.7 25.9

ν˜ TA (L) ν˜ LA (L) ν˜ TO (L) ν˜ LO (L) ν˜ TA (X) ν˜ LA (X) ν˜ TO (X) ν˜ LO (X)

266 610 766 838 373 640 761 829

Table 4.1-10 Phonon dispersion relations of Group IV

semiconductors and IV–IV compounds

Silicon carbide (6H-SiC) ν TA νLA ν TO νLO

Silicon carbide (3C-SiC) 6.00 (6) 1.00 (4) 4.15 (4) 4.89 (8) 5.74 (12) 1.25 (6) 4.67 (6) 5.51 (8)

9.8 16.7

10.6 18.6

11.2

Crystal

12.9

Phonon dispersion curves

Diamond Silicon Germanium Gray tin Silicon carbide

C Si Ge α-Sn 3C-SiC 6H-SiC

Fig. 4.1-18 Fig. 4.1-19 Fig. 4.1-20 Fig. 4.1-21 Fig. 4.1-22

ν (THz)

Diamond

45 ∆'2 (0) 40 X1 ∆5 (0)

35 30

Γ'25

Σ1(0)

X4

W2

L'2

X1

25

Λ3(0)

Σ2(0)

X4 W1

L'3 L1

Σ3(0) Σ1(A)

∆1 (A) X3

Λ1(0)

X3

W2

Λ1(A)

Σ 3(A)

20

L3 ∆5 (A)

15

Σ 4(A) Λ3(A)

10 5 0

[00ξ] 0

0.2 0.4 0.6 0.8 1.0 ξ

W 0

[1ξ0]

0.2 0.4 0.6 0.8 1.0 1.0 ξ ξ

[ξξ0]

[ξξξ] Γ15

0.8

0.6

0.4

0.2

0

0 0.1 0.2 0.3 0.4 0.5 ξ

Fig. 4.1-18 Diamond. Phonon dispersion curves. Symbols, experimental data from neutron scattering; solid curves, shell model calculation [1.16]

Part 4 1.1

Table 4.1-9 Phonon frequencies at symmetry points. Diamond (C) (ν in THz, 300 K, from Raman spectroscopy); silicon

585

586

Part 4

Functional Materials

Part 4 1.1

Wavenumber ν– (cm–1) 600 Si

400

200

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-19 Si. Phonon dispersion curves (left panel) and phonon density of states (right panel) [1.16]. Experimental data

points [1.17, 18] and ab initio calculations [1.16] Wavenumber ν– (cm–1) 400 Ge

300

200

100

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-20 Ge. Phonon dispersion curves (left panel) and phonon density of states (right panel) [1.16]. Experimental

data points [1.19] and ab initio calculations [1.16]

Semiconductors

1.1 Group IV Semiconductors and IV–IV Compounds

Part 4 1.1

Wavenumber ν– (cm–1) 300 α-Sn

200

100

0

Γ

K

X

Γ

L

X

W L Wave vector q

587

DOS

Fig. 4.1-21 α-Sn. Phonon dispersion curves (left panel) and phonon density of states (right panel) [1.20]. Experimental

data points from inelastic neutron scattering at 90 K [1.21]. Solid lines, ab initio pseudopotential calculation [1.20]

588

Part 4

Functional Materials

Part 4 1.1

Wavenumber ν-- (cm–1)

Wavenumber ν-- (cm–1)

1000

1000

3C-SiC

750

750

500

500

250

250

0

A

Γ

K

M

L

A Wave vector q

0

750

750

500

500

250

250

Γ

K

1000

4H-SiC

A

A Γ

A Wave vector q

M L

Wavenumber ν-- (cm–1)

Wavenumber ν-- (cm–1) 1000

0

6H-SiC

K

M

L

A Wave vector q

0

2H-SiC

A

Γ

K

M

L

A Wave vector q

Fig. 4.1-22 SiC. Phonon dispersion curves for the 3C, 2H, 4H, and 6H modifications obtained from a bond-charge model calculation [1.22]. Symbols represent experimental data. The different types of lines indicate different polarization states

1.1 Group IV Semiconductors and IV–IV Compounds

Semiconductors

Table 4.1-11 First Brillouin zones of Group IV semicon-

kz

ductors and IV–IV compounds Crystal

L Λ ∆

Γ kx

Σ K

U

Q

S W

Z

X

Figures

Diamond Silicon Germanium Gray tin Silicon carbide ky

C Si Ge α-Sn 3C-SiC 2H-SiC

Fig. 4.1-23 Fig. 4.1-23 Fig. 4.1-23 Fig. 4.1-23 Fig. 4.1-23 Fig. 4.1-24

kz

A R L

S H S'

Fig. 4.1-23 Brillouin zone of the diamond and of the zinc

P

T

U ky

Σ

blende lattice K

∆ Γ

T'

M

kx

Fig. 4.1-24 Brillouin zone of the Wurtzite lattice Table 4.1-12 Band structures of Group IV semiconductors and IV–IV compounds Diamond (C) (Fig. 4.1-25) Diamond is an indirect-gap semiconductor, the lowest minima of the conduction band being located along the ∆ axes. The valence band has the structure common to all group IV semiconductors, namely three bands degenerate at Γ. The spin–orbit splitting of these bands is negligible. Silicon (Si) (Fig. 4.1-26) The conduction band is characterized by six equivalent minima along the [100] axes of the Brillouin zone located at about k0 = 0.85(2π/a) (symmetry ∆1 ). The surfaces of constant energy are ellipsoids of revolution with their major axes along [100]. Higher minima are located at Γ and along the [111] axes about 1 eV above the [100] minima. The valence band has its maximum at the Γ point (symmetry Γ8 ), the light- and heavy-hole bands being degenerate at this point. Both bands show warping. The third, spin–orbit split-off band has Γ7 symmetry. The spin–orbit splitting energy at Γ is small compared with most interband energy differences. Thus, spin–orbit interaction is mostly neglected in band structure calculations and the notation of the single group is used to denote the symmetry of a band state.

Part 4 1.1

B. Electronic Properties Tables 4.1-11 – 4.1-18.

589

590

Part 4

Part 4 1.1

Table 4.1-12 Band structures of Group IV semiconductors and IV–IV compounds, cont.

Functional Materials

Germanium (Ge) (Fig. 4.1-27) The conduction band is characterized by eight equivalent minima at the end points L of the [111] axes of the Brillouin zone (symmetry L6 ). The surfaces of constant energy are ellipsoids of revolution with their major axes along [111]. Higher energy minima of the conduction band are located at the Γ point and (above these) on the [100] axes. The valence band has its maximum at the Γ point (symmetry Γ8 ), the light- and heavy-hole bands being degenerate at this point. Both bands are warped. The third, spin–orbit split-off band has Γ7 symmetry. In contrast to silicon the spin–orbit splitting energies are considerable. Thus, the symmetry notation of the double group of the diamond lattice is mostly used for Ge. Gray tin (α-Sn) (Fig. 4.1-28) The band structure of gray tin (α-Sn) is qualitatively different from those of the other Group IV elements. The s-like Γ7 conduction band edge, which decreases drastically with atomic number in the sequence C → Si → Ge, is situated below the p-like Γ8 valence band edge in α-Sn. This causes an inversion of the curvature of the Γ8 light-hole band. Consequently, α-Sn is a zero-gap semiconductor, with its lowest conduction band and its highest valence band being degenerate at Γ (symmetry Γ8 ). A second conduction band, with minima at L6 , follows at a slightly higher energy. This second hand determines the properties of n-type samples for n > 1017 cm−3 (T > 77 K for intrinsic samples). Silicon carbide Band structure calculations show that the conduction band minima are situated along the cubic axes at the border of the Brillouin zone. The band structure of 3C-SiC is shown in Fig. 4.1-29, and that of 2H-SiC in Fig. 4.1-30. Silicon–germanium alloys The band structure is characterized by a crossover in the lowest conduction band edge from Ge-like [111] symmetry to Si-like [100] symmetry at the composition x = 0.15. The shape of the band edge (and hence the effective masses) varies only slightly as a function of composition.

15

E (eV) 6 Γ2'

10 L1 L3 5

K1

E (eV) Γ2'

L3

Γ2'

K1 3

Diamond

Γ15

X1

K3

Si

Γ15 L1

Γ15

X1

Γ25'

0 L3'

Γ25'

0 Γ25'

L'3

X4 –3

K2 K1

–6

K3

K2 X4

–5

K1 – 10 L1

X1

L1 X1

–9

K3

L2'

K1

– 15

Γ1

Γ1

– 20

L

Λ

Γ

∆

X

Fig. 4.1-26 Band structure of silicon

– 25 L

Λ

Γ

∆

X

Fig. 4.1-25 Band structure of diamond

U,K

Σ Γ Wave vector k

K1

Γ1'

–12

L'2

K3

U,K

Σ Γ Wave vector k

E (eV) L4,5 4 L6 Ge 2 L6 0 L4,5 –2 L

591

E (eV) 4

Γ8

Γ8

Γ6 Γ7

Γ6

2 Γ7 Γ8 Γ7

X5

Γ8 Γ7

6

1.1 Group IV Semiconductors and IV–IV Compounds

Part 4 1.1

Semiconductors

X5

L4,5 –2 L 6

–4

–4

–6

–6

– 8 L6 – 10 L6 Γ6 Λ

L

Γ6

Γ

∆

Γ7 X5

– 10 L6

Theory Ge (111) c(2 × 8) Ge (111) (1 × 1)H Ge (110) (2 × 1) Typical error

– 12

Γ6

– 8 L6

X5

– 12

Γ8

0

X

Σ Γ Wave vector k

U,K

Λ

L

Γ

X5

∆ X Wave vector k

Fig. 4.1-27 Band structure of germanium

4

E (eV)

E (eV) L6 L 4,5

2

20 2

Γ6 Γ8 Γ8

X5

16 X5

Γ8

L4,5

– 2 L6

Γ7

X5

1

5

14

X5 –4

1

2

1 2

1

3 1

1

4 3

1

8

1 3

2

6

1

2

3,4

3

1

2

1

1

2 1

1

1

15 1

1

1

4

–6

2

L6

X5

X5

–8

1 15

0 3,4

L6

–2

– 10 Γ6 Γ6

3

1

1

Λ

Γ

∆

X

U,K Σ ΓΓ X Wave vector k Wave vector k

Fig. 4.1-28 Band structure of gray tin

1 3

2

–8 – 10

1

1

2 1

2

1

1

2

2

–6 3

L

3

5

–4 Γ6

2

3

3

1

1

– 12

1 12

2

10

Γ7 Γ7

1

2

3

12

Γ7 Γ 7

3

3C-SiC

1

18

Γ6

α-Sn Γ6 L6

0

Γ8

Γ8

1

4

1

1

1 1

– 12

1

1

– 14

1 1

– 16

Fig. 4.1-29 Band structure of 3C silicon carbide

Γ

∆

X Z W

Q

L

Λ

Γ

Σ K X Wave vector k

592

Part 4

Part 4 1.1

16

Functional Materials

E (eV) 3

1

2H-SiC 1

14

2

1 1

1

12

3

2 1 1

2 1

2

1 1

8

1

4 3

1

1

1

1

2

1

1 1,2 1,3

1,3

1

3

3

1,2

1

1

3

2

4

3

1,3 2

1,3

1

3

1

2,4

2

1,2

5,6

2 6 1

1,3

1 4

1

1

2

2

6

1

1

5

3

3

1,2 1

2

1 1,2

3

1

2

3

1,2

5,6

1

3

1

3 3

10

6 3

2

2

2 2

2 2

3

1,2

3

3 2

1,3

1 1

2

2 6

0

2

–2

1

5

1

2

1

2

1 1

3

2

3

1

1

1

2

–4 –6

3 2

1,2

2,4

1,2

2 1,3 1

2 1,2

1 1,2

1

3

3

2

3

1

3

1

1 3

1

1

3

3

1,3

1

3 3

1,3

– 12

3

1

1 2

2

3

1,3

1 3

– 10

2

1

2

1

–8

4 3

2 2

5,6 4

3

1,2 1

1

– 14

1,3

1 1

– 16

M T' K

Γ

T

Σ

MU L

R

A

S H PK Wave vector k

Fig. 4.1-30 Band structure of 2H silicon carbide Table 4.1-13 Energy gaps of Group IV semiconductors and IV–IV compounds Crystal

Between

Gap

bands Diamond

C

Γ25 v and ∆1c

Energy

Temperature

(eV)

(K)

E g, indir

5.50 (5)

E gx, indir

5.416 (2)

RT 100

5.409 (2) Silicon

Si

Γ25 v and ∆1c

E g, ind

Remarks Quantum photoyield Indirect exciton gap with lower valence band Indirect exciton gap with upper valence band

1.1700

0

1.1242

300

Extrapolated, wavelength-modulated transmission

E g, th

1.205

0

E g, dir

4.185 (10)

4.2

Wavelength-modulated transmission Extrapolated from temperature dependence of conductivity above 200 K

Γ25 v and Γ2 c

4.135

190

Electroreflection

1.1 Group IV Semiconductors and IV–IV Compounds

Semiconductors

Crystal Germanium

Ge

Between bands

Gap

Energy (eV)

Temperature (K)

Remarks

Γ8v and L6c

E g, ind

0.744 (1) 0.664 0.785

1.5 291 0

E g, dir E gx

0.898 (1) 0.805 (1) 2.417 (1) 2.2 6.0 2.390

1.5 293 2 300 300 2

Magnetotransmission Optical absorption Extrapolated from temperature dependence of intrinsic conductivity Magnetoabsorption

E gx E g, ind E gx

3.330 2.86 3.023

4 300 4

E g, th

Silicon carbide

Silicon carbide Silicon carbide

3C-SiC

Γ8v and Γ7c

E g, dir

Γ15v and X1c

E g, ind

2H-SiC 6H-SiC

Wavelength-modulated absorption Optical absorption Optical absorption Excitonic energy gap, wavelength-modulated absorption Excitonic energy gap; optical absorption Optical absorption

Table 4.1-14 Exciton energies of Group IV semiconductors and IV–IV compounds (E b = exciton binding energy) Crystal

Quantity

Diamond

E b (1S)

0.19 (15)

Eb

0.07

E(1S)

1.1552 (3)

1.8

Wavelength-modulated absorption

Eb

0.01412

4.2

Calculated binding energy

2.1, 5.1

Optical absorption at 2.1 K and

Silicon Germanium

State

Exciton energy (eV)

3/2

Remarks 1S core exciton Indirect exciton binding energy

E(1S)

1S3/2 (L4 + L5 )

0.74046 (3)

(L6 )

0.74158 (3)

Eb

3/2 1S1/2 3/2 1S3/2 3/2 1S1/2

(L4 + L5 )

0.00418

(L6 )

0.00317

Silicon carbide (3C-SiC) E b

Temperature (K)

luminescence at 5.1 K

0.027

2

Wavelength-modulated absorption

Table 4.1-15 Spin–orbit splitting energies of Group IV semiconductors and IV–IV compounds Crystal

Quantity

Diamond

∆(Γ25 v )

Silicon

∆0 (Γ25 v )

Germanium

∆0

Bands

Splitting energy (eV)

Temperature (K)

0.006 (1)

Cyclotron resonance

0.0441 (3) Γ7v to Γ8v

0.297

Γ6v to Γ8c

0.200

Silicon carbide (3C-SiC) ∆0

Remarks

1.8

Wavelength-modulated absorption

10

0.010

Electroreflectance

2

Wavelength-modulated absorption

Table 4.1-16 Effective masses of electrons (in units of the electron mass m 0 ) for Group IV semiconductors and IV–IV compounds Crystal

Quantity

Value

Diamond

m n, parall

1.4

m n, perpend

0.36

m n, parall

0.9163 (4)

m n, perpend

0.1905 (1)

Silicon

Temperature (K)

Remarks Field dependence of electron drift velocity

1.26

Cyclotron resonance with uniaxial stress

Part 4 1.1

Table 4.1-13 Energy gaps of Group IV semiconductors and IV–IV compounds, cont.

593

594

Part 4

Part 4 1.1

Table 4.1-16 Effective masses of electrons for Group IV semiconductors and IV–IV compounds, cont.

Functional Materials

Crystal

Quantity

Value

Germanium

m n, perpend (L6 )

0.0807 (8)

Temperature (K) 30–100

0.0823 m n, parall (L6 )

Silicon carbide (3C-SiC) Silicon carbide (6H-SiC)

Cyclotron resonance magnetophonon resonance

120

1.57 (3)

30–100

1.59 Gray tin

Remarks

Cyclotron resonance magnetophonon resonance

120

m n (Γ7 )

0.0380 (5)

m n, light (Γ8 )

0.0236 (2)

1.3

m n, heavy (L6 )

0.21

4.2

m n, parall

0.677 (15)

m n, perpend

0.247 (11)

m n, parall

3–6

m n, perpend

0.48 (2)

30

Piezomagnetoreflectance Density-of-states mass

45

Cyclotron resonance Cyclotron resonance

Table 4.1-17 Effective masses of holes (in units of the electron mass m 0 ) for Group IV semiconductors and IV–IV compounds Crystal

Quantity

Value

Diamond

m p, heavy

1.08

Calculated from valence band

m p, light

0.36

parameters

m spin–orbit split

0.15

m p, dens stat

0.75

m p, heavy

0.537

m p, light

0.153

m spin–orbit split

0.234

m p, dens stat

0.591

m p, light

0.0438 (3)

Silicon

Germanium

m p, heavy

Temperature (K)

300

Cyclotron resonance

Density-of-states mass 4

B parallel to [100]

0.0426 (2)

B parallel to [111]

0.0430 (3)

B parallel to [110]

0.284 (1)

B parallel to [100]

0.376 (1)

B parallel to [111]

m spin–orbit split

0.095 (7)

m p (Γ8 )

0.195

m p (Γ7 )

0.058

Silicon carbide (3C-SiC)

mp

0.45

Silicon carbide (6H-SiC)

m p, parall

1.85 (3)

m p, perpend

0.66 (2)

Diamond Silicon Germanium

gc 2.0030 (3)

Piezomagnetoabsorption Interband magnetoreflection

45

High-field cyclotron resonance Cyclotron resonance

Temperature (K)

Remarks

140–300

Electron spin resonance

1.99893(28) −3.0 (2)

Electron spin resonance 30

Cyclotron resonance

B parallel to [110] 30

Table 4.1-18 g-factor gc of conduction electrons for Group IV semiconductors Crystal

Remarks

Hall effect

4.2

0.352 (4) Gray tin

Field direction

Piezomagnetoabsorption

Semiconductors

Electronic Transport, General Description.

Diamond (C). Owing to the large band gap, most diamonds are insulators at room temperature, and

so electronic transport is extrinsically determined and therefore strongly dependent on the impurity content. Natural (type IIb) and synthetic semiconducting diamonds are always p-type. The electron mobility can be derived only from photoconductivity experiments.

Table 4.1-19 Intrinsic carrier concentration n i and electrical conductivity σi of Group IV semiconductors and IV–IV

compounds Crystal

ni (cm−3 )

σi (
−1 cm−1 )

T (K)

Temperature dependence

Silicon

1.02 × 1010

3.16 × 10−2

300

Fig. 4.1-31 a

Germanium

2.33 × 1013

2.1 × 10−2

300

Figs. 4.1-32 and 4.1-33

3C-SiC

Fig. 4.1-34

Si–Ge alloys

Composition dependence of intrinsic conductivity: Fig. 4.1-36 Composition dependence of the mobilities: Figs. 4.1-35 and 4.1-37

a

The intrinsic conductivity of Si up to 1273 K is given by the phenomenological expression log10 σi = 4.247 − 2.924 × 103 T −1 (σi in Ω−1 cm−1 , T in K).

σ (Ω–1 cm–1) 103

T (K) 1200 800 600 500

400

300 Si

102

104 RH (cm3 C –1) 103

T (K) 1000 800 600 103

500

400

350

σi (Ω–1 cm–1)

300

273 250

Ge

102

RH 102

10

10 10

1 σ

1

10 –1

1 10 –1 p-type

10 –2

10 –1

10 –3

10 –2

n-type Computed 10 –2

0

0.5

1.0

1.5

2.0

2.5

3.0 3.5 T–1 (10 –3 K–1)

Fig. 4.1-31 Si. Conductivity and Hall coefficient vs. re-

ciprocal temperature in the range of intrinsic conduction; n- and p-type samples with doping concentrations of 1.7 × 1014 cm−3 and above [1.23]. The different symbols show results from different samples

10 –3 0.8

1.2

1.6

2.0

2.4

2.8

3.2 3.6 4.0 T–1 (10 –3 K–1)

Fig. 4.1-32 Ge. Conductivity vs. reciprocal temperature in the range of intrinsic conduction [1.24]

595

Part 4 1.1

C. Transport Properties Tables 4.1-19 – 4.1-21.

1.1 Group IV Semiconductors and IV–IV Compounds

596

Part 4

Functional Materials

Part 4 1.1

T (K) 1000 800

600 500

1019 ni Ge (cm–3)

400 350

300 273 250

Carrier concentration (cm–3) 1000 500 200 1017

T (K) 70

100

8

3C - SiC

6 4

1018

Si / C: 0.33 2

0.37 1017

1016 8 6 4

1016

0.40

2

1015

1015 8 6

1014

p-type n-type computed

1013

1012 0.8

4 × 1014 0

2.5

5.0

7.5

10.0

12.5 15.0 T–1 (10–3 K–1)

Fig. 4.1-34 3C-SiC. Temperature dependence of carrier

concentration for n-type films grown by CVD on Si(100) substrates [1.25]. Solid lines, calculated values. Si/C = ratio of source gases 1.2

1.6

2.0

2.4

2.8

3.2 3.6 4.0 T–1 (10 –3 K–1)

µH,n (cm2/V s) 3000 SixGe1–x

Fig. 4.1-33 Ge. Intrinsic carrier concentration vs. recipro-

cal temperature [1.24] 10 –1

2000

σ –1 (Ω –1 cm–1) SixGe1–x

1000

10 –2

10 –3

0

10 –4

0

0.2

0.4

0.6

0.8

1.0 x

Fig. 4.1-35 Six Ge1−x . Composition dependence of the

electron Hall mobility at room temperature [1.26] 10 –5

10 –6

0

0.2

0.4

0.6

0.8

1.0 x

Fig. 4.1-36 Six Ge1−x . Composition dependence of the in-

trinsic conductivity at room temperature [1.26]

Semiconductors

1.1 Group IV Semiconductors and IV–IV Compounds

Crystal

µn (cm2 /V s)

µp (cm2 /V s)

T (K)

Remarks

Diamond Silicon

2000 1450 3800 µn (Γ8 ) 0.12 × 106 µn (L6 ) 1.6 × 103 510

293 300 20 300 100

See Figs. 4.1-38 and 4.1-39 for temperature dependence See Figs. 4.1-40 and 4.1-41 for temperature dependence

Germanium Gray tin

2100 370 2 × 105 1800 10 × 103 15–21

296

Silicon carbide (3C-SiC) µH,p (cm2/V s)

See Figs. 4.1-33 and 4.1-42 for temperature dependence From Hall and magnetoresistance data, via conductivity and Hall coefficient Epitaxial film grown on Si(100)

µn (cm2/V s)

2000

4×104

SixGe1–x

Diamond

2

1000 104 8 6

0 0

0.2

0.4

0.6

0.8

1.0 x

Fig. 4.1-37 Six Ge1−x . Composition dependence of the

4

2

hole Hall mobility at room temperature [1.26] 103

µn (cm2/V s)

8

2 ×104

Diamond

6 4

104 8 6

2

4

102 60

2

8

102

2

4

6

103 T (K)

Fig. 4.1-38 Diamond. Electron mobility vs. temperature. Open circles, drift mobility data from [1.27]; filled triangles and filled circles, Hall mobility data from [1.28] and [1.29, 30], respectively. Continuous curve, theoretical drift mobility [1.27]

103 8 6 4

2

102 8 6

40 60

8

102

2

4

6

103 T (K)

8

Fig. 4.1-39 Diamond. Hole mobility vs. temperature. Open circles, drift mobility data from [1.31]; filled circles and filled triangles, Hall mobility data from [1.29, 30] and [1.32], respectively. Solid and dashed curves: calculated drift and Hall mobilities, respectively [1.33]

Part 4 1.1

Table 4.1-20 Electron mobilities µn and hole mobilities µp of Group IV semiconductors and IV–IV compounds

597

598

Part 4

Functional Materials

Part 4 1.1

µH,p (cm2/ V s)

µn (cm2/V s) 6

10

Si nd
1012cm–3

1086 6 4

Light-hole band

2

4 × 10

13

Total

105

105

8

6 4

T

Heavyhole band

–2.42 2

104 8

4

10

6

1.3 × 1017

4

2

Spin-orbit band

3

10

8

103

6 4

2

102 10 102

4

10

102

103 T (K)

2

4

6

8

102

4 ×102 T (K)

Fig. 4.1-41 Si. (b) Hall hole mobility vs. temperature; cir-

Fig. 4.1-40 Si. Electron mobility vs. temperature [1.34].

cles from [1.37], solid lines calculated contributions from the three valence bands

Silicon (Si). The electronic transport is due exclusively to electrons in the [100] conduction band minima and holes in the two uppermost (heavy and light) valence bands. In samples with impurity concentrations below 1012 cm−3 , the mobilities are determined by pure lattice scattering down to temperatures of about 10 K (n-type) or 50 K (p-type), for electrons and holes, respectively. Higher impurity concentrations lead to deviations from the lattice mobility at corresponding higher temperatures. For electrons, the lattice mobility below 50 K is dominated by deformation-potential coupling

to accoustic phonons. At higher temperatures, intervalley scattering between the six equivalent minima of the conduction band is added to the intravalley process, modifying the familiar T −1.5 dependence of the acoustic-mode-dominated mobility to T −2.42 . At temperatures below 100 K, the lattice mobility of holes is dominated by acoustic scattering, but does not follow a T −1.5 law, owing to the nonparabolicity of the valence bands. The proportionality of µp to T −2.2 around room temperature is a consequence of optical-phonon scattering. Germanium (Ge). Low-field electronic transport is provided by electrons in the L6 minima of the conduction band and holes near the Γ8 point in the valence bands. At room temperature, the mobility of samples with impurity concentrations below 1015 cm−3 is limited essentially by lattice scattering; higher donor or acceptor concen-

Data points for n d ≤ 1012 cm−3 obtained by time-offlight technique [1.35]. Other experimental values taken from [1.36] (4 × 1013 cm−3 ) and [1.23] (1.3 × 1017 cm−3 ). Continuous line, theoretical lattice mobility, after [1.35]. Dash–dotted line, T −2.42 dependence of µn around room temperature

Semiconductors

104

100 90 80 70 60

κ (W/cm K) Diamond

Ge

50

103

40 30 102 20

µn Slope = –1.66

15

10 10 9 8 7 6 1

5

µp Slope = –2.33

4

1

10

102

103 T (K)

Fig. 4.1-43 Diamond. Thermal conductivity vs. tempera-

ture for three type Ia diamonds [1.39]

3

2 30

40

50 60

80

100

150

200

300 T (K)

Fig. 4.1-42 Ge. Electron and hole mobilities vs. tem-

perature for a constant carrier concentration (high-purity samples) [1.38]

trations result in an increasing influence of impurity scattering. At 77 K, even for doping concentrations below 1013 cm−3 , the mobilities depend on the impurity

concentration. Low temperatures and high concentrations lead to the replacement of free-carrier conduction by impurity conduction. Gray Tin (α-Sn). In intrinsic samples, light electrons and holes in the Γ8 bands determine the transport properties. When the Fermi level crosses the energy of the L6 minima, heavy electrons have an influence. This leads, for example, to a screening enhancement of the lightelectron mobility and, in heavily doped n-type samples, to a dominant role of the L electrons. Consequently,

Table 4.1-21 Thermal conductivity κ of Group IV semiconductors and IV–IV compounds κ (W/cm K)

Temperature (K)

Remarks

Diamond

C

6–10

293

See Fig. 4.1-43 for temperature dependence

Silicon

Si

1.56

300

See Fig. 4.1-44 for temperature dependence

Germanium

Ge

Silicon carbide

3C-SiC

Crystal

6H-SiC

See Fig. 4.1-46 for temperature dependence 4.9

300

Perpendicular to c axis; See Fig. 4.1-45 for temperature dependence

599

Part 4 1.1

µ (103 cm2/V s)

1.1 Group IV Semiconductors and IV–IV Compounds

600

Part 4

Functional Materials

Part 4 1.1

κ (W/cm K)

102

102

8

Si

6

κ (W/cm K)

8 6

SiC

4

4

2 2

10

2κ T

102

8 6

8

4

6 4

2

κL

1 8 6

2

4

1

8

2

6

10

4

2

–1 8 6 4

–1

2

10

4

2

6 8

2

10

4

6 8

102

2

4

103 T (K)

6 8

Fig. 4.1-44 Si. Lattice thermal conductivity vs. temperature, according to [1.40] (filled circles), [1.41] (open circles), and [1.42] (triangles). The curves marked κL and 2κT represent the contributions of the longitudinal and transverse phonons, respectively [1.43]

10

–2

1

2

4

6 8

10

2

4

102

6 8

2

4

6 8 103 T (K)

Fig. 4.1-45 6H-SiC. Thermal conductivity (⊥c axis) vs.

temperature for two different samples [1.44]

a) κ (W/cm K)

b) κ (W/cm K)

20

Ge 10

0.7 0.6 0.5

8 6

0.4

4

0.3

2

T –1 1 8 6

0.2

4

2

10–1

2

4

6

8

10

2

4

6

8

102

2

4 × 102 T (K)

0.1 400

500

600

800

1000

1200 T (K)

Fig. 4.1-46a,b Ge. Thermal conductivity vs. temperature. (a) 3–400 K, (b) 400–1200 K. Solid curve in (a) and data in (b) from [1.40]; experimental data in (a) from [1.45]. Dashed line in (b), extrapolated lattice component

Semiconductors

tals. The mobility is influenced by alloy scattering, which makes a contribution µalloy ∝ T 0.8 x −1 (1 − x)−1 . Near the band crossover (x = 0.15), intervalley scattering has to be taken into account.

D. Electromagnetic and Optical Properties Tables 4.1-22 – 4.1-25. Table 4.1-22 High-frequency dielectric constant ε (real part of the complex dielectric constant) of Group IV semiconductors and IV–IV compounds Crystal Diamond Silicon

C Si

Germanium

Ge

Gray tin Silicon carbide

α-Sn 3C-SiC

Silicon carbide

6H-SiC

ε

T (K)

Frequency

Method

5.70 (5) 12.1 11.97 16.5 16.0 16.2 15.8 24 9.52 6.38 9.66 10.03 6.52 6.70

300 4.2 300 4.2 4.2 300 77 300 300

1–10 kHz 750 MHz

Capacitance bridge Capacitance bridge

750 MHz 9200 MHz

Capacitance bridge Microwave measurement Capacitance bridge Infrared reflectance measurement Infrared transmission

300

1 MHz Infrared Low frequency High frequency Low frequency

300

High frequency

Optical Constants. The real part (ε1 ) and imaginary part (ε2 ) of the dielectric constant at optical frequencies were measured by spectroscopic ellipsometry. The refractive index n, the extinction coefficient k, the absorption coefficient K , and the reflectivity R have been calculated from ε1 and ε2 . The frequency dependences of ε1 , ε2 , n, and K are shown in Figs. 4.1-48 and 4.1-47. Diamond. The refractive index n is equal to 3.5 at λ = 177.0 nm. The spectral dependence of the refractive index n can be approximated by the empirical formula     n 2 − 1 = aλ2 / λ2 − λ21 + bλ2 / λ2 − λ22 ,

εperp εparall εperp εparall

with the parameters a = 0.3306, b = 4.3356, λ1 = 175.0 nm, and λ2 = 106.0 nm. Silicon. (See Table 4.1-23). Germanium. (See Fig. 4.1-48). Gray Tin (α-Sn). The index of refraction n, extinction coefficient k, and absorption coefficient K versus photon energy are shown in Fig. 4.1-47. Silicon Carbide (SiC).

601

Part 4 1.1

heavily doped n-type samples behave as indirect-gap semiconductors with an E g of about 0.09 eV. Silicon–Germanium Alloys (Six Ge1−x ). The transport properties have been investigated mostly on single crys-

1.1 Group IV Semiconductors and IV–IV Compounds

602

Part 4

Functional Materials

Part 4 1.1

ε1 , ε2

K (105 cm–1)

n, k 6

12 α-Sn

10

5

30

Ge

20 ε2

k 10

ε1

8

4

0 6

3

– 10

k 2

4

n

2

3

4

5

6 hω (eV)

Fig. 4.1-48 Ge. Real and imaginary parts of the dielectric 2

1

0

1

2

3

4

5

constant vs. photon energy [1.47]

0

hω (eV)

Fig. 4.1-47 α-Sn. Index of refraction n, extinction coefficient k, and absorption coefficient K vs. photon energy [1.46] Dielectric constant ε (∞) 19 Ge 18

17

16

Fig. 4.1-49 Ge. Temperature dependence of the high15

14

0

100

200

300

400

500 T (K)

frequency dielectric constant [1.48]. Experimental data points [1.49] and ab initio calculations (solid line); the dotted line is the theoretical result without the effect of thermal expansion, and the dashed line is the solid line shifted to match the experimental data

Semiconductors

1.1 Group IV Semiconductors and IV–IV Compounds

hν (eV)

ε1

ε2

n

k

K (103 /cm)

Part 4 1.1

Table 4.1-23 Optical constants of silicon R

1.5

13.488

0.038

3.673

0.005

0.78

0.327

2.0

15.254

0.172

3.906

0.022

4.47

0.351

2.5

18.661

0.630

4.320

0.073

18.48

0.390

3.0

27.197

2.807

5.222

0.269

81.73

0.461

3.5

22.394

33.818

5.610

3.014

1069.19

0.575

4.0

12.240

35.939

5.010

3.586

1454.11

0.591

4.5

−19.815

24.919

2.452

5.082

2317.99

0.740

5.0

−10.242

11.195

1.570

3.565

1806.67

0.675

5.5

−9.106

8.846

1.340

3.302

1840.59

0.673

6.0

−7.443

5.877

1.010

2.909

1769.27

0.677

Table 4.1-24 Optical constants of germanium hν (eV)

ε1

ε2

n

k

K (103 /cm)

R

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

21.560 30.361 13.153 12.065 9.052 4.123 −14.655 −8.277 −6.176 −6.648

2.772 10.427 20.695 17.514 21.442 26.056 16.782 8.911 7.842 5.672

4.653 5.588 4.340 4.082 4.020 3.905 1.953 1.394 1.380 1.023

0.298 0.933 2.384 2.145 2.667 3.336 4.297 3.197 2.842 2.774

45.30 189.12 604.15 652.25 946.01 1352.55 1960.14 1620.15 1584.57 1686.84

0.419 0.495 0.492 0.463 0.502 0.556 0.713 0.650 0.598 0.653

Table 4.1-25 Optical constants of silicon carbide Crystal

Refractive index

Wavelength range (nm)

3C-SiC 6H-SiC

n(λ) = 2.55378 + 3.417 × 104 /λ2 n o (λ) = 2.5531 + 3.34 × 104 /λ2 n e (λ) = 2.5852 + 3.68 × 104 /λ2

467–691

603

604

Part 4

Functional Materials

Part 4 1.2

4.1.2 III–V Compounds 4.1.2.1 Boron Compounds A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-26 – 4.1-32.

Table 4.1-26 Crystal structures of boron compounds Crystal

Space group

Crystal system

Structure type

Remarks

Figure

Stable under normal conditions Metastable under normal conditions Metastable under all conditions Stable under normal conditions Stable in presence of As vapor up to 920 ◦ C Stable under normal conditions

Fig. 4.1-50 Fig. 4.1-2 Fig. 4.1-3 Fig. 4.1-2 Fig. 4.1-2

Boron nitride, hexagonal Boron nitride, cubic Boron nitride, wurtzite Boron phosphide Boron arsenide

BNhex BNcub BNw BP BAs

Td2 4 C6v Td2 Td2

P63 /mmc F43m P63 mc F43m F43m

hex fcc hex fcc fcc

h-BN Zinc blende Wurtzite Zinc blende Zinc blende

Boron antimonide

BSb

Td2

F43m

fcc

Zinc blende

Fig. 4.1-2

Table 4.1-27 Lattice parameters of boron compounds Crystal Boron nitride, cubic Boron nitride, hexagonal

BNcub BNhex

Boron phosphide Boron arsenide Boron antimonide

BP BAs BSb

Lattice parameters (nm)

Temperature (K)

Remarks

a = 0.36160 (3) a = 0.25072 (1) c = 0.687 (1) a = 0.45383 (4) a = 0.4777 a = 0.512

RT 297 297 297

X-ray diffraction Prepared from amorphous BN in N2 atmosphere at room temperature

Ab initio pseudopotential calculation

Table 4.1-28 Densities of boron compounds Crystal

Fig. 4.1-50 The hexagonal lattice of h-BN (BNhex )

Density (g/cm3 )

Remarks X-ray diffraction X-ray density

Boron nitride, cubic

BNcub

3.4863

Boron nitride, hexagonal Boron phosphide Boron arsenide

BNhex BP BAs

2.279 5.22

Semiconductors

1.2 III–V Compounds

Melting point Tm (K)

Crystal

Remarks

Boron nitride, cubic

BNcub

> 3246

Boron nitride, hexagonal

BNhex

3200–3400

N2 ambient; pyrometric measurement

Boron phosphide

BP

1400

Decomposition temperature

Table 4.1-30 Linear thermal expansion coefficient α of boron compounds Expansion coefficient α (K−1 )

Crystal

Remarks

BNcub

1.15 × 10−6

Boron nitride, hexagonal

BNhex

40.6 (4) × 10−6

Boron phosphide

BP

3.65 × 10−6

At 400 K

BAs

4.1 × 10−6

Calculated

Boron nitride, cubic

Boron arsenide

X-ray measurement

Table 4.1-31 Heat capacities and Debye temperatures of boron compounds Crystal

Debye temperature ΘD (K)

Remarks See Fig. 4.1-51 for temp. dependence of c p

Boron nitride, cubic

BNcub

1730 (70)

Boron nitride, hexagonal

BNhex

598 (7)

Calorimetry

Boron phosphide

BP

985

See Fig. 4.1-52 for temp. dependence of c p

Boron arsenide

BAs

800

Table 4.1-32 Phonon wavenumbers/frequencies of boron compounds. Values for hexagonal boron nitride (BNhex )

obtained from infrared reflectivity; values for boron phosphide (BP) from ab initio pseudopotential calculations Phonon wavenumbers (cm−1 )

Crystal Boron nitride, cubic

BNcub

ν˜ LO

Boron arsenide

BAs

ν˜ LO (Γ)

1305 (1) 714

Table 4.1-32 Phonon wavenumbers/frequencies, cont. BNhex Phonon branch

Remarks

ν˜ TO ν˜ TO (Γ)

1054.7 (6) 695

RT; Raman scattering Raman scattering

Table 4.1-32 Phonon wavenumbers/frequencies, cont. BP

Wavenumber (cm−1 )

Phonon branch

Frequency (THz)

ν˜ TO1

783

ν˜ LO1

ν TO (Γ)

24.25

828

ν˜ TO2

νLO (X)

24.00

1510

ν˜ LO2

1595

ν TO (X)

15.81

ν˜ TO1

767

νLO (X)

21.04

ν˜ LO1

778

ν TO (X)

9.20 22.91 15.18

ν˜ TO2

1367

νLO (L)

ν˜ LO2

1610

ν TO (L)

Part 4 1.2

Table 4.1-29 Melting point Tm or decomposition temperature of boron compounds

605

606

Part 4

Functional Materials

Part 4 1.2

Heat capacity c p (J K–1 mol –1) 24 1.0

1.5

Heat capacity cp (J g–1 K–1)

Debye temperature ΘD (K) ΘD

c p (J K–1 mol –1)

BP

1.4

0.8

20

1000

1.3

0.6 0.4

16

1.2

900

0.2 0

1.1 0

10

20

30

12

40

50 T (K)

800

cp 1.0

700

0.9

8

0.8 4

0

1100

h-BN r-BN c-BN w-BN 0

50

100

150

200

250 300 Temperature T (K)

600

0.7 320

400

500

600

700 T (K)

Fig. 4.1-52 BP. Temperature dependence of specific heat capacity and Debye temperature [1.51]

Fig. 4.1-51 BN. Heat capacities for four polymorphic boron nitride modifications. Data taken from [1.50]

B. Electronic Properties Tables 4.1-33 – 4.1-35. Band Structures of Boron Compounds.

Boron Nitride, Cubic (BNcub ). All band structure calculations lead to an indirect-gap structure (Fig. 4.1-53). Boron Nitride, Hexagonal (BNhex ). All recent band structure calculations yield an indirect gap (Fig. 4.1-54). The conduction band minimum is located at P. Boron Phosphide (BP). BP is an indirect-gap semiconductor (Fig. 4.1-55). Boron Arsenide (BAs). The calculated band structure shows an indirect (Γ–X) gap of a few eV. The conduction

E (eV) 21 c-BN 14

7

0

–7

Table 4.1-33 First Brillouin zones of boron compounds Crystal

Figure

Boron nitride, cubic

BNcub

Fig. 4.1-23

Boron nitride, hexagonal

BNhex

Fig. 4.1-24

Boron phosphide

BP

Fig. 4.1-23

Boron arsenide

BAs

Fig. 4.1-23

– 14

– 21

L

Γ

X

K

Γ Wave vector k

Fig. 4.1-53 Band structure of cubic boron nitride

Semiconductors

1.2 III–V Compounds

Crystal Boron nitride, cubic

BNcub

Boron nitride, hexagonal

BNhex

Boron phosphide

BP

Bands

E g, ind

Γ15v to X1c

6.2

E g, dir

Γ15v to Γ1c

14.5

BAs

Boron antimonide

BSb

Remarks Soft-X-ray emission spectroscopy Reflectivity

Eg

5.9 (1)

Inelastic electron scattering

E g, th

7.1 (1)

Temperature dependence of electrical resistivity

E g, ind

2.1

X-ray emission and absorption

E g, dir

Boron arsenide

Energy (eV)

Quantity

Part 4 1.2

Table 4.1-34 Energy gaps of boron compounds

Γ

4.4

X

6.5

L

6.5

E g, ind

0.67

E g, dir

1.46

Eg

Γ to ∆

Absorption

0.527

Calculated

Table 4.1-35 Effective masses of electrons (m n ) and holes (m p ) for cubic boron nitride (in units of the electron mass m 0 ) Crystal

mn

Boron nitride, cubic

BNcub

mp, heavy

mp, light

Remarks

0.375

0.150

Parallel to [100]

0.926

0.108

Parallel to [111]

0.752

Calculated from band structure data

band minimum is on the ∆ axis close to the X point. As in silicon, the Γ15c level is below the Γ1c level (Fig. 4.1-56). Boron Antimonide (BSb). Boron antimonide is an indirect-gap semiconductor (Fig. 4.1-57).

E (eV) 20 Σ1

E (eV) 21

L1

K1

Γ12

Γ12

K2

Σ2

∆5

10 14 5 h-BN

Σ1

K1

Σ2

Σ1 Σ1

Γ1

X3

Γ15

∆1

Γ1 Γ15

Σ2

–5

–7

– 14

– 10

– 21

– 15

K H

A Γ

M L A Wave vector k

Fig. 4.1-54 Band structure of hexagonal boron nitride Fig. 4.1-55 Band structure of boron phosphide I

Σ1

K2

Λ3 Λ1

Γ15

Σ1

Γ

K1

∆1

X1

0

0

Λ3 Λ1

Γ15

7

L3

X5

K2

15

BP

K1

Λ3

L3 L1

L3

∆5 X5

K1

Λ1 ∆1

K1

X3

K1

X1

Σ1

L1

L1 ∆1

Λ1 Γ1

Γ1

– 20

Γ

Σ

K

X

∆

Γ

607

Λ L Wave vector k

608

Part 4

Functional Materials

Part 4 1.2

Energy E (eV)

Energy E (eV) 12

12 9

K2c

6 L3c 3

K1c

X5c

L1c

L1c 6

L3c

Γ15c K1c K2v

–3 X5v

–6

X3v – 9 L1v

Γ1c

3 X3c

Γ15v

0 L3v

Γ1c

X1c

Γ15c

X5c

9

K1c

Γ1c

L1c

BSb

BAs

Xv1

Γ15v

X5v L1v

X3v

–9 K1v K1v

L1v

X1v

– 12 Γ1v

– 12 – 15 – 18

X3c

Γ15v

–3 –6

K1v

X1c

Γ15c

L1c L3v

0

– 15

L1v Γ1v L

Λ

Γ

∆

X

U,K

Σ Γ Wave vector k

– 18

L

Γ

V

∆ X Wave vector k

Fig. 4.1-57 Band structure of boron antimonide

Fig. 4.1-56 Band structure of boron arsenide

C. Transport Properties Electronic Transport, General Description. Boron Nitride, Cubic (BNcub ). Owing to the large gap, all literature data refer to extrinsic conduction. For the temperature dependence of the conductivity, see Fig. 4.1-58. Hall measurements on nominally undoped thin films yield values of the carrier mobility of around 500 cm2 /V s. Boron Nitride, hexagonal (BNhex ). Figure 4.1-59 shows the temperature dependence of the electrical resistivity at high temperatures. In an undoped nanocrystalline film, resistivity values of the order of 2 × 1011 Ω cm have been found. Boron Phosphide (BP). Boron phosphide is extrinsic at room temperature, and the transport is limited by impurity scattering. Figure 4.1-60 shows the temperature dependence of the conductivity, carrier concentration, and Hall mobility of several samples. In n-doped single crystals, electron mobilities of the order of 30–40 cm2 /V s have been found at 300 K; in p-doped single crystals, mobilities around 500 cm2 /V s have been measured at 300 K. Boron Arsenide (BAs). There is almost no information about the semiconducting properties of BAs.

σ (Ω–1 cm–1) BNcub

10 –3

10 –4

10 –5

10 –6

10 –7 1

2

3 T–1 (10 –3 K–1)

Fig. 4.1-58 c-BN (BNcub ). Electrical conductivity vs. reciprocal temperature for several different polycrystalline samples above RT [1.52, 53]

Semiconductors

ρ (Ω cm)

Concentration n (cm–3 ) 800 400 2×1018

BNhex 1013

200

T (°C) 25

100

10189

1012

8 7 6

A 1011

5 4

1010

C

109

3

B 2

D

108

10179

E

107

8 7 6

106

5 4

105 104

3

5

6

7

8

9 T–1

10 11 (× 10 –4 K–1)

2 ×1016

above 700 ◦ C. A, from bulk resistance of a disk measured in the c direction; B – E, earlier literature data for comparison [1.54]

Hall mobility µH,n (cm2 (V s)–1) 2×102 µH,n No. 3 No. 1

Conductivity σ (Ω–1 cm–1 )

Fig. 4.1-59 h-BN (BNhex ). Resistivity vs. temperature

σ No. 1

1092

10 9 8 7 6

8 7 6

5

5

4

4

3

3

2

σ No. 3

2

10

19

9 8 7 6

8 7 6 5

5

4×10 –1 1.0

1.5

2.0

2.5

3.0 3.5 T–1 (10–3 Κ–1)

609

Part 4 1.2

1014

1.2 III–V Compounds

4

Fig. 4.1-60 Temperature dependence of the conductivity σi , the carrier concentration n, and the mobility µH,n of n-type BP(100) wafers [1.55]. Sample No. 1 contains autodoped Si with a concentration of 5 × 1018 atoms/cm3 and sample No. 3 contains 5 × 1019 atoms/cm3

610

Part 4

Functional Materials

Part 4 1.2

D. Electromagnetic and Optical Properties Table 4.1-36. Table 4.1-36 Dielectric constant ε and refractive index n of boron compounds Crystal

Temperature (K)

ε(0)

ε(∞)

n

at

BNcub

300

7.1

Boron nitride, hexagonal

BNhex

300

5.09

4.10

2.13

Parallel to c axis, IR reflectivity

7.04

4.95

1.65

Perpendicular to c axis, IR reflectivity

Boron phosphide

BP

300

11

2.097

λ (nm) Remarks

Boron nitride, cubic

712.5

7.8

IR reflectivity

Schottky barrier reflectance

RT

3.34 (5)

454.5

3.34 (5)

458

3.32 (5)

488

3.30 (5)

496

3.26 (5)

514.5

3.00 (5)

632.8

Brewster angle method

4.1.2.2 Aluminium Compounds A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-37 – 4.1-44. Table 4.1-37 Crystal structures of aluminium compounds Crystal

Space group

Crystal system

Aluminium nitride

AlN II

4 C6v Oh5

AlP I

Td2

AlP II AlAs

AlN I

Structure type

Remarks

Figure

P63 mc hex

Wurtzite

At normal pressure

Fig. 4.1-3

Fm3m

fcc

NaCl structure

At 21 GPa (shock

F43m

fcc

Zinc blende

At normal pressure

Oh5

Fm3m

fcc

NaCl structure

High-pressure phase

Td2

F43m

fcc

Zinc blende

Transition to NiAs structure

compression) Aluminium phosphide Aluminium arsenide

Fig. 4.1-2 Fig. 4.1-2

at high pressure Aluminium antimonide

AlSb I AlSb II

Td2

F43m

fcc

Cmcm

Zinc blende

At normal pressure

Orthorhombic

At high pressure

Fig. 4.1-2

Table 4.1-38 Lattice parameters of aluminium compounds Crystal Aluminium nitride

AlN

Lattice parameters (nm)

Temperature

Remarks

a = 0.31111

300 K

X-ray diffraction on ultrafine powder

c = 0.49788 25 ◦ C

Aluminium phosphide

AlP

a = 0.54635 (4)

Aluminium arsenide

AlAs

a = 0.566139

291 K

High-resolution X-ray diffraction

Aluminium antimonide

AlSb

a = 0.61355 (1)

291.15 K

Powder, X-ray measurement

Epitaxial film on GaP

Semiconductors

1.2 III–V Compounds

Density (g/cm3 )

Crystal Aluminium nitride

AlN

3.255

Aluminium phosphide

AlP

2.40 (1)

Aluminium arsenide

AlAs

3.760

Aluminium antimonide

AlSb

4.26

Temperature (K)

Part 4 1.2

Table 4.1-39 Densities of aluminium compounds Remarks X-ray diffraction

Calculated from lattice parameter 293

Table 4.1-40 Elastic constants cik of aluminium compounds Crystal

c11 (GPa)

c12 (GPa)

c13 (GPa)

c33 (GPa)

c44 (GPa)

Remarks

130 (11)

158 (06)

267 (18)

241 (20)

a

Aluminium nitride

AlN

296 (18)

Aluminium phosphide

AlP

140.50 (28)

62.03 (24)

70.33 (7)

Ultrasound ( f = 10 and 30 MHz)

Aluminium arsenide

AlAs

190 (1)

53.8 (1)

59.5 (1)

T = 300 K

122.1 (3)

56.6 (3)

59.9 (1)

T = 77 K

112.6

57.1

60.0

T = 0 K; extrapolated data

40.23

43.22

T = 296 K; ultrasound

Aluminium antimonide a

AlSb

88.34

Calculated from the mean square displacement of the lattice atoms measured by X-ray diffraction.

Table 4.1-41 Melting point Tm of aluminium compounds 6 Crystal

α (10 –6 K–1)

Melting point Tm (K)

Aluminium nitride

AlN

3025

4

Aluminium phosphide

AlP

2823

2

Aluminium arsenide

AlAs

2013 (20)

Aluminium antimonide

AlSb

1327 (1)

AlSb

0 –2

0

40

80

120

160

200

240

280

320 360 T (K)

Fig. 4.1-61 AlSb. Coefficient of linear thermal expansion

vs. temperature [1.56, 57] Table 4.1-42 Linear thermal expansion coefficient α of aluminium compounds Expansion coefficient α (K−1 )

Crystal Aluminium nitride

AlN

Aluminium phosphide

AlP

Aluminium arsenide

AlAs

Aluminium antimonide

AlSb

αperpend

4.35 × 10−6

αparallel

3.48 × 10−6

5.20 (5) × 10−6

Temperature

Remarks

300 K

Powder; X-ray diffraction

15–840 ◦ C

X-ray diffraction Fig. 4.1-61

611

612

Part 4

Functional Materials

Part 4 1.2

Table 4.1-43 Phonon wavenumbers of aluminium compounds: aluminium nitride (300 K, from Raman scattering); aluminium

Phosphide (from Raman spectroscopy); aluminium arsenide (from Raman spectroscopy; 0.5 µm layer of AlAs on GaAs; T = 37 K); aluminium antimonide (from Raman spectroscopy) AlN

AlP

AlAs

AlSb

Symmetry

Wave-

Symmetry

Wave-

Temperature

Symmetry

Wave-

Symmetry

Wave-

point,

number

point,

number

(K)

point,

number

point,

number

polarization

ν˜ E(1) 2

(cm−1 )

polarization

(cm−1 )

polarization

(cm−1 )

polarization

(cm−1 )

248.6

ν˜ LO (Γ)

504.5 (4)

5

ν˜ LO (Γ)

404 (1)

ν˜ LO (Γ)

334 a

ν˜ TO (A1 )

ν˜ E(2) 2

611.0

ν˜ LO (Γ)

501.0 (2)

300

ν˜ TO (Γ)

361 (1)

ν˜ TO (Γ)

316 a

657.4

ν˜ TO (Γ)

442.5 (2)

5

ν˜ LO (X)

403 (8)

ν˜ TA (X)

64 a

ν˜ TO (E1 )

670.8

ν˜ TO (Γ)

439.4 (2)

300

ν˜ TO (X)

335 (8)

ν˜ LA (X)

153 a

ν˜ LO (A1 )

890.0

ν˜ TA (X)

109 (8)

ν˜ TO (X)

290 a

ν˜ LO (E1 )

912.0

ν˜ LA (X)

222 (12)

ν˜ LO (X)

343 a

Table 4.1-43 Wavenumbers of aluminium compounds, cont. Table 4.1-44 Phonon dispersion curves of aluminium

compounds

AlSb Wave-

Crystal

point,

number

polarization

(cm−1 )

Aluminium nitride Aluminium phosphide Aluminium arsenide Aluminium antimonide

Symmetry

ν˜ TA (L)

49 a

ν˜ LA (K)

149 a

ν˜ TO (L)

306 a

ν˜ LO (L)

327 a

ν˜ LO (Γ)

340.0 (7) b

ν˜ TO (Γ)

318.7 (7) b

a

Ab initio pseudopotential calculation.

b

First-order Raman scattering.

Figure AlN AlP AlAs AlSb

Fig. 4.1-62 Fig. 4.1-63 Fig. 4.1-64 Fig. 4.1-65

Wavenumber ν– (cm–1) 1000 AlN

500

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-62 AlN (wurtzite structure). Phonon dispersion curves (left panel) and phonon density of states (right panel), from a rigid-ion model calculation [1.58, 59]

Semiconductors

Wavenumber ν– (cm–1) AlP

400

200

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-63 AlP. Phonon dispersion curves (left panel) and phonon density of states (right panel), from ab initio

calculations [1.60]. The data points were obtained from Raman scattering [1.61]

500

Wavenumber ν– (cm–1) AlAs

250

0

Γ

K

X

Γ

L

X

W L Wave vector q

613

Part 4 1.2

600

1.2 III–V Compounds

DOS

Fig. 4.1-64 AlAs. Phonon dispersion curves (left panel) and phonon density of states (right panel). Experimental data points [1.61, 62] and ab initio calculations [1.16]. From [1.16]

614

Part 4

Functional Materials

Part 4 1.2

Wavenumber ν– (cm–1) 400 AlSb

300

200

100

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-65 AlSb. Phonon dispersion curves (left panel) and phonon density of states (right panel). Experimental data points [1.63] and ab initio calculations [1.16]. From [1.16]

B. Electronic Properties Tables 4.1-45 – 4.1-48. Band Structures of Aluminium Compounds. Alu-

Table 4.1-45 First Brillouin zones of aluminium com-

minium Nitride (AlN). Aluminium nitride is a direct-gap semiconductor. Since it crystallizes in the wurtzite structure, the band structure (Fig. 4.1-66) differs from that of most of the other III–V compounds. Aluminium Phosphide (AlP). Aluminium phosphide is an indirect, wide-gap semiconductor. The minima of the conduction bands are located at the X point of the Brillouin zone. The top of the valence band has the structure common to all zinc blende semiconductors (Fig. 4.1-67). Aluminium Arsenide (AlAs). Aluminium arsenide is a wide-gap semiconductor with a band structure (Fig. 4.1-68) similar to that of AlP. Measurements have revealed a camel’s back structure near X.

pounds Crystal Aluminium nitride Aluminium phosphide Aluminium arsenide Aluminium antimonide

Figure AlN AlP AlAs AlSb

Fig. 4.1-24 Fig. 4.1-23 Fig. 4.1-23 Fig. 4.1-23

Aluminium Antimonide (AlSb). Aluminium antimonide (like AlAs) is an indirect-gap semiconductor with camel’s back conduction band minima near X (Fig. 4.1-69).

Semiconductors

E (eV) 10

E (eV)

AlP

AlN L3

15

K1

Γ15 L1'3'

Γ1', Γ6 A56 H3

L13

10

Γ15

X3

5 L1

Γ3

Γ1

X1

K1

Γ1

A13 Γ1

5

Γ15

Γ15

0

K2

L3 Γ1', Γ6

0

L13

A56

H3

Γ5

L24

H12

A13

–5

X5

K3 K2 K1

K1 –5 L1

X3

K1

X1

K1

Γ3

L1'3'

H3'

K3'

– 10 – 10 L1 – 15

Γ1

Γ1

Γ3' Γ1

– 20

A

R

L UM

Σ

Γ∆A

S

HP K T Γ Wave vector k

Fig. 4.1-66 AlN. Band structure calculated by a semiempirical tight-binding method [1.64]

– 15 L

Λ

Γ

∆

X

K

Σ Γ Wave vector k

Fig. 4.1-67 AlP. Band structure calculated by an orthogonalized

LCAO method [1.65]

615

Part 4 1.2

20

1.2 III–V Compounds

616

Part 4

Functional Materials

Part 4 1.2

E (eV) 10

10 AlAs

E (eV) L1

AlSb

X5 K1

L3 Γ15

5

5 L3

X3

L1 X1

Γ15 X5

K2

Γ1

X1

Γ15

0

K2

Γ15

X3

Γ1

L1

Γ1

Γ15

L3

Γ15

Γ15 K1

Γ1 0

K1

K1

L3

Γ15

X5

K1

X3

K1

X1

K1

K1 X3

–5

–5 K1

L1

X1

L1

L1

K1 – 10

– 10 L1

– 15

Γ1

Γ1

Γ1

Γ1

– 15 L

Λ

Γ

∆

X

K

Σ Γ Wave vector k

L

Fig. 4.1-68 AlAs. Band structure calculated by an orthog-

Λ

Γ

∆

X

K

Σ Γ Wave vector k

Fig. 4.1-69 Band structure of aluminium antimonide

onalized LCAO method [1.65] Table 4.1-46 Energy gaps of aluminium compounds Crystal

Quantity

Bands

Aluminium nitride

AlN

E g, dir

Aluminium phosphide

AlP

E g, ind

Γ15v to X1c

E g, dir

Γ15v to Γ1c

E g, ind

Γ15v to X1c

E g, ind E g, dir

Γ15v to L1c Γ15v to Γ1c

E g, ind

Γ15v to ∆1c

E g, ind

Γ15v to L1c

E g, dir

Γ15v to Γ1c

Aluminium arsenide

Aluminium antimonide

AlAs

AlSb

Energy (eV)

Temperature (K)

Remarks

6.19 6.13 2.5 (1) 2.45 3.63 (2) 3.62 (2) 2.229 (1) 2.153 (2) 2.363 3.13 (1) 3.03 (1) 3.14 (1) 1.615 (3) 1.686 (1) 2.211 2.327 2.300 2.384

7 300 2 300 4 77 4 300 295 4 300 300 300 27 295 35 295 25

Optical absorption Excitonic gap; Absorption Excitonic gap; Photoluminescence Excitonic gap; Photoluminescence Transport Excitonic gap; Photoluminescence Transmission Excitonic gap Electroreflectance Electroreflectance

Semiconductors

1.2 III–V Compounds

Crystal

Spin–orbit splitting

Symmetry points

Energy (eV)

Temperature (K)

Remarks

AlAs

∆0

Γ15v

0.275

300

Electroreflectance

∆1

L15v

0.20

∆0

Γ15c

0.15

∆0

Γ8v to Γ7v

0.673

295

Splitting of Γ15v

∆1

L4,5v to L6v

0.426

AlSb

Splitting of L3v

Table 4.1-48 Effective masses of electrons (m n ) and holes (m p ) for aluminium compounds (in units of the electron mass m 0 ). Aluminium nitride (AlN), calculated values; aluminium phosphide (AlP), calculated from band structure; aluminium arsenide (AlAs), calculated from band structure data; Aluminium antimonide (AlSb), theoretical estimates AlN

AlP

AlAs

AlSb 1.1a

m n, parall

0.33

m n, parall

3.67

m n, parall (X)

m n, perpend

0.25

m n, perpend

0.212

m n, perpend (X) 0.19a

m n, perpend (∆1 ) 0.26 estimated m n, parall (∆1 )

1.0

m p, A, parall

3.53

m p, heavy

0.513

m n, parall (L)

1.32

m p, heavy

0.336

m n, perpend (L)

0.15b

m p, heavy

m p, heavy

0.409

m p, light

parallel to [100] m p, A, perpend

11.14

m p, heavy

1.372

parallel to [100]

parallel to [111] m p, B, parall

3.53

m p, light

0.211

parallel to [111]

parallel to [100] m p, B, perpend

0.33

m p, light

0.145

0.872

parallel to [100] m p, heavy

parallel to [111]

1.022 parallel to [111]

m p, C, parall

0.26

m p, light

m p, C, perpend

4.05

m p, light

0.123 parallel to [100]

m p, light

0.091 parallel to [111]

0.153 parallel to [100] 0.109 parallel to [111]

a

Effective masses at X, neglecting camel’s back structure.

b

Effective masses at L.

C. Transport Properties Tables 4.1-49 and 4.1-50. Electronic Transport, General Description. Aluminium Nitride (AlN). Owing to the large energy gap, transport is always extrinsic. Typical numerical values for the electrical conductivity of undoped single crystals lie in the range 10−13 Ω−1 cm−1 < σ < 10−11 Ω−1 cm−1 . Aluminium Phosphide (AlP). At room temperature, electrical conductivities σ of bulk crystals and layers between 1 and 105 Ω−1 cm−1 have been measured. For the temperature dependence of the electrical conductivity, see Fig. 4.1-70.

Aluminium Arsenide (AlAs). Only a small amount of reliable data exists on the transport properties of AlAs. Most results are extrapolations from data obtained from the technologically more important solid solutions of type Alx Ga1−x As. At roomtemperature, values of the electrical conductivity of around 10 Ω−1 cm−1 have been found. Aluminium Antimonide (AlSb). Aluminium antimonide grown without intentional doping is p-type and becomes intrinsic at about 1000 K. For the temperature dependence of the electrical conductivity, see Fig. 4.1-71.

Part 4 1.2

Table 4.1-47 Spin–orbit splitting energies of aluminium compounds

617

618

Part 4

Functional Materials

Part 4 1.2

Table 4.1-49 Electron and hole mobilities µn and µp of aluminium compounds Crystal

Temperature (K)

Aluminium nitride Aluminium phosphide Aluminium arsenide Aluminium antimonide

AlN AlP AlAs AlSb

290 298 300 295 77 300 77

µn (cm2 /V s)

µp (cm2 /V s) 14

10–80 293–75 200 700

Remarks Doped single crystal Single crystals Single crystal layers, MBE-grown, Be-doped Single crystal, Te-doped, n = 4.7 × 1016 cm−3 Single crystal, p = 1016 cm−3

105

400 2000

Table 4.1-50 Thermal conductivity κ of aluminium compounds Crystal Aluminium nitride Aluminium phosphide Aluminium arsenide Aluminium antimonide

8

AlN AlP AlAs AlSb

Temperature (K)

κ (W/cm K)

Remarks

300 300 300

3.19 0.9 0.91

See Fig. 4.1-72

See Fig. 4.1-73

ln σ AlP

σ (Ω–1 cm–1 ) 1000 100 0 102

–100

–150

6

T (°C) –200 AlSb

0.37 eV 4 0.15 eV

2 0 1.5

2.5

3.5

4.5

5.5

6.5 T–1

7.5 8.5 (10 –3 K–1)

10

Fig. 4.1-70 AlP. Natural logarithm of electrical conductiv-

ity vs. reciprocal temperature for an undoped sample [1.66]. σ in Ω−1 cm−1 . Activation energies are also shown

1 0

2

4

6

8

12 10 T –1 (10–3 K–1)

Fig. 4.1-71 AlSb. Electrical conductivity vs. reciprocal temperature for three different polycrystalline p-type samples [1.67]

Semiconductors

κ (W/cm K)

10

κ (W/cm K)

AlN Upper limit 1

1 1 2

10 –1

7

4

3

8 5

10 –1

9 6

Ceramic

10 10 –2 10 –2

10 –3

1

102

10

103

104 T (K)

1

102

10

103 T (K)

Fig. 4.1-73 AlSb. Thermal conductivity vs. temperature for an n-type and a p-type sample, low-temperature range [1.69, 70]

Fig. 4.1-72 AlN. Temperature dependence of the thermal conductivity for two single crystals (curves 1 and 2) and several ceramic samples (curves 3 – 6). Other published results are included (curves 7 – 10), as well as a theoretical estimate of the upper limit [1.68]

D. Electromagnetic and Optical Properties Table 4.1-51. Table 4.1-51 Dielectric constant ε and refractive index n of aluminium compounds Crystal Aluminium nitride

Temperature (K) AlN

300

ε(0) 9.14

ε(∞)

n

at

λ (µm) Remarks

εperpend 4.71 (22) 2.17–2.34

0.25

Reflectivity and optical inter-

εparall

0.30

ferometry, λ = 589.0 nm,

4.93 (22) 2.04–2.18

CVD films a Aluminium phosphide

AlP

9.8

7.5

From refractive index b

Aluminium arsenide

AlAs

10.1

8.2

From infrared reflectivity c

Aluminium antimonide

AlSb

121.04

10.24

300 300

a

See Fig. 4.1-74 for the spectral dependence of the refractive index.

b

See Fig. 4.1-75 for the spectral dependence of the refractive index.

c

See Fig. 4.1-76 for the spectral dependence of the refractive index.

d

See Fig. 4.1-77 for the spectral dependence of the refractive index.

619

Part 4 1.2

10

1.2 III–V Compounds

IR reflectance, 3.652

40

2.995

20

2.080

15

3.100

10

3.182

4

3.300

2

3.445

1.1

transmission and reflectance d

620

Part 4

Functional Materials

Part 4 1.2

2.8

n AlN

2.6 2 2.4

1

2.2

2.0 200

250

300

350

400

450

500

550

600 λ (nm)

Fig. 4.1-74 AlN. Spectral dependence of the refractive index (1, ordinary ray; 2, extraordinary ray) [1.71]

3.1

n

n, k 6

AlP

AlAs

3.0

5 n

2.9

4

2.8

3

2.7 0.5

1.0

1.5

2.0

2.5

3.0 hω (eV)

Fig. 4.1-75 AlP. Refractive index vs. photon energy at

300 K [1.72] 15

n

k

15

AlSb 12

12

2 k 1

0

2

3

4

5

6 hω (eV)

Fig. 4.1-76 AlAs. Spectral variation of the complex refrac-

tive index calculated from the dielectric function [1.73] 9

9

6

6 k

3

0 20

3

n

23

26

29

32

35

0 38 λ (µm)

Fig. 4.1-77 AlSb. Refractive index n and extinction co-

efficient k vs. wavelength in the region of lattice absorption [1.74]

Semiconductors

1.2 III–V Compounds

Part 4 1.2

4.1.2.3 Gallium Compounds A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-52 – 4.1-60. Table 4.1-52 Crystal structures of gallium compounds Crystal

Space group

Crystal system

Structure type

Remarks

Figure

Gallium nitride

GaN

4 C6v Td2

P63 mc F43m

hex fcc

Wurtzite Zinc blende

Stable at ambient pressure Epitaxial growth on cubic substrate

Fig. 4.1-3 Fig. 4.1-2

Gallium phosphide

GaP

Td2 19 D4h

F43m I41 /amd

fcc

Zinc blende β-tin structure

Stable at normal pressure Pressure > 21–30 GPa

Fig. 4.1-2

Gallium arsenide

GaAs I GaAs II

Td2

F43m

fcc

Zinc blende Orthorhombic

Stable at normal pressure Pressure > 17 GPa

Fig. 4.1-2

Gallium antimonide

GaSb I GaSb II

Td2 19 D4h

F43m I41 /amd

fcc

Zinc blende β-tin structure

Stable at normal pressure Pressure > 8–10 GPa

Fig. 4.1-2

Table 4.1-53 Lattice parameters of gallium compounds Crystal

Lattice parameters (nm)

Temperature (K)

GaN

a = 0.3190 (1) c = 0.5189 (1)

Gallium phosphide

GaP

a = 0.54506 (4)

RT

Gallium arsenide

GaAs

a = 0.565359

RT

Gallium antimonide

GaSb

a = 0.609593 (4)

298.15

Gallium nitride

Remarks X-ray diffraction, monocrystal Single crystal X-ray powder diffraction

Table 4.1-54 Densities of gallium compounds Crystal

Density (g/cm3 )

Temperature (K)

Gallium nitride

GaN

6.07

Gallium phosphide

GaP

4.138

300

Gallium arsenide

GaAs

5.3161 (2)

298.15

Gallium antimonide

GaSb

5.6137 (4)

300

Table 4.1-55 Elastic constants cik of gallium compounds Crystal

621

c11 (GPa)

c12 (GPa)

c13 (GPa)

c33 (GPa)

c44 (GPa)

Temperature (K)

Remarks

160

114

209

81.4

300

Ultrasound resonance technique

Gallium nitride

GaN

377

Gallium phosphide

GaP

140.50 (28)

62.03 (24)

−

−

70.33 (7)

Gallium arsenide

GaAs

119 (1) 112.6

53.8 (1) 57.1

− −

− −

59.5 (1) 60.0

300 0

Extrapolated data

Gallium antimonide

GaSb

88.34

40.23

−

−

43.22

296

Ultrasound

Ultrasound ( f = 10 and 30 MHz)

622

Part 4

Functional Materials

Part 4 1.2

Table 4.1-56 Melting point Tm of gallium compounds Crystal

Melting point Tm (K)

Remarks GaN sublimes without decomposition around 800 ◦ C

Gallium nitride

GaN

2791

Gallium phosphide

GaP

1749

Gallium arsenide

GaAs

1511

Gallium antimonide

GaSb

7

991 (1)

α (10 –6 K–1)

5

α (10 –6 K–1) GaP

GaN 6

4

1

3

5 2 4

2

3

1 0

2 0

100

200

300

400

500

600

700

800 T (K)

Fig. 4.1-78 GaN. Coefficient of linear thermal expansion vs. temperature (curve 1, α⊥ ; curve 2, α ) [1.75] α (10– 6 K–1)

0

GaAs

100

150

200

250

300 T (K)

Fig. 4.1-79 GaP. Linear thermal expansion coefficient vs. temperature between 0 K and 300 K [1.76] 8

8

50

α (10 –6 K–1) GaSb

6 4

6

2 2

0 ∆ α (10 –8 K–1)

–2

0

0 –3

–6 0

–2

0

100

0

40

80

120

160

200

240

280

320 360 T (K)

Fig. 4.1-81 GaSb. Linear thermal expansion coefficient vs. 5

10

200

15

20 T (K)

300 T (K)

Fig. 4.1-80 GaAs. Coefficient of linear thermal expansion.

Experimental data points, and curves from an ab initio pseudopotential calculation [1.77]

temperature measured with a quartz dilatometer. Hightemperature range [1.56, 57]

Semiconductors

1.2 III–V Compounds

Expansion coefficient α

Crystal

Remarks

Temperature dependence

X-ray diffraction

Fig. 4.1-78

(10−6 K−1 ) Gallium nitride

GaN

αparall

5.59

αperpend

3.17

Gallium phosphide

GaP

4.65

300 K

Fig. 4.1-79

Gallium arsenide

GaAs

5.87

300 K

Fig. 4.1-80

Gallium antimonide

GaSb

7.75 (50)

Around 300 K; X-ray diffraction

Fig. 4.1-81

Table 4.1-58 Heat capacity c p and Debye temperature ΘD of gallium compounds Heat capacity (J/mol K)

Crystal

Temperature (K)

Debye temperature (K)

Remarks

600

Estimated

Gallium nitride

GaN

Gallium phosphide

GaP

49.65

800

445

Gallium arsenide

GaAs

46.90

300

344

Gallium antimonide

GaSb

266

Wavenumber ν– (cm–1) 800 E1(LO) GaN

E1(LO) A1(LO)

700 B1

B1

600 E2

E2

500

A1(TO)

A1(TO) E1(TO)

400 B1

B1 300 200

E2

E2

100 0

Γ

K

M

Γ

A

H

L A Wave vector q

DOS

Fig. 4.1-82 GaN (wurtzite structure). Phonon dispersion curves (decomposed according to different irreducible representations along the main symmetry directions) and density of states, from a model-potential calculation. The circles show Raman data from [1.78]. From [1.79]

Part 4 1.2

Table 4.1-57 Linear thermal expansion coefficient α of gallium compounds

623

624

Part 4

Functional Materials

Part 4 1.2

Table 4.1-59 Phonon wavenumbers of gallium compounds. Gallium nitride (GaN), T = 300 K, from Raman spec-

troscopy; gallium phosphide (GaP), RT, from an analysis of Raman, neutron, luminescence, and absorption data; gallium arsenide (GaAs), T = 296 K, from coherent inelastic neutron scattering; gallium antimonide (GaSb), T = 300 K, from second-order Raman effect GaN Symmetry

GaP Branch

point ν˜ low (E2 )

Wavenumber

Symmetry

(cm−1 )

point

145

ν (Γ)

ν˜ (A1 )

TO

533

ν˜ (E1 )

TO

560

ν˜ high (E2 )

ν (X)

Branch

Frequency (THz)

TO

10.95 (1)

LO

12.06 (1)

TA

3.13 (3)

567

LA

7.46 (6)

ν˜ (A1 )

LO

735

TO

10.58 (3)

ν˜ (E1 )

LO

742

LO

11.09 (6)

TA

2.58 (3)

LA

6.45 (3)

TO

10.64 (3)

LO

11.24 (3)

Branch

Wavenumber

ν (L)

GaAs

GaSb Frequency

Symmetry

(THz)

point

LO

8.55 (20)

ν˜ (L)

TA

46

TO

8.02 (8)

ν˜ (X)

TA

56

TA

2.36 (2)

ν˜ (W)

TA

75

LO

7.22 (15)

ν˜ (L)

LA

155

ν (X3 )

LA

6.80 (6)

LO

204

ν (X5 )

TO

7.56 (8)

ν˜ (X)

LO

210

ν (L1 )

LA

6.26 (10)

ν˜ (L, X, Σ)

TO

218

LO

7.15 (7)

TA

1.86 (2)

TO

7.84 (12)

Symmetry

Branch

point ν (Γ15 ) ν (X1 )

ν (L3 )

Table 4.1-60 Phonon dispersion curves of gallium com-

pounds Crystal

Figure

Gallium nitride

GaN

Fig. 4.1-82

Gallium phosphide

GaP

Fig. 4.1-83

Gallium arsenide

GaAs

Fig. 4.1-84

Gallium antimonide

GaSb

Fig. 4.1-85

(cm−1 )

Semiconductors

1.2 III–V Compounds

Part 4 1.2

Wavenumber ν– (cm–1) GaP

400

300

200

100

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-83 GaP. Phonon dispersion curves (left panel) and density of states (right panel). Experimental data points from [1.80] (open symbols) and from [1.81] (filled symbols) and theoretical curves from ab initio calculations [1.82]. From [1.82] Wavenumber ν– (cm–1) 400 GaAs

300

200

100

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-84 GaAs. Phonon dispersion curves (left panel) and phonon density of states (right panel) [1.16]. Experimental

data points [1.83] and ab initio calculations [1.16].

625

626

Part 4

Functional Materials

Part 4 1.2

Wavenumber ν– (cm–1) 300 GaSb

200

100

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-85 GaSb. Phonon dispersion curves (left panel) and phonon density of states (right panel) [1.16]. Experimental

data points [1.84] and ab initio calculations [1.16]

B. Electronic Properties Tables 4.1-61 – 4.1-66. Band Structures of Gallium Compounds. Gallium Nitride (GaN). The band structure is shown in Fig. 4.1-87. Owing to spin–orbit interaction, the two top valence bands (Γ6 and Γ1 ) are split into three spin-degenerate bands, one with quantum number Jz = 3/2(Γ9 ) and two with Jz = 1/2(Γ7 )’. For convenience, the notation A, B, C is used for these bands. Gallium Phosphide (GaP). Gallium phosphide is an indirect-gap semiconductor. The lowest set of conduction bands shows a camel’s back structure; the band minima are located on the ∆ axes near the zone boundary. The valence bands show the usual structure characteristic of zinc blende semiconductors. The spin–orbit splitting of the top of the valence band is negligible compared with most other energy separations in the band structure. Therefore, Fig. 4.1-86 shows the band structure calculated without inclusion of spin–orbit splitting; the symmetry symbols of the highsymmetry band states are symbols of the single group of the zinc blende structure. Gallium Arsenide (GaAs). Gallium arsenide is a directgap semiconductor. The minimum of the lowest

Table 4.1-61 First Brillouin zones of gallium compounds Crystal Gallium nitride Gallium phosphide Gallium arsenide Gallium antimonide

Figure GaN GaP GaAs GaSb

Fig. 4.1-24 Fig. 4.1-23 Fig. 4.1-23 Fig. 4.1-23

conduction band is located at Γ; higher sets of minima at L and near X (about 10% away from the zone boundary) are also important for the optical and transport properties. The minimum near X most probably has a camel’s back-like structure similar to that of GaP, AlAs, and AlSb. The valence bands have the usual structure characteristic of zinc blende crystals (Fig. 4.1-88). Gallium Antimonide (GaSb). The conduction band of GaSb is characterized by two types of minima, the lowest minimum at Γ and slightly higher minima at the L points at the surface of the Brillouin zone. A third set of minima at the X points has been detected in optical experiments. The valence bands show the usual structure common to zinc blende semiconductors (Fig. 4.1-89).

1.2 III–V Compounds

Semiconductors

10

E (eV)

Γ15

X3

3 Γ1

L1

X1

Γ15

0 L3

5

GaN

GaP

L3

Γ15

8

K1

Γ1 Γ15

6

1,3

4

1,3

1

1

4

K1

1,2 5,6

6 3

3

3

2

K2

X5

1,3

3 1 1

–3 2

K1 –6 L2 –9

X3

K1

X1

K1

6

0 –2

5,6

1

4

L1

3 5

1,3

3

2,4

L

Λ

Γ

2

–4 ∆

X

U,K

Σ Γ Wave vector k

1,2

–6 –8

Γ7

X6

Γ6 Γ8

L4,5 Γ7 X6

–6

X6

LU M

E (eV) L6

Σ

Γ ∆A

H P K T Γ Wave vector k

S

GaSb

Γ8

L4,5 L6

L6

X7

Γ7

L6

Γ7

X6

Γ8

0 L4,5

Γ8 X7

Γ7 Γ6

3

Γ7

X7

R

3

1

3

3

Fig. 4.1-87 Band structure of gallium nitride

6

–4

–3

Γ8 Γ7

X6

L6 –6

L

X6

–9

L6

Γ6 Λ

Γ

L6

Γ6 ∆

X

U,K

Σ Γ Wave vector k

Fig. 4.1-88 Band structure of gallium arsenide

X6

L6

X6

– 10 – 12

A

Γ7

X7

Γ8

– 2 L6

–8

Γ8

Γ6

2 L6 0

GaAs

Γ8

L6

1

3 1,3

E (eV)

2

1,3

1

Fig. 4.1-86 Band structure of gallium phosphide

6 L4,5

3

Γ1

Γ1

–12

4

Part 4 1.2

E (eV) 6

L6

Γ6 –12

L

Λ

Γ

∆

X

U,K

Σ Γ Wave vector k

Fig. 4.1-89 Band structure of gallium antimonide

627

628

Part 4

Part 4 1.2

Table 4.1-62 Energy gaps of gallium compounds

Functional Materials

Crystal Gallium nitride

Gallium phosphide

Quantity GaN

GaP

Energy (eV)

Bands

3.503 (2)

E g, dir

E g, ind

1.6

GaAs

Remarks Photoluminescence

A exciton

3.4751 (5)

Transition from Γ9v

B exciton

3.4815 (10)

Transition from upper Γ7v

C exciton

3.493 (5)

Transition from lower Γ7v

Γ8v to ∆5c

2.350 (1)

0

2.272 Gallium arsenide

Temperature (K)

E g, ind

Γ15v to L1c

2.637 (10)

E g, dir

Γ8v to Γ6c

1.51914

78

Electroabsorption

0

1.424 (1) E g, th

Extrapolated, from exciton data

300 Extrapolated, photoluminescence

300

1.604

0

0.822

0

Differentiated reflectivity Extrapolated, intrinsic carrier concentration

Gallium antimonide

GaSb

E g, dir

Γ8v to Γ6c

0.75

Extrapolated, electroreflectance

300

Table 4.1-63 Exciton binding energies of gallium compounds Crystal

Quantity

Energy (meV)

Remarks

Gallium nitride

E bA E bB E bC

20

A exciton, photoreflectance

18.5

B exciton, photoreflectance

22.4

C exciton, photoluminescence

Gallium antimonide

GaN

GaSb

Eb

1.6

Calculated ground-state binding energy

Table 4.1-64 Spin–orbit splitting energies of gallium compounds Crystal

Gallium nitride

Gallium phosphide

Quantity

GaN

GaP

Bands

Energy

Temperature

(meV)

(K)

Remarks

∆1

9.8

Epitaxial films,

∆2

5.6

reflectance measurements

∆3

5.6

∆0

Γ8v to Γ7v

80 (3)

100–200

Splitting of Γ15v into Γ8v (upper level) and Γ7v (lower level)

Gallium arsenide

GaAs

∆0

Γ15v

346.4 (5)

1.7

Splitting of Γ15v valence band state into Γ7v and Γ8v , magnetoabsorption splitting of Γ15 conduction band state into Γ7c and Γ8c ,

Gallium antimonide

GaSb

∆0

Γ15c

171 (15)

∆0

Γ8v to Γ7v

756 (15)

∆0

Γ7c to Γ8c

213 (10)

∆1

L4,5v to L6v

430 (10)

∆1

L4,5c to L6c

130

4.2 10

electroreflectance Electroreflectance

Semiconductors

1.2 III–V Compounds

GaN

GaP 6K

Near ∆min

7.25

m n, perp

Near ∆min

0.21

Luminescence

m n, parall

Away from ∆min Parallel to [111] Parallel to [111]

2.2

High above bottom of camel’s back Cyclotron resonance at 1.6 K

0.22

m n, parall

0.20 (6)

m n, perp

0.20 (2)

m (A) p

1.01

m (B) p

1.1

m p, light

m (C) p

1.6

m p, so

7K

Cyclotron resonance, polaron mass From reflectance spectrum

m n, parall

mn

Estimated from binding energies

m p, heavy

1–20 K

0.67 (4)

1.6

0.17 (1)

Parallel to [111] 0

0.4649

At bottom of camel’s back

Spin–orbit mass, calculated from k · p model

GaAs m n (Γ) m p, heavy m p, light

0.0662 (2) 0.34 0.75 0.094 0.082

Parallel to [100] Parallel to [111] Parallel to [100] Parallel to [111]

1.6 10 K

Cyclotron resonance Electronic Raman scattering

GaSb m n (Γ) m n (L6c )

m p, heavy

m p, light

0.039 (5) 0.11 0.95 0.226 0.29 (9) 0.36 (13) 0.40 (16) 0.042 (2)

2K

30 K

B parallel to [100] B parallel to [110] B parallel to [111]

Optically detected cyclotron resonance Transverse mass Longitudinal mass Density-of-states mass Stress-modulated magnetoreflectance

Table 4.1-66 Electron g-factor gc of gallium antimonide Crystal Gallium antimonide

GaSb

gc

Temperature (K)

Remarks

− 9.1 (2)

4.2–50

Magnetoluminescence

C. Transport Properties Tables 4.1-67 and 4.1-68. Electronic Transport, General Description. Gallium Nitride (GaN). Undoped GaN is normally an n-type conductor. Carrier concentrations in undoped films can vary from 5 × 1019 cm−3 to 5 × 1016 cm−3 because of unintentional incorporation of extrinsic impurities, mainly silicon and oxygen. In the purest α-GaN material (n = 1017 cm−3 ), conductivities of the order of

10 Ω cm have been found at 300 K. For the temperature dependence of the electrical resistivity, see Fig. 4.1-90. Gallium Phosphide (GaP). Even in high-purity samples, intrinsic conduction occurs in gallium phosphide only above 500 ◦ C. Thus, the transport properties are in general determined by the properties of impurities and lattice defects. The data for the electrical conductivity σ of pure n-type material are found to lie around 0.5 Ω cm at 300 K.

Part 4 1.2

Table 4.1-65 Effective masses of electrons (m n ) and holes (m p ) for gallium compounds (in units of the electron mass m 0 )

629

630

Part 4

Functional Materials

Part 4 1.2

As in the case of GaAs, semi-insulating GaP can be obtained by doping with shallow donors and acceptors and with deep centers. Resistivities at room temperature are of the order of 108 –1011 Ω cm. Typical data at high temperatures are shown in Fig. 4.1-91. Gallium Arsenide (GaAs). At low fields, the electrons are in the Γ6 minima at the zone center. The dominating scattering process at room temperature is polar optical scattering, while below 60 K the most important contribution to the lattice mobility is from piezoelectric potential scattering. At room temperature, the hole mobility of samples with p < 5 × 1015 cm−3 is governed by lattice scattering alone. An intrinsic carrier concentration of n i = 2.1 × 106 cm−3 has been found at T = 300 K (Fig. 4.1-92). Owing to the very low intrinsic carrier concentration, the electrical conductivity of GaAs at 300 K is deterρ (Ω cm) 100 50 1 8

T (K) 30

20

15

10

1

mined by charge carriers provided by impurities. Only under certain doping conditions (e.g. compensation of shallow acceptor levels by donor impurities and overcompensation by deep Cr levels) can the Fermi level be pinned in the middle of the energy gap and nearly intrinsic conduction achieved (semi-insulating GaAs, ρ = 105 –109 Ω cm). Gallium Antimonide (GaSb). Transport in n-type GaSb is complicated by the contribution of three sets of conduction bands with minima located at Γ, L, and X. The data on transport coefficients can be consistently explained by a three-band model, the X bands contributing to transport above 180 ◦ C. Intrinsic carrier concentrations n i of the order of 1014 cm−3 have been estimated for a temperature T = 365 K. In p-type GaSb, a multiellipsoidal model has to be used at low temperatures, taking into account the shift of the heavy- and light-hole bands away from k = 0. At high temperatures, a warped-sphere model (as in the case of Si and Ge) is adequate.

GaN

6

2 4

3

1012

n/T 3/2 (cm–3 /K3/2)

107 GaP

2

ρ (Ω cm)

n/T 3/2

4 1011

10 –1

106

8

ρ

6 4

5

1010

105

109

104

108

103 103 µH, n (cm2 /V s)

107

102 102

6 2

7 10 –2 8 6 4

8 2

10 –3 0

µH, n 20

40

60

80

100

120

T –1 (10–3 Κ–1)

Fig. 4.1-90 GaN. Resistivity of several undoped samples (1 – 7) and a Zn-doped sample (8) vs. reciprocal temperature [1.85]

106

1.0

1.5

2.0

10 2.5 T–1 (10 –3 K–1)

10

Fig. 4.1-91 GaP. Resistivity, Hall mobility, and electron

concentration (divided by T −3/2 ) vs. temperature for a semi-insulating sample [1.86]

Semiconductors

1.2 III–V Compounds

Crystal

Temperature (K)

Carrier concentration (cm−3 )

µn (cm2 /V s)

Gallium nitride

300

n = 3 × 1016 p = 5 × 1013

900

Gallium phosphide

RT

160

Gallium arsenide

300 300 300 300

2400–3300

Gallium antimonide a b c

µp (cm2 /V s)

Hall mobility a β-GaN, Hall mobility Thin films, Hall mobility, maximum mobility b Bulk GaAs, Hall mobility c Hall mobility MBE-grown on GaSb substrates Hall mobility

350 135

400 n = 1.2 × 1016

Remarks

7620 680

See Fig. 4.1-93 for the temperature dependence of the electron mobility in GaN. See Figs. 4.1-94a,b for the temperature dependence of the electron and hole mobilities in GaP. See Figs. 4.1-95 and 4.1-96 for the temperature dependences of the electron and hole mobilities in GaAs.

1017

ni (cm–3)

ni (cm–3) 1019 8

GaAs

6

1016

4

C

1015

2

D 1014

D 1018

B

A

8 6

1013 A

4

1012 2

1011 1017 8

1010

6

G

4

L

109

2

108

B

D 1016

107

8

G

6

F

106

B

4

A 2

105 104 10

15

20

25

30

35 40 (10 –4 K–1)

T–1

1015 800

900

1000

1100

1200

1300

1400 1500 T (K)

Fig. 4.1-92 GaAs. Intrinsic carrier concentration vs. reciprocal temperature for the range 250–1000 K and vs. temperature

for the range 800–1500 K. The solid curves (A) are the result of a critical discussion of the literature data. The other curves (B – G) represent data from other sources [1.87]

Part 4 1.2

Table 4.1-67 Electron and hole mobilities µn and µp of gallium compounds

631

632

Part 4

Functional Materials

Part 4 1.2

µH,n (cm2/ V s) 3

10

8

GaN

6 4

2 2

4 2

10

8 6 4

2

10 10

2

4

6

8

102

2

4

6

8

103 2×103 T (K)

Fig. 4.1-93 GaN. Electron Hall mobility vs. temperature

for two samples [1.85] a) µH,n (cm2/ V s)

b) µH,p (cm2/ V s)

300 GaP

300

200

200

100

100

90 80

90 80

70

70

60 50 40 30

20 100

60

nA = 5 × 1016 c m–3 2 × 1017 c m–3 2.5 × 1018 c m–3 7.5 × 1018 c m–3 1.2 × 1019 c m–3 8 × 1018 c m–3

200

50 40

nA = 5 × 1016 cm–3 3 × 1017 cm–3 6 × 1017 cm–3 1 × 1018 cm–3 2 × 1018 cm–3

30

300

400

500 600 T (K)

20 100

200

300

400

Fig. 4.1-94a,b GaP. Hall mobility in n-type (a) and p-type (b) LPE-grown layers vs. temperature [1.86]

500 600 T (K)

1.2 III–V Compounds

Semiconductors

105

4×10

10

GaAs Deformation potential mobility

6

µH,n (cm2(V s)–1 )

8 6

GaAs

4

Polar mobility

2

104 8 6

a 10

4

b

5

2

Ionized-impurity mobility

103 8 6

c

MBE

4

104

MOCVD

2

4×103 4

6

8

10

2

4

6

8

102

2

4 ×102 T (K)

Fig. 4.1-95 GaAs. Temperature variation of Hall mobility at 5 kG for three n-GaAs samples. In the temperature range from 300 K to 77 K, the electron mobility of sample a is dominated by polar optical scattering. Samples b and c show increased effects of ionized-impurity scattering [1.88]

102 10

4

6

8

102

4 ×102 T (K)

2

Fig. 4.1-96 GaAs. Hall mobility of holes vs. temperature for MBE- and MOCVD-grown samples. The solid line represents the empirical relation µH,n = 450 × (300/T)2.3 [1.89]

10

κ (W/cm K)

2

κ (W/cm K) GaP

8 6

4 GaN

4 2

1 8 6

1

4

8 2

6

10 –1

4

8 6 4

2

2

2×10 2×10 –1 10

T 3.8

–2

1 2

4

6

8

2

10

2

4 ×10 T (K)

Fig. 4.1-97 GaN. Thermal conductivity along the c axis vs.

temperature [1.90]

2

4

6 8

10

2

2

4

6

102

8

2

4

6 103 T (K)

Fig. 4.1-98 GaP. Thermal conductivity vs. temperature for

a p-type sample [1.69, 70]

Part 4 1.2

µ H,n (cm2(V s)–1 ) 6

633

634

Part 4

Functional Materials

Part 4 1.2

Table 4.1-68 Thermal conductivity κ of gallium compounds Crystal

κ (W/cm K)

Temperature (K)

Remarks

Gallium nitride Gallium phosphide Gallium arsenide Gallium antimonide

1.3 0.77 0.455

300 300 300

See Fig. 4.1-97 for temperature dependence. See Fig. 4.1-98 for temperature dependence. See Fig. 4.1-99 for temperature dependence. See Fig. 4.1-100 for temperature dependence.

40

κ (W/cm K)

κ (W/cm K) GaAs

10 8 6

GaSb

4

10 8

2

6 4

1 8 6

2

4

1 8

2

6 4

10 –1 8

2

1 2 3 4

6 4

10 –1 8

2

6 4

10 –2

Doping (cm3) 2

10

8

6×10–3 1

7 × 1015 5 × 1017 Te 14 × 1018 Cd 2.7 × 1017 Zn 2.6 × 1018 Zn ≈ 5 × 1016 Mn ≈ 5 × 1017 Mn

–2 8 6 4

10 –3 2

4

6

8

10

2

4

6

8

102

4

6

8

10

2

4

6

8

102

2

4×102 T (K)

Fig. 4.1-100 GaSb. Thermal conductivity of two n-type samples with impurity contents of 4 × 1018 cm−3 (1) and 1.4 × 1018 cm−3 (2) and of two p-type samples with impurity contents of 1 × 1017 cm−3 (3) and 2 × 1017 cm−3 (4) [1.92]

2

1

2

2

4 ×102 T (K)

Fig. 4.1-99 GaAs. Thermal conductivity vs. temperature

for seven samples with impurity concentrations between 7 × 1015 cm−3 and 2.6 × 1018 cm−3 [1.91]

Semiconductors

1.2 III–V Compounds

Part 4 1.2

D. Electromagnetic and Optical Properties Tables 4.1-69 – 4.1-72 and Figs. 4.1-101 – 4.1-105.

Table 4.1-69 Dielectric constant ε and refractive index n of gallium compounds Crystal Gallium nitride

GaN

Temperature (K)

ε(0)

300

9.5 (3) 10.4 (3)

ε(∞)

n

at or

5.8 (4) 5.35 (20) 2.29 (5) Gallium phosphide

GaP

300 75.7 300

11.11 10.86

300

12.80 (5)

9.11 3.334

Gallium arsenide

GaAs

10.86 3.878 Gallium antimonide GaSb

300

15.7

λ (nm) Remarks hν (eV)

Figure

E perpendicular to c E parallel to c E parallel to c E perpendicular to c 500 nm Optical interference Low-frequency capacitance measurements Derived from refractive index 2.0 eV Spectroscopic ellipsometry Microwave technique Optical-transmission interference 2.0 eV Spectroscopic ellipsometry Reflectance and oscillator fit

Fig. 4.1-101

Fig. 4.1-103

Fig. 4.1-102

Fig. 4.1-105

14.44 5.239

2.7

n

3.8

2.0 eV

Spectroscopic ellipsometry

n GaAs

GaN 3.7 2.6 3.6 2.5

3.5

2.4

3.4 1.0

1.1

1.2

1.3

1.4

1.5

1.6 1.7 hω (eV)

Fig. 4.1-102 GaAs. Refractive index vs. photon energy in 2.3 1.0

1.5

2.0

2.5

3.0

3.5 hω (eV)

Fig. 4.1-101 GaN. Refractive index vs. photon energy at 300 K; E⊥c [1.93]

635

the range 1.0–1.7 eV [1.94]. Solid line, calculated; symbols, experimental data from three sources

636

Part 4

Functional Materials

Part 4 1.2

Table 4.1-70a Optical constants of gallium phosphide hν (eV)

ε1

ε2

n

k

R

K (103 cm−1 )

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

10.102 11.114 12.996 16.601 24.833 9.652 11.073 0.218 −10.266 −5.521

0.000 0.000 0.046 1.832 8.268 16.454 17.343 26.580 10.974 7.041

3.178 3.334 3.605 4.081 5.050 3.790 3.978 3.661 1.543 1.309

0.000 0.000 0.006 0.224 0.819 2.171 2.180 3.631 3.556 2.690

0.272 0.290 0.320 0.369 0.458 0.452 0.461 0.580 0.677 0.583

0.00 0.00 1.63 68.26 290.4 880.1 994.3 1840 1983 1636

Table 4.1-71 Optical constants of gallium arsenide hν (eV)

ε1

ε2

n

k

R

K (103 cm−1 )

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

13.435 14.991 18.579 16.536 8.413 9.279 6.797 −11.515 −6.705 −4.511

0.589 1.637 3.821 17.571 14.216 13.832 22.845 18.563 8.123 6.250

3.66 3.878 4.333 4.509 3.531 3.601 3.913 2.273 1.383 1.264

0.080 0.211 0.441 1.948 2.013 1.920 2.919 4.084 2.936 2.472

0.327 0.349 0.395 0.472 0.425 0.421 0.521 0.688 0.613 0.550

12.21 42.79 111.7 592.5 714.2 778.7 1331 2070 1637 1503

Table 4.1-72a Optical constants of gallium antimonide hν (eV)

ε1

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

19.135 25.545 13.367 9.479 7.852 −1.374 −8.989 −5.693 −5.527 −4.962

ε2

n

k

R

K (103 cm−1 )

3.023 14.442 19.705 15.838 19.267 25.138 10.763 7.529 5.410 4.520

4.388 5.239 4.312 3.832 3.785 3.450 1.586 1.369 1.212 0.935

0.344 1.378 2.285 2.109 2.545 3.643 3.392 2.751 2.645 2.416

0.398 0.487 0.484 0.444 0.485 0.583 0.561 0.585 0.592 0.610

52.37 279.4 579.1 641.2 902.8 1477 1547 1394 1475 1469

Table 4.1-70b GaP. Refractive index in the infrared

Table 4.1-72b GaSb. Refractive index in the infrared

Wavelength Refractive Remarks (µm) index n

Wavelength Refractive (µm) index n

Temperature (K)

Remarks

20 10 5 2 1

14.9

3.880

300

Reflectance and transmission

10 4 2 1.9 1.8

3.843 3.833 3.789 3.802 3.820

2.529 2.90 2.94 3.02 3.17

Reflectance and transmission at 300 K

Prism method

1.2 III–V Compounds

Semiconductors

ε (0) 11.5

30

ε1, ε2 GaP

GaP

ε2

1 kHz 11.4

20

10 kHz

11.3

10

ε1

100 kHz 11.2 tan δ 10 –1

ε (0)

0

11.1 100 kHz

– 10

10 kHz 10 –2

11.0

2

1 kHz tan δ 10.9 10 –3 10.8

b)

0

100

200

300

400

500

600 T (K)

3

4

5

6 hω (eV)

Fig. 4.1-104 GaP. Real and imaginary parts of the dielectric constant vs. photon energy [1.47]

30

ε GaSb ε2

∆ε (0) 0 20

–0.04

T = 75.4 K 298.4 K

ε1

10

–0.08

–0.12

0 0

0.2

0.4

0.6

0.8

1.0 p (GPa)

Fig. 4.1-103a,b GaP. (a) Static dielectric constant ε(0) and

dielectric loss tan δ vs. temperature, obtained from lowfrequency capacitance measurements. For clarity, the actual data points at only one frequency (100 kHz) are shown. The data have been corrected for dimensional changes due to thermal expansion. (b) Change in static dielectric constant vs. pressure at two temperatures [1.95]

– 10 2

3

4

5

6 hω (eV)

Fig. 4.1-105 GaSb. Real and imaginary parts of the dielec-

tric constant vs. photon energy [1.47]

Part 4 1.2

a)

637

638

Part 4

Functional Materials

Part 4 1.2

4.1.2.4 Indium Compounds A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-73 – 4.1-81.

Table 4.1-73 Crystal structures of indium compounds Crystal

Space group

Crystal system

Structure type

Remarks

Figure

Indium nitride

InN

4 C6v

P63 mc

hex

Wurtzite

Fig. 4.1-3

Indium phosphide

InP I InP II InAs I InAs II InSb I

Td2 Oh5 Td2 Oh5 Td2

F43m Fm3m F43m Fm3m F43m

fcc fcc fcc fcc fcc

Zinc blende NaCl Zinc blende NaCl Zinc blende

Phase transition to NaCl structure under pressure Stable at normal pressure Pressure > 34 GPa Stable at normal pressure Pressure > 4 GPa, RT Stable at normal pressure a

Indium arsenide Indium antimonide a

Fig. 4.1-2 Fig. 4.1-2 Fig. 4.1-2

Quite a number of phase transitions have been observed at high pressures (> 2.1 GPa).

Table 4.1-74 Lattice parameters of indium compounds Crystal

Lattice parameters (nm)

Indium nitride

InN

Indium phosphide Indium arsenide Indium antimonide

InP InAs InSb

a = 0.35446 c = 0.57034 a = 0.58687 (10) a = 0.60583 a = 0.647937

Temperature (K)

Remarks Epitaxial layers, X-ray diffraction Powder, X-ray diffraction

291.15 298.15 298.15

Powder, X-ray diffraction

Table 4.1-75 Densities of indium compounds Density (g/cm3 )

Crystal Indium nitride Indium phosphide Indium arsenide Indium antimonide

InN InP InAs InSb

Temperature (K)

6.78 (5) 4.81 5.667 5.7747 (4)

Remarks Pycnometric

300 300

X-ray diffraction X-ray diffraction

Table 4.1-76 Elastic constants cik (in GPa) of indium compounds Crystal

c11

c12

c13

c33

190 (7)

104 (3)

121 (7)

182 (6)

Indium phosphide InP 101.1 Indium arsenide InAs 83.29 Indium antimonide InSb 69.18

56.1 45.26 37.88

− − −

− − −

Indium nitride

InN

c44 9.9 (11) 45.6 39.59 31.32

Remarks Calculated from the mean square displacements of the lattice atoms measured by X-ray diffraction Ultrasonic-wave transit times, RT Ultrasound, f = 15 MHz, n-type, RT T = 0 K, extrapolated from 4.2 K, ultrasound, f = 10 MHz

1.2 III–V Compounds

Semiconductors

Table 4.1-77 Melting point Tm of indium compounds Melting point Tm (K)

Remarks Estimated; at 80 kbar N2 Optimized

Indium nitride

InN

1900

Indium phosphide Indium arsenide Indium antimonide

InP InAs InSb

1327 1221 (1) 800 (1)

Part 4 1.2

Crystal

α (10 –6 K–1) 6 InN 5 α⊥ 4

Drop calorimetry

α⏐⏐ 3

2 0

100

200

300

400

500

600 T (K)

Fig. 4.1-106 InN. Coefficient of linear thermal expansion vs. temperature [1.75] Table 4.1-78 Linear thermal expansion coefficient α of indium compounds Crystal Indium nitride

InN

Indium phosphide Indium arsenide Indium antimonide

InP InAs InSb

Expansion coefficient α (10−6 K−1 )

Temperature (K)

Temperature dependence

Remarks

αa αc

100–673

Fig. 4.1-106

X-ray diffraction

298 20–250 283–343

Fig. 4.1-107 Fig. 4.1-108 Fig. 4.1-109

Average value, X-ray diffraction X-ray diffraction

3.6 (2) 2.6 (3) 4.75 (10) 4.52 5.37 (50)

α (10 –6 K–1)

0

α (10 –8 K–1)

InP – 30

4.0

InAs – 60

– 90 2.0

InSb – 120

– 150 0 –0.5

0

5

10

15

20

25

30

35

40 45 T (K)

Fig. 4.1-108 InAs, InSb. Linear thermal expansion coeffi0

100

200

300

T (K)

Fig. 4.1-107 InP. Temperature dependence of the coeffi-

cient of linear thermal expansion, obtained by the Bond method [1.96]

639

cient vs. temperature, measured with a variable-transformer dilatometer [1.97]

640

Part 4

Functional Materials

Part 4 1.2

Table 4.1-79 Heat capacity c p and Debye temperature ΘD of indium compounds Crystal

Indium nitride Indium phosphide Indium arsenide Indium antimonide

InN InP InAs InSb

Heat capacity (J/mol K)

Temperature (K)

Debye temperature (K)

Remarks

41.74

300

660 321 247 206

Calorimetry

Average value

Table 4.1-80 Phonon wavenumbers of indium compounds. Indium nitride (InN), T = 300 K; indium phosphide (InP),

RT, from coherent inelastic neutron scattering, carrier concentration n = 1012 cm−3 ; indium arsenide (InAs), from Raman scattering; indium antimonide (InSb), T = 300 K, from inelastic neutron scattering, carrier concentration n = 8 × 1013 cm−3 InN Symmetry

InP Branch

point

Wave-

Temperature

number

(K)

Remarks

Symmetry

Branch

point

(cm−1 ) ν˜ (Γ)

TO

Frequency (THz)

478

300

Reflectivity,

ν (111)(0.05)

LO

10.3 (3)

ν (Γ15 )

TO

9.2 (2)

ν (X5 )

TA

2.05 (10)

Kramers–Kronig analysis LO

694

Reflectivity, Kramers–Kronig analysis

ν˜ (A1 )

ν˜ E1

ν˜ E(1) 2 ν˜ (E(2) 2 )

TO

400

Experimental data

TO

484

ν (X3 )

LA

5.8 (3)

LO

570

ν (X5 )

TO

9.70 (10)

TO

190

ν (X1 )

LO

9.95 (20)

TO

590

ν (L3 )

TA

1.65 (2)

ν (L1 )

LA

5.00 (10)

ν (L3 )

TO

9.50 (15)

ν (L1 )

LO

InAs Symmetry

InSb Branch

point

Wave-

Temperature

Symmetry

number

(K)

point

Branch

(cm−1 ) ν˜ (Γ) ν˜ (X)

ν˜ (L)

10.2 (3)

TO

217.3

LO

238.6

Frequency (THz)

300

ν (Γ15 )

LO

5.90 (25)

TO

5.54 (5)

TA

53

ν (X5 )

TA

1.12 (5)

LA

160

ν (X3 )

LA

4.30 (10)

TO

216

ν (X1 )

LO

4.75 (20)

LO

203

100

ν (X5 )

TO

5.38 (17)

TA

44

300

ν (L3 )

TA

0.98 (5)

LA

139.5

ν (L1 )

LA

3.81 (6)

TO

216

LO

4.82 (10)

LO

203

TO

5.31 (6)

100

ν (L3 )

Semiconductors

b) α (10 –6 K–1) 6

InSb – 40

4

– 80

2

–120

0

–160

–2 0

10

20

30

0

100

200

300 T (K)

T (K)

Fig. 4.1-109a,b InSb. Linear thermal expansion coefficient vs. temperature: (a) low-temperature region [1.97], (b) high-

temperature region [1.98]

Table 4.1-81 Phonon dispersion curves of indium com-

pounds

12

Crystal Indium phosphide Indium arsenide Indium antimonide

Frequency ν (THz) InP

Figure InP InAs InSb

Fig. 4.1-110 Fig. 4.1-111 Fig. 4.1-112

8

4

0

Γ

641

Part 4 1.2

a) 0α (10 –8 K–1)

1.2 III–V Compounds

K

X

Γ

L

X

W L Wave vector q

Fig. 4.1-110 InP. Phonon dispersion curves. Experimental neutron data (diamonds) [1.99] and Raman data (triangles) [1.100] and ab initio pseudopotential calculations (solid curves) [1.101]. From [1.101]

642

Part 4

Functional Materials

Part 4 1.2

Wavenumber ν– (cm–1) 250

InAs

200

150

100

50

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-111 InAs. Phonon dispersion curves (left panel) and density of states (right panel) [1.82]. Experimental neutron

data (circles, T = 300 K) [1.102], thermal-diffuse-scattering X-ray data (diamonds, T = 80 K) [1.102], Raman data (squares, T = 330 K) [1.103], and ab initio calculations (solid curves [1.82]). From [1.82]

Wavenumber ν– (cm–1) 200

InSb

100

0

Γ

K

X

Γ

L

X

W L Wave vector q

DOS

Fig. 4.1-112 InSb. Phonon dispersion curves (left panel) and density of states (right panel). Experimental neutron data

(circles) [1.21] and ab initio pseudopotential calculations (solid curves) [1.60]. From [1.60]

1.2 III–V Compounds

Semiconductors

Band Structures of Indium Compounds. Indium Ni-

tride (InN). The band structure (Fig. 4.1-114) shows a direct gap at Γ very similar to that of GaN. A low-lying many-valley conduction band leading to an indirect gap has been suggested. Indium Phosphide (InP). Indium phosphide is a directgap semiconductor. The conduction band minimum is situated at Γ. Higher conduction band minima at L and X have been detected in optical experiments. The X-band minima show no camel’s back structure, in contrast to most other III–V compounds with the zinc blende structure. The valence band has the structure common to all zinc blende-type semiconductors (Fig. 4.1-113). Indium Arsenide (InAs). Indium arsenide resembles InSb in its band structure, having only a slightly larger energy gap and a smaller spin–orbit splitting of the top of the valence band. The conduction band minimum (Γ6 ) is situated in the center of the Brillouin zone. Near the minimum, E(k) is isotropic but nonparabolic. The valence band shows the usual structure common to all zinc blende-type III–V compounds (Fig. 4.1-116).

E (eV) 6 L4,5 L6

Γ7 Γ6

3

X7

Γ7

X6

L6

Γ8

Figure

Indium nitride Indium phosphide Indium arsenide Indium antimonide

X7

–3

InN InP InAs InSb

Γ7

E (eV) 12 InN M3

9

Γ6

6 3

M4 K3

L6

K2 K1

Γ6

–6

– 12 L

Λ

Γ

∆

X

U,K

Σ Γ Wave vector k

K3

M3

A5,6

H3

L1,3

M2 A1,3

M1

H1,2

M3

L1,3

–9

M1

Fig. 4.1-113 Band structure of indium phosphide – 12

Γ1 Γ5

L2,4

–3

Γ6

L1,3

Γ1 Γ6

0

X6

L1,3

H3

Γ3

L6

–9

H1,2

A5,6

A1,3

M1

X6 X6

Fig. 4.1-24 Fig. 4.1-23 Fig. 4.1-23 Fig. 4.1-23

Indium Antimonide (InSb). Indium antimonide is a directgap semiconductor. The minimum of the conduction band (Γ6 ) is located in the center of the Brillouin zone. Near the minimum, E(k) is isotropic but nonparabolic. Thus the effective mass of the electrons is scalar and depends strongly on the electron concentration. Higher band minima (about 0.63 eV above the lowest minimum) seem to have been established by transport measurements in heavily doped n-InSb. The valence band shows the structure common to all zinc blende semiconductors, i. e. two subbands degenerate at Γ8 and one spin-split band at Γ7 (Fig. 4.1-115).

K2

Γ7

L6

Crystal

M3

Γ6

Γ8

0 L4,5

–6

Γ8

InP

Γ8

Table 4.1-82 First Brillouin zones of indium compounds

Γ

T

K

M

H3

Γ3

Σ

Γ∆ A

S

H

L

Fig. 4.1-114 Band structure of indium nitride

R

AL U MH P K Wave vector k

Part 4 1.2

B. Electronic Properties Tables 4.1-82 – 4.1-87.

643

644

Part 4

Functional Materials

Part 4 1.2

E (eV)

E (eV) L4,5

6

InAs

Γ8

Γ8

L6

3

L6

Γ7

X7

Γ7

Γ6

X6

Γ6 Γ8

Γ8

0 L4,5 Γ7

L6

E (eV)

21

X7

L6

15

0 L 4,5

Γ7

X6

Γ8

X6

–6

X6

L6

Γ7

X6 L6

9

X6

6 X6

–9 L 6

3

Γ6

Γ6 0

– 12 L

–9

X6

Λ

Γ

∆

X

U,K

–3

Σ Γ Wave vector k

Fig. 4.1-115 Band structure of indium antimonide

L6

– 12

Γ6

Γ6

L

Γ8

X7

Γ7

–3

–6 –3

Γ8 Γ6

X7

Γ6

L6

Γ8

InSb

Γ7

18

12

Γ8

L6 L4,5

3

Λ

Γ

∆

–6

X U,K Σ Γ Wave vector k

X Σ Γ Wave vector k

Fig. 4.1-116 Band structure of indium arsenide

Table 4.1-83 Energy gaps of indium compounds Crystal

Quantity

Indium nitride

InN

E g, dir

Indium phosphide

InP

E g, dir

Bands Γ8v to Γ6c

Energy (eV)

Temperature (K)

Remarks

1.95

300

Polycrystalline film, absorption edge

1.4236 (1) 1.344

Indium arsenide

InAs

E g, dir

Γ8v to Γ6c

0.4180 (5) 0.354 (3) 0.41565 (1)

E g, x Indium antimonide

InSb

E g, dir

Γ8v to Γ6c

0.2352 0.180

1.6 300 4.2 295

From excitonic gap Absorption, photoluminescence Magnetotransmission Electroreflectance

1.4

Excitonic band gap, photoluminescence

1.7

Emission spectra, from exciton data

300

Reflectance, magnetoabsorption

Table 4.1-84 Spin–orbit splitting energies of indium compounds Crystal Indium phosphide

InP

Indium arsenide

InAs

Indium antimonide

InSb

Spin–orbit splitting

Bands

Numerical value (eV)

Temperature (K)

Remarks

∆0 ∆1

Γ8v to Γ7v Λ4,5v to Λ6v

∆0 ∆0 ∆1 ∆0 ∆0 ∆1

Γ8c to Γ7c Γ8v to Γ7v L4,5v to L6v Γ8v to Γ7v Γ7v to Γ8c Λ4,5v to Λ6v

0.108 (8) 0.13 0.15 (5) 0.07 0.38 (1) 0.267 0.81 (1) 0.39 0.495

4.2 77 300 300 1.5 5 1.5 5

Wavelength-modulated photovoltaic effect Thermoreflectance Electroreflectance Electroreflectance Magnetoelectroreflectance Wavelength-modulated reflectance Magnetoelectroreflectance Wavelength-modulated reflectance

Semiconductors

1.2 III–V Compounds

InSb

InAs 0.23

1.42

0.22

1.41

0.21 1.40 Band gap

Exciton peak

0.20 1.39 0.19 1.38 0.18 1.37 0.17 1.36

0.16

Emission Absorption

1.35

1.34

0

80

160

240

320 T (K)

Fig. 4.1-119 InSb. Energy gap vs. temperature below RT,

0

50

100

150

200

250

300 T (K)

measured by resonant two-photon photo-Hall effect (filled circles); the open circles and triangles show earlier literature data for comparison. Solid curve: fit by Varshni’s formula [1.106]

Fig. 4.1-117 InP. Energy gap and exciton peak energy vs.

temperature from absorption and emission data [1.104] Table 4.1-85 Temperature dependence of the energy gaps of indium compounds

Eg (eV) 0.45 InAs 0.40

0.35

0.30

0.25

0

100

200

300

400

500

600 T (K)

Fig. 4.1-118 InAs. Band gap vs. temperature. Solid line,

optical band gap calculated from parameters used for fitting various transport data; symbols, thermal band gap of six samples, obtained from conductivity and Hall coefficient [1.105]

Crystal

Figure

Indium phosphide

InP

Fig. 4.1-117

Indium arsenide

InAs

Fig. 4.1-118

Indium antimonide

InSb

Fig. 4.1-119

Part 4 1.2

Eg (eV) 0.24

E (eV) 1.43

645

646

Part 4

Functional Materials

Part 4 1.2

Table 4.1-86 Effective masses of electrons (m n ) and holes (m p ) for indium compounds (in units of the electron mass m 0 ) InN mn

0.11

m n, calc

0.12

m p, heavy

0.5

m p, light

0.17

300 K

Optical mass, plasma edge Calculated effective mass

InP mn

0.0808(10) 0.073

0K

Magnetophonon resonance

300 K

m p, heavy

0.45 (5)

4.2 K

m p, light

0.12 (1)

4.2 K

m p, so

0.121 (1)

Faraday rotation Piezomodulated photovoltaic effect

110 K

B parallel to [111] and [100]

InAs mn

0.0265

4.2 K

0.023

300 K

m p, heavy

0.57

300 K

m p, [100]

0.35

m p, [111]

0.85

InSb Faraday effect, n = 4.6 × 1013 cm−3 Cyclotron resonance

m n (Γ6c )

0.01359 (3) 0.0118

m p, heavy

0.44 0.42 0.32

20 K

Parallel to [111], magnetoabsorption, Faraday rotation Parallel to [110] Parallel [100]

m p, light

0.016

20 K

Magnetoabsorption, Faraday rotation

4.2 K 300 K

Table 4.1-87 Electron g-factor gc of indium compounds Crystal Indium phosphide

gc 1.48 (5)

Temperature (K)

Remarks

4.2

Modulated photovoltaic effect

Indium arsenide

−15.3 (2)

1.4

Magnetoluminescence

Indium antimonide

−51.31 (1)

1.4

Electron spin resonance

Semiconductors

1.2 III–V Compounds

Electronic Transport, General Description. Indium

Phosphide (InP). The transport properties are determined mainly by the electrons in the Γ6c minimum. Above 800 K, multivalley conduction, where the L6c minimum is involved, becomes important. Indium Arsenide (InAs). The transport properties are determined mainly by the electrons in the Γ6 minimum. Pure material with intrinsic conduction down to 450 K is available.

Indium Antimonide (InSb). The transport properties are mainly determined by the extremely high mobility of the electrons in the Γ6 minimum of the conduction band. Pure material with intrinsic conduction down to 200 K is available. At low temperatures and in doped material, impurity scattering limits the electron mobility.

1028

ni2/T3 (cm–6 K–3) nd, na (cm–3)

InAs T (°C) 500 200 100

10 4

0

– 50

σ (Ω–1 cm–1) 10 3

– 100 InAs

D

E

1027

C

10 2

2

1026

B 1

10

0.45 eV

0.49 eV

1025

1

10 –1

a 1.2 × 1015 b 1.7 × 1016 n c 3 ×1016 16 d 7 ×10 2 ×1017 p 1

A

1

2

3

4

5

6 7 T–1 (10 –3 K–1)

Fig. 4.1-120 InAs. Electrical conductivity vs. recipro-

1024 1.0

1.4

1.8

1.2 × 1015 cm−3 ;

B, cal temperature [1.107]. A, n = n = 1.7 × 1016 cm−3 ; C, n = 4 × 1016 cm−3 ; D, n = 7 × 1016 cm−3 ; E, n = 2 × 1018 cm−3 ; 1, p = 2 × 1017 cm−3 ; 2, p = 7 × 1018 cm−3

2.2

2.6 3.0 T–1 (10 –3 K–1)

Fig. 4.1-121 InAs. Square of the intrinsic carrier concentration

divided by T 3 vs. reciprocal temperature for several different samples [1.107]

Table 4.1-88 Carrier concentrations n i and electrical conductivity σ of indium compounds Crystal

Temperature (K)

Indium nitride

InN

300

Indium phosphide Indium arsenide Indium antimonide

InP InAs InSb

300 300 300

Carrier concentration ni (cm−3 )

Conductivity σ (
−1 cm−1 ) 2 –3 × 102

6.3 × 1015 1.9 × 1016

4 –5 50 220

Remarks Temperature coefficient of resistivity 3.7 × 10−3 K−1 at 200–300 K for pressed powder n-type pure material See Fig. 4.1-120 for temperature dependence See Fig. 4.1-122 for temperature dependence

Part 4 1.2

C. Transport Properties Tables 4.1-88 – 4.1-90.

647

648

Part 4

Functional Materials

Part 4 1.2

σ (Ω–1 cm–1 ) 1000 500 104

T (K) 300

200

104

150

µn (cm2/V s) InN

8

InSb

6 4

1 2

2

103

103

B

8 6

3

A 4

102

2×102 10

2

4

6

8

102

2

4

6

8 3 10 T (K)

4

Fig. 4.1-123 InN. Electron mobility vs. temperature

for three samples with RT carrier concentrations of 5.3 × 1016 (1), 7.5 × 1016 (2), and 1.8 × 1017 cm−3 (3). Left broken line, calculated ionized-impurity-scattering mobility; right broken line, empirical high-temperature mobility (µ ∝ T −3 ) for sample 1. Solid lines, total mobility calculated for each sample [1.109]

3 10

2

1 V

1 1

2

3

4

5

6

7 8 9 T –1 (10–3 Κ–1)

Fig. 4.1-122 InSb. Electrical conductivity vs. recipro-

cal temperature [1.108]. Curve V , n ≈ 1013 cm−3 ; A, n = 1.3 × 1016 cm−3 ; B, n = 1 × 1016 cm−3 ; 1, p = 4 × 1015 cm−3 ; 2, p = 2.2 × 1016 cm−3 ; 3, p = 6 × 1016 cm−3 ; 4, p = 2 × 1017 cm−3 Table 4.1-89 Electron and hole mobilities µn and µp of indium compounds Crystal

Indium nitride Indium phosphide

Indium arsenide

Indium antimonide

Temperature

Carrier concentration

µn

µp

(K)

(cm−3 )

(cm2 /V s)

(cm2 /V s)

300 300 300 77 300 300 77 300 300 300

5–18 × 1016

250 (50) 20 4–5.4 × 103 130 × 103

n = 0.5–1 × 1016 n = 6 × 1013

Remarks

Fig. 4.1-123 Pure material, Hall mobilities 190

n ∼ 1016

Temperature dependence of mobilities

2–3.3 × 104 0.8–1 × 105

Pure material

Fig. 4.1-124 Fig. 4.1-125 Fig. 4.1-121

100–450 70 × 103

Hall mobilities 850

Fig. 4.1-126 Fig. 4.1-127

Semiconductors

5

2 ×10

3

InP

InP

8 6

103

Ionized impurity

8

4 6

Polar scattering

4

Total

nion = 5 × 1015 cm–3 2

2

104 Ionized impurity

8 6

102 8

nion = 5 × 10 cm 17

–3

6

4×10 6×10

4

Total 2×103 20

4

6

8

10

2

4×10 T(K)

2

2

Fig. 4.1-124 InP. Electron mobility vs. temperature, calcu-

lated for two concentrations of ionized impurities [1.110]

8

102

2

4

6×102 T (K)

Fig. 4.1-125 InP. Hole Hall mobility vs. temperature for pure p-type samples, after [1.111] µH,p (cm2/V s) 104 8

InSb

6 4

µn (cm2/V s) 2×10

5

InSb

2

103

105

8 6

8

4

6

2

4

2×103 60 2

104 200

8

102

2

4

6

103 T (K)

8

Fig. 4.1-127 InSb. Hole Hall mobility vs. temperature [1.111]. The vertical bars indicate the ranges of the experimental values. The solid line has a slope −1.8 400

600

800 T (K)

Fig. 4.1-126 InSb. Electron mobility vs. temperature. The

experimental data are Hall mobilities. Triangles, [1.112]; filled circles [1.113]; open circles, [1.114, 115]; solid line, calculated drift mobility [1.116]

649

Part 4 1.2

µH,p (cm2/V s)

µn (cm2/V s) 10

1.2 III–V Compounds

650

Part 4

Functional Materials

Part 4 1.2

40

κ (W/cm K)

40

InP

κ (W/cm K) InSb

8

κL+ κT

10 8 6

10 8

4

T

6

3

4

2

T –3/2

1 8 6

2

4

1

κT κL

8 2

6

10–1

4

1

2

4

6 8

10

2

4

6 8

102

2

4

103 T (K) 6

Fig. 4.1-128 InP. Thermal conductivity vs. tempera-

ture [1.117, 118]

2

10–1

pounds

2

1

Table 4.1-90 Thermal conductivity κ of indium com-

4

6

8

10

2

4

6

8

102 2 ×102 T (K)

Fig. 4.1-129 InSb. Thermal conductivity vs. temperature κ (W/m K)

Crystal Indium nitride

InN

Indium phosphide

InP

Indium arsenide

InAs

Indium antimonide

InSb

for an n-type sample, and theoretical curve showing the contributions of the longitudinal and transverse phonons [1.119]

Remarks

38.4 See Fig. 4.1-128

See Fig. 4.1-129

D. Electromagnetic and Optical Properties Tables 4.1-91 – 4.1-93. Table 4.1-91 Dielectric constant ε and refractive index n of indium compounds Crystal Indium nitride

Temperature (K) InN

ε(0)

ε(∞)

n

at

λ (µm) Remarks

9.3

Infrared reflectivity, heavily doped film 8.4

Indium phosphide

InP

Indium arsenide Indium antimonide

InAs InSb

300 77 297 300

2.56 1.0 µm Interference method, n = 3 × 1020 cm−3 2.93 0.82 µm 3.12 0.66 µm Table 4.1-92 Capacitance measurements

12.56 (20) 11.93 (20) 15.15 16.8 (2)

10.9 (10) 12.37 15.68

Table 4.1-92 Table 4.1-92

Film interference Infrared reflectance and oscillator fit Gyroscopic sphere resonance, infrared reflectance, and oscillator fit

Semiconductors

1.2 III–V Compounds

InP λ (µm)

n

Remarks

14.85

3.03

Transmission and reflectance

5 2

3.08 3.134

1

3.327

0.652

3.410

0.399 0.200 0.062

4.100 1.525 0.793

Prism method

Reflectance and dispersion relations

InAs λ (µm)

n

Remarks

InSb λ (µm)

n

Remarks

25

3.26

Interference

45

2.57

Reflectance and transmission, n = 6 × 1015 cm−3

10 3.74

3.42 3.52

21.15 19.98

3.814 3.826

1.38

3.516

0.517

4.558

10.06 7.87 2.07

3.953 4.001 4.03

0.282 0.049

3.800 1.139

Reflectance and dispersion relations

0.689 0.062

Interference technique, n = 2 × 1016 cm−3

Reflectance and dispersion relations

5.13 1.17

Table 4.1-93 Energy dependence of optical constants of indium compounds. Real and imaginary parts of the complex dielectric

constant measured by spectroscopic ellipsometry; n, k, R, K calculated from these data InP hν (eV) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 InAs hν (eV) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 InSb hν (eV) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

ε1 11.904 12.493 14.313 17.759 5.400 6.874 8.891 −7.678 −4.528 −2.681 ε1 13.605 15.558 15.856 6.083 5.973 7.744 −1.663 −5.923 −3.851 −2.403 ε1 19.105 14.448 7.811 7.354 5.995 −6.722 −6.297 −4.250 −4.325 −3.835

ε2

n

k

R

K (103 cm−1 )

1.400 2.252 3.062 10.962 12.443 10.871 16.161 14.896 7.308 5.644

3.456 3.549 3.818 4.395 3.193 3.141 3.697 2.131 1.426 1.336

0.203 0.317 0.511 1.247 1.948 1.730 2.186 3.495 2.562 2.113

0.395 0.317 0.349 0.427 0.403 0.376 0.449 0.613 0.542 0.461

30.79 64.32 129.56 379.23 691.21 701.54 996.95 1771.5 1428.1 1285.1

ε2

n

k

R

K (103 cm−1 )

3.209 5.062 15.592 13.003 10.550 11.919 22.006 8.752 6.008 6.005

3.714 3.995 4.364 3.197 3.008 3.313 3.194 1.524 1.282 1.434

0.432 0.634 1.786 2.034 1.754 1.799 3.445 2.871 2.344 2.112

0.337 0.370 0.454 0.412 0.371 0.393 0.566 0.583 0.521 0.448

65.69 128.43 452.64 618.46 622.13 729.23 1571.2 1455.3 1306.6 1284.2

ε2

n

k

R

K (103 cm−1 )

5.683 14.875 15.856 13.421 17.673 19.443 8.351 6.378 4.931 3.681

4.418 4.194 3.570 3.366 3.511 2.632 1.443 1.307 1.057 0.861

0.643 1.773 2.221 1.994 2.517 3.694 2.894 2.441 2.333 2.139

0.406 0.443 0.447 0.416 0.474 0.608 0.598 0.537 0.563 0.572

97.79 359.46 562.77 606.27 892.82 1497.8 1320.2 1237.0 1300.6 1300.9

Part 4 1.2

Table 4.1-92 Wavelength dependence of refractive index n of indium compounds at T = 300 K

651

652

Part 4

Functional Materials

Part 4 1.3

4.1.3 II–VI Compounds 4.1.3.1 Beryllium Compounds A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-94 – 4.1-99. Table 4.1-94 Crystal structures of beryllium compounds Crystal

Space group

Crystal system

Structure type

Figure

Beryllium oxide

BeO

Beryllium sulfide

BeS

Beryllium selenide

BeSe

Beryllium telluride

BeTe

4 C6v 2 Td Td2 Td2

P63 mc

hex

Wurtzite

Fig. 4.1-130

F43m

fcc

Zinc blende

Fig. 4.1-131

F43m

fcc

Zinc blende

Fig. 4.1-131

F43m

fcc

Zinc blende

Fig. 4.1-131

c

a

a

Fig. 4.1-130 The wurtzite lattice (a and c are the lattice

Fig. 4.1-131 The zinc blende lattice (a is the lattice param-

parameters)

eter)

Table 4.1-95 Lattice parameters of beryllium compounds Crystal

Lattice parameters (nm)

Temperature (K)

Remarks

Beryllium oxide

BeO

a = 0.26979 c = 0.4380

Beryllium sulfide

BeS

a = 0.48630 (5)

RT

X-ray diffraction

Beryllium selenide

BeSe

a = 0.51520 (23)

RT

Epitaxial film, X-ray diffraction

Beryllium telluride

BeTe

a = 0.56270 (15)

300

Epitaxial film, X-ray diffraction

X-ray diffraction

Table 4.1-96 Elastic constants cik (in GPa) of beryllium oxide Crystal Beryllium oxide

BeO

c11

c12

c13

c33

c44

Remarks

460.6

126.5

88.5

491.6

147.7

Ultrasonic data, RT

1.3 II–VI Compounds

Semiconductors

Crystal

Density

Beryllium oxide Beryllium sulfide

BeO BeS

beryllium compounds

(g/cm3 )

Crystal

3.01 2.36

Table 4.1-98 Melting point Tm of beryllium oxide Crystal

Beryllium oxide Beryllium telluride

Melting point Tm

Beryllium oxide

BeO BeTe

Expansion coefficient α (K−1 )

Temperature (K)

9.7 × 10−6 7.66 (21) × 10−6

373 300

2507 ◦ C

BeO

B. Electronic Properties Tables 4.1-100 – 4.1-102. kz

Table 4.1-100 First Brillouin zones of beryllium com-

pounds Crystal

Figures

Beryllium oxide

BeO

Fig. 4.1-132

Beryllium sulfide

BeS

Fig. 4.1-133

Beryllium selenide

BeSe

Fig. 4.1-133

Beryllium telluride

BeTe

Fig. 4.1-133

L Λ

U ∆ Q

Γ Σ

S W

K

Z

X

ky

kx kz

A

S

R

H ∆

S' P

U

Fig. 4.1-133 The Brillouin zone of the zinc blende and rock

Γ

T K

L

ky

Σ T'

M

salt lattices E (eV) 15

kx

BeS 10

Fig. 4.1-132 The Brillouin zone of the wurtzite lattice Table 4.1-101 Band structures of beryllium compounds Crystal Beryllium oxide Beryllium sulfide Beryllium selenide Beryllium telluride a

b

Figure BeO BeS BeSe BeTe

Fig. 4.1-135 Fig. 4.1-134 Fig. 4.1-136 Fig. 4.1-137

Remarks

5 0

a b

According to theory, BeS is an indirect-gap material with the highest valence band edge at Γ and the lowest conduction band edge at X. According to theory, BeSe is an indirect-gap material with the highest valence band edge at Γ and the lowest conduction band edge at X.

–5 – 10 – 15

Γ

∆

X U,K

Σ

Γ

Λ

L

K WZ X Wave vector k

Fig. 4.1-134 Band structure of beryllium sulfide

Part 4 1.3

Table 4.1-99 Linear thermal expansion coefficient α of

Table 4.1-97 Densities of beryllium compounds

653

654

Part 4

Functional Materials

Part 4 1.3

E (eV) 15

E (Ry) 0.50

BeO

BeSe 10

0.25 5 0 0 – 0.25 –5 – 0.50 – 10 – 0.75 – 15 Γ

∆

X U,K

Σ

Γ

Λ

L

– 1.00

K WZ X Wave vector k

Fig. 4.1-136 Band structure of beryllium selenide – 1.25 – 1.50 A 0,0, π c

15 M 0, 2π ,0 3a Wave vector k

Γ(0,0,0)

Fig. 4.1-135 Band structure of beryllium oxide

E (eV) BeTe

10 5 0 –5 – 10 – 15 Γ

∆

X U,K

Σ

Γ

Λ

L

K WZ X Wave vector k

Fig. 4.1-137 Band structure of beryllium telluride Table 4.1-102 Energy gaps of beryllium compounds Crystal Beryllium oxide Beryllium sulfide Beryllium selenide Beryllium telluride

BeO BeS BeSe BeTe

Band gap

Remarks

10.585 eV >5.5 eV 5.6 eV E g, ind 2.8 eV

Absorption RT 300 K optical reflection, ellipsometry

E g, dir 4.1 eV

Semiconductors

1.3 II–VI Compounds

Part 4 1.3

C. Transport Properties Table 4.1-103. Table 4.1-103 Electronic transport in beryllium compounds, general description Crystal Beryllium oxide Beryllium sulfide Beryllium telluride

Transport properties BeO

BeO, synonym beryllia, is an electrical insulator like a ceramic, but conducts heat like a metal. The electrical resistivity is larger than 1016 Ω cm BeS The electrical conductivity of polycrystalline BeS disks was found to be p-type. This is attributed to Be vacancies or S interstitials BeTe BeTe, like ZnTe, tends towards p-type conductivity. Using plasma-assisted nitrogen doping during molecular-beam epitaxy, very high p-type concentrations above 1020 cm−3 could be achieved; n-type doping of BeTe has not yet been reported

D. Electromagnetic and Optical Properties Table 4.1-104. Table 4.1-104 Dielectric constants ε of beryllium compounds Temperature (K) ε(0)

Crystal Beryllium oxide Beryllium selenide Beryllium telluride a b

c

BeO BeSe BeTe

ε(∞)

εparall 7.65

300 300 RT

εperpend 6.94

Method

Remarks

Reflectance

Crystalline BeOa b

7

Infrared reflection

c

BeO is transparent up to 9.4 eV (vacuum UV) and quite resistant to UV damage. The interest in BeSe originates from the fact that ternary BeZnSe and quaternary BeMgZnSe alloys can be lattice-matched to silicon substrates and can also be used as base materials for blue–green-emitting ZnSe-based laser diodes grown on GaAs. The ternary alloy has a band gap of approximately 4 eV if lattice-matched to silicon. BeTe is used in efficient pseudomorphic p-contacts for ZnSe laser diodes.

4.1.3.2 Magnesium Compounds A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-105 – 4.1-111. Table 4.1-105 Crystal structures of magnesium compounds Crystal

Space group

Crystal system

Structure type

Figure

Magnesium oxide Magnesium sulfide Magnesium selenide Magnesium telluride

Oh5 Oh5 Oh5 4 C6v

fcc fcc fcc hex

NaCl NaCl NaCl Wurtzite

Fig. 4.1-138 Fig. 4.1-138 Fig. 4.1-138 Fig. 4.1-130

MgO MgS MgSe MgTe

Fm3m Fm3m Fm3m P63 mc

655

656

Part 4

Functional Materials

Part 4 1.3

14

α (×10 –6 K–1) BaO

12 10 8

MgO 6 4 2 T3 0

a

0

40

80

120

160

200

240

280

Fig. 4.1-138 The rock salt lattice

320 T (K)

Fig. 4.1-139 MgO, BaO. Linear thermal expansion coefficient α vs. temperature. Open circles, [1.120]; filled circles, [1.121] Table 4.1-106 Lattice parameters of magnesium compounds Crystal

Lattice parameters (nm)

Temperature (K)

Remarks

Magnesium oxide

MgO

a = 0.4216

298

X-ray diffraction, powder samples

Magnesium sulfide

MgS

a = 0.5203

300

X-ray diffraction

Magnesium selenide

MgSe

a = 0.546

300

X-ray diffraction

Magnesium telluride

MgTe

a = 0.45303

300

c = 0.74056

Table 4.1-107 Densities of magnesium compounds Crystal

Density

Temperature

(g/cm3 )

(K) 298

Magnesium oxide

MgO

3.576

Magnesium sulfide

MgS

2.86

Magnesium selenide

MgSe

4.21

Magnesium telluride

MgTe

Table 4.1-108 Melting point Tm of magnesium oxide Crystal

Melting point Tm

Magnesium oxide

MgO

2827 ◦ C

Table 4.1-109 Elastic constants cik (in 1012 dyn/cm2 ) of magnesium oxide Crystal Magnesium oxide

MgO

c11

c12

c44

Temperature (K)

Remarks

2.971 (6)

0.965 (7)

1.557 (2)

293

Single crystals

Table 4.1-110 Linear thermal expansion coefficient α of magnesium oxide Crystal Magnesium oxide a

MgO

Expansion coefficient α (K−1 )

Temperature (K)

Remarks

9.84 × 10−6

283

Capacitance cell a

See Fig. 4.1-139 for the temperature dependence.

Semiconductors

1.3 II–VI Compounds

Crystal Magnesium oxide

MgO

Magnesium telluride

MgTe

νTO (THz)

νLO (THz)

12.05

21.52

ν˜ TO (cm−1 )

235

ν˜ LO (cm−1 )

292

Temperature (K)

Symmetry point

Remarks

300

Γ

Thin films, polarized reflectance Raman spectroscopy

300

B. Electronic Properties Tables 4.1-112 – 4.1-114. Table 4.1-112 First Brillouin zones of magnesium com-

E (Ry)

pounds Crystal Magnesium oxide Magnesium sulfide Magnesium selenide Magnesium telluride

Figure MgO MgS MgSe MgTe

Fig. 4.1-133 Fig. 4.1-133 Fig. 4.1-133 Fig. 4.1-132

Λ3

1.0 L1 0.8

Γ15 ∆2

Λ1

MgO

∆5

Γ12

Λ1

Γ2'

∆1

Γ25'

∆5

L2 0.4 L3'

Λ3

Magnesium oxide Magnesium sulfide Magnesium selenide Magnesium telluride a

Figure MgO MgS MgSe MgTe

Fig. 4.1-140 a Fig. 4.1-141 Fig. 4.1-142 Fig. 4.1-143

Disagreement exists about the position of the minimum of the lowest conduction band. Some authors place the minimum at Γ1 and anticipate a direct gap; others claim that the minimum is at X3 , indicating an indirect gap.

Σ3 K1

Σ1

Γ2' X1

Σ3

Γ25'

X5

Table 4.1-113 Band structures of magnesium compounds Crystal

Σ4 Σ1

L1 0.6

Γ12

∆2'

Λ3

Γ15

Σ4

∆1

0.2 Λ1

∆2'

0 L1

X4

Σ1

∆1

– 0.4 L2'

L3

Λ3

Σ1

X1

Λ1

– 0.6

K1

K1 K4

X3

– 0.2

K3

Γ1

Γ1

Γ15

Γ15

Σ4

– 1.2

K1

K4

∆1 X5'

– 1.4

Σ3 K1

– 1.6 L1

Λ1

L

X4'

∆1

X1

Σ1

K3 K1

– 1.8 – 2.8 L2' L2' – 4.8 L3'

∆1

Λ1 Λ1

Γ1

∆5 X4' X5'

Γ15

Λ3 Λ

Γ1 Γ15

∆

Σ4 Σ3 Σ1

∆1 Γ

Σ1

X Γ

Fig. 4.1-140 Band structure of magnesium oxide

K1K4

K3 Σ K Wave vector k

Part 4 1.3

Table 4.1-111 Phonon frequencies/wavenumbers of magnesium compounds

657

658

Part 4

Functional Materials

Part 4 1.3

1.8

E (eV)

1.8

E (Ry)

MgS

MgSe

1.2

1.2

0.6

0.6

0

0

EF

– 0.6

– 1.2

EF

– 0.6

Γ

X

W

– 1.2

L Wave vector k

Γ

X

W

L Wave vector k

Fig. 4.1-141 Band structure of magnesium sulfide, rock salt

Fig. 4.1-142 Band structure of magnesium selenide, rock

structure

salt structure

E (eV) 12 MgTe 8

4

0

–4

–8

– 12 L

Γ

X

U(K)

Fig. 4.1-143 Band structure of magnesium telluride

Γ

X W0 Wave vector k

0.04

0.08 0.12 DOS (arb. units)

1.3 II–VI Compounds

Semiconductors

Band gap (eV)

Crystal Magnesium oxide

MgO

Magnesium sulfide Magnesium selenide Magnesium telluride

MgS MgSe MgTe

7.672 (10) 7.9 (7)

E gx, dir E g, theor 4.5 4.05 3.49

Temperature (K)

Remarks

85 0 77 300 RT

Exciton states Temperature dependence of microwave conductivity Zinc blende structure Zinc blende structure Epitaxial films, photoluminescence, zinc blende structure

C. Transport Properties Electronic Transport, General Description. Magnesium

Oxide (MgO). Electrical transport measurements on alkaline earth oxides encounter several difficulties, such as high resistance at low temperatures, a strong influence of surface layers, and high-temperature thermionic emission. The partly contradictory results depend considerably on the purity and nature of the samples (pressed porous powders, sintered samples, polycrystals, and single crystals) and on the experimental conditions.

σ (Ω–1 cm–1) 10 –4 MgO 100 Hz

As in several semiconducting oxides, the conductivity and the type of conduction are determined by the oxygen partial pressure of the ambient atmosphere. In high-purity MgO crystals, temperatures below 1600 K favor ionic conduction, whereas at temperatures above 2000 K, electronic conduction is increasingly predominant. At low oxygen pressures (< 10−3 mbar) the conduction is ntype; at high pressures (> 10−1 mbar) ionic and electronic hole conduction seem to be superimposed. See Fig. 4.1-144 for the temperature dependence of the electrical conductivity of MgO and Fig. 4.1-145 for the thermal conductivity of MgO.

1873 K – 1– 4

– 1– 6

10 –5

102

κ (W/cm K) MgO

1773 a 10

1673

b

10 –6 c

1573 1 1473

10 –7

10 –1

1373

10 –8

10 –2 1273 K

10 –9 10 –24

10 –3 10 –20

10 –16

10 –12

10 –8

10 –4 1 p02 (bar)

Fig. 4.1-144 MgO. Electrical conductivity σ of a highpurity single crystal at various temperatures vs. oxygen partial pressure pO2 [1.122]. The numbers between the curves for 1673 K and 1773 K indicate the slopes of the dashed straight lines

4 × 10 –4 4 × 10 –1

1

10

102 T (K)

Fig. 4.1-145 MgO. Thermal conductivity κ vs. temperature [1.123]. Curve a, high-purity crystal; b, after additive coloration in Mg vapor; c, after subsequent bleaching with UV light

Part 4 1.3

Table 4.1-114 Energy gaps of magnesium compounds

659

660

Part 4

Functional Materials

Part 4 1.3

D. Electromagnetic and Optical Properties Table 4.1-115. Table 4.1-115 Dielectric constant ε of magnesium compounds Crystal Magnesium oxide Magnesium sulfide Magnesium selenide Magnesium telluride

MgO MgS MgSe MgTe

ε(0)

ε(∞)

Temperature (K)

Remarks

9.830

2.944

300

Single crystals

3.8

RT

Zinc blende structure, Raman scattering

4.1.3.3 Oxides of Ca, Sr, and Ba A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-116 – 4.1-123. Table 4.1-116 Crystal structures of oxides of Ca, Sr, and Ba Crystal

Space group

Crystal system

Structure type

Figure

Calcium oxide Strontium oxide Barium oxide

Oh5 Oh5 Oh5

fcc fcc fcc

NaCl NaCl NaCl

Fig. 4.1-138 Fig. 4.1-138 Fig. 4.1-138

CaO SrO BaO

Fm3m Fm3m Fm3m

Table 4.1-117 Lattice parameters of oxides of Ca, Sr, and Ba Crystal Calcium oxide Strontium oxide Barium oxide

CaO SrO BaO

Lattice parameters (nm)

Temperature (K)

Remarks

a = 0.48110 (2) a = 0.5159 a = 0.55363 (8)

297

Single crystal, X-ray diffraction Semiempirical calculation Powder samples, negligible oxygen pressure

300

Table 4.1-118 Densities of oxides of Ca, Sr, and Ba Crystal Calcium oxide Strontium oxide Barium oxide

Density CaO SrO BaO

Table 4.1-119 Melting point Tm of oxides of Ca, Sr, and Ba

(g/cm3 )

Crystal

3.335 4.75 5.68

Calcium oxide Strontium oxide Barium oxide

Melting point Tm (K) CaO SrO BaO

2900 2930 (30) 2290 (30)

Table 4.1-120 Elastic constants cik of oxides of Ca, Sr, and Ba Crystal Calcium oxide Strontium oxide Barium oxide

CaO SrO BaO

c11 (GPa)

c12 (GPa)

c44 (GPa)

Temperature (K)

Remarks

221.89 (60) 175.47 (37) 126.14 (66)

57.81 (66) 49.08 (35) 50.03 (60)

80.32 (10) 55.87 (13) 33.68 (30)

298 298 298

Calculated from sound velocities

Table 4.1-121 Linear thermal expansion coefficient α of oxides of Ca, Sr, and Ba Crystal Calcium oxide Strontium oxide Barium oxide

CaO SrO BaO

Expansion coefficient α (K−1 )

Temperature (K)

Remarks

15.2 × 10−6 13.72 × 10−6 12.8 (9) × 10−6

293–593 200–400

Single crystal, X-ray diffraction Mean value, X-ray diffraction Powder samples, X-ray diffraction

Semiconductors

1.3 II–VI Compounds

Crystal

Calcium oxide

CaO

Strontium oxide Barium oxide

SrO BaO

Heat capacity c p (J/mol K)

Debye temperature ΘD (K)

Remarks

14.70 at 100 K 42.21 at 300 K

605 (2)

ΘD (0) from heat capacity at low temperatures

446 (5) 370 (4)

ΘD from heat capacity at very high temperatures ΘD from heat capacity at very high temperatures

47.28 at 298 K

Table 4.1-123 Phonon frequencies at symmetry points for oxides of Ca, Sr, and Ba. Calcium oxide (CaO), 293 K;

strontium oxide (SrO), 300 K; barium oxide (BaO), 300 K. All data from inelastic thermal-neutron scattering CaO Mode ν˜ LO ν˜ TO ν˜ LO ν˜ TO ν˜ TA

Symmetry point

Frequency (THz)

q/qmax = 0.2 Γ X X X

16.40 (25) 8.8 (4) 12.00 (22) 9.4 (5) 6.48 (11)

SrO Mode ν˜ TO ν˜ LO ν˜ TA ν˜ LA ν˜ TO ν˜ LO

Symmetry point

Frequency (THz)

Γ Γ L L L L

7.02 (10) 14.47 (15) 3.33 (5) 7.14 (10) 8.35 (12) 12.94 (24)

BaO Mode ν˜ TO ν˜ LO ν˜ TA ν˜ LA ν˜ TO

Symmetry point

Frequency (THz)

Γ Γ L L L

4.32 (6) 13.02 (3) 1.99 (7) 4.88 (27) 6.58 (9)

B. Electronic Properties Tables 4.1-124 – 4.1-127. Table 4.1-124 First Brillouin zones of oxides of Ca, Sr, and Ba Crystal

Figure

Calcium oxide Strontium oxide Barium oxide

CaO SrO BaO

Fig. 4.1-133 Fig. 4.1-133 Fig. 4.1-133

Table 4.1-125 Energy gaps of oxides of Ca, Sr, and Ba Band gap (eV)

Crystal Calcium oxide

CaO

Strontium oxide

SrO

Barium oxide

BaO

E g, dir E g, theor E g, opt E g, theor E g, theor

6.931 (6) 7.8 5.22 6.4 4.4

Temperature (K)

Remarks

85 0 300 0 0

Exciton states

Estimated from temperature dependence of conductivity Estimated from temperature dependence of conductivity

Table 4.1-126 Effective masses of electrons for oxides of Ca, Sr, and Ba (in units of the electron mass m 0 ) Crystal Calcium oxide

CaO

Strontium oxide

SrO

Barium oxide

BaO

Quantity

Mass

Temperature (K)

Remarks

mn m n, polaron mn m n, polaron mn m n, polaron

0.50 0.68 0.54 0.77 0.59 0.86

700 700–800 600–700

From Hall mobility Polaron mass, Hall mobility From Hall mobility Polaron mass, Hall mobility From Hall mobility Polaron mass, Hall mobility

600 500–700

Part 4 1.3

Table 4.1-122 Heat capacity and Debye temperature of oxides of Ca, Sr, and Ba

661

662

Part 4

Functional Materials

Part 4 1.3

Table 4.1-127 Band structure of calcium oxide

E (Ry) 1.2 L3' L3 1.0 L1

Λ1 Λ1

Γ15

Λ3 Λ3

Γ15

Λ1

Γ1

∆5 ∆1 ∆1

X2

K1 Σ3 Σ1

Σ4 Σ1

X5 ∆5

Γ15 Γ1

Σ4 Σ1

∆1

0.8 0.6 L3' L3 0.4

Σ3 Γ15

CaO

L2'

Λ3 Λ1

Γ12

X1

∆2

Σ2

X5' Σ1

Γ2'

Γ2' ∆5

Λ3

Σ3

Γ25'

Γ25'

0.2

∆1 X4'

Σ1

∆2'

L1

L2'

∆1

Λ1

K3 K1

K4 K1

X1 – 0.2

K3 K1

Σ4

Λ1 0

K4

Γ12

∆2'

Σ1 X3

K1

Γ1

Γ1 – 0.4 Λ3

– 0.9

Γ15

Γ15

Σ4

∆5

L3

Σ3

X5'

K4

– 1.1 Λ1

Σ1

∆1

K1

– 1.3 K3

X4' L1

– 1.5

L2'

– 2.5

L2' – 2.7 L3' L

Λ1

Γ1

∆1

X1

Λ1 Λ3

Γ15

∆5 ∆1 ∆

X5' X4'

Λ

Γ

Γ1 Γ15

X Γ

Σ1

K1

Σ1Σ4 Σ3 K4,1 K3 Σ K Wave vector k

Fig. 4.1-146 Band structure of calcium oxide

Calcium oxide a

K2

Σ3

Crystal CaO

Figure

Remarks

Fig. 4.1-146

a

Some controversy exists in the literature about the positions of the lowest conduction band minima. One result shows the lowest minimum at Γ1 and the minimum of the d states at X3 , below some s states but above Γ1 . Other results claim the symmetry point of the conduction band bottom is at X3 instead of Γ1 , whereas according to other authors Γ1 and X3 are nearly degenerate.

Semiconductors

1.3 II–VI Compounds

Part 4 1.3

C. Transport Properties Tables 4.1-128 – 4.1-130.

Table 4.1-128 Electronic transport in oxides of Ca, Sr, and Ba, general description Crystal

Transport properties

Calcium oxide

CaO

Strontium oxide

SrO

Barium oxide

BaO

For general remarks, see the comments on the transport properties of MgO on p. 659. The transport of charge carriers in CaO has been discussed in various models, e.g. polaron band conduction and hopping conduction through compensated semiconducting samples, and also a considerable contribution from ionic conductivity has been taken into account. From measurements of the oxygen pressure dependence of the conductivity of undoped CaO, it is concluded that n-type conduction occurs at low pressures (< 10−2 –10−4 mbar) and that p-type conduction occurs at higher pressures (> 10−2 –1 mbar). In some cases this conclusion is confirmed by Hall and thermoelectric measurements. For intermediate pressures, it is supposed that the lattice disorder (presumably of Schottky type) gives rise to predominantly ionic conduction The transport of charge carriers has been discussed in various models as in the case of CaO (see above). It is supposed that the dominating scattering mechanism is optical-mode scattering The electrical transport has been discussed mainly on the assumption that it is due to electronic conduction. The ionic contribution is small. Polaron conduction and predominant optical-mode scattering are assumed

Table 4.1-129 Electrical conductivity σ and electron mobility µn of oxides of Ca, Sr, and Ba Crystal

Calcium oxide Strontium oxide Barium oxide

Conductivity

CaO SrO BaO

Fig. 4.1-148

Electron mobility µn at temperature (cm2 /V s) (K)

at O2 pressure (mbar)

8 5 5

< 10−6 < 10−6 < 10−6

700 700 600

Remarks

Single crystals, Hall mobility Single crystals, Hall mobility Polycrystals, Hall mobility

Table 4.1-130 Thermal conductivity κ of oxides of Ca, Sr, and Ba Crystal Calcium oxide Strontium oxide Barium oxide

CaO SrO BaO

663

Temperature (K)

κ (W/cm K)

Remarks

300 300 300

0.3 0.1 0.03

See Fig. 4.1-147 for temperature dependence See Fig. 4.1-147 for temperature dependence See Fig. 4.1-147 for temperature dependence

664

Part 4

Functional Materials

Part 4 1.3

κ (W/cm K)

σ (Ω–1 cm–1) 1

10

BaO 10 –1

1 10 –2 σ 10 –3

MgO CaO

S (mV K–1) 2.0

10 –4

SrO

S

10–1 10 –5

1.5

BaO σ

10 –6 10–2 80 102

2

4

6

8

10 –7

103 T (K)

Fig. 4.1-147 MgO, CaO, SrO, BaO. Temperature de-

pendence of the thermal conductivity κ of single crystals [1.124]. Dashed lines, κ ∝ T −1

10 –8 0.5

1.0

0.5

S

0.7

0.9

1.1

0 1.3 1.5 –3 –1 (10 K )

T–1

Fig. 4.1-148 BaO. Electrical conductivity σ (solid lines)

and thermoelectric power S (dashed lines) of two crystals vs. 1/T [1.125]. pO = 3 × 10−5 mbar. n-type conduction 2 at temperatures below the discontinuity

D. Electromagnetic and Optical Properties Table 4.1-131. Table 4.1-131 Dielectric constant ε of oxides of Ca, Sr, and Ba Crystal Calcium oxide Strontium oxide Barium oxide

Temperature (K) CaO SrO BaO

273

296

ε(0)

ε(∞)

Remarks

3.27

Capacitance measurement at 1 kHz and 10 kHz Compilation

12.01 (10)

3.903–4.197

Calculated from refractive-index values in the spectral range 624–436 nm

Semiconductors

1.3 II–VI Compounds

Part 4 1.3

4.1.3.4 Zinc Compounds A. Crystal Structure, Mechanical and Thermal Properties Tables 4.1-132 – 4.1-139.

Table 4.1-132 Crystal structures of zinc compounds Crystal Zinc oxide Zinc sulfide Zinc selenide Zinc telluride a

ZnO ZnS ZnSe ZnTe

Space group

Crystal system

Structure type

Figure

4 C6v Td2 Td2 Td2

hex fcc fcc fcc

Wurtzite Zinc blende Zinc blende Zinc blende

Fig. 4.1-130 Fig. 4.1-131a Fig. 4.1-131 Fig. 4.1-131

P63 mc F43m F43m F43m

At room temperature, ZnS bulk material consists predominantly of the cubic phase, often with hexagonal inclusions, leading to polytypic material. Epitaxial ZnS has mostly been grown on GaAs and thus has pseudomorphically assumed the cubic structure of the substrate material. In this section, all data refer to the cubic modification unless explicitly stated otherwise.

Table 4.1-133 Lattice parameters of zinc compounds Crystal

Lattice parameters (nm)

Zinc oxide

Temperature

a = 0.3249 (6)

ZnO

Remarks X-ray diffraction

c = 0.52042 (20) Zinc sulfide

ZnS

a = 0.54053

RT

X-ray diffraction

Zinc selenide

ZnSe

a = 0.5667 (4)

300 K

X-ray diffraction

Zinc telluride

ZnTe

a = 0.60882

RT

X-ray diffraction

Table 4.1-134 Densities of zinc compounds Crystal

Density (g/cm3 )

Temperature

Remarks Hydrostatic weighing

Zinc oxide

ZnO

5.67526 (19)

293 K

Zinc sulfide

ZnS

Cubic: 4.088

RT

Hexagonal: 4.087

RT

Zinc selenide

ZnSe

5.266

Zinc telluride

ZnTe

5.636

Shock wave experiment 298 K

Table 4.1-135 Elastic constants cik (in GPa) of zinc compounds Crystal Zinc oxide

ZnO

c11 (GPa)

c13 (GPa)

c33 (GPa)

c44 (GPa)

c66 (GPa)

Remarks

206 (4)

118 (10)

211 (4)

44.3 (10)

44.0 (10)

ZnO film on Si substrate, Brillouin scattering

Table 4.1-135 Elastic constants cik (in GPa) of zinc compounds, cont. Crystal Zinc sulfide

ZnS

Zinc selenide

ZnSe

Zinc telluride

ZnTe

c11 (GPa)

c12 (GPa)

c44 (GPa)

Temperature

Remarks

103.2 (5)

64.6 (5)

46.2 (4)

293 K

Resonance method

53.6 (23)

39.4 (12)

40.9 (6)

30.8 (3)

90.3 (19) 72.2 (2)

665

Brillouin scattering RT

Brillouin scattering

666

Part 4

Functional Materials

Part 4 1.3

a)

a (Å)

c (Å) 6.264

3.825 ZnS (hex)

c

3.823

6.256

3.821

6.248

Fig. 4.1-149a,b ZnS, hexagonal. (a) Lattice parameters a and c vs. temperature; (b) molar volume and c/a ratio vs. temperature [1.126]

a 3.819

3.817

b) Vm (cm3)

Two points With silicone grease

23.84 Vm c/a 1.640

23.80 c/a 23.76

1.638

23.72 0

70

140

210

280

1.636 350 T (K)

Table 4.1-136 Melting point Tm of zinc compounds Crystal

Melting point Tm (K) ZnO

2242 (5)

Zinc sulfide

ZnS

1991

Zinc selenide

ZnSe

1799

Zinc telluride

ZnTe

1563 (8)

Zinc oxide

Remarks

Under normal pressure, ZnS sublimes before melting

Table 4.1-137 Linear thermal expansion coefficient α of zinc compounds Crystal Zinc oxide

ZnO

Expansion coefficient α (K−1 )

Temperature (K)

Remarks

αparall c :2.92 × 10−6

399

Interferometric and capacitance methods

αperpend c :4.75 × 10−6

300

Zinc sulfide

ZnS

See Fig. 4.1-149

Zinc selenide

ZnSe

7.4 × 10−6

300

ZnTe

0.083 × 10−6

300

Zinc telluride

Polycrystal, capacitance dilatometer

1.3 II–VI Compounds

Semiconductors

Crystal

Zinc oxide

ZnO

Zinc sulfide

ZnS

Zinc selenide ZnSe

Heat capacity

Debye temperature ΘD

Temperature Remarks

c p (J/mol K)

(K)

(K)

440 (25)

300

45.358

352

77

45.882

351

298

51.88

339 (2)

298

180 (6)

Zinc telluride ZnTe

93–298

Part 4 1.3

Table 4.1-138 Heat capacities and Debye temperatures of zinc compounds

Calorimetric data Zinc blende lattice, ΘD calculated from c p Wurtzite lattice; ΘD calculated from c p ΘD from X-ray intensities from powders

Table 4.1-139 Phonon frequencies/wavenumbers at symmetry points for zinc compounds. Zinc oxide (ZnO), fundamental

optical modes, T = 300 K, from Raman spectroscopy; zinc sulfide (ZnS), T = 300 K; zinc selenide (ZnSe), from Raman spectroscopy and luminescence; zinc telluride (ZnTe), RT, from neutron scattering ZnO Mode

Symmetry point

Wavenumber (cm−1 )

ν˜

E2

101

ν˜

E2

437

ν˜ TO

E1, perp c

ν˜ TO

ZnS Mode

Symmetry point

Wavenumber (cm−1 )

ν˜ LO

Γ

350

ν˜ TO

Γ

274

407

ν˜ LO

X

332 (1)

A1, parall c

380

ν˜ TO

X

318 (1)

ν˜ LO

E1, perp c

583

ν˜ LA

X

212 (1)

ν˜ LO

A1, parall c

574

ν˜ TA

X

88 (1)

ν˜ LO

L

334 (1)

ν˜ TO

L

298 (1)

ν˜ LA

L

192 (1)

ν˜ TA

L

72 (1)

ZnSe Mode

Symmetry point

Phonon energy (meV)

hνLO

Γ1

30.99

hν TO

Γ15

25.17

hνLA

Γ

hν TA hνLO

ZnTe Mode

Symmetry point

Frequency (THz)

νLO

Γ

6.20 (5)

ν TO

Γ

5.30 (7)

19.8

νLO

X

5.51 (10)

Γ

8.0

ν TO

X

5.21 (10)

X

27.64

νLA

X

4.29 (5)

hν TO

25.54

ν TA

X

1.62 (2)

hνLA

23.55

νLO

L

5.39 (5)

27.77

ν TO

L

5.20 (9)

25.54

νLA

L

4.06 (5)

ν TA

L

1.25 (2)

hνLO

L

hν TO hν

W3

24.9

hν

W1

18.59

hν

W2

11.53

hν hν hν

W2 W4

W4

26.53 14.26 26.41

667

668

Part 4

Functional Materials

Part 4 1.3

B. Electronic Properties Tables 4.1-140 – 4.1-145. Table 4.1-140 First Brillouin zones of zinc compounds

Band Structures of Zinc Compounds.

Zinc oxide (ZnO) (Fig. 4.1-150) The topmost valence band (Γ5 + Γ1 ) is split owing to crystal-field splitting and spin–orbit coupling into three spin-degenerate states (Γ7 , Γ9 , Γ7 ). The exciton states formed with holes in these valence band states are referred to as the A, B, and C excitons, respectively. Owing to the negative spin–orbit coupling (there is a contribution from Zn 3d states), the positions of the edges of the two highest valence band states are reversed as compared with other II–VI compounds with the wurtzite structure. The conduction band edge, originating from the 4s states of Zn, possesses Γ7 symmetry. Zinc sulfide ZnS (Fig. 4.1-150) Cubic ZnS is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin zone (Γ). When spin–orbit splitting is taken into account, the topmost valence band state Γ15v splits into Γ8v and Γ7v ; further splitting into A, B, and C levels is caused by the crystal field. E (eV) 12.5

M6 L1,3

10.0

Γ1

M4

L1,3

H1,2

A1,3

ZnO

M1

Γ3

L2,4 L1,3

–5.0

Zinc sulfide

ZnS

Fig. 4.1-133

Zinc selenide

ZnSe

Fig. 4.1-133

Zinc telluride

ZnTe

Fig. 4.1-133

Zinc selenide ZnSe (Fig. 4.1-151) Zinc selenide is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin zone (Γ). The topmost valence band (Γ15 ) is split owing to spin–orbit coupling into a fourfold (Γ8 ) and a twofold (Γ7 ) state. Zinc telluride ZnTe (Fig. 4.1-152) Zinc telluride is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin zone (Γ). The topmost valence band (Γ15 ) is split owing to spin–orbit coupling into a fourfold (Γ8 ) and a twofold (Γ7 ) state.

10.0

K2

A ∆ Γ

M4 M3

5.0

S H P K

Σ M

H3 Γ6

H1,2

A1,3

M1

H3

Γ3

Eg

0 K3

A5,6

M2 M3 M1

2.5

– 2.5

K2 K1

– 5.0

K3

–7.5

– 7.5

–10.0

– 10.0

–12.5 A

E (eV) ZnS (cubic)

A1,3

Γ5 Γ1

–2.5

Fig. 4.1-132

K1 K3

H3

Γ1

2.5

L1,3

ZnO

7.5

5.0

0

Figure

Zinc oxide

Γ5 A5,6

M3 M3

7.5

Γ6

Crystal

– 12.5 R

L U M

Σ

Γ ∆ A

S

H P K

T

Γ – 15.0 L

Fig. 4.1-150 Band structure of zinc oxide and cubic zinc sulfide

Γ

X

W

Γ K Wave vector k

1.3 II–VI Compounds

Semiconductors

E (eV)

E (eV)

L4,5

Γ8

L6

10

Γ8

ZnSe

Γ7

8

Γ7

6

X7 L6

Γ12

∆1

6

X6

3 Γ6

Γ6

4

Γ8

2

Γ8 Γ7

L6

X7

Γ7

0

Γ15

∆1

Σ1 Γ15

V1 X1

L1

V2

Λ1

K2 K1 Σ1 K1

Σ1

K1

Σ2

K2

Σ1

K1

Γ1

Λ3 ∆3+∆4 ∆1

–4

Γ15

L3

V1

–2

X6

Γ1

K Σ1 K2 1

X3

L6 –6

Σ2

Λ1 L3 Λ3

∆3+∆4 ∆1

Γ15

X6

–3

Λ1

L1

a = 6.089 Å

Γ1

0 L4,5

Λ3

X5

ZnTe

Γ1

Γ12

L1

∆1

∆2

Λ1

X5 V 1

Σ1

X3 V2

L1 K1

–6 Zn 3d

–9

–8 X6

L6

– 10 Γ6

– 12

Γ6 – 12

L

Λ

Γ

∆

X U,K

Σ Γ Wave vector k

Fig. 4.1-151 Band structure of zinc selenide

∆1

Γ1

Γ

X1 V1

X

L1

W

Λ1

L

Γ1

Γ

Σ1

K1

K Wave vector k

Fig. 4.1-152 Band structure of zinc telluride

Table 4.1-141 Energy gaps of zinc compounds Band gap (eV)

Crystal Zinc oxide

ZnO

Zinc sulfide

ZnS

Zinc selenide Zinc telluride

ZnSe ZnTe

E gA E gB E gC E g, dir E g, dir E g, dir E g, dir E g, dir

Between bands

3.4410 (1) 3.4434 (1) 3.4817 (2) 3.723 (1) 3.78 3.76 2.8222 (1) 2.3945 2.35

Temperature (K) 6

Γ15v and Γ1c Γ8v and Γ6c Γ7v and Γ6c Γ8v and Γ6c Γ8v and Γ6c Γ8v and Γ6c

300 295 298 6 1773

Cadmium sulfide

CdS

1750

Under pressure p > 3.85 bar

Cadmium selenide

CdSe

1537

Assessed

Cadmium telluride

CdTe

1366.6 (70)

Mean of experimental values

Table 4.1-155 Linear thermal expansion coefficient α of cadmium compounds Crystal

Expansion coefficient α (K−1 )

Temperature (K)

Remarks

Cadmium oxide

CdO

14 × 10−6

300–770

Dilatometer measurements

Cadmium sulfide

CdS

See Fig. 4.1-165 for temperature dependence

Cadmium selenide

CdSe

Cadmium telluride

CdTe

4.96 × 10−6

20–420

677

Part 4 1.3

9.0

1.3 II–VI Compounds

678

Part 4

Functional Materials

Part 4 1.3

Table 4.1-156 Heat capacity c p and Debye temperature ΘD of cadmium compounds Crystal

Cadmium oxide

CdO

Heat capacity c p (J/mol K)

Temperature (K)

43.639

298.15

Debye temperature ΘD (K)

See Fig. 4.1-166 for temperature dependence Calculated from X-ray diffraction measurements T = 298–1678 K From elastic constants Monocrystalline sample, T = 400–700 K T = 0K Polycrystalline sample, T = 300–530 K Single crystal, X-ray diffraction

255 (6) Cadmium sulfide

CdS

55.10

300

Cadmium selenide

CdSe

49.58

300

Cadmium telluride

CdTe

25.63

300

Remarks

219.32 181.7 140 (3)

Table 4.1-157 Phonon frequencies/wavenumbers at symmetry points for cadmium compounds. Cadmium oxide (CdO), Fundamental optical-mode frequencies; cadmium sulfide (CdS), 25 K; cadmium selenide (CdSe), 300 K, from infrared and Raman spectroscopy; cadmium telluride (CdTe), 300 K, from inelastic neutron scattering CdO Mode ν˜ O ν˜ ΛO ν˜ LO ν˜ LO ν˜ TO CdSe Mode ν¯ LO, 1 ν¯ TO, 1 ν¯ LO, 2 ν¯ TO, 2 ν¯ TA

Symmetry point

Frequency (THz)

Temperature (K)

Γ Γ L X X

7.85 15.83 14.4 15.6 7.2

300 300 2 2 2

Symmetry point

Wavenumber (cm−1 )

Γ1 , parallel to c Γ5 , perpendicular to c Γ5 , perpendicular to c Γ1 , parallel to c A3

210 169 212 166 43.5

B. Electronic Properties Tables 4.1-158 – 4.1-164. Table 4.1-158 First Brillouin zones of cadmium com-

pounds Crystal Cadmium oxide

Figure CdO

Fig. 4.1-133

Cadmium sulfide

CdS

Fig. 4.1-132

Cadmium selenide

CdSe

Fig. 4.1-133

Cadmium telluride

CdTe

Fig. 4.1-133

CdS Mode

Symmetry point

Wavenumber (cm−1 )

ν¯ LO ν¯ LO, 1 ν¯ TO, 1 ν¯ TO, 1 ν¯ LO, 2 ν¯ TO, 3 CdTe Mode

Γ5 , perpendicular to c Γ1 , parallel to c Γ5 , perpendicular to c Γ1 , parallel to c Γ6 , perpendicular to c Γ6 , perpendicular to c

307 305 242 234 256 43

Symmetry point

Frequency (THz)

νLO ν TO νLO ν TA νLO ν TAO νLA ν TA

Γ Γ X X L L L L

5.08 (10) 4.20 (10) 4.44 (6) 1.05 (3) 4.33 (6) 4.33 (7) 3.25 (8) 0.88 (3)

Semiconductors

1.3 II–VI Compounds

Cadmium oxide (CdO) (Fig. 4.1-167) The lowest conduction band has its minimum at the Γ1 point in the center of the Brillouin zone. Within an energy range of a few tenths of an electron volt above its bottom, the band is isotropic but highly nonparabolic. The nonparabolicity is revealed by the strong dependence of the optical electron mass on the electron concentration. The lowest conduction band is separated from the higher bands by a small gap. The valence band consists of several branches, with maxima at L3 and Σ. Cadmium sulfide (CdS) (Fig. 4.1-168) Hexagonal CdS is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin zone (Γ). The topmost valence band (Γ5 + Γ1 ) is split owing to the crystal field and spin–orbit coupling into three spin-degenerate states. The exciton states formed with holes in these valence band states are referred to as the A, B, and C excitons, respectively. Cadmium selenide (CdSe) See Fig. 4.1-170. Cadmium telluride (CdTe) (Fig. 4.1-169) Cadmium telluride is a direct-gap semiconductor with the smallest energy gap at the center of the Brillouin zone (Γ). The topmost valence band is split owing to spin–orbit coupling into a fourfold (Γ8 ) and a twofold (Γ7 ) state. E (Ry) 1.5

E (eV)

∆2

L5'

Z4

K1

Γ25' Z1 K4 ∆2 ∆1 L4' Z 3 Γ2' W2 1.0 K3 L3 Z4 W3 K 1 W1 K1 L1 0.5 Z1 Γ1

0

Γ15

∆5

– 0.5

Λ1 Γ25'

Λ3

Γ2'

Λ1

L4'

Z4

L1

Q1'

8

Q1 Q1

L1,3

CdS (hex) 6

L1,3

Γ15

W1 K4 K1 W3 K3

Λ1 L2'

Q1'

4

Λ3 L3

Q1

2

Q1 Q1

0

– 1.0 Γ12 Γ25

– 1.5

∆5 ∆2'

Γ1

∆1

Γ

∆

L1 Z1 L2,5 Z2 L3 Z3 Z4 L1 Z1

X Z W

K

Γ12

Λ3 L3

Γ25'

Λ3 L3 Λ1

Γ1

W2' K1

Σ

Γ

A1,3

Γ6

A5,6

H1,2

K1 K3 K2

M3 M1

H3 Γ3

Γ1

Λ1 L1

W2' K1 W1' K2 W1 K4 W3 K3 K1

Γ5 Γ1

A1,3

L1,3

Z3 ∆1 ∆2

M3 M4

M3

Γ1 L5' Z1

CdO

L3'

∆1

∆1

– 2.0

Σ2

Σ3

Λ1

L2'

Q1' Q1 Q1 Q1' Q1 Q1'

Λ L Q W Wave vector k

Fig. 4.1-167 Band structure of cadmium oxide

L2,4

M2 M1 M3

L1,3

M3

–2 –4 A

R

Γ6 Γ1

M4 M3

L U M

Γ5

A5,6

H3

A5

H1,2

Γ ∆ A

K3K2

H3 K1

Γ3

Σ

K3

S

H P K T Γ Wave vector k

Fig. 4.1-168 Band structure of hexagonal cadmium sulfide

Part 4 1.3

Table 4.1-159 Band structures of cadmium compounds

679

680

Part 4

Functional Materials

Part 4 1.3

a) E (eV)

b)

L4,5 6 L6

Γ8

Γ8 CdTe

Γ7

L6

X6

2 0 L4,5 –2

Γ7

X7

4 Γ6

Γ6

Γ8

Γ8 X7

Γ7

L6

Γ7

X6

–4

X6

L6 –6 –8

X6

L6 – 10

Γ6

– 12 L

Λ

Γ

Γ6 ∆

X

U,K

Σ

Γ0 Wave vector k

0.5

1.0 1.5 g (states/eV atom)

Fig. 4.1-169a,b CdTe. (a) Band structure and (b) electron E (eV) 12 W2 9 W2 W4 6 W3

L1

density of states from a pseudopotential calculation [1.144]. Dashed curve: Experimental data

Γ1

Γ1 X3

CdSe (cubic) L1 Γ15 L3

X3

Σ1

W1 3

X1

L1

0 W3 – 3 W2 W1

L3

Γ15

Γ1 Γ15

Γ1 Σ2

X5

Γ15

X3 L1

–6

–9

L1 W4

X1 Γ1

Γ1

– 12 Cd 4d energy – 15

W

L

Γ

X

K

Γ Wave vector k

Fig. 4.1-170 Band structure of cubic cadmium selenide

Semiconductors

1.3 II–VI Compounds

Crystal Cadmium oxide

CdO

Band gap (eV)

Between bands

Temperature (K)

Remarks

(1) E g, ind

1.09 (5)

Σ3v and Γ1c

100

Thermoreflectance

300

Band gaps of the three subbands;

(2) E g, ind

Cadmium sulfide

CdS

Cadmium selenide CdSe Cadmium telluride CdTe

0.84

L3v and Γ1c

E g, dir A E g, dir

2.28 2.482

Γ15v and Γ1c Γ9v and Γ7c

E gB E gC E g, dir E g, dir

2.496 2.555 1.74 1.475

Γ7v and Γ7c Γ7v and Γ7c E0 Γ8v and Γ6c

Ellipsometry 300 RT

Ellipsometry Photoelectrochemistry

Table 4.1-161 Spin–orbit splitting energy ∆so of cadmium compounds Splitting energy (meV)

Crystal Cadmium selenide Cadmium telluride

CdSe CdTe

Bands

470 950 (20)

Γ7v to Γ78

Temperature (K)

Remarks

300

Calculation Photoemission

Table 4.1-162 Effective masses of electrons (in units of the electron mass m 0 ) for cadmium compounds Crystal

Quantity

Mass

Cadmium oxide

CdO

mn

0.33–0.46

Temperature (K) 81

Cadmium sulfide Cadmium selenide Cadmium telluride

CdS CdSe CdTe

mn mn m n [110] m n [100] m n [111]

0.25 0.12 0.096 (3) 0.094 (4) 0.095 (4)

300

Remarks Comparison of low-temperature mobilities, n = 0.4–6.3 × 1019 cm−3 Thermoelectric power Calculation Cyclotron resonance

1.5 1.8 1.8

Table 4.1-163 Effective masses of holes (in units of the electron mass m 0 ) for cadmium compounds Crystal Cadmium sulfide

CdS

Cadmium selenide

CdSe

Cadmium telluride

CdTe

Quantity

Mass

Temperature (K)

Remarks

mA p, perpend

0.7 (1)

1.6

Exciton magnetoabsorption

mA p, parall

5 2.14 0.9 1.7 0.16 0.18 0.16 0.81 (5) 0.12 (2)

m p, heavy [111] m p, heavy [100] m p, heavy [110] m p, light [111] m p, light [100] m p, light [110] m p, heavy [110] m p, light [110]

Calculation

1.5

Cyclotron resonance

Table 4.1-164 g-factors in the conduction band (gc ) and valence band (gv ) for cadmium compounds Crystal Cadmium oxide Cadmium sulfide

Cadmium selenide Cadmium telluride

CdO CdS

CdSe CdTe

Quantity

g-factor

Temperature (K)

Remarks

gc gc, perpend gc, parall A gv, parall

1.806 (5) 1.78 (5) 1.72 (10) 1.15 (5)

77 1.6

Electron spin resonance measurements Exciton absorption (for the letters A, B, C see CdS band structure, Fig. 4.1-168)

B gv, perpend g gc

0.8 0.23 1.652

16 1.8 1.5

Lineshape analysis of excitonic polaron reflectivity Calculation Spin-flip Raman measurements

Part 4 1.3

Table 4.1-160 Energy gaps of cadmium compounds (for the letters A, B, C see CdS band structure, Fig. 4.1-168)

681

682

Part 4

Functional Materials

Part 4 1.3

C. Transport Properties Tables 4.1-165 – 4.1-167. Table 4.1-165 Electronic transport, general description

Cadmium oxide (CdO) Owing to a high degree of nonstoichiometry, CdO is generally a highly degenerate n-type semiconductor. The conductivity is related to an excess of Cd in the lattice. Usually the electron concentration is several times 1019 cm−3 . Values of the electrical resistivity at 300 K range from 1.2 to 1.5 × 10−3 Ω cm. Cadmium sulfide (CdS) Electrical transport in CdS is performed by electrons in the Γ7 conduction band and holes in the Γ9 valence band. Because of compensation effects during the preparation of the samples and the large ratio µn /µp > 10, CdS is normally n-type conducting; p-type conductivity is observed only in a few special cases. The carrier concentration depends on the impurity or defect content and on temperature. Furthermore, the carrier concentration can be changed markedly by illumination: CdS is known to be a model substance for photoconductivity. Cadmium selenide (CdSe) Electrical transport in CdSe is governed by electrons in the Γ7 conduction band and holes in the Γ9 valence band. CdSe is mainly n-type conducting, owing to compensation effects during the preparation of the samples and to a ratio of the mobilities of electrons and holes of order 10. The carrier concentration depends on the impurity or defect content and on temperature. Furthermore, it depends strongly on irradiation. Photoconductivity in CdSe can be produced by electromagnetic illumination (photon energy > band gap) and by high-energy particles. Cadmium telluride (CdTe) CdTe bulk crystals can be doped to become n- or p-type conductive. High-resistivity crystals (ρ > 109 Ω cm) can be obtained under various growth and doping conditions. Table 4.1-166 Electron and hole mobilities µn and µp of cadmium compounds µn (cm2 /V s)

Crystal Cadmium oxide Cadmium sulfide

CdO CdS

180 160 >10 000

Cadmium selenide CdSe

660 5000 200

µp (cm2 /V s)

15

40 Cadmium telluride CdTe 38 000

Ga

46 500

Hf

80

Hg

10.49

ΘD (K)

99.9999

1390

0.21

0.517

2.805

209

0.69

1.0833

5.93

325

0.60

0.128

1.27

256

2.21

4.154

41.1

87

1.81

In

9000

3.4087

28.15

109

1.672

Ir

>2000

0.1125

1.6

425

3.19

4.87

9.8

151

9.8

0.1

35.0

210

10.2

La

>99.9

Lu

15

Mo

17 000

Nb

0.916

500–16 500

9.25

Os

0.66

Pa

1.4

9.686

460

1.83

276

7.80

7.0

500

2.35

206

Pb

15 000

7.196

80.34

105

3.36

Re

1700

1.697

20.1

415

2.35

0.493

6.9

580

2.8

Ru Sn

3.722

30.55

195

1.78

Ta

29–120

4.47

82.9

258

6.15

Tc

80–100

7.77

411

6.28

Th Ti

1200 >99.9

1.374

16.0

165

4.32

0.40

5.6

415

3.3

17.65

Tl

53

2.38

V

24–430

5.46

U

0.68

W

57 000

141

140 10.0

87.5

1.47

383

9.82

206

10.60

0.0154

0.115

383

0.90

Zn

99.9999

0.857

5.41

310

0.66

Zr

99.9

0.63

4.7

290

2.77

Table 4.2-2 Pressure dependence of the superconductivity of metals [2.1] Metal Al As I

Pressure range a (102 MPa) 0–62 Θf ), ν0 decreases as the temperature decreases toward Θf , that is, the phonon mode softens

Ferroelectrics and Antiferroelectrics

ferroelectrics, as seen in Figs. 4.5-8 and 4.5-9. The dielectric constant at the Curie point at 1 GHz is not so small in displacive ferroelectrics, as seen in Fig. 4.5-10, where the critical slowing-down seems to be related to cluster boundary motion, and the dielectric constant at the Curie point at 1 GHz contains a contribution from the soft phonon as observed in millimeter spectroscopy (Fig. 4.5-11).

4.5.3.1 The 72 Families of Ferroelectrics

a. Perovskite-Type Family (Family Number 1). The name of this group is derived from the mineral perovskite (CaTiO3 ). The perovskite-type oxides are cubic (e.g. CaTiO3 above 1260 ◦ C and BaTiO3 above 123 ◦ C) or pseudocubic with various small lattice distortions (e.g. CaTiO3 below 1260 ◦ C and BaTiO3 below 123 ◦ C). Ceramics made from solid solutions of perovskitetype oxides are the most useful ferroelectrics in high-capacitance capacitors, piezoelectric elements, and infrared sensors. Ceramic thin films are useful in memory devices. The pure compounds are divided into simple perovskite-type oxides and complex perovskite-type oxides. Simple perovskite-type oxides have the chemical formula A1+ B5+ O3 or A2+ B4+ O3 . Complex perovskite-type oxides have chemical formu3+ 2+ 2+ 6+ las expressed by (A1+ 1/2 A1/2 )BO3 , A (B1/2 B1/2 )O3 ,

909

5+ 2+ 2+ 5+ 2+ 3+ 6+ A2+(B3+ 1/2B1/2 )O3 , A (B1/3 B2/3 )O3 , A (B2/3 B1/3 )O3 , A(B, B,B )O3 , or (A, A )(B, B )O3 . Among the complex perovskite-type oxides, most of the Pb(B, B )O3 type oxides show a diffuse phase transition such that the transition point is smeared out over a relatively wide temperature range and exhibits a characteristic dielectric relaxation; these materials therefore are called “relaxors”.

b. LiNbO3 Family (Family Number 2). This family contains LiNbO3 and LiTaO3 . Their chemical formulas are similar to those of the simple perovskite oxides, but their structures are trigonal, unlike the perovskite oxides. c. Stibiotantalite Family (Family Number 5). The members of this family are isomorphous with the mineral stibiotantalite Sb(Ta, Nb)O4 . They have the common chemical formula ABO4 , where A stands for Sc, Sb, or Bi and B for Ta, Nb, or Sb. d. Tungsten Bronze-Type Family (Family Number 6).

The tungsten bronzes are a group of compounds having the chemical formula Mx WO3 , where M stands for an alkali metal, an alkaline earth metal, Ag, Tl, etc. (e.g. Nax WO3 , where x = 0.1–0.95). Most of them exhibit a bronze-like luster. The tungsten bronze-type oxides consist of crystals isomorphous with tungsten bronze, including a simple type (e.g. Pb1/2 NbO3 ) and a complex type (e.g. Ba2 NaNb5 O15 ). Single crystals (not ceramics) are used for technological applications. e. Pyrochlore-Type Family (Family Number 7). The members of this family are isomorphous with the mineral pyrochlore, CaNaNb2 O6 F. Most of the members have the general chemical formula A2 B2 O7 or A2 B2 O6 (anion-deficient compounds), where A stands for Cd, Pb, Bi, etc. and B for Nb, Ta, etc. f. Sr2 Nb2 O7 Family (Family Number 8). This family contains high-temperature ferroelectrics such as Nb2 Ti2 O7 and La2 Ti2 O7 . Their Curie points are higher than 1500 ◦ C. g. Layer-Structure Family (Family Number 9). The common chemical formula of these oxides is (Bi2 O2 )(An−1 Bn O3n−1 ), where A stands for Ca, Sr, Ba, Pb, Bi, etc., B stands for Ti, Nb, Ta, Mo, W, etc., and n varies from 1 to 9. The crystal structure is a repeated stacking of a layer of (Bi2 O2 )2+ and a layer of (An−1 Bn O3n−1 )2− , which can be approximately repre-

Part 4 5.3

In the Landolt–Börnstein data collection, ferroelectric and antiferroelectric substances are classified into 72 families according to their chemical composition and their crystallographic structure. Some substances which are in fact neither ferroelectric nor antiferroelectric but which are important in relation to ferroelectricity or antiferroelectricity, for instance as an end material of a solid solution, are also included in these families as related substances. This subsection surveys these 72 families of ferroelectrics presented in Landolt–Börnstein Vol. III/36 (LB III/36). Nineteen of these families concern oxides [5.1, 2], 30 of them concern inorganic crystals other than oxides [5.3], and 23 of them concern organic crystals, liquid crystals, and polymers [5.4]. Table 4.5-1 lists these families and gives some information about each family. Substances classified in LB III/36 as miscellaneous crystals (outside the families) are not included. In the following, remarks are made on 13 of the families, labeled by the letters a – m in Table 4.5-1. The corresponding family numbers are repeated in the headings.

5.3 Classification of Ferroelectrics

910

Part 4

Inorganic Crystals Oxides [5.1, 2] Family Name Nr. 1 Perovskite-type family (90, 40; 11) a 2 LiNbO3 family (2, 2; 1) b 3 YMnO3 family (6, 6; 0) 4 SrTeO3 family (1, 1; 1) 5 Stibiotantalite family (7, 6; 0) c

Inorganic Crystals other than Oxides [5.3] Family Name Nr.

Organic Crystals, Liquid Crystals, and Polymers [5.4] Family Name Nr.

20 SbSI family (11, 4; 1)

50 SC(NH2 )2 family (1, 1; 1)

21 22 23 24

51 52 53 54

TlS family (1, 1; 0) TlInS2 family (5, 2; 0) Ag3 AsS3 family (2, 1; 0) Sn2 P2 S6 family (2, 2; 0)

Part 4 5.3

6 Tungsten bronze-type family (141, 21; 2) d 7 Pyrochlore-type family (19, 2; 0) e 8 Sr2 Nb2 O7 family (6, 5; 1) f 9 Layer-structure family (36, 16; 0) g 10 BaAl2 O4 -type family (1, 1; 0)

25 KNiCl3 family (3, 3; 0)

55

26 BaMnF4 family (6, 6; 1)

56

27 HCl family (2, 2; 1) 28 NaNO2 family (2, 2; 1)

57 58

29 CsCd(NO2 )3 family (2, 2; 0)

59

11 LaBGeO5 family (1, 1; 0)

30 KNO3 family (4, 3; 1)

60

12 LiNaGe4 O9 family (2, 2; 0)

31 LiH3 (SeO3 )2 family (7, 5; 0)

61

13 Li2 Ge7 O15 family (1, 1; 1)

32 KIO3 family (3, 3; 0)

62

14 Pb5 Ge3 O11 family (1,1; 0)

33 KDP (KH2 PO4 ) family (12, 12; 3)

63

15 5PbO · 2P2 O5 family (1, 1; 0) (exact chemical formula unknown) 16 Ca3 (VO4 )2 family (2, 2; 0)

34 PbHPO4 family (2, 2; 1)

64

35 KTiOPO4 family (23, 15; 0)

65

17 GMO (Gd2 (MoO4 )3 ) family (5, 5; 1) 18 Boracite-type family (28, 14; 1) h

36 CsCoPO4 family (5, 5; 0)

66

37 NaTh2 (PO4 )3 family (2, 2; 0)

67

19 Rb3 MoO3 F3 family (4.4; 0)

38 Te (OH)6 · 2NH4 H2 PO4 · (NH4 )2 HPO4 family (1, 1; 0) 39 (NH4 )2 SO4 family (22, 21; 1) 40 NH4 HSO4 family (9, 4; 1)

68

41 NH4 LiSO4 family (9, 6; 1) 42 (NH4 )3 H(SO4 )2 family (2, 2; 1) 43 Langbeinite-type family (16, 5; 1) i 44 Lecontite (NaNH4 SO4 · 2H2 O) family (2, 2; 0) 45 Alum family (16, 15; 0) j 46 GASH (C(NH2 )3 Al(SO4 )2 · 6H2 O) family (9, 9; 0) 47 Colemanite (Ca2 B6 O11 · 5H2 O) family (1, 1; 0) 48 K4 Fe(CN)6 · 3H2 O family (4, 4; 0) 49 K3 BiCl6 · 2KCl · KH3 F4 family (1, 1; 0)

71 72

69 70

CCl3 CONH2 family (1, 1; 0) Cu(HCOO)2 · 4H2 O family (1, 1; 0) N(CH3 )4 HgCl3 family (6, 5; 0) (CH3 NH3 )2 AlCl5 · 6H2 O family (3, 2; 0) [(CH3 )2 NH2 ]2 CoCl4 family (3, 2; 0) [(CH3 )2 NH2 ]3 Sb2 Cl9 family (5, 5; 0) (CH3 NH3 )5 Bi2 Cl11 family (2, 2; 0) DSP (Ca2 Sr(CH3 CH2 COO)6 ) family (3, 3; 1) (CH2 ClCOO)2 H · NH4 family (2, 2; 0) TGS ((NH2 CH2 COOH)3 · H2 SO4 ) family (3, 3; 1) NH2 CH2 COOH · AgNO3 family (1, 1; 0) (NH2 CH2 COOH)2 · HNO3 family (1, 1; 0) (NH2 CH2 COOH)2 · MnCl2 · 2H2 O family (1, 1; 0) (CH3 NHCH2 COOH)3 · CaCl2 family (2, 2; 1) (CH3 )3 NCH2 COO · H3 PO4 family (3, 3; 0) (CH3 )3 NCH2 COO · CaCl2 · 2H2 O family (1, 1; 1) Rochelle salt (NaKC4 H4 O6 · 4H2 O) family (3, 2; 1) LiNH4 C4 H4 O6 · H2 O family (3, 2; 1) k C5 H6 NBF4 family (1, 1; 0) 3C6 H4 (OH)2 · CH3 OH family (1, 1; 0) Liquid crystal family (97, 90; 2) l Polymer family (5, 5; 1) m

Ferroelectrics and Antiferroelectrics

J

5.3 Classification of Ferroelectrics

911

Table 4.5-1 The 72 families of ferroelectric materials. The number assigned to each family corresponds to the number used in LB III/36. The numbers in parentheses (NSub , NF+A ; n) after the family name serve the purpose of conveying some information about the size and importance of the family. The numbers indicate the following: NSub , the number of pure substances (ferroelectric, antiferroelectric, and related substances) which are treated as members of this family in LB III/36; NF+A , the number of ferroelectric and antiferroelectric substances which are treated as members of this family in LB III/36; n, the number of representative substances from this family whose properties are surveyed in Sect. 4.5.4. For some of these families, additional remarks are needed: for instance, because the perovskite-type oxide family has many members and consists of several subfamilies; because the liquid crystal and polymer families have very specific properties compared with crystalline ferroelectrics; and because the traditional names of some families are apt to lead to misconceptions about their members. Such families are marked by letters a–m following the parentheses, and remarks on these families are given under the corresponding letter in the text in Sect. 4.5.3.1

sented by a chain of n perovskite-type units of ABO3 perpendicular to the layer. h. Boracite-Type Family (Family Number 18). Bo-

racite is a mineral, Mg3 B7 O13 Cl. The boracite-type family contains crystals isomorphous with the mineral, 1− and has the chemical formula M2+ 3 B7 O13 X , where M2+ stands for a divalent cation of Mg, Cr, Mn, Fe, Co, Ni, Cu, Zn, or Cd, and X1− stands for an anion of Cl, Br, or I.

j. Alum Family (Family Number 45). The alums are compounds with the chemical formula M1+ M3+ (SO4 )2 · 12 H2 O, where M1+ is a monovalent cation and M3+ is a trivalent cation. Ferroelectricity has been found for the monovalent cations of NH4 , CH3 NH3 , etc. and the trivalent cations of Al, V, Cr, Fe, In, and Ga. This family contains a few isomorphous selenates, M1+ M3+ (SeO4 )2 · 12 H2 O. k. LiNH4 C4 H4 O6 · H2 O Family (Family Number 68). This

family contains two ferroelectrics, LiNH4 C4 H4 O6 · H2 O and LiTlC4 H4 O6 · H2 O. The polar directions of the two ferroelectrics are different from each other.

l. Liquid Crystals (Family Number 71). Ferroelectric and antiferroelectric liquid crystals are very useful as fast display elements.

A. Ferroelectric liquid crystals (family number 71A). Ferroelectric liquid crystals are defined as liquid

m. Polymers (Family Number 72). Polyvinylidene flu-

oride (CH2 CF2 )n and its copolymers with trifluoroethylene (CHFCF2 )n , etc. are ferroelectric. Ferroelectric polymers are usually prepared as thin films in which crystalline and amorphous regions coexist. The ferroelectric hysteresis loop originates from reversal of the

Part 4 5.3

i. Langbeinite-Type Family (Family Number 43). This family consists of crystals which are basically isomorphous with K2 Mg2 (SO4 )3 (langbeinite), and have 2+ the common chemical formula M1+ 2 M2 (SO4 )3 , where 1+ M stands for a monovalent ion of K, Rb, Cs, Tl, or NH4 , and M2+ stands for a divalent ion of Mg, Ca, Mn, Fe, Co, Ni, Zn, or Cd.

crystals which exhibit a ferroelectric hysteresis loop like that shown in Fig. 4.5-1. Unlike ferroelectric crystals, however, ferroelectric liquid crystals generally have no spontaneous polarization in the bulk state. The chiral smectic phase denoted by Sm C∗ (e.g. of DOBAMBC) consists of many layers, each of which has a spontaneous polarization parallel to the layer plane, but the spontaneous polarization varies helically in different directions from layer to layer, so that the bulk has no spontaneous polarization as a whole. A sufficiently strong electric field causes a transition from the helical phase to a polar phase. Under an alternating electric field, the helical structure does not have a chance to build up owing to the delay in the transition. Instead, a direct transition occurs between the induced polar phases, resulting in a hysteresis loop of the type shown in Fig. 4.5-1. Accordingly, the hysteresis loop may be regarded as one in which the linear part of the antiferroelectric hysteresis shown in Fig. 4.5-2 is eliminated. It should be noted, however, that the helical structure disappears and two stable states with parallel and antiparallel polarizations appear, similar to the domain structure of a ferroelectric crystal, when a liquid crystal is put in a cell which is thinner than the helical pitch [5.52]. B. Antiferroelectric liquid crystals (family number 71B). The phase denoted by Sm C∗A (e.g. of MHPOBC) exhibits a double hysteresis of the type shown in Fig. 4.5-2, and a liquid crystal showing this phase is called antiferroelectric [5.53].

912

Part 4

spontaneous polarization in the crystalline regions. The electric-field distribution is expected to be complex in the thin film because of the interposition of the amorphous regions. A ferroelectric hysteresis loop can be observed when the ratio of the volume of the crystalline regions to the total volume is relatively large (e.g. more than 50%). The coercive field is larger (e.g.

> 50 MV/m) than that of solid ferroelectrics (usually a few MV/m or smaller). The ferroelectric properties depend sensitively upon the details of sample preparation, for example the use of melt quenching or melt extrusion, the annealing temperature, or the details of the poling procedure. Polymer ferroelectrics are useful for soft transducers.

4.5.4 Physical Properties of 43 Representative Ferroelectrics

Part 4 5.4

This section surveys the characteristic properties of 43 representative ferroelectrics with the aim of demonstrating the wide variety in the behavior of ferroelectrics. The 43 representative ferroelectrics are selected from 29 of the above-mentioned families. The presentation is mainly graphical. Most of the figures are reproduced from LB III/36, where the relevant references can be found. Table 4.5-2 summarizes the meaning of the symbols frequently used in the figure captions and indicates the units in which the data are given. To facilitate to get more information on each representative substance in LB II/36, the number assigned to the substance in LB III/36 is given in parenthesis fol-

lowing its chemical formula, e.g., KNbO3 (LB number 1A-2).

4.5.4.1 Inorganic Crystals Oxides [5.1, 2] Perovskite-Type Family KNbO3 (LB Number 1A-2). This crystal is ferroelec-

tric below about 418 ◦ C. Further phase transitions take place at about 225 ◦ C and about −10 ◦ C, retaining ferroelectric activity. The crystal has large electromechanical coupling constants and is useful in lead-free piezoelectric elements and SAW (surface acoustic wave) filters in communications technology (Fig. 4.5-13,4.5-14).

Table 4.5-2 Symbols and units frequently used in the figure captions

a, b, c a∗ , b∗ , c∗ Ec f Ps T κ κ  , κ  κij κa , κb , κc κ(hkl) κ[uvw] κT κS Θf

unit cell vector, units Å unit cell vector in reciprocal space, units Å−1 coercive field, units V/m frequency, units Hz = 1/s spontaneous polarization, units C/m2 temperature, units K or ◦ C dielectric constant (or relative permittivity) = ε/ε0 , where ε is the permittivity of the material and ε0 is the permittivity of a vacuum. κ is a dimensionless number real and imaginary parts of the complex dielectric constant κ ∗ = κ  + iκ  . κ  and κ  are both dimensionless numbers component of dielectric-constant tensor; dimensionless numbers κ measured along a, b, c axes; dimensionless numbers κ measured perpendicular to the (hkl) plane; dimensionless number κ measured parallel to the [uvw] direction; dimensionless number κ of free crystal, i. e. κ measured at constant stress T; dimensionless number κ of clamped crystal, i. e. κ measured at constant strain S; dimensionless number ferroelectric transition temperature, units K or ◦ C

5.4 Physical Properties of 43 Representative Ferroelectrics

Ferroelectrics and Antiferroelectrics

913

κ

Dielectric constant  5000 f = 10 kHz

3850

–1

E = 500 Vm 4000

3845 3000 3840 2000 3835 1000

0 –200 –100

3830 0

100

200

300 400 500 Temperature T (° C)

Fig. 4.5-12 KNbO3 . Dielectric constant κ versus tempera-

0

1

2

3

4

5

6

7 T (K)

Fig. 4.5-14 KTaO3 . Real part of dielectric constant κ  ver-

sus T . f = 1 kHz

ture T KTaO3 (LB Number 1A-5). KTaO3 is cubic at all tem-

1.50

νp (1012 Hz)

Part 4 5.4

peratures, and its dielectric constant becomes very large at low temperatures without a phase transition (Fig. 4.5-14). It is generally believed that this behavior is related to the zero-point lattice vibrations. Replacement of Nb by Ta generally lowers drastically the ferroelectric Curie temperature , as seen by comparing Fig. 4.5-14 with Fig. 4.5-12. (This effect is well demonstrated later in Figs. 4.5-39 and 4.5-40).

1.25 1.00 0.75

SrTiO3 (LB Number 1A-8). This crystal is cubic at room

temperature and slightly tetragonal below 105 K. The phase transition at 105 K is caused by softening of the lattice vibration mode at the (1/2, 1/2, 1/2) Bril-

0.50 0.25

40

Ps (10–2 C m–2)

Ec (102 V m–1)

0 100

30

Ps

Ec 10 150

140

160

180

200

220

240 T (K)

Fig. 4.5-15 SrTiO3 . νP versus T . νP is the frequency of the

20

0 100

120

200

250

300

350

2000

R25 (Γ25 ) optical phonon

1000

louin zone corner (Fig. 4.5-15) without an appreciable dielectric anomaly. At very low temperatures, the dielectric constants become extraordinarily high without a phase transition (Fig. 4.5-16), owing to softening of the optical phonon at the origin of the Brillouin zone (Fig. 4.5-17). It is generally believed that the absence of a low-temperature transition is related to zero-point lat-

0 400 T (° C)

Fig. 4.5-13 KNbO3 . Ps and E c versus T . Measurements were made by applying the electric field parallel to the pseudocubic [100] direction

914

Part 4

Fig. 4.5-16 SrTiO3 . κ(111) , κ(110) , and κ(100) versus T at

κ (104)

f = 50 kHz. κ(111) , κ(110) , and κ(100) are slightly different from each other in the tetragonal phase

2.25

2.00

tice vibrations as in KTaO3 . Solid solutions of SrTiO3 are useful as ceramic thin films in memory devices. 1.75 50 kHz 1.50

κ ( 103)

10 1.25

8

1.00

6

κa

4 0.75

κ(111) κ (110)

0.50

κc

0

κ(100)

0.25

Part 4 5.4

0

2

0 –160 –120

– 80

– 40

0

40

80

120 T (° C)

Fig. 4.5-18 BaTiO3 . κa and κb versus T . κa and κb are

0

50

100

150

200

250

300 T (K)

the values of κ along the a and b axes, respectively, of the tetragonal phase

0.30

Ps (C m–2)

ν0 (1012 Hz) 3

0.25

0.20

2

0.15 1

0.10 0 0

50

100

150

200

250

300

350 T (K)

Fig. 4.5-17 SrTiO3 . ν0 versus T . ν0 is the frequency of

the soft phonon at q = 0. Open circles: inelastic neutron scattering. Filled circles: Raman scattering. The solid curve is 194.4 κ 1/2 and the dashed curve is 0.677(T − T0 )1/2 , with T0 = 38 K

0.05

0

0

20

40

60

80

100

120

140 T (°C)

Fig. 4.5-19 BaTiO3 . Ps versus T in the tetragonal phase.

Ps is parallel to the c axis

5.4 Physical Properties of 43 Representative Ferroelectrics

Ferroelectrics and Antiferroelectrics

BaTiO3 (LB Number 1A-10). BaTiO3 is the most exten-

sively studied ferroelectric crystal. It is ferroelectric below about 123 ◦ C, where the crystal symmetry changes from cubic to tetragonal. Further phase transitions take place from tetragonal to orthorhombic at about 5 ◦ C and to rhombohedral at about −90 ◦ C (Figs. 4.5-18 to 4.5-20). It is believed that the ferroelectric transition

4.840

ν (1012 Hz) T= 230 ° C 430 ° C

3.872

[ζ 00] LA

2.904

Ps (10–2 C m–2)

Zone boundary

TA

30 20

915

1.936

10

TO 0.968

0 –140 –120 –100

– 80

– 60

– 40

– 20

0 20 T (°C)

Fig. 4.5-20 BaTiO3 . Ps[001] versus T below 20 ◦ C, where

Ps[001] is the component of the spontaneous polarization parallel to the c axis in the tetragonal phase

κ '' (arb. units) 0

10

20 20

40

60

80

100

10 8 6

T = 408 K T = 423 K T = 473 K T = 553 K

4 2

1 8 6 4 2

10–1 8 6 4 2 –2

10

0

3

66

12

18

24

30

36 42 ν (1011 Hz)

Fig. 4.5-21 BaTiO3 . κ  versus ν. Parameter: T . κ  is

the imaginary part of κ obtained from the hyper-Raman spectrum. Curves: calculations based upon the classical dispersion oscillator model. c: light velocity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 0.9 ζ (Å–1)

Fig. 4.5-22 BaTiO3 . Phonon dispersion relation deter-

mined by neutron scattering along the [100] direction in the cubic phase. ν is the phonon frequency. LA, longitudinal acoustic branch; TA, transverse acoustic branch; TO, transverse optical branch. The frequency of the TO branch is lower (softer) at 230 ◦ C than at 430 ◦ C, indicating mode softening

is caused by softening of an optical mode at the center of the Brillouin zone. Hyper-Raman scattering studies support this model (Figs. 4.5-21 and 4.5-22). The results of neutron scattering studies favor this model (Fig. 4.5-23), but the measurement was not easy owing to the intense elastic peaks (Fig. 4.5-24a). These elastic peaks indicate marked cluster formation in the vicinity of the Curie point. As discussed in Sect. 4.5.3, there seem to be two components contributing to the dielectric constant measured in the vicinity of the Curie point: a component due to the soft mode and another one due to the motion of the cluster boundaries. Presumably the two components suggested by infrared and hyper-Raman scattering data correspond to these two components. For theoretical studies of the phase transitions, readers should refer to [5.7]. Solid solutions of BaTiO3 are the most useful ferroelectrics in ceramic condensers and as thin films in memory devices. When the temperature is raised above 1460 ◦ C, cubic BaTiO3 performs another phase transition to a hexagonal structure. This hexagonal phase can be quenched

Part 4 5.4

40

ν / c (cm–1) 120 140

0

916

Part 4

∆ν0, Γ (1012Hz) 8

∆ν0 / c (cm–1) 250

7 200

6

Fig. 4.5-23 BaTiO3 . ∆ν0 and Γ versus T , obtained from hyper-Raman scattering in the cubic phase. ∆ν0 and Γ are the optical mode frequency and damping constant, respectively. The different symbols (brown and gray) show results from different authors. ∆ν0 decreases as the temperature decreases to the Curie point, showing the presence of mode softening. c: ligth velocity

5 150

10 000

κ

4

8000 100

3

6000 2 50 1 0

∆ν0 Γ 300

400

500

600

2000

700

0

800 T (K)

0 0

a) I (103 counts)

100

200

300

400

500

600 T (° C)

Part 4 5.4

Fig. 4.5-25 PbTiO3 . κ versus T

3.6 3.2

4000

Q = (H, K, O) a*

Cubic BaTiO3 150 °C

80

K = 0.1 K = 0.2 K = 0.3

2.8 K

Ps (10–2 C m–2)

60

2.4 ν=0

H

2.0

40

L

1.6

20

1.2 0

0.8

100

200

300

400

500 T (° C)

Fig. 4.5-26 PbTiO3 . Ps versus T

0.4 0

Fig. 4.5-24a,b BaTiO3 . Triple-axis neutron spectrometer

b) 0.50

ν = 0.97 × 1012 Hz

0.25 0 3.7

0

3.8

3.9

4.0

4.1

4.2

4.3 H

scans at constant frequency across the sheet of diffuse scattering at 150 ◦ C. The path of the scans is shown in the inset. (a) shows the elastic scan (ν = 0), where the high background level is due to nuclear incoherent scattering. (b) Ineleastic scan (ν = 0.97 × 1012 Hz)

Ferroelectrics and Antiferroelectrics

4000

κc

κ –1c (10–4)

7

f = 1 MHz

3500

5.4 Physical Properties of 43 Representative Ferroelectrics

the crystal useful in infrared sensors. Solid solutions with other perovskite-type oxides provide good dielectric and piezoelectric materials (see PZT, PLZT, and (PbTiO3 )x (Pb(Sc1/2 Nb1/2 )O3 )1−x below).

6

κc

κ –1c

3000

5 2500 4 2000 3 1500 2 1000

PbZrO3 (LB Number 1A-15). This crystal is antiferroelectric below about 230 ◦ C (Fig. 4.5-27), exhibiting a typical antiferroelectric hysteresis loop (Fig. 4.5-28). Solid solutions of this substance are very important in technological applications (see PZT and PLZT below). Pb(Mg1/3 Nb2/3 )O3 (LB Number 1B-d4). This crystal

exhibits a broad ferroelectric phase transition with an average transition temperature of −8 ◦ C determined by the maximum of the low-frequency dielectric constant. A marked frequency dispersion of the

1

500

κ (10–3)

ΘP

0 175

200

225

250

275

0 300 325 T (°C)

20 16 12

PbTiO3 (LB Number 1A-11). This crystal is ferroelec-

Hz kHz kHz kHz kHz MHz

κ 0.16

8 tan δ

4

tric below about (Figs. 4.5-25, 4.5-26). The spontaneous polarization is large (Fig. 4.5-26) and thus the pyroelectric coefficient is large, which makes 5

0

–150

–100

–50

0

0 100 T (° C)

50

Fig. 4.5-29 Pb(Mg1/3 Nb2/3 )O3 (ceramic). κ and tan δ versus T . Parameter: f

–1

Ecrit (10 V m )

50

20

40

Ps (10–2 C m–2)

15 x= 0.05

30 P

0.04 0.03 0.02

10

20 E

10 0 200

0.08

κ

500 ◦ C

5

Ecrit

205

210

0.005

215

220

225

230

0 75

T (°C)

Fig. 4.5-28 PbZrO3 . E crit versus T . E crit is the critical field of the antiferroelectric hysteresis loop

100

125

150

175

200

225

250 T (°C)

Fig. 4.5-30 Pb(Zr1−x Tix )O3 (ceramic). Ps versus T . Pa-

rameter: x

Part 4 5.4

to room temperature by relatively rapid cooling. This hexagonal BaTiO3 also shows ferroelectric activity below −199 ◦ C.

tan δ 100 2 10 60 600 1

Fig. 4.5-27 PbZrO3 (single crystal). κc and κc−1 versus T

60

917

918

Part 4

dielectric constant occurs around the transition temperature. These is a typical behavior of a relaxor (Fig. 4.5-29).

35

Pb(Zr,Ti)O3 (LB Number 1C-a62). PbZrO3 is antiferro-

30

electric, as described above, while a small addition of PbTiO3 induces a ferroelectric phase (Fig. 4.5-30). PZT (LB Number 1C-a63). Solid solutions Pb(Ti1−x Zrx )O3 with x = 0.5–0.6 are commonly called PZT. They have very large electromechanical coupling constants and are widely utilized as piezoelectric elements. Thin ceramic films are useful in memory devices (Fig. 4.5-31).

κ

– d31 (10–12 C/N)

1000

Ps (10–2 C m–2)

25 20 15 10 5 0 –25

0

25

50

75

100

800

125 150 T (° C)

Fig. 4.5-32 (Pb0.92 La0.08 )(Zr0.40 Ti0.60 )0.98 O3 (PLZT). Ps

Part 4 5.4

600

100

versus T

400

80

200

60

PLZT (LB Number 1C-c66). The acronym PLZT means La-modified PZT. Hot-pressed ceramic PLZT is transparent and useful for optical switches and similar devices (Fig. 4.5-32).

0

40 d31

These solid solutions have very large electromechan20

0 pi (10–4 C/(K m2)) 4

Pr (10–2 C/m2) 45

(PbTiO3 )x (Pb(Sc1/2 Nb1/2 )O3 )1−x (LB Number 1C-b34).

Pi

35

3

25

2

0.5

kp T = 25 °C

0.4 0.3 0.2 0.1

Pr

15 0.3

0.4

0.5

0.6

1 0.7 0.8 x (PbZrO3)

Fig. 4.5-31 Pb(Ti1−x Zrx )O3 2% Zr(Mn1/3 Bi2/3 )O3 as an

additive (ceramic). κ, pi , d31 , and Pr versus x. pi is the pyroelectric coefficient, d31 is the piezoelectric strain constant, and Pr is the remanent polarization (see Fig. 4.5-1)

0 0 0.1 0.2 0.3 0.4 x = 0 corrsponds to Pb(Sc1/2Nb1/2) O3

0.5

0.6 0.7 x (PbTiO3)

Fig. 4.5-33 (PbTiO3 )x (Pb(Sc1/2 Nb1/2 )O3 )1−x (ceramic).

kp versus x. kp is the planar electromechanical coupling factor

Ferroelectrics and Antiferroelectrics

105

5.4 Physical Properties of 43 Representative Ferroelectrics

919

ical coupling factors, and are utilized for piezoelectric actuators and similar devices (Fig. 4.5-33).

κT

8 6

LiNbO3 Family LiTaO3 (LB Number 2A-2). This crystal is ferroelectric

4

below 620 ◦ C. The coercive field is large. The crystal is useful for piezoelectric elements, for linear and nonlinear optical elements, and for SAW filters in communications technology (Figs. 4.5-34 and 4.5-35).

f = 10 kHz 2

104

8 6

SrTeO3 Family SrTeO3 (LB Number 4A-1). This crystal is ferroelectric

4

κ

T 11

between 312 and 485 ◦ C (Figs. 4.5-36 and 4.5-37).

2

103

κ

8

104

6 4

2

103

κ'22T

102 8 6

10

κ11T

4

κ'11T

2

κ'33T

Part 4 5.4

2

10 10 0

100

200

300

400

500

600

700 800 T (°C)

T and κ T versus T . f = 10 kHz Fig. 4.5-34 LiTaO3 . κ11 33

1.0

Ps /Ps(0)

1 0

100

200

300

400

500

600 T (° C)

Fig. 4.5-36 SrTeO3 . κ versus T . f = 10 kHz

Ps (C m–2)

0.8 0.04

0.6

0.03

0.4

0.02

0.2

0 –100

0.01

0

100

200

300

400

500

600 700 T (°C)

0 200

320

360

400

Fig. 4.5-35 LiTaO3 . Ps /Ps (0) versus T . Ps (0) is the value

of Ps at 0 K (about 0.5 C m−2 )

Fig. 4.5-37 SrTeO3 . Ps versus T

440

480

520 T (° C)

920

Part 4

Tungsten Bronze-Type Family Ba2 NaNb5 O15 (BNN) (LB Number 6B-a7). This crystal is

l33 (10–5 m) 3.5

ferroelectric below about 580 ◦ C. The crystal structure is modulated below 300 ◦ C. This material is utilized for optical second-harmonic generation and in optical parametric oscillators (Fig. 4.5-38).

l33 3.0 2.5 50

Ba2 Na(Nb1−x Tax )5 O15 (BNNT) (LB Number 6C-b30). The transition temperature varies over a wide temperature range as x varies from 0 to 1.0 (Fig. 4.5-39).

d33 (relative)

d33 (relative)

40

Sr2 Nb2 O7 Family Sr2 (Nb1−x Tax )2 O7 (LB Number 8B-6). These solid solu-

tions can be made over the whole range of x = 0–1.0, and the Curie point varies over a wide temperature range from 1342 ◦ C to −107 ◦ C (Fig. 4.5-40). The solid solutions are very useful as high-temperature dielectric materials, especially because they do not contain Pb, which is volatile at high temperatures.

30

20

10

Li2 Ge7 O15 Family Li2 Ge7 O15 (LB Number 13A-1). This crystal is ferroelectric

0 0

100

300

200

400

500

600 T (° C)

below 283.5 K. The sign of the spontaneous polarization is reversed around 130 K (Figs. 4.5-41 and 4.5-42).

Fig. 4.5-38 Ba2 NaNb5 O15 . d33 and l33 versus T . d33 is the

Part 4 5.4

nonlinear optical susceptibility (relative value), and l33 is the coherence length

GMO (Gd2 (MoO4 )3 ) Family Gd2 (MoO4 )3 (GMO) (LB Number 17A-3). Three crys-

tal structures of GMO are known, α, β, and γ . The β structure is stable above 850 ◦ C but can be obtained at room temperature as a metastable state by 1000

Θ (K) 1500

Θ (° C)

750 1000

500

Θf 500

250 0 0 0.0

0.2

0.4

0.6

0.8

1.0 x

Fig. 4.5-39 Ba2 Na(Nb1−x Tax )5 O15 . Ferroelectric transi-

tion temperature Θ versus x. Brown circles and gray circles represent data measured by different authors

– 273

0

0.2

0.4

0.6

0.8

1.0 x

Fig. 4.5-40 Sr2 (Nb1−x Tax )2 O7 . Ferroelectric transition temperature Θf versus x. The lower curve shows another phase transition temperature

Ferroelectrics and Antiferroelectrics

κc

5.4 Physical Properties of 43 Representative Ferroelectrics

921

Ps (10–2 C m–2)

50

0.30 f = 10 kHz

40

Ps (10–2 C m–2)

0.25

0.08

0.20

0.06

0.15

0.04

0.10

0.02

30

20

10 Θf 0 270

275

280

285

290

295

300

305

310 315 T (K)

0.05

Near the transition

0 426

428

430

432

Fig. 4.5-41 Li2 Ge7 O15 . κc versus T . f = 10 kHz 0 Ps (10 C m ) –5

–2

50

Ebias= 420 kV m–1

0

50

434

T (K)

100 150 200 250 300 350 400 450 T (K)

Fig. 4.5-43 Gd2 (MoO4 )3 . Ps versus T

0

Boracite-Type Family Ni3 B7 O13 I (LB Number 18A-23). This crystal is

ferroelectric and ferromagnetic below about 60 K (Figs. 4.5-44, 5-45, 5-46): a rare example where both ferroelectric and ferromagnetic spontaneous polarizations

–25

Ebias= – 420 kV m–1

75

Ps (10–5 C m–2)

–50 0

50

100

150

200

250

300 T (K)

Fig. 4.5-42 Li2 Ge7 O15 . Ps versus T . Ps was determined

60 45

by pyroelectric-charge measurement 30

rapid cooling. Ferroelectric activity takes place in this metastable β-GMO below 159 ◦ C. The phase transition is the indirect type IIIop discussed in Sect. 4.5.3. S The dielectric constant of the clamped crystal (κc in Fig. 4.5-6) shows no anomaly at the transition point. The ferroelectric phase results from a phonon instability at the (1/2, 1/2, 0) Brillouin zone corner of the parent tetragonal phase. Anharmonic coupling to the

15 0

0

20

40

60

80

100 T (K)

Fig. 4.5-44 Ni3 B7 O13 I. Ps versus T . Ps was measured

with the specimen parallel to the cubic (001) plane

Part 4 5.4

25

resulting antiparallel displacements produces a spontaneous strain, which in turn causes a spontaneous polarization through the normal piezoelectric coupling (Fig. 4.5-43).

922

Part 4

Fig. 4.5-45 Ni3 B7 O13 I. σr versus T . σr is the remanent

σr (A m2 kg–1) 140 [110]

Hc = 20 × 106 Am–1  [110]

120 100

take place simultaneously. There is a magnetoelectric effect, where the magnetic polarization is reversed by reversal of the electric polarization and vice versa.

80 60 40

4.5.4.2 Inorganic Crystals Other Than Oxides [5.3]

20 0

23

magnetization. The sample was cooled down to 4.2 K in a magnetic field of 1.6 × 106 A/m parallel to [100] prior to the measurement

30

0

40

50

60

70 T (K)

low 20 ◦ C. The phase transition is of the displacive type, a relatively rare characteristic in nonoxide materials. The crystal is photoconductive (Figs. 4.5-47 and 4.5-48).

' , κ ''33 κ 33 ' κ 33

BaMnF4 Family BaMnF4 (LB Number 26A-2). This crystal exhibits a di-

19.93

22 19.66

100 kHz

21

55

' κ 33

SbSI Family SbSI (LB Number 20A-7). SbSI is ferroelectric be-

60

65 T (K)

' κ 33

Part 4 5.4

20

electric anomaly at about 242 K (Fig. 4.5-49). The coercive field is very large. The crystal is antiferromagnetic below 25 K (Fig. 4.5-50). The dielectric constant varies depending upon the magnetic field at low temperatures (Fig. 4.5-51).

21.60

19 21.15

8

18

κc (104)

1 MHz

55

60

65 T (K)

(1/κc ) (10– 4) 2.0

f = 1 kHz

7

17

6

1.5

κc

16

1/κc

5 15

1.0

4 14 1.0

3

κ ''33 0.5

2

0.5

1

0 0

50

100

150  κ33

200

250

300 T (K)

 versus T . f = Fig. 4.5-46 Ni3 B7 O13 I. and κ33  100 kHz. The insets show details of κ33 versus T at 100 kHz and 1 MHz around Θf

0

Θp 0

10

20

30

40

Fig. 4.5-47 SbSI. κc and 1/κc versus T

50

0 60 T (°C)

5.4 Physical Properties of 43 Representative Ferroelectrics

Ferroelectrics and Antiferroelectrics

923

χ magn m (10–9 m3/ mol)

Ps (10–2 C m–2)

25

χ⊥

350

H⊥b H  b

300

20

250

15 200

χ 150

10



100

5

50 0

0 5

0

10

15

20 T (° C)

100

150

200

250

300 T (K)

Fig. 4.5-50 BaMnF4 . χmagn m versus T . χmagn m is the

magnetic susceptibility, and χ⊥ and χ are the magnetic susceptibilities measured perpendicular and parallel, respectively, to the b axis

Fig. 4.5-48 SbSI. Ps versus T

κa

50

0

κc

21 12.095

17

12.090

f = 9.75 kHz

Part 4 5.4

κa

f = 100 kHz

19

H = 8.36 × 104 A/m 2.51 ×105 A/m

8.8

15

κa

12.085

13

8.6

11

8.4

H=0 12.080

κc

9 0

50

100

150

200

8.2 300 250 T (K)

12.075 12.070

Fig. 4.5-49 BaMnF4 . κa and κc versus T 12.065 0

20

22

24

26 T (K)

Fig. 4.5-51 BaMnF4 . κa versus T . Parameter: magnetic field H. f = 9.75 kHz

924

Part 4

HCl Family HCl (LB Number 27A-1). This crystal is ferroelectric be-

low 98 K. The chemical formula is the simplest one among all known ferroelectrics. The coercive field is large (Figs. 4.5-52 and 4.5-53).

κ0

30

NaNO2 Family NaNO2 (LB Number 28A-1). This crystal is ferroelectric

below 163.9 ◦ C (Figs. 4.5-54 and 4.5-55). The spontaneous polarization results from orientational order of ◦ the NO− 2 ions. Between 163.9 and 165.2 C, the crystal structure is incommensurately modulated with a wave vector δa∗ , where δ varies from 0.097 to 0.120 with increasing temperature.

20

κ

Tmelt

f = 10 kHz

10 8 6 5

103

4 3 0

80

100

120

140

160

180

200 T (K)

Fig. 4.5-52 HCl (polycrystalline). κ0 versus T . κ0 is the

static dielectric constant

Part 4 5.4

4.0

κb 102

Ps (10–2 C m–2)

κc

3.5

10

κa

3.0 120

130

140

150

160

170

2.5

180 190 T (°C)

Fig. 4.5-54 NaNO2 . κa , κb , and κc versus T

2.0

Ps (10–2 C m–2)

1.5

12

1.0

9 0.5 0 0.97

6 0.98

0.99

1.00

Fig. 4.5-53 HCl.

1.01

1.02

Ps versus T/Θf obtained pyroelectric-current measurement. Θf = 98 K

1.03 T/Θf

3

from 0

Fig. 4.5-55 NaNO2 .

Ps versus pyroelectric-charge measurement

T , determined by

0

30

60

90

120

150

180 T (°C)

Ferroelectrics and Antiferroelectrics

κc

105

70 f = 100 kHz 60

104

50

103

40 II

III

5.4 Physical Properties of 43 Representative Ferroelectrics

925

κ κc

102

I

30

10

20

κa 50

100

150

200

250

300 T (K)

Fig. 4.5-58 KH2 PO4 . κa and κc versus T . f = 800 Hz

10 0 0

25

50

75

100

125

150

175 200 T (° C)

Ps (10–2 C m–2)

4

Fig. 4.5-56 KNO3 . κc versus T

10.0

3

Ps (10–2 C m–2)

2 7.5

1

5.0

1.25

0 115.0

117.5

120.0

122.5

125.0

127.5 130.0 T (° C)

Fig. 4.5-57 KNO3 . Ps versus T

KNO3 Family KNO3 (LB Number 30A-2). This crystal is ferroelectric

between about 115 and 125 ◦ C in a metastable phase III which appears on cooling. Hydrostatic pressure stabilizes this phase (Figs. 4.5-56 and 4.5-57).

KDP (KH2 PO4 ) Family KH2 PO4 (KDP) (LB Number 33A-1). KH2 PO4 is a classical and extensively studied ferroelectric crystal. It is ferroelectric below 123 K (Figs. 4.5-58 and 4.5-59). The transition is a typical ferroelectric phase transition, related to a configuration change in a three-dimensional hydrogen-bond network. Figures 4.5-61 and 4.5-60 demonstrate changes in the proton configuration associated with the phase transition. The transitions related

1.00

0.75

0.50

0.25

0 Θ f – T (K)

Fig. 4.5-59 KH2 PO4 . Ps versus (Θf − T ). Θf = 123 K

to hydrogen atom rearrangement in the hydrogen-bond network are characterized by sensitivity to deuteration and hydrostatic pressure, as demonstrated in Figs. 4.5-62 and 4.5-63, respectively. For theoretical studies of the phase transition, readers should refer to [5.7]. The crystal is useful in nonlinear optical devices. CsH2 PO4 (LB Number 33A-3). This crystal is ferroelectric below about 151.5 K. The crystal system of its paraelectric phase (monoclinic) is different from that of KH2 PO4 (tetragonal). The temperature dependence of the dielectric constant above the Curie point deviates considerably from the Curie–Weiss law, suggesting that the transition is related to one-dimensional ordering of hydrogen atoms in a hydrogen-bond network. Deuteration changes the transition temperature from 151.5 to 264.7 K (Fig. 4.5-64).

Part 4 5.4

0

2.5

926

Part 4

κ c (103) O (1) K,P O(1)

100 80 60 40

x=0

0.08 0.17

f = 3 kHz 0.29

30

O (2)

0.46 0.78

20 10 0 90

110

130

150

170

190

210

O (1)

230 250 T (K)

Fig. 4.5-62 KH2(1−x) D2x PO4 . κc versus T . Parameter: x

O(2) K,P

RbH2 PO4 -NH4 H2 PO4 (LB Number 33B-5). The mixed crystals Rb1−x (NH4 )x H2 PO4 , where 0.2 < x < 0.8, show a characteristic temperature dependence of the dielectric constants, suggesting that at low temperatures

Part 4 5.4

Fig. 4.5-60 KH2 PO4 . Fourier map of the projection of the proton distribution on (001) in the ferroelectric phase (77 K), determined by neutron diffraction. The proton distribution lies approximately on a line joining two oxygen atoms O(1) and O(2) and closer to O(1)

κ c (102) 8

7

6

8.4 × 108

p = 1.8× 108 Pa

5

a) Θf + 2 K

16.9 ×108

b) Θf – 1.3 K 4

0.2 Å

15.4 ×108

3

2

c) Θf – 10 K

d) Θf – 20 K

19.3 × 108 1 21.0 ×108 Pa

Fig. 4.5-61a–d KH2 PO4 . Change of proton distribution

above and below the Curie point Θ f , determined by neutron diffraction. Contours are all equally spaced. (a) Θf + 2 K; (b) Θf − 1.3 K; (c) Θf − 10 K; (d) Θf − 20 K

0

0

20

40

60

80

100

120

140

160

180 T (K)

Fig. 4.5-63 KH2 PO4 . κc versus T . Parameter: hydrostatic

pressure p

Ferroelectrics and Antiferroelectrics

κb

106

103

x=0 x = 0.03 x = 0.15 x = 0.57

5.4 Physical Properties of 43 Representative Ferroelectrics

927

κ f = 1592 Hz

κ(100)

102

κb

105

10

κc

4

10

1

0

60

120

180

240

360 T (K)

Fig. 4.5-66 PbHPO4 . κ(100) , κb , and κc versus T . κ(100) is

103

the dielectric constant perpendicular to the (100) plane Ps (10–2 C m–2 ) 2.0

102

300

0

100

150

200

250

300 T (K)

p (10–2 C / K m2 ) 0.15

1.6

0.12

1.2

0.09

0.8

0.06

0.4

0.03

Fig. 4.5-64 CsH2 PO4 and CsH2(1−x) D2x PO4 . κb versus

T . Parameter: x κ ''c

60 40 20

8

0 f= 6.0 MHz 31.6 MHz 218.8 MHz 1000.0 MHz 0

20

40

60

80

6 4 2 0 100 T (K)

Fig. 4.5-65 Rb0.65 (NH4 )0.35 H2 PO4 . κc and κc versus T .

Parameter: f

a local order becomes predominant in a configuration of hydrogen atoms without definite long-range order, i. e. a dipole glass state develops (Fig. 4.5-65). PbHPO4 Family PbHPO4 (LB Number 34A-1). This crystal is ferroelec-

tric below 37 ◦ C (Figs. 4.5-66 and 4.5-67). It exhibits

0 – 60

– 40

–20

0

20

40

0 60 T (°C)

Fig. 4.5-67 PbHPO4 . Ps and p versus T , measured on (100) planar specimen. p = − dPs / dT is the pyroelectric coefficient

characteristic critical phenomena, suggesting that the spontaneous polarization results from an ordered arrangement of hydrogen atoms in a one-dimensional array of hydrogen bonds. (NH4 )2 SO4 Family (NH4 )2 SO4 (LB Number 39A-1). This crystal is fer-

roelectric below − 49.5 ◦ C. The dielectric constant is practically independent of temperature above the Curie point (Fig. 4.5-68). The spontaneous polarization changes its sign at about −190 ◦ C (Fig. 4.5-69), suggesting a ferrielectric mechanism for the spontaneous polarization.

Part 4 5.4

κ c'

928

Part 4

κc 150

1450

κc

f = 10 kHz 5 × 10 2 V m–1 1400

100 200

50 150

0 –200

–150

–100

–50

0

50 T (°C)

100

Fig. 4.5-68 (NH4 )2 SO4 . κc versus T 50 Ps (10–2 C m–2) 0.7 0.62 0.6 0.5

0 –200

0.61

–150

–100

–50

0

50 T (°C)

Fig. 4.5-70 NH4 HSO4 . κc versus T . f = 10 kHz

0.60

0.4 0.59

Ps (10–2 C m–2)

0.3

Part 4 5.4

0.2

0.58 –60

–55

–50 T (°C)

0.8

0.1 0.4

0 –0.1 –260 –230 –200 –170 –140 –110

–80

–50 –20 T (°C)

Fig. 4.5-69 (NH4 )2 SO4 . Ps versus T

0 –125

–75

–50

–25

0 T (°C)

Fig. 4.5-71 NH4 HSO4 . Ps versus T

(NH4 )HSO4 Family (NH4 )HSO4 (LB Number 40A-5). This crystal is ferroelec-

−3 ◦ C

30

(NH4 )LiSO4 Family (NH4 )LiSO4 (LB Number 41A-5). This crystal is ferroelectric in the temperature range between 10 and 186.5 ◦ C (Figs. 4.5-72 and 4.5-73).

20

tric in the temperature range between −119 and (Figs. 4.5-70 and 4.5-71).

–100

(NH4 )3 H(SO4 )2 Family (NH4 )3 H(SO4 )2 (LB Number 42A-1). This crystal is ferroelectric in its phase VII below −211 ◦ C. Another Fig. 4.5-72 NH4 LiSO4 . κa and κb versus T . f = 3 kHz

κ

κa

10

0

κb

0

50

100

150

200 T (°C)

Ferroelectrics and Antiferroelectrics

Ps (10–2 C m–2)

2.5

5.4 Physical Properties of 43 Representative Ferroelectrics

929

Ps (10–2 C m–2) VII

0.8 2.0 0.6

VI

1.5 x = 0.93

x = 0.40

1.0 0.4 0.5 0.2

x = 0.90

0 –200 –175 –150 –125 –100

0 0

40

80

120

160

200 T (°C)

Fig. 4.5-73 NH4 LiSO4 . Ps versus T

–75

–50

–25 0 T (°C)

Fig. 4.5-75 ((NH4 )3 H)1−x ((ND4 )3 D)x (SO4 )2 . Ps versus

T . Parameter: x. Gray circles (for Phase VI), determined by pyroelectric measurements. Brown circles (for phase VII), determined by hysteresis loop measurements

ferroelectric phase, VI, is induced by hydrostatic pressure (Fig. 4.5-74). When H is substituted by D, phase VI appears at atmospheric pressure and the temperature of the transition to phase VII becomes higher. Figure 4.5-75

T (°C) 140 I 120

80

Ebias = at 10 kHz 0 (600 V m–1) 2000 kV m–1 3.3 GHz

12

60 II

11

40 20

10 0 –20

9

κ ''[100]

–40

0.4

VI

III –60

VII –80 –100 0

1

2

3

4

5

6

7

8 9 p (108 Pa)

Fig. 4.5-74 (NH4 )3 H(SO4 )2 . T versus p phase diagram.

0.3

0.2

0.1

p is the hydrostatic pressure. Phases VI and VII are ferroelectric   Fig. 4.5-76 (NH4 )2 Cd2 (SO4 )3 . κ[100] and κ[100] versus T

0 –200

–190

–180

–170

–160

–150

140 T (°C)

Part 4 5.4

κ '[100]

100

930

Part 4

Ps (10–2 C m–2)

104

0.8

κb f = 1 kHz E = 10 V m–1

0.6 V

103

0.4

IV II

III

0.2

I

102 0 80

82

84

86

88

90

92

94 T (K)

Fig. 4.5-77 (NH4 )2 Cd2 (SO4 )3 . Ps versus T

10

Q12 (103 m4 C–2)

100

0

140

180

220

220

300 T (K)

Fig. 4.5-79 SC(NH2 )2 . κb versus T

3

2

Ebias (106 V/m) 6 Method Pyroelectric response Hysteresis loops Dielectric constant Polarization

1

Part 4 5.4

5

Θf 0 –186

–184

–182

–180

–178

–176

–174 T (°C)

Fig. 4.5-78 (NH4 )2 Cd2 (SO4 )3 . Q 12 versus T . Q 12 is the

4

electrostrictive constant

shows temperature dependence of Ps for three values of x in ((NH4 )3 H)1−x ((ND4 )3 D)x (SO4 )2 . Langbeinite-Type Family (NH4 )2 Cd2 (SO4 )3 (LB Number 43A-13). This crystal is fer-

roelectric below about −184 ◦ C. The dielectric constants are insensitive to temperature above the transition point (Fig. 4.5-76), and the spontaneous polarization does not depend upon temperature (Fig. 4.5-77). The electrostrictive constant Q 12 , however, exhibits an anomaly at the transition point (Fig. 4.5-78).

4.5.4.3 Organic Crystals, Liquid Crystals, and Polymers [5.4]

I (Paraelectric)

3

2 Inc. 1

V (Ferroelectric) δ = 1–9

0 165

170

Inc.

175

III (δ= 1–8 ) 180

185

190

195

200 T (K)

Fig. 4.5-80 SC(NH2 )2 . E bias versus T phase diagram.

SC(NH2 )2 Family SC(NH2 )2 (LB Number 50A-1). This crystal exhibits at least five phases, I, II, III, IV, and V (Figs. 4.5-79

The value of δ means that the phase is commensurately modulated with a vector of wavenumber δc∗ . Inc., incommensurate phase

Ferroelectrics and Antiferroelectrics

5.4 Physical Properties of 43 Representative Ferroelectrics

931

κ

Ps (10–2 C m–2)

f = 10 kHz 103

3.0 2.5

κb

102

2.0 1.5

κa'

κc' 10

1.0

–160

–120

–80

–40

0

40

0.5

80 T (°C)

Fig. 4.5-83 (NH2 CH2 COOH)3 · H2 SO4 . κa , κb , and κc 0 90

110

130

150

170 T (K)

versus T . These quantities are referred to the unit cell vectors: a = a + c, b = −b, and c = −c

Fig. 4.5-81 SC(NH2 )2 . Ps versus T for phase V Ps (10–2 C m–2)

and 4.5-80). The crystal is ferroelectric in phase V (Fig. 4.5-81), and slightly ferroelectric with a very small spontaneous polarization in phase III. The crystal structure is modulated commensurately or incommensurately except for phases I and V, as indicated in Fig. 4.5-80.

4.5

DSP (Ca2 Sr(CH3 CH2 COO)6 ) Family Ca2 Sr(CH3 CH2 COO)6 (DSP) (LB Number 58A-1). This crys-

2.5

Part 4 5.4

tal is ferroelectric below about 4 ◦ C (Fig. 4.5-82). The Curie–Weiss constant is small (60 K). Critical slowingdown (see Sect. 4.5.3) takes place (Fig. 4.5-8).

4.0 3.5 3.0

2.0 1.5 1.0

Ps (10–2 C m–2)

0.5

0.3 0 100 0.2

125

150

175

200

225

250

275

300 325 T (K)

Fig. 4.5-84 (NH2 CH2 COOH)3 · H2 SO4 . Ps versus T . Ps

is parallel to the b axis. Gray circles: values determined by pyroelectric measurements. Triangles and brown circles: determined from hysteresis loop by different authors

0.1 1 3 0 –25

–20

–15

–10

–5

0

5

2 10 T (°C)

Fig. 4.5-82 Ca2 Sr(CH3 CH2 COO)6 . Ps versus T . The three curves show the effect of annealing: 1, unannealed; 2, annealed at 330 ◦ C for 60 h; 3, annealed at 330 ◦ C for 60 h and at 390 ◦ C for 5 h

932

Part 4

TGS ((NH2 CH2 COOH)3 · H2 SO4 ) Family (NH2 CH2 COOH)3 · H2 SO4 (TGS) (LB Number 60A-1). This

crystal is ferroelectric below 49.4 ◦ C (Figs. 4.5-83 and 4.5-84). Critical slowing-down takes place (Fig. 4.5-9).

(CH3 NHCH2 COOH)3 · CaCl2 Family (CH3 NHCH2 COOH)3 · CaCl2 (LB Number 64A-1). This crys-

tal is ferroelectric below 127 K (Figs. 4.5-85 and 4.5-86). The Curie–Weiss constant is small (40 K). As discussed in Sect. 4.5.3, two components are expected in the dielectric constants of displacive-type ferroelectrics: one contribution from the soft optical phonon and one contribution from cluster boundary motion. This crystal provides a good example of this situation. Softening of the optical phonon mode B2u occurs (Fig. 4.5-11), indicating that the transition is of the displacive type,

80

while critical slowing-down takes place in the GHz region (Fig. 4.5-10); this seems to take place in the contribution from cluster boundary motion. The value of the dielectric constant at the Curie point at 1.0 GHz seems to contain a contribution from the optical phonon mode. (CH3 )3 NCH2 COO · CaCl2 · 2H2 O Family (CH3 )3 NCH2 COO · CaCl2 · 2H2 O (LB Number 66A-1). This

crystal is ferroelectric below 46 K. It exhibits at least ten phase transitions (eight can be recognized in Fig. 4.5-87), and the crystal structure is commensurately or incommensurately modulated between 46 and 164 K, with a feature known as a devil’s staircase. Multiple hysteresis loops are observed in the modulated phases, as shown in Fig. 4.5-88. Rochelle Salt (NaKC4 H4 O6 · 4H2 O) Family NaKC4 H4 O6 · 4H2 O (Rochelle Salt, RS) (LB Number 67A-1). Rochelle salt was the first ferroelectric crys-

κb

tal to be discovered. It is ferroelectric between −18 and 24 ◦ C (Figs. 4.5-89 and 4.5-90). It is rare that an ordered ferroelectric phase of lower symmetry (P21 in this case) appears in an intermediate temperature range between disordered phases of the same higher symmetry (P21 21 2). Figure 4.5-91 shows X-ray evidence for such space group changes. For theoretical studies, readers should refer to [5.7].

60

Part 4 5.4

40

20

LAT (LiNH4 C4 H4 O6 · H2 O) Family LiNH4 C4 H4 O6 · H2 O (LAT) (LB Number 68A-1). Ferro-

0 50

100

150

200

250 T (K)

Fig. 4.5-85 (CH3 NHCH2 COOH)3 · CaCl2 . κb versus T .

f = 10 kHz

electric activity appears along the b axis below 106 K (Fig. 4.5-92). The dielectric constant of the clamped 105

κb f = 10 kHz

Ps (10–2 C m–2)

E = 1.2 kV/m

104

0.3 103 0.2 102 0.1 10 0 0

75

100

125

T (K)

Fig. 4.5-86 (CH3 NHCH2 COOH)3 · CaCl2 . Ps versus T

50

100

150

200

250

300 T (K)

Fig. 4.5-87 (CH3 )3 NCH2 COO · CaCl2 · 2H2 O. κb ver-

sus T

Ferroelectrics and Antiferroelectrics

Ps

P3

5.4 Physical Properties of 43 Representative Ferroelectrics

933

P

P2

P1 E5 E4

Ec

E

E3, E4

E1, E2

P (10–2 C/m2) P3 2

Ps

1 P2

P1

0 15

E (105 V/m) E2

10 E6

E5

E4

E3

E1

5 Ec 0

30

40

50

60

70

80

90

100

110

120

130 T (K)

S

crystal κ22 shows no anomaly at the transition temperature (Fig. 4.5-7), while the elastic compliances

104

103

κ 11T

exhibit a pronounced anomaly (Fig. 4.5-93). These data indicate that the ferroelectric phase transition is of the indirect type IIIac triggered by an elastic anomaly (see Sect. 4.5.3). The crystal is piezoelectric in the paraelecPs (10–3 C m–2)

f = 1 kHz 900 Hz

4

Deuterated RS

3 RS

2

10

RS

2

Deuterated RS

10 1 1 –180 –160 –140 –120 –100 –120 –80 –40 –20

0

20

40

60

0 –30

–20

–10

0

10

T (°C)

Fig. 4.5-89 NaKC4 H4 O6 · 4H2 O (RS) and NaKC4 H2 D2 O6 T versus T · 4D2 O (deuterated RS). κ11

20

30

40 T (°C)

Fig. 4.5-90 NaKC4 H4 O6 · 4H2 O (RS) and NaKC4 H2 D2 O6

· 4D2 O (deuterated RS). Ps versus T

Part 4 5.4

Fig. 4.5-88 (CH3 )3 NCH2 COO · CaCl2 · 2H2 O. Ps , E c , Pi , and E i versus T . Definitions of Pi (i = 1, 2, 3) and Ei are shown in the top figure

934

Part 4

P 2s (10–4 C2 m–4) 0.07

I (050) (arb. units) 7

14

E s 44 (10–11 m2 N–1)

12 6

0.06

E s 44

10 5

0.05

8 0.04

4

0.03

3

P 2s

E s 66 (10–11 m2 N–1)

7

320

I (050) 0.02

2

0.01

1

E s 66

5

–1 9 –2 (s55 – s (0) 55 ) (10 N m )

E s 55 (10–11 m2 N–1)

180 E s 55

15 140 0 –20

–10

0

10

20

30 T (°C)

0 200

Fig. 4.5-91 NaKC4 H4 O6 · 4H2 O. I(050) versus T . I(050) is

Part 4 5.4

the integrated intensity of the X-ray (050) reflection, which should disappear in the space group P21 21 2 below −18 ◦ C and above 23 ◦ C. The solid line is Ps2 normalized to fit to I(050)

tric phase and the elastic anomaly causes a dielectric T anomaly in the free crystal (κb in Fig. 4.5-92 and κ22 in Fig. 4.5-7), but no dielectric anomaly in the clamped S in Fig. 4.5-7). crystal (κ22

10

160

120 E E (0) –1 (s 55 – s 55 )

80

(s D55 – s D55(0))–1

5

40 ΘII–I

160

κb

0 75

100

125

150

175

200

225

0 250 T (K)

E , s E , and s E verFig. 4.5-93 LiNH4 C4 H4 O6 · H2 O. s44 55 66

120

E , s E , and s E are the shear components of the sus T . s44 55 66 elastic compliance tensor at constant electric field. The two 



E E (0) −1 and s D − s D (0) −1 , straight lines show s55 − s55 55 55 D is s where s55 55 at constant electric displacement, E (0) = 18.0 m2 N−1 , and s D (0) = 17.0 m2 N−1 s55 55

80

40

0 80

120

160

200

240

Fig. 4.5-92 LiNH4 C4 H4 O6 · H2 O. κb versus T

280 T (K)

Liquid Crystal Family DOBAMBC, p-decyloxybenzylidene p-amino 2-methylbutyl cinnamate (LB Number 71A-1 (A)) (Liquid Crystal). This liquid crystal is ferroelectric in the smec-

tic C∗ phase between about 76 and 92 ◦ C on heating. On cooling, the C∗ phase is transformed into a smectic H∗

5.4 Physical Properties of 43 Representative Ferroelectrics

Ferroelectrics and Antiferroelectrics

7.0

κ

θ (°) f = 30 Hz

+ 20

6.5

+ 10 –10

6.0

–5 0

f =110 Hz

5.5

+5

+ 10

–10

f =330 Hz

–20 E

f = 1 Hz

5.0

Fig. 4.5-97 MHPOBC. θ versus E. θ is the apparent tilt

angle. Sample cell thickness = 3 µm

f = 3 kHz

4.5 4.0

phase at about 63 ◦ C, retaining the ferroelectric activity (Figs. 4.5-94 and 4.5-95).

f = 10 kHz

3.5 50

60

70

80

90

100 T (°C)

Fig. 4.5-94 DOBAMBC. κ versus T . Parameter: f . Sample cell thickness = 2.3 µm Ps (10–5 C m–2)

Θ (deg) 30

10

MHPOBC, 4-(1-methylheptyl oxycarbonyl)phenyl 4octyloxybiphenyl-4-carboxylate (LB Number 71B1 (A)) (Liquid Crystal). Seven phases are known for this

liquid crystal. It exhibits an antiferroelectric hysteresis loop at low frequency, as shown in Fig. 4.5-96a, between a)

D

Part 4 5.4

f = 2 Hz

Θ 25

8

20 6 15

Ps 4

10 2 5 0 –35

935

–30

–25

–20

–15

–10

–5 00 T– ΘII–I (°C)

E

b) D f = 100 Hz

Fig. 4.5-95 DOBAMBC. Ps and θ versus T − ΘII−I . θ is

the apparent tilt angle, and ΘII−I is the ferroelectric transition temperature

Fig. 4.5-96a,b MHPOBC. D − E hysteresis loops ob-

tained from switching-current measurements. D is the electric displacement. Sample cell thickness = 3 µm. (a) Double hysteresis loop at 2 Hz. (b) Single hysteresis loop at 100 Hz

E

936

Part 4

κ'

Ps (10–3 C m–2) 100

0.59

80

x = 0.75

60

x = 0.65

60

40

x = 0.59

0.65

40

0.69 0.73

20 20

x=1 0

40

60

80

100

120

140 T (°C)

0

κ' 0.47

Fig. 4.5-98 ((CH2 CF2 )x (CF2 CHF)1−x )n . Ps versus T . Pa-

rameter: x. Thickness of specimen film = 50 µm

65 and 119.7 ◦ C. The antiferroelectric behavior can be best demonstrated by measuring the apparent tilt angle, as shown in Fig. 4.5-97. The hysteresis loop turns into a triple one between 119.7 and 120.6 ◦ C, and into a normal ferroelectric hysteresis loop between 120.6 and 122.1 ◦ C. The phase exhibiting the triple hysteresis loop is called “ferrielectric” by several authors.

Part 4 5

Polymer Family ((CH2 CF2 )x (CF2 CHF) 1−x )n ,Vinylidene fluoride–trifluoroethylene Copolymer, ((VDF)x (TrFE)1−x )n (LB Number 72-2) (Polymer). Random polymers (CH2 CF2 )x (CF2 CHF)1−x exhibit a ferroelectric hysteresis loop for

40 0.37 20 0.13 x=0 0

–50

0

50

100 T (°C)

κ

Fig. 4.5-99 ((CH2 CF2 )x (CF2 CHF)1−x )n . versus T . Parameter: x. f = 1 kHz. Thickness of specimen film = 50 µm

x > 0.5 (Figs. 4.5-98 and 4.5-99). Ferroelectric activity is preserved up to the melting point for x > 0.8.

References 5.1

5.2

5.3

5.4

Y. Shiozaki, E. Nakamura, T. Mitsui (Eds.): Ferroelectrics and Related Substances: Oxides: PerovskiteType Oxides and LiNbO3 Family, Landolt–Börnstein, New Series III/36 (Springer, Berlin, Heidelberg 2001) Y. Shiozaki, E. Nakamura, T. Mitsui (Eds.): Ferroelectrics and Related Substances: Oxides: Oxides Other Than Perovskite-Type Oxides and LiNbO3 Family, Landolt–Börnstein, New Series III/36 (Springer, Berlin, Heidelberg 2002) Y. Shiozaki, E. Nakamura, T. Mitsui (Eds.): Ferroelectrics and Related Substances: Inorganic Crystals Other Than Oxides, Landolt–Börnstein, New Series III/36 (Springer, Berlin, Heidelberg 2004) Y. Shiozaki, E. Nakamura, T. Mitsui (Eds.): Ferroelectrics and Related Substances: Organic Crystals, Liquid Crystals and Polymers, Landolt–Börnstein,

5.5 5.6 5.7

5.8 5.9

5.10

New Series III/36 (Springer, Berlin, Heidelberg 2005) in preparation J. Valasek: Piezoelectric and Allied Phenomena in Rochelle Salt, Phys. Rev. 15, 537 (1920) J. Valasek: Piezo-Electric and Allied Phenomena in Rochelle Salt, Phys. Rev. 17, 475 (1921) T. Mitsui, E. Nakamura, I. Tatsuzaki: An Introduction to the Physics of Ferroelectrics (Gordon and Breach, New York 1976) F. Jona, G. Shirane: Ferroelectric Crystals (Dover Publications, New York 1993) B. A. Strukov, A. P. Levanyuk: Ferroelectric Phenomena in Crystals: Physical Foundations (Springer, Berlin, Heidelberg 1998) M. E. Lines, A. M. Glass: Principles and Applications of Ferroelectrics and Related Materials (Clarendon, Oxford 1979)

Ferroelectrics and Antiferroelectrics

5.11 5.12 5.13 5.14 5.15 5.16

5.17 5.18

5.19

5.20

5.21

5.23

5.24 5.25

5.26

5.27 5.28

5.29 5.30

5.31

5.32

5.33

5.34

5.35

5.36 5.37

5.38 5.39

5.40

5.41 5.42

5.43

5.44

5.45

5.46

5.47 5.48

5.49

C. P. Araujo, J. F. Scott, G. W. Taylor (Eds.): Ferroelectric Thin Films: Synthesis and Basic Properties (Gordon and Breach, New York 1996) R. Ramesh (Ed.): Thin Film Ferroelectric Materials and Devices, Electronic Materials Science and Technology, Vol. 3 (Kluwer, Dordrecht 1997) J. F. Scott: The physics of ferroelectric ceramic thin films for memory applications, Ferroelectr. Rev. 1, 1 (1998) D. Damjanovic: Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics, Rep. Prog. Phys. 62, 1267 (1998) J. F. Scott: Ferroelectric Memories, Springer Series in Advanced Microelectronics, Vol. 3 (Springer, Berlin, Heidelberg 2000) R. M. White: Surface elastic waves, Proc. IEEE 58, 1238 (1970) G. W. Farnell, E. L. Adler: Acoustic Wave Propagation in Thin Layers. In: Physical Acoustics, Vol. 9, ed. by W. P. Mason, R. N. Thurston (Academic Press, New York 1972) pp. 35–127 A. A. Oliner (Ed.): Acoustic Surface Waves (Springer, Berlin, Heidelberg 1978) K.-Y. Hashimoto: Surface Acoustic Wave Devices in Telecommunications, Modeling and Simulation (Springer, Berlin, Heidelberg 2000) J. M. Herbert: Ferroelectric Transducers and Sensors, Electrocomp. Sci. Mon., Vol. 3 (Gordon and Breach, New York 1982) W. H. de Jeu: Physical Properties of Liquid Crystalline Materials (Gordon and Breach, New York 1980) J. W. Goodby, R. Blinc, N. A. Clark, S. T. Lagerwall, M. A. Osipov, S. A. Pikin, T. Sakurai, K. Yoshino, B. Zeks: Ferroelectric Liquid Crystals: Principles, Properties and Applications, Ferroelectrics and Related Phenomena, Vol. 7 (Gordon and Breach, New York 1991) G. W. Taylor (Ed.): Ferroelectric Liquid Crystals: Principles, Preparations and Applications (Gordon and Breach, New York 1991) L. M. Blinov, V. G. Chigrinov: Electric Effects in Liquid Crystal Materials (Springer, Berlin, Heidelberg 1994) A. Fukada, Y. Takanishi, T. Isozaki, K. Ishikawa, H. Takezoe: Antiferroelectric Chiral Smectic Liquid Crystals, J. Mater. Chem. 4, 997 (1994) P. J. Collings, J. S. Patel (Eds.): Handbook of Liquid Crystal Research (Oxford Univ. Press, Oxford 1997) S. T. Lagerwall: Ferroelectric and Antiferroelectric Liquid Crystals (Wiley VCH, Weinheim 1999) T. Furukawa: Ferroelectric Properties of Vinylidene Fluoride Copolymers, Phase Transitions 18, 143 (1989) D. K. Das-Gupta (Ed.): Ferroelectric Polymer and Ceramic-Polymer Composites (Trans Tech Publications, Aedermannsdorf 1994)

937

Part 4 5

5.22

Y. Xu: Ferroelectric Materials and Their Applications (North-Holland, Amsterdam 1991) B. Jaffe, W. R. Cook Jr., H. Jaffe: Piezoelectric Ceramics (Academic Press, London 1971) J. Zelenka: Piezoelectric Resonators and Their Applications (Elsevier, Amsterdam 1986) T. Ikeda: Fundamentals of Piezoelectricity (Oxford Univ. Press, Oxford 1990) R. A. Cowley: Structural Phase Transitions (Consultant Bureau, New York 1980) K. A. Miller, H. Thomas (Eds.): Structural Phase Transitions I, Topics in Current Physics, Vol. 23 (Springer, Berlin, Heidelberg 1981) M. Fujimoto: The Physics of Structural Phase Transitions (Springer, Berlin, Heidelberg 1997) R. Blinc, A. P. Levanyuk (Eds.): Incommensurate Phases in Dielectrics, Modern Problems in Condensed Matter Science 14 (Elsevier, Amsterdam 1986) F. J. Scott: Soft-mode spectroscopy: Experimental studies of structural phase transitions, Rev. Mod. Phys. 46, 83 (1974) G. Shirane: Neutron scattering studies of structural phase transitions, Rev. Mod. Phys. 46, 437 (1974) C. H. Wang: Raman and Brillouin scattering spectroscopy of phase transitions in solids. In: Vibrational Spectroscopy of Phase Transitions, ed. by Z. Iqbal, F. J. Owens (Academic Press, Orlando 1984) pp. 153–207 J. M. Herbert: Ceramic Dielectrics and Capacitors, Electrocomp. Sci. Mon., Vol. 6 (Gordon and Breach, New York 1985) B. E. Vugmeister, M. D. Glinchuk: Dipole glass and ferroelectricity in random-site electric dipole systems, Mod. Phys. 62, 993 (1990) L. E. Cross: Relaxor ferroelectrics, Ferroelectrics 76, 241 (1987) S. Singh: Nonlinear optical materials. In: Handbook of Lasers with Selected Data on Optical Technology, ed. by R. J. Pressley (The Chemical Rubber Co., Cleveland 1971) pp. 489–525 V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan: Handbook of Nonlinear Optical Crystals, Springer Series in Optical Science, Vol. 64, ed. by A. E. Siegman (Springer, Berlin, Heidelberg 1991) P. Yeh: Introduction to Photorefractive Nonlinear Optics (Wiley, New York 1993) G. Rosenman, A. Skliar, A. Arie: Ferroelectric domain engineering for quasi-phase-matched nonlinear optical devices, Ferroelectr. Rev. 1, 263 (1999) N. Setter, E. L. Colla: Ferroelectric Ceramics (Birkhäuser, Basel 1993) B. A. Tuttle, S. B. Desu, R. Ramesh, T. Shiosaki: Ferroelectric Thin Films IV (Materials Research Society, Pittsburgh 1995)

References

938

Part 4

5.50

5.51

H. S. Nalva (Ed.): Ferroelectric Polymers: Chemistry, Physics and Applications (Marcel Dekker, New York 1995) H. Kodama, Y. Takahashi, T. Furukawa: Effects of Annealing on the Structure and Switching Characteristics of VDF/TrFE Copolymers, Ferroelectrics 205, 433 (1997)

5.52

5.53

N. A. Clark, S. T. Lagerwall: Submicrosecond Bistable Electro-Optic Switching in Liquid Crystals, Appl. Phys. Lett. 36, 899 (1980) A. D. L. Chandani, E. Gorecka, Y. Ouchi, H. Takezoe, A. Fukuda: Antiferroelectric Chiral Smectic Phases Responsible for the Tristable Switching in MHPOBC, Jpn. J. Appl. Phys. 28, L1265 (1989)

Part 4 5

939

Part 5

Special Stru Part 5 Special Structures

1 Liquid Crystals Sergei Pestov, Moscow, Russia Volkmar Vill, Hamburg, Germany

2 The Physics of Solid Surfaces Gianfranco Chiarotti, Roma, Italy 3 Mesoscopic and Nanostructured Materials Fabrice Charra, Gif-sur-Yvette, France Susana Gota-Goldmann, Fontenay aux Roses, France

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Liquid crystals (LCs) are widely used in informationprocessing devices, for optical visualization of physical influences (heat, IR, high-frequency radiation, pressure, etc.), for nondestructive testing, and for thermography.

5.1.1 Liquid Crystalline State ....................... 5.1.1.1 Chemical Requirements ........... 5.1.1.2 Physical Properties of Liquid Crystals ..................... 5.1.1.3 Applications of Liquid Crystals... 5.1.1.4 List of Abbreviations ................ 5.1.1.5 Conversion Factors .................. 5.1.2 Physical Properties of the Most Common Liquid Crystalline Substances ............... 5.1-2 Acids ..................................... 5.1-3 Two-ring Systems without Bridges .................................. 5.1-4 Two-ring Systems with Bridges . 5.1-5 Three and Four-ring Systems .... 5.1-6 Ferroelectric Liquid Crystals ...... 5.1-7 Cholesteryl (cholest-5-ene) Substituted Mesogens .............. 5.1-8 Discotic Liquid Crystals ............. 5.1-9 Liquid Crystal Salts ..................

941 943 943 944 944 945 946 946 947 955 964 967 968 972 973

5.1.3 Physical Properties of Some Liquid Crystalline Mixtures ...... 975 5.1-10 Nematic Mixtures .................... 975 5.1-11 Ferroelectric Mixtures .............. 975 References .................................................. 977

5.1.1 Liquid Crystalline State Liquid crystals represent an intermediate state of order (mesophase) between crystals and liquids. Crystals have a three-dimensional long-range order of both position and orientation (Fig. 5.1-1a). Liquids, in contrast, do not show any long-range order (Fig. 5.1-1b). In plastic crystals (disordered crystals, Fig. 5.1-1c), positional order is maintained, but orientational order is lost. In mesophases, imperfect long-range order is observed, and thus they are situated between crystals and liquids. The reasons for the formation of a mesophase can be the molecular shape or a microphase separation of amphiphilic compounds. More than 100 000 individual liquid crystals have been prepared until now [1.1–4]. About 2000 of them have been tested for physical properties and technical applications [1.5–14]. These materials can be classified

by chemical structures and physical characteristics (see Table 5.1-1). Generally, molecules of liquid crystalline substances have the following shapes:

• • •

rod-like molecules, which form calamitic liquid crystals (nematicand smectic phases); disk-like molecules, which form discotic liquid crystals (discoid nematic and discotic phases); amphiphilic compounds, which form layered columnar or cubic phases in the pure state and in solution.

The simplest and most widespread liquid crystalline phase is the nematic phase. The molecules are statistically distributed within the medium, but the long axes are orientated in one direction, the director (Fig. 5.1-2a). A special class of nematic phases is the cholesteric phase

Part 5 1

Liquid Crystal 5.1. Liquid Crystals

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Part 5

Special Structures

Part 5 1.1

Table 5.1-1 Classifications of liquid crystals

Shape Phase structure Mesophase units Mesophase origin

a)

Rod-like molecules Calamitic liquid crystals Thermotropic liquid crystals Amphiphilic liquid crystals

Disk-like molecules Discotic liquid crystals Lyotropic liquid crystals Monophilic liquid crystals

b)

c)

Fig. 5.1-1a–c Types of states: (a) crystal, (b) isotropic liquid, (c) plastic crystal

(Fig. 5.1-2b). Here the orientation of the director does not apply to the whole medium but rather to a virtual layer. Perpendicular to this layer, the director follows a helix with a certain pitch. In the case of the blue phases, such a helical structure is formed not in one but in all three dimensions. Thus, highly complex arrangements, with chiral cubic symmetry in most cases, are generated. Not only rod-like but also disk-like molecules can form nematic phases. The discoid nematic phase is shown in Fig. 5.1-2c. Rod-like molecules arranged in layers form smectic phases. They are subdivided into a considerable number of different species. These classifications result from various arrangements of the molecules within the layers and different restrictions on their movement. The smectic A phase, the simplest smectic phase, can be regarded as a two-dimensional liquid. The molecules are arranged normal to the layers (Fig. 5.1-2d). The smectic B phase can be interpreted as the closest packing of rod-like molecules, so that within a layer each molecule has a hexagonal environment (Fig. 5.1-2e). The smectic A phase and the smectic C phase are similar, except that in the latter the molecules are tilted within the layers by a tilt angle (Fig. 5.1-2f). A particular case of smec-

a)

b)

c)

d)

e)

f)

g)

Fig. 5.1-2a–g Types of mesophase: (a) nematic, (b) cholesteric, (c) discoid nematic, (d) smectic A, (e) smectic B, (f) smectic C, (g) discotic

tic C is the chiral smectic C∗ phase, where the tilt angle varies from layer to layer, forming a helical structure. For discussion of other smectic phases, as well as their further subclassification, the reader should consult the references [1.15, 16]. In discotic phases, the disk-like molecules are arranged in columns. In this group, again various phases are possible, depending of the orientation of

Liquid Crystals

5.1.1.1 Chemical Requirements A liquid crystalline compound can be divided into the mesogenic group and the side groups. The mesogenic group is subdivided into fragments of rings and bridges. The side groups are subdivided into links and terminal groups. Many other types of liquid crystalline compounds exist besides those with rod-like molecules e.g. compounds with disk-shaped, banana-shaped, and bowlshaped molecules. However, over 80% of all liquid crystals have a rod-like form (e.g. the molecule shown in Fig. 5.1-3).

5.1.1.2 Physical Properties of Liquid Crystals The order parameter S = 0.5(3cos2 Θ − 1) characterizes the long-range order of molecules in a mesophase, where Θ is the momentary angle between the long axis of the molecule and the director. In an ideal crystal the order parameter S equals 1, and it equals 0 in an isotropic liquid. In a nematic phase the order parameter lies in the range 0.5–0.7. One of the most useful properties for the application of liquid crystals is the anisotropy of their refractive index ∆n = n e − n o , where n e is the extraordinary and n o Link C6H13 O Side group L

Bridge

Ring

O C O N CH Mesogenic group

Terminal group O C6H13 Side group R

Fig. 5.1-3 Structure of a calamitic mesogenic compound

is the ordinary refractive index. For nematics, n e corresponds to n and n o = n ⊥ . For n ⊥ the vibration vector of plane-polarized light is perpendicular to the optical axis, i. e. the director, while for n the vibration vector of plane-polarized light is parallel to the director. For the majority of LCs the value of ∆n is positive, but cholesteryl-substituted compounds are optically negative (∆n < 0). On increasing the wavelength, ∆n usually decreases. For homologues ∆n decreases as the length of the alkyl chains increases. The orientation of molecules in an electric field is determined by the sign of the dielectric anisotropy (∆ε = ε − ε⊥ ); ε and ε⊥ are the dielectric constants measured parallel and perpendicular to the director. Some nematic LCs can change their sign of ∆ε depending upon the frequency of the applied field. The majority of mesogens are diamagnetic. The diamagnetic anisotropy (∆χ) characterizes the behavior of a LC under the influence of a magnetic field; ∆χ = χ − χ⊥ , where χ and χ⊥ are the diamagnetic susceptibilities parallel and perpendicular to the director. The basic methods for the determination of phase transition temperatures (T tr ) are DSC (differential scanning calorimetry), DTA (differential thermal analysis), and polarization microscopy. Every method has its advantages and restrictions. DSC allows one to determine the enthalpies of phase transitions (∆H tr ). Microscopy allows one both to determine the phase transition temperatures and to identify the type of mesophase. DTA gives reliable results for melting temperatures of LCs that show solid-state polymorphism, and of LC mixtures. The differences in T tr that can be found in publications by different authors arise from different measurement techniques and the presence of impurities. We have selected the data with the higher T tr values in such cases. The temperature dependence of the density ( ) is practically linear, with the exception of jumps near phase transitions. The volume changes are 3–9%, 0.1–0.4%, and 0.01–0.2% for the crystal–mesophase, nematic–isotropic, and smectic A–nematic transitions, respectively. The kinematic and dynamic viscosities ν and η, respectively, can be determined by a capillary viscometer of the Ubbelohde or Ostwald type (ν = η/ ). The surface tension (γ LV ) influences the angle between the surface and the nematic-phase director. It plays an important role in the selection of coatings for the creation of homeotropic alignment (where the molecules are perpendicular to the cell surfaces) or planar alignment (where the molecules are parallel to the surfaces) of LCs. The Friedel–Creagh–Kmetz rule states that if

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Part 5 1.1

the molecules within the columns and the order between the columns. The simplest phase is the hexagonal columnar discotic phase. It can be regarded as a onedimensional liquid. The columns have a hexagonal order (Fig. 5.1-2g). Lyotropic liquid crystals are formed by aggregation of micelles. They are multicomponent systems. Normally they consist of an amphiphilic substance and a solvent. In contrast, thermotropic liquid crystals are individual compounds. Enantiotropic LC phases are formed during both the heating and the cooling process. Monotropic LC phases exist only in the supercooled state below the melting point. Thus, these phases are observed during cooling only.

1.1 Liquid Crystalline State

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Special Structures

Part 5 1.1

γL (energy of LC–surface interaction ) > γS (solid surface energy), then a homeotropic alignment is induced; otherwise, a parallel alignment is induced.

5.1.1.3 Applications of Liquid Crystals The main requirements on LC materials (LCMs) for electro-optics are a high clearing temperature (T N-Is ) and low melting temperature, i. e. a wide temperature range of definite liquid crystalline phases, and a low viscosity for reducing the switching time of electro-optical effects. Wide usage of LCMs in displays became possible after the discovery of mesogenic cyanobiphenyls. At present many of homologous LCs are synthesized for display applications. Phenylcyclohexane- and bicyclohexanesubstituted LCs are used as components in LCMs; they have low viscosity and, accordingly, fast switching. Fluorinated three-ring LCs containing two cyclohexane rings and a phenyl ring are used in LCMs with high dielectric anisotropy, which are used at low voltages. For the application of a LCM as a material in LC displays, many properties have to correspond to rigid specifications. For this reason LCMs consist typically of 7 to 15 components. Sometimes LCMs contain nonmesogenic additives, e.g. to reduce the viscosity of the mixture. In the twist structure, the molecules are parallel to the cell surfaces and the angle between the boundary directors is 90◦ . In the S effect (Frederics effect), a planar structure is transformed to a homeotropic one, and in the B effect, a homeotropic structure is transformed to a planar one. In the twist effect (or twisted nematic, TN, effect) a twist structure turns into a homeotropic one. The disadvantage of the TN effect is the necessity to use polarizers. The “dynamic scattering mode” of use of LCs depends on the influence of an electric current on the orientation of the molecules. At a high enough voltage, transparent nematic cells becomes turbid. A disadvantage of this effect is that the lower the voltage, the longer the time of switching. One of the modern uses of this effect is use of the dynamic scattering mode for data storage. After the applied voltage is switched off,

5.1.1.4 List of Abbreviations Cr, Cr S A, B, C, E, F, G, H C* D

crystalline phases smectic specific smectic mesophases chiral smectic C (ferroelectric) discotic

the mode of the planar cell does not return to its initial state. The cell can be stored in the turbid state for a long time (from some minutes to some months). The host–guest effect results from a reorientation of dye dopants (1–2% in the LC matrix) in an electric field. In this case the wavelength of maximum absorption of light is shifted and the color of the LC cell changes. The sign of the dielectric anisotropy of a LCM determines the type of electro-optical effect. LCMs with ∆ε > 0 are used for the TN (twisted nematic), STN (supertwisted nematic), and TFT (thin-film transistor) effects. LCMs with low negative values of ∆ε were formerly used for the dynamic scattering mode. Now LCMs with negative anisotropy ∆ε are utilized for MVA-TFT (multidomain vertical-alignment thin-film transistor) displays. The higher the value of ∆ε > 0, the smaller the working voltage. Electric current leads to degradation of a LCM and reduces the lifetime of the display. Impurities influence the stability of the material and accelerate electrodegradation. Therefore a multistage purification, consisting for example of recrystallization, and column chromatography, to remove conducting impurities (intermediate products, water, and CO2 ), is necessary. Usually the specific conductivity of a LCM is lower than 10−11 –10−12 C m/cm and corresponds to the intrinsic conductivity. The elastic constants (K i ) determine the switching time of the electro-optical effects. The elastic constant K 1 corresponds to the S effect, K 3 to the B effect, and K 2 to the TN effect; here K 1 corresponds to splaying K 2 to twisting, and K 3 to bending [1.11, 12]. Cholesteryl compounds were the first materials that found application in thermography. A huge number of other applications exist, where the chemical and physical requirements are totally different. These applications include reflectors, temperature measurement with thermochromic materials, nonlinear optics, polymer materials, SAMs (self-assembled monolayers) and LB (Langmuir–Blodgett) films, the use of liquid crystals in template synthesis of porous materials, drug delivery, and many more.

Liquid Crystals

Examples Cr 95.0 C 99.0 N 107.5 Is Cr 5.0 Cr 67.3 (N 30.3) Is

(extra) dec

hexagonal columnar discotic (ordered or disordered) rectangular, tilted columnar discotic nematic cholesteric isotropic Crystals melt at 95 ◦ C, smectic C transforms to nematic at 99 ◦ C and to isotropic liquid at 107.5 ◦ C. Crystals melt at 67.3 ◦ C. Compound has a monotropic nematic phase on cooling below 30.3 ◦ C and polymorphism (solid–solid transition) at 5 ◦ C. Data were extrapolated from 10–20 wt% solution in nematic mixture. Substance decomposes on heating.

Common names are historical names, and trade names of BDH, Licristal® Merck, and Hoffmann-La Roche [1.8, 9, 17]. CAS-RN T tr T N–Is

Registration number of the Chemical Abstract Service (CAS) temperatures of phase transitions temperature of nematic–isotropic transition (in Kelvin)

Relative temperatures (e.g. T = 0.977T N–Is ) are assumed to be in K only. Inverse temperatures are always given in 1/Kelvin (e.g. 1000/T = 2.4). Some data are given for supercooled mesophases (T < Tmelting ). ∆H tr Cp v p ∆n ∆ε Ps D C6 H12

enthalpies of phase transitions (kJ/mol) heat capacity at constant pressure (J/(mol K)) sound velocity (m/s) helix pitch (for N* phase) (µm) anisotropy of the refractive index (n e − n o ) dielectric anisotropy spontaneous polarization (for ferroelectric LC) (nC/cm2 ) diffusion coefficient (m2 /s) cyclohexane

5.1.1.5 Conversion Factors Molar mass Dipole moment (µ) Density Temperatures of phase transitions T tr Dynamic viscosity η Kinematic viscosity ν = η/ Diamagnetic anisotropy ∆χ Thermal conductivity

1 g/mol = 1 × 10−3 kg/mol 1 D (Debye) = 3.33564 × 10−30 Cm (Coulomb meter) 1 g/cm3 = 1 × 103 kg/m3 T(◦ C) = T(K) − 273.15 1 mPa s = 1 × 10−3 Pa s = 1 cP (centi-Poise) 1 mm2 /s = 1 × 10−6 m2 /s = 1 cSt (centi-Stokes) 1 m3 /kg = 1 × 103 cm3 /g (CGS unit) 1 W/(m K) = 1 × 10−2 W/(cm K)

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Part 5 1.1

Dh, Dho, Dhd Dr, Dt N N* Is

1.1 Liquid Crystalline State

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Part 5

Special Structures

Part 5 1.2

5.1.2 Physical Properties of the Most Common Liquid Crystalline Substances The compounds are arranged in the tables on the basis of the number and priority of fragments. The order principles for mesogenic groups are the number of rings and bridges, and the priority of rings, bridges, and side groups. Priority of rings:

Priority of bridges: Cn Hm > CH=N > N=N > N=N(O) > COO . Homologues are arranged in order of increasing number of carbon atoms in the alkyl chains. We have attempted to include all of the most common liquid crystals, from the traditional “model substances” (e.g. 5CB, MBBA, and PAA) to substances used in modern applications.

benzene > cyclohexane > heterocycles > halogen-substituted benzenes . Table 5.1-2 Acids Number/common name

1

Substance

2

O

COOH

3

O

COOH

O

COOH

H7C3

H9C4

H11C5

C10 H12 O3 180.205 5438-19-7 Cr 146.0 N 156.0 Is

C11 H14 O3 194.232 1498-96-0 Cr 147.5 N 161.0 Is

C12 H16 O3 208.26 15872-41-0 Cr 124.4 N 151.4 Is

16.7 (Cr–N), 2.5 (N–Is)

19.7 (Cr–N), 2.4 (N–Is)

18.0 (Cr–N), 1.8 (N–Is)

Dielectric anisotropy ∆ε Dynamic viscosity η (mPa s) Diffusion coefficient D (m2 /s)

P21 /c 0.533 (149 ◦ C) 1.0095 (N, 150 ◦ C), 1.0008 (Is, 159 ◦ C) n e 1.632, n o 1.457 (N, 546 nm, 140.5 ◦ C) − 1.81 (149 ◦ C), 2.63 (159 ◦ C) −

P1 0.538 (154 ◦ C) 1.0079 (N, 150 ◦ C), 0.9883 (Is, 165 ◦ C) n e 1.615, n o 1.449 (N, 589 nm, 149 ◦ C) 0.079 (T = 0.977 T N–Is ) 1.88 (151 ◦ C), 2.62 (165 ◦ C) D⊥ = 4 × 10−10 , D = 14 × 10−10 (1000/T = 2.38)

P21 0.587 (137 ◦ C) 0.9945 (N, 145 ◦ C), 0.9721 (Is, 155 ◦ C) n e 1.602, n o 1.456 (N, 546 nm, 140.5 ◦ C) 0.042 (T = 0.977 T N–Is ) 2.37 (145 ◦ C), 3.30 (155 ◦ C) D⊥ = 4 × 10−10 , D = 12 × 10−10 (1000/T = 2.45)

Number/common name

4

5 (HOBA)

6 (OOBA)

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group Order parameter S Density (g/cm3 ) Refractive index n

Substance

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol)

O

COOH

O

COOH

O

COOH

H13C6

H15C7

H17C8

C13 H18 O3 222.287 1142-39-8 Cr 75 Cr 105.4 N 153.2 Is

C14 H20 O3 236.314 15872-42-1 Cr 94.0 C 102.0 N 147.5 Is

C15 H22 O3 250.341 2493-84-7 Cr 100.5 C 107.5 N 147.0 Is

13.8 (Cr–N), 3.3 (N–Is), 6.7 (Cr –Cr)

19.2 (Cr–C), 2.5 (N–Is)

12.7 (Cr–C), 1.1 (C–N), 2.1 (N–Is)

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Liquid Crystals

Number/common name

5 (HOBA)

6 (OOBA)

P21 /c (Cr), P1 0.611 (129 ◦ C) 0.983 (N, 146 ◦ C), 0.969 (Is, 156 ◦ C) n e 1.595, n o 1.453 (546 nm, N, 142.5 ◦ C) 0.052 (T = 0.977 T N–Is ) 2.61 (146 ◦ C), 3.46 (157 ◦ C) 0.137 (N, 115 ◦ C), 0.159 (Is, 157 ◦ C) 972 (3.36 GHz, 141 ◦ C) D⊥ = 2 × 10−10 , D = 8 × 10−10 (1000/T = 2.45)

P1 0.626 (123 ◦ C) 0.970 (N, 140 ◦ C), 0.959 (Is, 150 ◦ C) n e 1.580, n o 1.452 (546 nm, N, 137.5 ◦ C) 0.038 (T = 0.977 T N–Is ) 3.02 (137 ◦ C), 3.95 (150 ◦ C) 0.146 (N, 130 ◦ C), 0.162 (Is, 159 ◦ C) 1021 (3.40 GHz, 135 ◦ C) −

P1 0.615 (128 ◦ C) 0.961 (N, 140 ◦ C), 0.945 (Is, 150 ◦ C) n e 1.578, n o 1.450 (546 nm, N, 138.5 ◦ C) 0.037 (T = 0.977 T N–Is ) 3.19 (140.5 ◦ C), 3.97 (151 ◦ C) −

Number/common name

7

8

9

Substance

H11C5

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) ∆ε (N, 90 ◦ C, 500 kHz)

C12 H22 O2 198.308 32829-29-1 Cr 53.0 (B 45.0) N 105.0 Is

C13 H24 O2 212.335 38289-30-4 Cr 31.7 B 47.2 N 96.4 Is

20.9 (Cr–N), 1.1 (N–Is)

15.7 (Cr–B), 1.0 (B–N), 0.5 (N–Is) −

Crystallographic space group Order parameter S Density (g/cm3 ) Refractive index n Dielectric anisotropy ∆ε Dynamic viscosity η (mPa s) Thermal conductivity (W/(m K)) Sound velocity v (m/s) Diffusion coefficient D (m2 /s)

4 (Cr )

COOH

0.05

H13C6

COOH

1050 (3.63 GHz, 137 ◦ C) −

H15C7

COOH

C14 H26 O2 226.362 32829-31-5 Cr 31.0 Cr 54.0 B 77.0 N 104.0 Is 13.4 (Cr –Cr), 5.2 (Cr–B), 2.3 (B–N), 1.1 (N–Is) 0.05

Table 5.1-3 Two-ring systems without bridges Number/common name

10 (2CB, K6, RO-CM-5106)

11 (3CB, K9, RO-CM-5109)

Substance

H5C2

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group Anisotropy of refractive index ∆n Dielectric constant ε Kinematic viscosity ν (mm2 /s) Dipole moment µ (D), 25 ◦ C

C15 H13 N 207.278 58743-75-2 Cr 75.0 (N 22.0) Is

C16 H15 N 221.305 58743-76-3 Cr 67.3 (N 30.3) Is

C17 H17 N 235.332 52709-83-8 Cr 48.0 (N 16.5) Is

17.2 (Cr–Is)

26.8 (Cr–Is), 0.3 (N–Is)

23.0 (Cr–Is)

− 0.206 ∆ε + 18.9 5 (70 ◦ C) 4.81 (CCl4 ), 4.96 (C6 H14 ), 4.90 (C6 H12 ), 5.01 (C6 H6 )

P21 /c 0.211 ε 25.8, ε⊥ 6.9 (20 ◦ C) 23 (extra, 20 ◦ C), 7 (70 ◦ C) 4.72 (CCl4 ), 5.02 (C6 H14 ), 4.93 (C6 H12 ), 4.93 (C6 H6 )

P21 /c 0.202 ∆ε +17 7.5 (70 ◦ C) 4.73 (CCl4 ), 5.04 (C6 H14 ), 4.94 (C6 H12 ), 4.99 (C6 H6 )

CN

H7C3

12 (4CB, K12, RO-CM-5112) CN

H9C4

CN

Part 5 1.2

Table 5.1-2 Acids, cont.

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Part 5 1.2

Table 5.1-3 Two-ring systems without bridges, cont.

Special Structures

Number/common name

13 (5CB, K15, RO-CM-5115)

14 (6CB, K18, RO-CM-5118)

15 (7CB, K21, RO-CM-5121)

Substance

H11C5

H13C6

H15C7

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group Order parameter S Density (g/cm3 )

C18 H19 N 249.359 40817-08-1 Cr 24.0 N 35.3 Is

C19 H21 N 263.386 41122-70-7 Cr 14.3 N 30.1 Is

C20 H23 N 277.413 41122-71-8 Cr 15.0 Cr 30.0 N 42.8 Is

17.2 (Cr–N), 0.4 (N–Is)

24.3 (Cr–N), 0.4 (N–Is)

25.9 (Cr–N), 0.9 (N–Is)

P21 /a 0.64 (24 ◦ C) 1.022 (N, 24 ◦ C), 1.016 (N, 30 ◦ C) n e 1.716, n o 1.533 (N, 24 ◦ C, 589 nm) ε 20, ε⊥ 7 (25 ◦ C, 1.5 kHz) η 28 mPa s (25 ◦ C) 33 (N, 20 ◦ C), 28 (N, 30 ◦ C), 28.3 (Is, 40 ◦ C) k⊥ 0.124, k 0.242

P1 − 1.017 (N, 20 ◦ C), n e 1.687, n o 1.531 (N, 20 ◦ C, 633 nm) ε 14.45, ε⊥ 7.2 (28 ◦ C, 1 kHz) ν 46 mm2 /s (20 ◦ C) 27.4 (N, 22 ◦ C), 28.0 (Is, 32 ◦ C)

P1 0.65 (29 ◦ C) 1.001 (N, 29 ◦ C), 0.991 (N, 39 ◦ C) n e 1.679, n o 1.522 (N, 32 ◦ C, 589 nm) ε 13.55, ε⊥ 6.8 (41 ◦ C, 1 kHz) ν 26 mm2 /s (20 ◦ C) 26.3 (N, 37 ◦ C), 27.5 (Is, 47 ◦ C)

k⊥ 0.126, k 0.223

k⊥ 0.127, k 0.269

113.5 (25.6 ◦ C)

101.5 (20 ◦ C)

102.0 (33 ◦ C)

v 1740, v⊥ 1680 (14.75 GHz, 30 ◦ C) D⊥ 6.8 × 10−8 , D 12.7 × 10−8 (25 ◦ C) 4.85 (CCl4 ), 5.08 (C6 H14 ), 4.95 (C6 H12 ), 4.93 (C6 H6 )

v 1776, v⊥ 1712 (14.75 GHz, 25 ◦ C) D⊥ 6.4 × 10−8 , D 10.9 × 10−8 (25 ◦ C) 4.83 (CCl4 ), 5.09 (C6 H14 ), 5.01 (C6 H12 ), 4.98 (C6 H6 )

v 1675, v⊥ 1640 (14.75 GHz, 38 ◦ C) D⊥ 6.8 × 10−8 , D 14.4 × 10−8 (25 ◦ C) 4.74 (CCl4 ), 5.11 (C6 H14 ), 4.94 (C6 H12 ), 4.97 (C6 H6 )

Number/common name

16 (8CB, K24)

17 (9CB, K27)

18 (10CB, K30)

Substance

H17C8

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group Density (g/cm3 )

C21 H25 N 291.44 52709-84-9 Cr 21.5 A 33.5 N 40.5 Is

C22 H27 N 305.467 52709-85-0 Cr 42.0 A 48.0 N 49.5 Is

C23 H29 N 319.494 59454-35-2 Cr 44.0 A 54.5 Is

28.3 (Cr–A), 0.2 (A–N), 0.7 (N–Is) P21 /n 0.991 (A, 32.5 ◦ C), 0.981 (N, 40 ◦ C), 0.978 (Is, 41 ◦ C) n e 1.657, n o 1.524 (N, 37.4 ◦ C) ε 12.8, ε⊥ 5.3 (N, 34 ◦ C), ε 12.4, ε⊥ 4.8 (A, 28 ◦ C) 35 (N, 33.5 ◦ C)

33.5 (Cr–A), 0.6 (A–N), 1.7 (N–Is) P1 0.973 (A, 47.7 ◦ C), 0.968 (N, 49.5 ◦ C) n e 1.638, n o 1.519 (N, 49 ◦ C) ε 12.5, ε⊥ 5.1 (44 ◦ C)

33.1 (Cr–A), 2.8 (N–Is)

−

−

Refractive index n (589 nm) Dielectric constant ε Viscosity Surface tension (mN/m) Thermal conductivity (W/(m K)) (N, 25 ◦ C) Magnetic susceptibility ∆χ (m3 /kg) (×10−12 ) Sound velocity v (m/s) Diffusion coefficient D (m2 /s) Dipole moment µ (D), 25 ◦ C

Refractive index n (589 nm) Dielectric constant ε (1 kHz) Dynamic viscosity η (mPa s)

CN

CN

H19C9

CN

CN

H21C10

P21 /n − − ε 8.8 (Is, 64.5 ◦ C)

CN

CN

Liquid Crystals

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Part 5 1.2

Table 5.1-3 Two-ring systems without bridges, cont. Number/common name

16 (8CB, K24)

17 (9CB, K27)

18 (10CB, K30)

Surface tension (mN/m) Thermal conductivity (W/(m K)) Magnetic susceptibility ∆χ(m3 /kg) (×10−12 ) Sound velocity v (m/s)

25.5 (N, 35 ◦ C), 26.2 (Is, 41 ◦ C) k⊥ 0.130, k 0.276 (A, 30 ◦ C), k⊥ 0.132, k 0.254 (N, 35 ◦ C) 88 (35 ◦ C)

− k⊥ 0.130, k 0.310 (40 ◦ C)

− −

88.5 (48.9 ◦ C)

−

v 1596, v⊥ 1545 (14.75 GHz, 39 ◦ C) D⊥ 6 × 10−8 , D 12 × 10−8 (A, 30 ◦ C), D⊥ 5.8 × 10−8 , D 10 × 10−8 (N, 35 ◦ C) 4.78 (CCl4 ), 5.12 (C6 H14 ), 4.93 (C6 H12 ), 5.00 (C6 H6 )

v 1740, v⊥ 1680 (14.75 GHz, 44.5 ◦ C) D⊥ 6.6 × 10−8 , D 15.2 × 10−8 (A, 40 ◦ C)

−

4.73 (CCl4 ), 5.11 (C6 H14 ), 4.94 (C6 H12 ), 4.94 (C6 H6 )

4.76 (CCl4 ), 5.10 (C6 H14 ), 5.00 (C6 H12 ), 5.00 (C6 H6 )

19 (3OCB, M9, RO-CM-5309)

20 (4OCB, M12)

21 (5OCB, M15, RO-CM-5315)

Diffusion coefficient D (m2 /s)

Dipole moment µ (D), 25 ◦ C Number/common name

O

Substance

CN

O

−

CN

O

CN

H7C3

H9C4

H11C5

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group Order parameter S Density (g/cm3 ) Refractive index n (589 nm) Dielectric constant ε (1 kHz)

C16 H15 NO 237.304 52709-86-1 Cr 71.5 (N 64.0) Is

C17 H17 NO 251.331 52709-87-2 Cr 78.0 (N 75.5) Is

C18 H19 NO 265.368 52364-71-3 Cr 48.0 Cr 53.0 N 68.0 Is

19.2 (Cr–Is)

23.4 (Cr–Is)

28.9 (Cr–N), 0.2 (N–Is)

P21 /c − 1.19 (Cr) − −

P21 /n 0.63 (55 ◦ C) 1.042 (N, 61.5 ◦ C), 1.029 (Is, 70 ◦ C) n e 1.697, n o 1.528 (N, 55 ◦ C) ∆ε + 8.5, ε 16.7 (T = 0.98T N–Is )

Kinemamic viscosity ν (mm2 /s) Surface tension (mN/m) Magnetic susceptibility ∆χ (m3 /kg) (×10−12 ) Dipole moment µ (D)

10 (Is, 80 ◦ C) − −

Pca21 − 1.14 (Cr) − ∆ε + 28.7, ε⊥ + 7.5 (20 ◦ C, extra) 10 (75 ◦ C) − −

−

5.1

−

Number/common name

22 (6OCB, M18)

23 (7OCB, M21)

24 (8OCB, M24, RO-CM-5324)

Substance

O H13C6

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol)

C19 H21 NO 279.385 41424-11-7 Cr 44.0 Cr 57.0 N 75.5 Is

C20 H23 NO 293.412 52364-72-4 Cr 45.5 Cr 53.5 N 75.0 Is

29.7 (Cr–N), 0.8 (N–Is)

28.9 (Cr–N), 0.6 (N–Is)

CN

O H15C7

20 (53 ◦ C), 10 (85 ◦ C) 33.2 (N, 51 ◦ C), 31.9 (Is, 70 ◦ C) 87 (58 ◦ C), 98 (50 ◦ C)

CN

O H17C8

949

CN

C21 H25 NO 307.44 52364-73-5 Cr 46.0 Cr 51.0 Cr 54.5 A 67.0 N 80.0 Is 28.5 (Cr–A), 0.1 (A–N), 0.8 (N–Is)

950

Part 5

Part 5 1.2

Table 5.1-3 Two-ring systems without bridges, cont.

Special Structures

Number/common name

22 (6OCB, M18)

23 (7OCB, M21)

24 (8OCB, M24, RO-CM-5324)

Crystallographic space group Order parameter S

−

P21 /c, P1

P1

−

0.61 (63 ◦ C)

Density (g/cm3 )

1.017 (N, 71 ◦ C), 1.025 (N, 63 ◦ C)

1.0051 (N, 63 ◦ C), 0.9869 (Is, 79.5 ◦ C)

0.990 (N, 75 ◦ C), 0.977 (Is, 85 ◦ C)

Refractive index n (589 nm)

n e 1.72, n o 1.50 (60 ◦ C)

n e 1.6734, n o 1.5155 (60 ◦ C)

n e 1.647, n o 1.509 (71 ◦ C)

Dielectric constant ε (1 kHz)

∆ε + 8.0, ε 15.8 (T = 0.98T N–Is )

∆ε + 7.5, ε 15.0 (T = 0.98T N–Is )

∆ε + 8.0 (N, 74 ◦ C)

Kinematic viscosity ν (mm2 /s)

17 (60 ◦ C), 12 (85 ◦ C)

10 (70 ◦ C), 30 (50 ◦ C)

16 (70 ◦ C), 12 (85 ◦ C)

Surface tension (mN/m)

−

−

36.5 (A, 60), 35.4 (N, 70), 30.5 (Is, 80)

Magnetic susceptibility ∆χ (m3 /kg) (×10−12 )

88 (67 ◦ C), 80 (71 ◦ C)

71 (70 ◦ C), 87.5 (60 ◦ C)

83 (70.6 ◦ C)

Dipole moment µ (D)

5.2

4.9

5.2 (CCl4 )

Number/common name

25 (PCH-3)

26 (PCH-4)

27 (PCH-5)

Substance

NC

Formula

C16 H21 N

C17 H23 N

C18 H25 N

Molar mass (g/mol)

227.352

241.38

255.407

CAS-RN

61203-99-4

61204-00-0

61204-01-1

Temperatures of phase transitions T tr (◦ C)

Cr 42.7 N 45.9 Is

Cr 41.0 N 39.0 Is

Cr 30.0 N 55.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

19.0 (Cr–N), 0.7 (N–Is)

22.2 (Cr–Is)

18.0 (Cr–N), 0.9 (N–Is)

Crystallographic space group

C2/c

P21 /c, P1

−

−

0.54 (43 ◦ C)

Order parameter S Density

(g/cm3 )

0.64

C3H7

(43 ◦ C)

0.9672 (N,

43 ◦ C),

0.9571 (Is,

46.5 ◦ C) 43 ◦ C)

Refractive index n (589 nm)

n e 1.582, n o 1.492 (N,

Dielectric constant ε (1 kHz)

ε 19.3, ε⊥ 5.5 (T = 0.95T N–Is )

(20 ◦ C)

NC

C4H9

0.962 (N,

35 ◦ C),

0.951 (Is,

43 ◦ C)

n e 1.579, n o 1.498 (N,

NC

C5H11

0.967 (N, 25 ◦ C), 0.932 (Is, 60 ◦ C) 37 ◦ C)

∆ε +11 (20 ◦ C)

n e 1.600, n o 1.492 (N, 40 ◦ C) ε 14.4, ε⊥ 5.2 (39 ◦ C)

η 19.2 mPa s

ν

Dipole moment µ (D)

3.9

−

4.1

Number/common name

28 (PCH-7)

29 (PCH-8)

30 (PCH-32, RO-CM-4232, ZLI-1484)

Substance

NC

Formula

C20 H29 N

C21 H31 N

C17 H26

Molar mass (g/mol)

283.461

297.488

230.397

CAS-RN

61204-03-3

83626-40-8

82991-47-7

Temperatures of phase transitions T tr (◦ C)

Cr 30.0 N 57.8 Is

Cr 37.0 N 55.0 Is

Cr −1 Is

Viscosity

C7H15

23 mm2 /s

NC

ν 23 mm2 /s

C8H17

H5C2

C3H7

Liquid Crystals

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Number/common name

28 (PCH-7)

29 (PCH-8)

30 (PCH-32, RO-CM-4232, ZLI-1484)

Enthalpies of phase transitions ∆H tr (kJ/mol)

25.5 (Cr–N), 1.0 (N–Is)

−

18.4 (Cr–Is)

Crystallographic space group

−

P21 /c, P1 (Cr )

−

−

−

(47 ◦ C)

Order parameter S

0.47

Density (g/cm3 )

0.952 (N, 30 ◦ C), 0.915 (Is, 67 ◦ C)

0.941 (N, 37 ◦ C), 0.915 (Is, 62 ◦ C)

0.909 (20 ◦ C)

Refractive index n (589 nm)

n e 1.590, n o 1.482 (47 ◦ C)

−

1.514 (20 ◦ C)

−

ε 2.293, ∆ε + 0.5 (20 ◦ C, extra)

−

4 (extra, 20 ◦ C)

32 (PCH-302, ZLI-1476)

33 (PCH-304, ZLI-1477)

Dielectric constant ε (1 kHz) Kinematic viscosity ν

(mm2 /s)

Number/common name

ε 12.9, ε⊥ 4.2 28 (extra,

(31 ◦ C)

20 ◦ C)

31 (PCH-301, ZLI-2446) O

Substance

C3H7

O

C3H7

O

H3C

H5C2

H9C4

Formula

C16 H24 O

C17 H26 O

C19 H30 O

Molar mass (g/mol)

232.369

246.396

274.45

CAS-RN

81936-32-5

80944-44-1

79709-84-5

Temperatures of phase transitions T tr (◦ C)

Cr 32.0 (N 10.0) Is

Cr 40.8 (N 37.8) Is

Cr 35.5 (N 33.0) Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

17.6 (Cr–Is)

26.4 (Cr–Is), 0.7 (N–Is)

30.6 (Cr–Is), 0.5 (N–Is)

Anisotropy of refractive index ∆n (20 ◦ C, 589 nm)

0.09 (extra)

0.09 (extra)

0.09 (extra)

Dielectric anisotropy ∆ε (20 ◦ C, 1 kHz)

− 0.5 (extra)

− 0.5 (extra)

− 0.5 (extra)

Kinematic viscosity ν (mm2 /s)

6 (extra, 20 ◦ C)

7 (extra, 20 ◦ C)

10 (extra, 20 ◦ C)

Number/common name

34 (H33, ZLI-1305)

35

36

Substance

O

O

C3H7

O

O C3H7

H7C3

C3H7

C5H11

H5C2

H5C2

Formula

C19 H28 O2

C18 H26 O

C20 H30 O

Molar mass (g/mol)

288.434

258.407

286.462

Temperatures of phase transitions T tr (◦ C)

Cr 11.0 B 26.1 N 30.3 Is

Cr 49.2 N 56.5 Is

Cr 56.6 N 68.8 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

16.4 (Cr–B), 4.9 (B–N), 0.4 (N–Is)

−

−

Refractive index n (589 nm)

∆n 0.09 (20 ◦ C)

n e 1.589, n o 1.497 (T = 0.95T N–Is )

n e 1.574, n o 1.487 (T = 0.95T N–Is )

Dielectric constant ε (1 kHz)

∆ε − 1.5 (20 ◦ C)

ε 9.0, ε⊥ 7.6 (T = 0.95T N–Is )

ε 8.3 ε⊥ 6.9 (T = 0.95T N–Is )

Viscosity ν (20 ◦ C)

15 mm2 /s (extra)

−

−

Diamagnetic anisotropy ∆χ (m3 /mol) (×10−12 )

−

25.3

26.1

Dipole moment µ (D)

−

3.02

3.1

Part 5 1.2

Table 5.1-3 Two-ring systems without bridges, cont.

951

952

Part 5

Part 5 1.2

Table 5.1-3 Two-ring systems without bridges, cont.

Special Structures

Number/common name

37

38

Substance

NC

Formula

C18 H23 N

C20 H27 N

C22 H31 N

Molar mass (g/mol)

253.391

281.445

309.499

CAS-RN

−

74385-67-4

−

Temperatures of phase

Cr 66.5 N 88.0 Is

Cr 62.0 N 100.0 Is

Cr 61.0 N 95.0 Is

17.4 (Cr–N)

20.7 (Cr–N)

32.7 (Cr–N)

C3H7

39

NC

C5H11

NC

C7H15

transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) 1.007 (N, 66 ◦ C)

Density (g/cm3 ) Refractive index n (633 nm)

n e 1.614, n o 1.492

0.993 (N, 60 ◦ C) (66 ◦ C)

n e 1.616, n o 1.490

(66 ◦ C)

ε⊥ 4.6, ε 13.1

0.975 (N, 65 ◦ C) (60 ◦ C)

n e 1.598, n o 1.489 (65 ◦ C)

(60 ◦ C)

ε⊥ 4.4, ε 12.0 (65 ◦ C)

Dielectric constant ε (10 kHz)

ε⊥ 5.2, ε 15.4

Viscosity ν (mm2 /s)

−

7.8 (70 ◦ C)

−

Dipole moment µ (D)

−

4.1

−

Number/common name

40 (CCH-3)

41 (CCH-5)

42 (CCH-7)

Substance

H7C3

Formula

C16 H27 N

C18 H31 N

C20 H35 N

Molar mass (g/mol)

233.4

261.454

289.509

CAS-RN

65355-35-3

65355-36-4

65355-37-5

Temperatures of phase

Cr 58.0 (S 18.0 S 44.0

Cr 59.2 Cr 63.4 (S 40.5 B 49.1)

Cr 71.0 N 83.0 Is

transitions T tr (◦ C)

S 48.0 B 57.0) N 80.0 Is

N 86.4 Is

Enthalpies of phase transitions

26.8 (Cr–N), 1.1 (N–Is)

26.8 (Cr–N), 1.3 (N–Is)

Crystallographic space group

P1

P21 /c, P21 21 21 (Cr )

P21 21 21

Density (g/cm3 )

0.902 (N, 73 ◦ C),

0.902 (N, 72 ◦ C)

0.893 (N, 70 ◦ C)

CN

H11C5

CN

H15C7

CN

33.9 (Cr–N), 0.9 (N–Is)

∆H tr (kJ/mol)

0.885 (Is, 87 ◦ C) 0.53 (73 ◦ C)

Order parameter S

0.62 (72 ◦ C) 73 ◦ C)

n e 1.502, n o 1.456 (N, 70 ◦ C)

Refractive index n (589 nm)

n e 1.4930, n o 1.4553 (N,

Dielectric constant ε (1 kHz)

ε⊥ 5.5, ε 10.0 (73 ◦ C)

ε⊥ 4.75, ε 9.25 (73 ◦ C)

ε⊥ 3.89, ε 7.17 (74 ◦ C)

Viscosity ν

(mm2 /s)

(20 ◦ C)

n e 1.5061, n o 1.4568 (N,

0.52 (71 ◦ C) 72 ◦ C)

63 (extra)

66 (extra)

78 (extra)

Dipole moment µ (D)

−

3.8 (xylene)

−

Number/common name

43 (RO-CM-4513)

44 (RO-CM-4535)

45 (CCH-301)

Substance

CN

CN

H7C3

H3C

H3C

Formula

C16 H25 N

C18 H29 N

C16 H30 O

Molar mass (g/mol)

231.384

259.439

238.417

CAS-RN

122705-86-6

−

−

CH3 O

Liquid Crystals

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Number/common name

43 (RO-CM-4513)

44 (RO-CM-4535)

45 (CCH-301)

Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Refractive index n (589 nm) Dielectric constant ε (1 kHz) Viscosity ν (mm2 /s) (20 ◦ C) Dipole moment µ (D)

Cr 64.9 N 99.7 Is

Cr 79.5 (A 45.0) N 100.0 Is

Cr 10.0 N 17.0 Is

−

−

18.8 (Cr–N)

∆n 0.066, n o 1.457 (89.7 ◦ C) ε⊥ 4.35, ∆ε + 5.03 (89.7 ◦ C) − 3.76

∆n 0.065, n o 1.456 (89.7 ◦ C) ε⊥ 4.12, ∆ε + 4.61 (89.7 ◦ C) − 3.83

− ∆ε − 0.3 (20 ◦ C) 7 (extra) −

Number/common name

46 (CCN55, ZLI-2395)

47 (C33)

48 (C35)

Substance

H11C5

O NC

C5H11

H7C3

O

C3H7

Part 5 1.2

Table 5.1-3 Two-ring systems without bridges, cont.

O H7C3

O

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Anisotropy of refractive index ∆n (extra, 20 ◦ C, 589 nm) Dielectric anisotropy ∆ε (20 ◦ C, 1 kHz) Viscosity ν (mm2 /s) (20 ◦ C)

C23 H41 N 331.59 88510-89-8 Cr 25.0 B 30.0 N 66.0 Is

C19 H34 O2 294.482 − Cr 41.0 B 69.0 N 73.0 Is

C21 H38 O2 322.536 − Cr 44.0 S 46.0 N 74.0 Is

22.6 (Cr–S)

22.6 (Cr–S)

23.8 (Cr–S)

0.03

0.04

0.03

− 8.4 (extra)

− 1.6 (extra)

− 0.8 (extra)

67 (extra)

11 (extra)

13 (extra)

Number/common name

49

50 (RO-CM-7035)

51 (RO-CM-7037, RO-CP-7037)

Substance

N

N H11C5

CN

H11C5

C5H11

N CN

H15C7

N

953

CN N

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Density (g/cm3 ) Anisotropy of refractive index ∆n Dielectric constant ε

C17 H18 N2 250.346 77782-82-2 Cr 33.6 N 43.5 Is

C16 H17 N3 251.334 59855-05-9 Cr 71.0 (N 52.0) Is

C18 H21 N3 279.388 59854-97-6 Cr 45.0 N 51.0 Is

20.9 (Cr–N)

−

0.4 (N–Is)

1.0483 (N, 30.0 ◦ C) 0.176 (T = 0.95T N–Is )

− 0.220 (extra, 20 ◦ C)

− 0.2098

ε 28.7, ∆ε + 17.8 (27.7 ◦ C)

∆ε + 16.0, ε 24.6 (T = 0.98T N–Is )

Viscosity Diamagnetic anisotropy ∆χ (m3 /kg) (×10−12 ) Dipole moment µ (D)

ν 50 mm2 /s (extra, 20 ◦ C) −

∆ε + 21.3, ε 31.3 (T = 0.98T N–Is , 1.592 kHz) ν 55 mm2 /s (extra, 20 ◦ C) −

6.0

6.0

6.7

η 25 mPa s (38 ◦ C) 90.7 (T = 0.98T N–Is )

954

Part 5

Part 5 1.2

Table 5.1-3 Two-ring systems without bridges, cont.

Special Structures

Number/common name

52 (PYP605, ZLI-2543)

Substance

H13C6

53 (PYP606, ZLI-2303)

C5H11 O

N N

C6H13 O

N H13C6

54 (PYP607, ZLI-2304)

N

N H13C6

C7H15 O

N

Formula

C21 H30 N2 O

C22 H32 N2 O

C23 H34 N2 O

Molar mass (g/mol)

326.486

340.513

354.54

CAS-RN

57202-28-5

51518-75-3

57202-29-6

Temperatures of phase transitions T tr (◦ C)

Cr 43.0 N 53.0 Is

Cr 30.5 N 60.8 Is

Cr 35.5 N 58.3 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

29.4 (Cr–N), 1.2 (N–Is)

19.2 (Cr–N), 1.4 (N–Is)

32.7 (Cr–N), 1.5 (N–Is)

Density (g/cm3 )

0.9899 (N, 48.0 ◦ C), 0.9673 (Is, 68.0 ◦ C)

0.9857 (N, 48.0 ◦ C), 0.9618 (Is, 68.0 ◦ C)

0.9806 (N, 48.0 ◦ C), 0.9562 (Is, 68.0 ◦ C)

Refractive index n (589 nm)

n e 1.6217, n o 1.5042 (48 ◦ C)

n e 1.6435, n o 1.4939 (48 ◦ C)

n e 1.6305, n o 1.4940 (48 ◦ C)

Dielectric constant (1 kHz) Viscosity ν

(mm2 /s)

(20 ◦ C)

∆ε + 1.2 (extra,

20 ◦ C)

ε 3.92, ε⊥ 3.14 (T

= 0.97T N–Is )

ε 3.79, ε⊥ 3.10 (T = 0.97T N–Is )

50 (extra)

43 (extra)

49 (extra)

Number/common name

55 (PYP609, ZLI-2306)

56 (PYP707, ZLI-2710)

57 (PYP909, ZLI-2713)

Substance

H13C6

N N

C9H19 O

H15C7

N N

C7H15 O

H19C9

N N

C9H19 O

Formula

C25 H38 N2 O

C24 H36 N2 O

C28 H44 N2 O

Molar mass (g/mol)

382.594

368.567

424.676

CAS-RN

51462-26-1

−

99895-85-9

Temperatures of phase transitions T tr (◦ C)

Cr 35.0 N 61.0 Is

Cr 44.0 C 44.0 A 49.0 N 68.0 Is

Cr 34.0 C 61.0 A 75.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

35.1 (Cr–N), 1.7 (N–Is)

35.5 (Cr–A), 2.0 (N–Is)

35.1 (Cr–C)

Density (g/cm3 )

0.9707 (N, 48.0 ◦ C), 0.9454 (Is, 68.0 ◦ C)

−

0.9650 (C, 48.0 ◦ C), 0.9494 (N, 68.0 ◦ C)

Refractive index n (589 nm)

n e 1.6191, n o 1.4886 (48 ◦ C)

∆n 0.14 (20 ◦ C)

∆n 0.13 (20 ◦ C)

Dielectric anisotropy ∆ε

+ 0.49 (56.0 ◦ C)

+ 1.1 (extra, 20 ◦ C)

+ 0.9 (extra, 20 ◦ C)

Viscosity ν

(mm2 /s)

(20 ◦ C)

63 (extra)

53 (extra)

110 (extra)

Number/common name

58 (PDX3, ZLI-1906)

59 (PDX5, ZLI-1908)

60 (PDX7, ZLI-1910)

Substance

H7C3

O

O CN

H11C5 O

O

O CN

H15C7

CN O

Formula

C14 H17 NO2

C16 H21 NO2

C18 H25 NO2

Molar mass (g/mol)

231.397

259.351

287.405

CAS-RN

−

−

97128-75-1

Temperatures of phase transitions T tr (◦ C)

Cr 52.9 (N 39.3) Is

Cr 56.0 (N 49.0) Is

Cr 54.0 (N 53.0) Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

20.9 (Cr–Is)

21.0 (Cr–Is), 0.4 (N–Is)

26.4 (Cr–Is), 0.8 (N–Is)

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Liquid Crystals

Part 5 1.2

Table 5.1-3 Two-ring systems without bridges, cont. Number/common name

58 (PDX3, ZLI-1906)

59 (PDX5, ZLI-1908)

Crystallographic space group

−

−

P21 21 21

Anisotropy of refractive index ∆n (589 nm, 20 ◦ C)

0.13

0.14

0.13

Dielectric constant ε (1 kHz)

∆ε +32 (20 ◦ C)

∆ε + 29.6, ε⊥ 8.2 (20 ◦ C)

∆ε +32 (20 ◦ C), ∆ε + 7.9 (T = 0.98T N–Is )

Kinematic viscosity ν (mm2 /s)

33 (20 ◦ C)

29.4 (25 ◦ C)

34.7 (25 ◦ C)

Dipole moment µ (D)

4.1

6.2 (C6 H12 )

6.2 (C6 H12 )

60 (PDX7, ZLI-1910)

62

63 (RO-CM-3952)

Table 5.1-4 Two-ring systems with bridges Number/common name Substance

61 C5H11

NC

C3H7 NC

O H5C2

C5H11

Formula

C20 H29 N

C20 H27 N

C21 H34 O

Molar mass (g/mol)

283.461

281.445

302.505

Temperatures of phase transitions T tr (◦ C)

Cr 31.0 N 52.5 Is

Cr 25.1 N 47.5 Is

Cr 27.0 (B 8.0) N 47.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

14.6 (Cr–N), 2.0 (N–Is)

15.2 (Cr–N)

−

Dielectric constant ε (1 kHz)

ε⊥ 4.98, ∆ε + 9.77 (42.5 ◦ C)

ε⊥ 4.61, ∆ε + 11.13 (22 ◦ C)

∆ε − 0.24, ε⊥ 2.98

(22 ◦ C)

η 22.8

(22 ◦ C)

η 12.0 (22 ◦ C)

Dynamic viscosity η (mPa s)

η 22.4

Number/common name

64

Substance

H11C5

Formula

C20 H22 O

C21 H24 O

C24 H30 O

Molar mass (g/mol)

278.398

292.425

334.506

Temperatures of phase transitions T tr (◦ C)

Cr 47.0 N 58.0 Is

Cr 60.0 N 80.0 Is

Cr 41.0 N 65.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

18.0 (Cr–N), 0.6 (N–Is)

23.2 (Cr–N), 1.0 (N–Is)

22.6 (Cr–N), 0.9 (N–Is)

Refractive index n (589 nm)

n e 1.735, n o 1.526 (44.5 ◦ C)

n e 1.726, n o 1.517 (70 ◦ C)

n e 1.683, n o 1.510 (60 ◦ C)

Dielectric constant ε (1 kHz)

ε⊥ 3.58, ∆ε − 0.11

(50 ◦ C)

Kinematic viscosity (mm2 /s)

−

ν 20 (extra, 20 ◦ C)

−

Surface tension (mN/m)

25 (22 ◦ C)

−

−

Number/common name

67 (MBBA)

68 (EBBA)

69 (CBOOA)

Substance

O H3C

65 O CH3

N

C4H9

66

H11C5

O C2H5

∆ε + 0.2, (extra,

O H5C2

N

20 ◦ C)

H11C5

O C3H7

ε⊥ 3.67, ∆ε − 0.18 (55 ◦ C)

C4H9 NC

N

Formula

C18 H21 NO

C19 H23 NO

C22 H26 N2 O

Molar mass (g/mol)

267.374

281.401

334.465

CAS-RN

26227-73-6

29743-08-6

65756-96-9

955

C8H17 O

956

Part 5

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

Special Structures

Number/common name

67 (MBBA)

68 (EBBA)

69 (CBOOA)

Temperatures of phase

Cr 22.0 N 48.0 Is

Cr 36.5 N 79.8 Is

Cr 73.1 A 83.3 N 107.9 Is

15.1 (Cr–N), 0.4 (N–Is)

17.2 (Cr–N), 0.6 (N–Is)

27.6 (Cr–N), 0.7 (N–Is)

−

P21 /c

P21 /c

transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group

(25 ◦ C)

−

Order parameter S

0.55

Density (g/cm3 )

1.042 (N, 25 ◦ C),

1.020 (N, 40 ◦ C),

60 ◦ C)

80 ◦ C)

1.015 (Is, Refractive index n Dielectric constant ε

0.39

(55 ◦ C)

0.988 (Is,

1.009 (A, 83 ◦ C), 1.003 (N, 90 ◦ C), 0.981 (Is, 110 ◦ C) −

n e 1.764, n o 1.549

n e 1.763, n o 1.524

(589 nm, 25 ◦ C)

(578 nm, N, 43.5 ◦ C)

ε 4.72, ε⊥ 5.31

ε 4.37, ε⊥ 4.50

ε 14.4, ε⊥ 7.5

(30 ◦ C, 1.6 kHz)

(73.8 ◦ C)

(95 ◦ C, 1 kHz)

30 ◦ C)

Dynamic viscosity η (mPa s)

23 (N,

Surface tension (mN/m)

34.0 (N, 22 ◦ C), 32.6 (Is, 50 ◦ C)

11 (N,

69 ◦ C)

13 (N, 84 ◦ C)

23.8 (N, 45 ◦ C), 23.3 (Is, 80 ◦ C)

26.1 (A, 80 ◦ C), 26.7 (N, 90 ◦ C), 26.6 (Is, 110 ◦ C)

20 ◦ C),

0.128

0.135 (N,

125 ◦ C),

Thermal conductivity

0.125 (N,

(W/(m K))

(N, 30 ◦ C), 0.145 (N, 50 ◦ C)

(Is, 140 ◦ C)

0.157

Heat capacity C p (J/(mol K))

509 (N, 37 ◦ C), 507 (Is, 49 ◦ C)

540 (N, 37 ◦ C), 590 (Is, 82 ◦ C)

− 401 (A, 80 ◦ C), 474 (N, 100 ◦ C), 514 (Is, 120 ◦ C)

116 (N, 23 ◦ C)

Magnetic susceptibility

47 (T = T N–Is )

−

∆χ (m3 /kg) (×10−12 ) 1200 (N, 33 ◦ C)

Sound velocity v (m/s) Diffusion coefficient D

(m2 /s)

D⊥

8 × 10−10 ,

D

1375 (N, 73 ◦ C, 4.8 GHz) 13 × 10−10

D

2.5 × 10−10

(Is,

89 ◦ C)

1340 (N, 90 ◦ C, 2 MHz) D⊥ 6.6 × 10−8 , D 13.5 × 10−8 (N, 88 ◦ C)

(1000/T = 3.3) Dipole moment µ (D)

3.2 (22 ◦ C)

µ 1.28, µ⊥ 1.35 (73.8 ◦ C)

5.21 (C6 H6 , 25 ◦ C)

Number/common name

70 (BBBA)

71 (HBT)

72 (OBT)

Substance

O H9C4

Formula

C21 H27 NO

C20 H25 NO

C22 H29 NO

Molar mass (g/mol)

309.455

295.428

323.483

CAS-RN

29743-09-7

25959-51-7

−

Temperatures of phase

Cr 8.0 G 41.0 B 45.0 A 45.5

Cr 58.0 (G 44.0 B 53.0)

Cr 70.0 (B 61.5 A 69.0)

transitions

T tr (◦ C)

C4H9

N

CH3

N

O H13C6

O H17C8

N 75.0 Is

N 76.0 Is

N 78.5 Is

Enthalpies of phase transitions

3.3 (Cr–G), 0.7 (G–B),

29.3 (Cr–N), 5.4 (B–N),

−

∆H tr (kJ/mol)

2.9 (B–A), 0.4 (A–N), 0.9 (N–Is)

1.0 (N–Is)

Crystallographic space group

−

−

P1

Order parameter S

0.36 (52 ◦ C)

−

−

Density (g/cm3 )

1.007 (B, 40 ◦ C), 0.990 (N,

Refractive index n (589 nm)

50 ◦ C),

0.964 (Is,

n e 1.670, n o 1.527

75 ◦ C)

(52 ◦ C)

0.985 (N, 70 ◦ C), 0.976 (Is,

CH3

0.9714 (N, 71 ◦ C),

77 ◦ C)

n e 1.692, n o 1.525

N

0.9576 (Is, 81 ◦ C) (71 ◦ C)

n e 1.688, n o 1.500 (72.5 ◦ C)

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Liquid Crystals

Number/common name Dielectric constant ε

(68 ◦ C)

Dynamic viscosity η (mPa s)

70 (BBBA)

71 (HBT)

72 (OBT)

ε 3.99, ε⊥ 4.01 (1 MHz)

ε 4.41, ε⊥ 4.25 (10 kHz)

−

18 (N, 57 ◦ C)

6.5 (N, 70 ◦ C), 7.0 (Is, 80 ◦ C)

8.6 (N, 71 ◦ C), 8.3 (Is, 80 ◦ C)

67 ◦ C),

Heat capacity C p (J/(mol K))

−

689 (N,

Magnetic susceptibility

49 (T = T N–Is )

−

1467 (G, 40 ◦ C), 1405

1358 (N, 70 ◦ C), 1328

624 (Is,

90 ◦ C)

− −

∆χ (m3 /kg) (×10−12 ) Sound velocity v (m/s)

(N,

60 ◦ C)

Number/common name

73

Substance

H3C

(2 MHz)

(Is,

82 ◦ C)

1360 (N, 70 ◦ C), 1332 (Is, 80 ◦ C) (2 MHz)

(2 MHz)

74

75

O NN O

CH3

H15C7

N N

C7H15

H13C6 O

NN O

Formula

C16 H16 N2 O2

C26 H38 N2

C24 H34 N2 O2

Molar mass (g/mol)

268.318

378.606

382.551

CAS-RN

2299-73-2

37592-97-5

10225-93-1

Temperatures of phase

Cr 173.0 N 186.0 Is

Cr 40.0 (A 21.4) N 47.3 Is

Cr 102.6 N 116.2 Is

38.7 (Cr–N), 1.6 (N–Is)

24.4 (Cr–N), 1.1 (N–Is)

39.0 (Cr–N), 1.5 (N–Is)

Cc

−

−

−

0.676 (105.7 ◦ C)

0.9430 (40.6 ◦ C)

0.9493 (Is, 115 ◦ C)

n o 1.5095, ∆n 0.191 (40.3 ◦ C)

−

ε 2.8, ε⊥ 2.5 (23 ◦ C, extra)

ε 3.254, ε⊥ 3.219

transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr

(kJ/mol)

Crystallographic space group Order parameter S Density (g/cm3 )

0.656

(154.2 ◦ C),

0.410

(180 ◦ C)

1.044 (N, 178 ◦ C), 1.023 (Is,

Refractive index n (589 nm) Dielectric constant ε

195 ◦ C)

n e 1.791, n o 1.549 (178 ◦ C) − 0.124

(172.5 ◦ C,

0.8 MHz)

(106 ◦ C, 650 kHz) Dynamic viscosity η (mPa s)

130 (N, 175 ◦ C),

−

−

−

−

−

−

−

10.0 (N, 35 ◦ C)

−

1.3 × 10−9 (N), 2.0 × 10−9

−

−

−

1.87 (C6 H6 )

170 (Is, 197 ◦ C) Surface tension (mN/m)

34.6 (N, 180 ◦ C), 32.9 (Is, 190 ◦ C)

Heat capacity C p (J/(mol K))

572 (N, 180 ◦ C), 606 (Is, 220 ◦ C)

Diamagnetic anisotropy ∆χ (10−11 m3 /kg) Diffusion coefficient D (m2 /s)

(1000/T = 2.15) (Is) Dipole moment µ (D)

−

C6H13

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

957

958

Part 5

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

Special Structures

Number/common name

76 (PAA)

77 (PAP)

78

Substance O H3C

O

(+)

N N

(-)

(-)

(-)

O

O CH3

N N

O

O

(+)

O C2H5

O

H5C2

H7C3

(+)

N N

O C3H7

Formula

C14 H14 N2 O3

C16 H18 N2 O3

C18 H22 N2 O3

Molar mass (g/mol)

258.279

286.333

314.388

CAS-RN

51437-65-1

51437-64-0

104746-32-9

Temperatures of phase

Cr 119.5 N 136.5 Is

Cr 136.8 N 168.4 Is

Cr 118.3 N 124.0 Is

29.6 (Cr–N), 0.6 (N–Is)

26.9 (Cr–N), 1.5 (N–Is)

26.9 (Cr–N), 0.7 (N–Is)

Crystallographic space group

P21 /c

Cc

P21 /n

Order parameter S

0.50 (N, 122 ◦ C)

0.57 (T = 0.90 × T N–Is )

0.605 (T = 0.90 × T N–Is )

Density (g/cm3 )

1.165 (N, 120 ◦ C),

1.096 (N, 142 ◦ C),

1.067 (N, 114 ◦ C),

1.140 (Is, 140 ◦ C)

1.032 (Is, 198 ◦ C)

1.046 (Is, 134 ◦ C)

n e 1.804, n o 1.572

n e 1.784, n o 1.522

n o 1.534 (N, 114 ◦ C, 546 nm)

transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol)

Refractive index n

(589 nm, N, Dielectric constant ε

130 ◦ C)

(589 nm, N,

ε 5.53, ε⊥ 5.69 (126 ◦ C)

Surface tension (mN/m)

2.5 (N, 120 ◦ C), 2.5 (151 ◦ C) 38.8 (N,

126 ◦ C),

∆ε − 0.22 (118.4 ◦ C, 0.8 MHz)

ε 4.77, ε⊥ 4.97 (160 ◦ C,

Dynamic viscosity η (mPa s)

160 ◦ C)

1.2 MHz)

5.2 (N, 164.6 ◦ C) 29.7 (N,

9.6 (N, 121.2 ◦ C)

159 ◦ C),

−

38.0 (Is, 136 ◦ C)

28.8 (Is, 170 ◦ C)

Thermal conductivity

0.135 (N, 125 ◦ C),

−

−

(W/(m K))

0.157 (Is, 140 ◦ C)

Heat capacity C p (J/(mol K))

399 (Cr, 100 ◦ C),

548 (Cr, 126 ◦ C),

609 (Cr, 100 ◦ C),

507 (N, 120 ◦ C),

682 (N, 160 ◦ C),

696 (N, 117 ◦ C),

508 (Is, 150 ◦ C)

643 (Is, 169 ◦ C)

665 (Is, 128 ◦ C)

136 ◦ C)

10.8 (N, 112 ◦ C)

Diamagnetic anisotropy ∆χ (10−11

9.7

(130.8 ◦ C)

13.7 (N,

m3 /kg)

Sound velocity v (m/s)

1240 (N, 130 ◦ C, 3 MHz)

1128 (N, 160 ◦ C, 4.2 MHz)

1247 (N, 121 ◦ C, 3.1 MHz)

D⊥ 5.5 × 10−10 , D 9 × 10−10

D⊥ 7.5 × 10−10 , D 12 × 10−10

D⊥ 4 × 10−10 , D 7 × 10−10

(1000/T = 2.55)

(1000/T = 2.45)

(1000/T = 2.60)

Dipole moment µ (D)

2.3

2.42

2.41

Number/common name

79

80

81

Diffusion coefficient D (m2 /s)

(-)

Substance O

O (+) N N

(-)

(-)

O C4H9

O

O (+) N N

O C5H11

O

H9C4

H11C5

H13C6

Formula

C20 H26 N2 O3

C22 H30 N2 O3

C24 H34 N2 O3

Molar mass (g/mol)

342.442

370.496

398.55

CAS-RN

113787-54-5

107266-21-7

122055-52-1

O (+) N N

O C6H13

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Liquid Crystals

Number/common name

79

80

81

Temperatures of phase transitions T tr (◦ C)

Cr 105.8 N 136.6 Is

Cr 68.0 Cr 76.0 N 124.0 Is

Cr 81.0 (C 74.0) N 129.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

20.9 (Cr–N), 1.0 (N–Is)

14.6 (Cr–N), 0.7 (N–Is)

41.4 (Cr–N), 1.0 (N–Is)

Crystallographic space group

−

P1

−

Order parameter S

0.590 around (T = 0.90 × T N–Is )

0.590 around (T = 0.90 × T N–Is )

1.031 (N, 1.007 (Is, 147 ◦ C)

1.072 (N, 1.063 (Is, 123 ◦ C)

0.990 (N, 125 ◦ C), 0.979 (Is, 132 ◦ C)

Refractive index n (589 nm)

n o 1.516 (127 ◦ C)

n e 1.812, n o 1.518 (103.3 ◦ C)

n e 1.731, n o 1.505 (107.5 ◦ C)

Density

127 ◦ C),

Dielectric anisotropy ∆ε Dynamic viscosity η (mPa s)

− 0.38

(110 ◦ C,

6.9 (N,

131.7 ◦ C)

120 ◦ C),

0.610 around (T = 0.90 × T N–Is )

(g/cm3 )

0.8 MHz)

− 0.29

(105 ◦ C)

13.5 (N,

− 0.65 (99.5 ◦ C, 0.8 MHz)

120 ◦ C)

10.5 (N, 128.1 ◦ C)

Surface tension (mN/m)

110 ◦ C),

32.0 (N, 29.4 (Is, 140 ◦ C)

120 ◦ C),

30.9 (N, 30.6 (Is, 140 ◦ C)

28.4 (N, 120 ◦ C), 27.4 (Is, 140 ◦ C)

Heat capacity C p (J/(mol K))

759 (N, 120 ◦ C), 761 (Is, 143 ◦ C)

718 (Cr, 70 ◦ C), 808 (N, 100 ◦ C), 854 (Is, 125 ◦ C)

828 (Cr, 69 ◦ C), 978 (N, 120 ◦ C), 917 (Is, 155 ◦ C)

Diamagnetic anisotropy ∆χ (10−11 m3 /kg)

10.2 (N, 122 ◦ C)

8.9 (N, 112 ◦ C)

9.5 (N, 109 ◦ C)

Sound velocity v (m/s)

1235 (N, 125 ◦ C, 3.1 MHz)

Diffusion coefficient D

(m2 /s)

5.5 × 10−8 ,

D⊥ D (N, 117.6 ◦ C)

Dipole moment µ (D)

2.38

Number/common name

82

12 × 10−8

1205 (N, 122 ◦ C, 3.1 MHz) 6.0 × 10−8 ,

D⊥ (N, 110 ◦ C)

O (+) N N

O

1160 (N, 125 ◦ C, 3.1 MHz) D⊥ 6.0 × 10−8 , D 13 × 10−8 (N, 113.6 ◦ C)

2.35

2.35

83 (EPAB)

84 (N-4)

(-)

Substance

D

12 × 10−8

(-)

O C7H15

H15C7

O (+) N N

O H5C2 O

(-)

O (+) N

O O C2H5

H9C4

N

Formula

C26 H38 N2 O3

C18 H18 N2 O5

C17 H20 N2 O2

Molar mass (g/mol)

426.604

342.355

284.361

CAS-RN

70906-50-2

6421-04-1

102135-46-6

Temperatures of phase transitions T tr (◦ C)

Cr 74.4 C 95.4 N 124.2 Is

Cr

Cr 16.0 N 76.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

40.9 (Cr–C), 1.6 (C–N), 1.0 (N–Is)

19.7 (Cr–A), 5.0 (A–Is)

−

Crystallographic space group

P1

C2/c, P1 (Cr )

−

−

0.65 (19 ◦ C)

Order parameter S

0.615 (T

= 0.90 × T N–Is )

0.994 (C, 0.985 (N, 105 ◦ C)

1.146 (Is, 1.138 (Is, 135 ◦ C)

1.1217 (N, 20 ◦ C), 1.1067 (N, 40 ◦ C)

Refractive index n

n e 1.673, n o 1.512 (589 nm, N, 117 ◦ C)

−

∆n 0.45 (450 nm), 0.34 (550 nm), 0.30 (650 nm) (20 ◦ C)

Dynamic viscosity η (mPa s)

15.1 (N, 123.5 ◦ C)

−

−

Surface tension (mN/m)

−

26.0 (A, 120 ◦ C), 26.3 (Is, 160 ◦ C)

37.3 (N, 23 ◦ C), 35 (N, 76 ◦ C)

Density

(g/cm3 )

94 ◦ C),

102.0 Cr 115.8 A 123.1 Is

123 ◦ C),

O CH3

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

959

960

Part 5

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

Special Structures

Number/common name

82

83 (EPAB)

84 (N-4)

Heat capacity C p (J/(mol K))

887 (C, 77 ◦ C), 1004 (N, 102 ◦ C), 987 (Is, 127 ◦ C)

675 (A, 116.2 ◦ C), 676 (Is, 130 ◦ C)

511 (N, 61 ◦ C)

Diamagnetic anisotropy ∆χ

7.5 × 10−11 m3 /kg (116 ◦ C)

−

6.9 × 10−10 m3 /mol (75.3 ◦ C)

(80 ◦ C),

(100 ◦ C)

117.4 ◦ C)

Sound velocity v (m/s)

1300 (12 MHz)

Diffusion coefficient D (m2 /s)

D⊥ 3.7 × 10−10 , D 6 × 10−10 (1000/T = 2.60)

−

−

Dipole moment µ (D)

2.36

−

−

Number/common name

85 (RO-CM-1500)

86 (RO-CM-1530)

87 (RO-CM-1510)

Substance

H9C4

1250

1276 (2 MHz,

O O

−

O CN

H11C5

O

O CN

H13C6

O

Formula

C18 H17 NO2

C19 H19 NO2

C20 H21 NO2

Molar mass (g/mol)

279.342

293.369

307.396

CAS-RN

38690-77-6

49763-64-6

50793-85-6

Temperatures of phase transitions T tr (◦ C)

Cr 67.1 (N 42.6) Is

Cr 64.4 (N 55.4) Is

Cr 44.4 N 48.6 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

28.0 (Cr–Is)

25.1 (Cr–Is)

40.2 (Cr–N)

Crystallographic space group

−

P21 /n

−

Density (g/cm3 )

1.095 (N, 40 ◦ C), 1.061 (Is, 80 ◦ C)

1.076 (N, 47.4 ◦ C), 1.053 (Is, 67.4 ◦ C)

1.064 (N, 36.6 ◦ C), 1.043 (Is, 56.6 ◦ C)

Refractive index n

n e 1.639, n o 1.525 (589 nm, N, 39 ◦ C)

n e 1.669, n o 1.512 (546 nm, N, 47.4 ◦ C)

n e 1.657, n o 1.514 (546 nm, N, 36.6 ◦ C)

Dielectric constant ε (1.592 kHz, T = 0.98T N–Is )

ε 34.3, ε⊥ 12.0

ε 30.2, ε⊥ 10.2

ε 29.3, ε⊥ 9.7

Surface tension (mN/m)

−

28.2 (N, 38 ◦ C), 30.7 (53 ◦ C)

−

Dipole moment µ (D)

5.77

−

−

Number/common name

88 (RO-CM-1540)

89

90

Substance

H15C7

O O

O CN

H17C8

O

O CN

H17C8

CN

O O

NO2

Formula

C21 H23 NO2

C22 H25 NO2

C21 H25 NO5

Molar mass (g/mol)

321.423

335.45

371.437

CAS-RN

38690-76-5

50793-86-7

52910-78-8

Temperatures of phase transitions T tr (◦ C)

Cr 44.0 N 56.5 Is

Cr 47.0 N 55.0 Is

Cr 47.5 Cr 50.5 A 61.4 N 68.1 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

31.5 (Cr–N), 1.0 (N–Is)

38.5 (Cr–N)

18.4 (Cr–A), 0.2 (A–N), 0.4 (N–Is)

Crystallographic space group

P21 /n

−

P21 /c

Order parameter S

0.574 (44 ◦ C), 0.42 (56 ◦ C)

−

0.605 (A, 44 ◦ C), 0.31 (N, 66 ◦ C)

Liquid Crystals

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Number/common name Density

(g/cm3 )

Refractive index n Dielectric constant ε

88 (RO-CM-1540) 1.050 (N,

48 ◦ C),

1.034 (Is,

60 ◦ C)

89

90

1.042 (N,

45.8 ◦ C),

1.123 (A, 52 ◦ C),

1.021 (Is,

65.8 ◦ C)

1.110 (N, 66 ◦ C), 1.106 (Is, 70 ◦ C)

n e 1.649, n o 1.505

n e 1.627, n o 1.508

n e 1.644, n o 1.504

(546 nm, N, 45 ◦ C)

(546 nm, N, 50.8 ◦ C)

(589 nm, N, 55 ◦ C)

ε 26.4, ε⊥ 8.7

ε 24.3, ε⊥ 8.5

∆ε 11.1 (60 ◦ C), ∆ε 11.4 (65 ◦ C)

(1.592 kHz, T = 0.98T N–Is )

(1.592 kHz, T = 0.98T N–Is )

(1 kHz)

(50 ◦ C),

(60 ◦ C)

Dynamic viscosity η (mPa s)

22

−

−

Surface tension (mN/m)

27 (22 ◦ C), 25.4 (45 ◦ C)

19.6 (43 ◦ C), 22.5 (58 ◦ C)

−

Sound velocity v (m/s)

1235 (N, 125 ◦ C, 3.1 MHz)

−

1372 (58 ◦ C, 4.74 GHz)

Dipole moment µ (D)

6.1 (CCl4 )

−

6.04

Number/common name

91

92

93

Substance

22

O

O

O

H11C5

CN

O

O

O

H15C7

CN

O

O

O

H17C8

Formula

C19 H19 NO3

C21 H23 NO3

C22 H25 NO3

Molar mass (g/mol)

309.368

337.422

351.449

CAS-RN

50649-73-5

50793-88-9

50793-89-0

Temperatures of phase

Cr 87.0 (N 78.0) Is

Cr 71.5 N 82.0 Is

Cr 75.6 N 88.0 Is

32.2 (Cr–Is)

34.3 (Cr–N)

40.6 (Cr–N)

CN

transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group

Pnam

P21 /a

P1

Density (g/cm3 )

1.093 (N, 69 ◦ C),

1.061 (N, 73 ◦ C),

1.044 (N, 79 ◦ C),

1.075 (Is, 85.5 ◦ C)

1.045 (Is, 88 ◦ C)

1.028 (Is, 94 ◦ C)

n e 1.662, n o 1.513 (76.7 ◦ C)

n e 1.633, n o 1.508 (73.3 ◦ C)

n e 1.627, n o 1.502 (79 ◦ C)

Refractive index n (546 nm)

(71.8 ◦ C)

Dielectric constant ε

ε 27.8, ε⊥ 11.7

Surface tension (mN/m)

29.1 (76 ◦ C), 26.4 (91 ◦ C)

25.0 (73 ◦ C), 22.9 (88 ◦ C)

23.2 (76 ◦ C), 21.1 (91 ◦ C)

Sound velocity v (m/s)

1359 (83 ◦ C, 2 MHz)

−

−

Dipole moment µ (D)

6.6 (CCl4 )

−

−

Number/common name

94 (ME105, ZLI-0245)

95 (ME605, ZLI-1004)

96

Substance

O H3C

O O

C5H11

O H13C6

O O

H9C4 C5H11

O O

Formula

C19 H22 O3

C24 H32 O3

C23 H30 O3

Molar mass (g/mol)

298.385

368.521

354.494

CAS-RN

−

38444-15-4

38454-28-3

Temperatures of phase

Cr 29.5 N 43.5 Is

Cr 50.0 N 63.0 Is

Cr 31.3 N 48.6 Is

17.6 (Cr–N), 0.6 (N–Is)

21.9 (Cr–N)

17.6 (Cr–N)

transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol)

O C6H13

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

961

962

Part 5

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

Special Structures

Number/common name

94 (ME105, ZLI-0245)

95 (ME605, ZLI-1004)

96

Density (g/cm3 ) Refractive index n (589 nm) Dielectric anisotropy ∆ε Kinematic viscosity ν (mm2 /s) Surface tension (mN/m) Dipole moment µ (D)

1.078 (N, 31 ◦ C), 1.061 (Is, 45 ◦ C) n e 1.639, n o 1.515 (35 ◦ C) + 0.11 (38 ◦ C) 38 (20 ◦ C) 24.5 (20 ◦ C) µ 2.18, µ⊥ 2.15 (38 ◦ C)

1.019 (N, 50 ◦ C), 1.001 (Is, 65 ◦ C) n e 1.613, n o 1.490 (47.4 ◦ C) + 0.1 (20 ◦ C, 1 kHz) 87 (20 ◦ C) − −

1.020 (N, 41 ◦ C), 1.006 (Is, 53 ◦ C) n e 1.599, n o 1.498 (41 ◦ C) − − 27.5 (41.5 ◦ C) 2.3 (CCl4 )

Number/common name

97

98

99

O

Substance

H13C6 Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Order parameter S Density (g/cm3 ) Refractive index n

O O

O C4H9

O H17C8

O O

O C6H13

O H21C10

O O

O C6H13

C23 H30 O4 370.493 38454-24-9 Cr 66.0 N 89.5 Is

C27 H38 O4 426.602 54963-63-2 Cr 55.0 C 66.0 N 89.0 Is

35.0 (Cr–N), 1.3 (N–Is)

Dielectric constant ε (1 kHz) Dynamic viscosity η (mPa s) Sound velocity v (m/s) Dipole moment µ (D), 25 ◦ C

0.49 (84 ◦ C) 1.015 (N, 88 ◦ C) n e 1.518, n o 1.394 (80 ◦ C, 650 nm) ∆ε − 0.27 (79 ◦ C) − − 2.67 (CCl4 )

38.0 (Cr–C), 0.4 (C–N), 2.1 (N–Is) 0.49 (84.5 ◦ C) 0.9821 (N, 83 ◦ C) n e 1.5811, n o 1.4828 (83.5 ◦ C, 589 nm) ∆ε − 0.20 (84 ◦ C) 11.4 (80 ◦ C) 1383 (83 ◦ C, 0.36 MHz) 2.86 (C6 H6 )

Number/common name

100 (D55, ZLI-1497)

101 (D301, ZLI-2469)

Substance

H11C5

Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Order parameter S Density (g/cm3 ) Refractive index n (589 nm) Dielectric constant ε (1 kHz) Kinematic viscosity ν (mm2 /s) 20 ◦ C Dipole moment µ (D)

C23 H36 O2 344.542 67589-72-4 Cr 36.0 (A 29.0) N 48.0 Is

C17 H24 O3 276.379 − Cr 55.5 N 62.5 Is

C18 H26 O3 290.406 67589-39-3 Cr 49.0 N 79.8 Is

28.9 (Cr–N), 0.55 (N–Is)

28.0 (Cr–N)

27.6 (Cr–N)

0.67 (39 ◦ C) 0.9508 (N, 36 ◦ C) n e 1.5304, n o 1.4730 (36 ◦ C) ε 2.958, ε⊥ 3.396 (40 ◦ C) 13 (extra)

− − ∆n 0.09 (20 ◦ C) ∆ε − 1.8 (20 ◦ C) 12 (extra)

0.71 (60 ◦ C) 1.0118 (51 ◦ C) n e 1.5304, n o 1.4684 (60 ◦ C) ε 3.28, ε⊥ 4.54 (51 ◦ C) 14 (extra)

1.99

−

2.17

O O

H7C3 C5H11

ε 3.85, ε⊥ 4.05 (85 ◦ C) − 1285 (80 ◦ C, 0.36 MHz) 3.31 (CCl4 ) 102 (D302, ZLI-1496)

O O

C29 H42 O4 454.656 68162-09-4 Cr 62.5 (E 38.0 B 44.5) C 77.5 A 83.3 N 88.9 Is 45.3 (Cr–C), 4.7 (B–C), 0.7 (A–N), 2.1 (N–Is) 0.51 (84 ◦ C) 0.9735 (N, 84.9 ◦ C) −

O CH3

H7C3

O O

O C2H5

Liquid Crystals

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Number/common name

103 (D401, ZLI-2470)

Substance

H9C4

Formula

C18 H26 O3

C19 H28 O3

C19 H28 O3

Molar mass (g/mol)

290.406

304.433

304.433

CAS-RN

67589-46-2

67589-47-3

67589-52-0

Temperatures of phase transitions T tr (◦ C)

Cr 42.0 N 59.0 Is

Cr 36.3 N 74.6 Is

Cr 40.9 N 71.3 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

23.0 (Cr–N)

21.4 (Cr–N)

21.0 (Cr–N), 0.5 (N–Is)

Order parameter S

−

0.73 (40 ◦ C)

0.71 (50 ◦ C)

Density

(g/cm3 )

104 (D402, RO-CM-1942, ZLI-1563)

O O

O CH3

−

1.059 (20 ◦ C)

Refractive index n (589 nm)

∆n 0.09

Dielectric constant ε (1 kHz)

∆ε − 1.8 (20 ◦ C) 14 mm2 /s

O

H9C4

O

O C2H5

(40 ◦ C) (40 ◦ C)

ε⊥ 4.20, ∆ε − 0.91 (65.4 ◦ C) η 20 mPa s

O

H11C5

O

O CH3

1.050 (48 ◦ C)

n e 1.5508, n o 1.4730

(20 ◦ C)

105 (D501, RO-CM-1951, ZLI-1495)

(22 ◦ C)

n e 1.5389, n o 1.4742 (50 ◦ C) ε 3.37, ε⊥ 4.28 (51 ◦ C)

Viscosity

ν

Diamagnetic anisotropy ∆χ (10−11 m3 /kg)

−

3.0 (52 ◦ C)

3.0 (52.5 ◦ C)

Dipole moment µ (D)

−

2.08 (C6 H6 )

2.23 (C6 H6 )

Number/common name

106 (OS33, RO-CM-1633, ZLI-2155)

107 (OS53, RO-CM-1653, ZLI-2256)

108 (OS55, ZLI-2495)

Substance

H7C3

O O

C3H7

−

O

H11C5

O

C3H7

O

H11C5

O

Formula

C19 H34 O2

C21 H38 O2

C23 H42 O2

Molar mass (g/mol)

294.482

322.536

350.59

CAS-RN

73255-62-6

73255-65-9

−

Temperatures of phase transitions T tr (◦ C)

Cr 22.8 N 36.6 Is

Cr 24.5 B 37.5 N 52.0 Is

Cr 52.0 B 72.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

−

29.3 (Cr–S)

31.0 (Cr–S)

Anisotropy of refractive index ∆n (589 nm)

0.036 (25 ◦ C)

0.05 (extra, 20 ◦ C)

−

Dielectric anisotropy ∆ε (1 kHz)

− 1.1 (25 ◦ C)

− 1.5 (20 ◦ C)

− 1.6 (20 ◦ C)

Kinematic viscosity ν (mm2 /s) (20 ◦ C)

11

14

15

Number/common name

109

110

111

Substance

H11C5

Formula

C25 H38 O2

O O

FO C5H11

H11C5 C23 H35 FO2

O

FO C5H11

NC

O

C19 H24 FNO2

C5H11

C5H11

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

963

964

Part 5

Part 5 1.2

Table 5.1-4 Two-ring systems with bridges, cont.

Special Structures

Number/common name

109

110

111

Molar mass (g/mol)

370.58

362.533

317.407

Temperatures of phase transitions T tr (◦ C)

Cr 31.0 N 64.5 Is

Cr 19.0 N 37.9 Is

Cr 75.5 N 93.5 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

29.8 (Cr–N)

33.5 (Cr–N)

−

Refractive index n

n e 1.5337, n o 1.4770 (T = 0.97 × T N–Is , 633 nm)

∆n 0.0608, n e 1.5273 (T = 0.97 × T N–Is , 633 nm)

∆n 0.093 (T = 0.95×T N–Is , 589 nm)

Dielectric constant ε (1 kHz)

ε 2.79, ε⊥ 3.18 (T = 0.97 × T N–Is )

−

∆ε + 4.4 (T = 0.95 × T N–Is )

Viscosity (20 ◦ C)

η 35 mPa s (extra)

ν 16 mm2 /s (extra)

−

113

114

Table 5.1-5 Three and four-ring systems Number/common name

112 (RO-CM-5515, T15)

Substance

H11C5

F

F CN

NC

C5H11

F

H7C3

C3H7

Formula

C24 H23 N

C24 H22 FN

C24 H24 F2

Molar mass (g/mol)

325.458

343.448

350.456

CAS-RN

54211-46-0

−

−

Temperatures of phase transitions T tr (◦ C)

Cr 80.0 Cr 115.0 Cr 131.0 N 240.0 Is

Cr 97.0 N 189.0 Is

Cr 95.0 N 131.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

17.2 (Cr–N), 0.9 (N–Is)

−

24.3 (Cr–N)

Anisotropy of refractive index ∆n (extra, 20 ◦ C, 589 nm)

0.30

0.343

0.24

Dielectric anisotropy ∆ε (1 kHz)

+13, ε 16.0 (T = 0.75 × T N–Is )

+10, (20 ◦ C, extra)

− 1.7, (20 ◦ C, extra)

Kinematic viscosity ν (mm2 /s)

86 (extra, 20 ◦ C)

195 (extra, 20 ◦ C)

31 (extra, 20 ◦ C)

Number/common name

115 (BCH5, ZLI-1131)

116 (BCH32, ZLI-1639)

117 (BCH52, ZLI-1409)

Substance

NC

Formula

C24 H29 N

C23 H30

C25 H34

Molar mass (g/mol)

331.505

306.496

334.55

Temperatures of phase transitions T tr (◦ C)

Cr 96.0 N 222.0 Is

Cr 66.0 S 134.0 N 166.0 Is

Cr 34.0 B 146.0 N 164.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

21.1 (Cr–N), 0.7 (N–Is)

−

18.5 (Cr–B), 6.8 (B–N), 0.5 (N–Is)

Crystallographic space group

P21 /c

−

C2/c

Density (g/cm3 )

1.196 (101 ◦ C)

−

−

Refractive index n

n e 1.734, n o 1.515 (101 ◦ C, 546 nm)

∆n 0.18 (20 ◦ C, 589 nm)

∆n 0.18 (20 ◦ C, 589 nm)

ε 16.8, ε⊥ 4.9 (20 ◦ C, extra)

∆ε + 0.5 (20 ◦ C, extra)

∆ε + 0.4 (20 ◦ C, extra)

Dielectric constant ε (1 kHz) Kinematic viscosity ν

(mm2 /s)

90 (extra,

C5H11

20 ◦ C)

H5C2

20 (extra,

C3H7

20 ◦ C)

H5C2

20 (extra, 20 ◦ C)

C5H11

Liquid Crystals

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Number/common name

118 (BCH52F)

119 F

Substance H11C5 Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Refractive index n

120 F

F C2H5

H11C5

CN

H11C5

F F

C25 H33 F 352.54 − Cr 37.0 N 117.0 Is

C24 H28 FN 349.496 − Cr 84.0 N 175.4 Is

C23 H27 F3 360.467 137019-95-5 Cr 30.4 N 58.0 Is

23.0 (Cr–N)

−

18.0 (Cr–N), 0.2 (N–Is)

∆n 0.201 (20 ◦ C, extra, 589 nm) ∆ε + 20.3 (20 ◦ C, extra)

∆n 0.134 (25 ◦ C, extra, 589 nm) ∆ε + 11.3 (20 ◦ C, extra)

Viscosity (20 ◦ C, extra)

∆n 0.096 (633 nm) (T = 0.97 × T N–Is ) ε 2.97, ε⊥ 2.85 (T = 0.97 × T N–Is ) ν 27 mm2 /s

ν 110 mm2 /s

η 32.1 mPa s

Number/common name

121

122 (BCN55, ZLI-2769)

123

Substance

H11C5

Dielectric constant ε (1 kHz)

F F

H11C5

CN

C5H11

C3H7

NC

F Formula Molar mass (g/mol) Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Anisotropy of refractive index ∆n (589 nm) Dielectric anisotropy ∆ε (extra, 20 ◦ C, 1 kHz) Kinematic viscosity ν (mm2 /s)

C23 H33 F3 366.515 Cr 87.3 N 101.2 Is

Number/common name Substance Formula Molar mass (g/mol) CAS-RN Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Density (g/cm3 ) Refractive index n (T = 0.95 × T N–Is , 633 nm)

C24 H35 N 337.553 Cr 69.0 N 196.0 Is

26.4 (Cr–N), 0.6 (N–Is)

C29 H51 N 413.737 Cr 33.0 B 176.0 A 185.0 N 198.7 Is 17.6 (Cr–B)

0.085 (25 ◦ C, extra)

0.06 (20 ◦ C, extra)

0.17 (20 ◦ C, extra)

+ 7.8

− 4.7

+12

20 (extra, 20 ◦ C)

110 (extra, 20 ◦ C)

75 (extra, 20 ◦ C)

124 (I32)

125 (I35)

126 (I52)

F H5C2 C25 H33 F 352.54

C3H7

F H11C5

−

C3H7

F H5C2

C5H11

Cr 27.0 N 97.0 Is

C28 H39 F 394.621 100497-33-4 Cr 30.0 N 106.0 Is

C27 H37 F 380.594 95379-18-3 Cr 24.0 (B 14.0) N 103.0 Is

−

−

14.2 (Cr–N), 1.3 (N–Is)

1.0156 (N, 25 ◦ C) n e 1.6108, n o 1.4893

0.9975 (N, 25 ◦ C) n e 1.6021, n o 1.4851

1.003 (N, 25 ◦ C) n e 1.6013, n o 1.4824

Part 5 1.2

Table 5.1-5 Three and four-ring systems, cont.

965

966

Part 5

Part 5 1.2

Table 5.1-5 Three and four-ring systems, cont.

Special Structures

Number/common name

124 (I32)

125 (I35)

126 (I52)

Dielectric constant ε Kinematic viscosity ν (mm2 /s)

ε 2.94, ε⊥ 2.93 (T = 0.95 × T N–Is , 0.5 kHz) 19 (20 ◦ C)

ε 2.92, ε⊥ 2.89 (T = 0.95 × T N–Is , 0.5 kHz) 24.5 (20 ◦ C)

∆ε − 0.06, ε (25 ◦ C, 1 kHz) 2.964, ε⊥ 3.024 25.1 (25 ◦ C)

Number/common name

127 (HP5N, ZLI-1226)

128 (HP33, ZLI-1222)

129 (HP35, ZLI-2429)

Substance

H11C5

Formula Molar mass (g/mol) Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Density (g/cm3 ) Refractive index n

C25 H29 NO2 375.515 Cr 82.0 Cr 111.5 N 226.0 Is

C25 H32 O2 364.533 Cr 87.0 N 186.0 Is

C27 H36 O2 392.587 Cr 83.0 (S 79.0) N 175.0 Is

5.4 (Cr–Cr ), 19.0 (Cr–N), 1.4 (N–Is) − ∆n 0.16 (20 ◦ C, 589 nm)

20.9 (Cr–N)

22.0 (Cr–N) − ∆n 0.14 (20 ◦ C, 589 nm)

Dielectric constant ε (1 kHz) Kinematic viscosity ν (mm2 /s)

ε 24.4, ε⊥ 7.5 (156.0 ◦ C) 220 (extra, 20 ◦ C)

1.141 (N, 99.5 ◦ C) n e 1.655, n o 1.509 (99.5 ◦ C, 546 nm) ∆ε + 0.4 (20 ◦ C) 60 (extra, 20 ◦ C)

Number/common name

130 (HH33, ZLI-1224)

131 (HH53, ZLI-1223)

132 (HD34, ZLI-1749)

Substance

H7C3

Formula Molar mass (g/mol) Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group Anisotropy of refractive index ∆n (extra, 589 nm) Dielectric anisotropy ∆ε (20 ◦ C, 1 kHz) Kinematic viscosity ν (mm2 /s)

C25 H38 O2 370.58 Cr 94.0 N 158.0 Is

O O

O O

CN

C3H7

H7C3

H11C5

O O

C3H7

O O

H7C3

C5H11

∆ε + 0.6 (20 ◦ C) 41 (extra, 20 ◦ C)

O O

C3H7

H9C4

O O

C3H7

18.1 (Cr–N)

C27 H42 O2 398.635 Cr 67.0 (S 43.0 A 55.0) N 155.0 Is 21.8 (Cr–N)

C26 H40 O2 384.63 Cr 64.0 S 97.0 S 116.0 N 189.0 Is 13.5 (Cr–S)

P1 0.19 (20 ◦ C)

P1 0.092 (N, 80 ◦ C)

0.11 (20 ◦ C)

−1

−1

− 1.4

130 (extra, 20 ◦ C)

119 (extra, 20 ◦ C)

40 (extra, 20 ◦ C)

Number/common name

133 (CH33)

134 (CH35)

135 (CH45)

Substance

H7C3

Formula Molar mass (g/mol) Temperatures of phase transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Anisotropy of refractive index ∆n (extra, 589 nm)

C25 H44 O2 376.628 Cr 58.0 S 155.0 N 189.0 Is

C27 H48 O2 404.682 Cr 53.0 S 169.0 N 188.0 Is

C28 H50 O2 418.71 Cr 38.0 S 181.0 N 186.0 Is

24.3 (Cr–S)

30.1 (Cr–S)

22.2 (Cr–S)

0.06 (20 ◦ C)

0.06 (20 ◦ C)

0.05 (20 ◦ C)

O O

C3H7

H7C3

O O

C5H11

H9C4

O O

C5H11

Liquid Crystals

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Number/common name

133 (CH33)

134 (CH35)

135 (CH45)

Dielectric anisotropy ∆ε (20 ◦ C, 1 kHz)

− 1.8

− 1.6

− 1.7

Kinematic viscosity ν (mm2 /s)

31 (extra, 20 ◦ C)

34 (extra, 20 ◦ C)

37 (extra, 20 ◦ C)

Number/common name

136 (CBC53, ZLI-1544)

137 (CBC33, ZLI-1987)

138

Substance

H7C3

Part 5 1.2

Table 5.1-5 Three and four-ring systems, cont.

F C5H11

H7C3

C3H7

H11C5

F F

Formula

C32 H46

C30 H42

C29 H37 F3

Molar mass (g/mol)

430.723

402.669

442.613

CAS-RN

80955-71-1

85600-56-2

−

Temperatures of phase transitions (◦ C)

Cr 54.0 Cr 58.0 B 232.0 A 251.0 N 311.0 Is

Cr 108.0 Cr 127.0 Cr 155.0 B 210.0 A 220.0 N 325.0 Is

Cr 87.8 N >250.0 Is

Enthalpies of phase transitions ∆H tr (kJ/mol)

5.1 (Cr–Cr ), 1.4 (Cr–B), 6.1 (B–A), 0.5 (A–N), 1.1 (N–Is)

12.0 (Cr–B), 5.2 (B–A), 1.2 (N–Is)

−

Anisotropy of refractive index ∆n (extra, 589 nm)

0.19 (20 ◦ C)

0.19 (20 ◦ C)

0.144 (25 ◦ C)

Dielectric anisotropy ∆ε (extra, 20 ◦ C, 1 kHz)

+ 0.4

+ 0.5

+ 11.3

Viscosity (extra, 20 ◦ C)

ν 42 mm2 /s

ν 53 mm2 /s

η 51.1 mPa s

140 (C-7)

141 (MHPOBC)

Table 5.1-6 Ferroelectric liquid crystals Number/common name

139 (DOBAMBC)

Substance

O H21C10

Formula

C31 H43 NO3

C25 H33 ClO3

C36 H46 O5

Molar mass (g/mol)

477.693

416.993

558.765

CAS-RN

97335-57-4

100497-43-6

103376-72-3

Temperatures of phase transitions T tr (◦ C)

Cr 74.6 (I* 62.0) C* 94.0 A 117.0 Is

Cr 55.0 C* 55.0 A 62.0 Is

Cr 84.0 CA* 118.4 Cγ 119.2 C* 120.9 Cα 122.0 A 148.0 Is

Enthalpies of phase transitions ∆H tr (J/mol)

2.58 × 104 (Cr–C*), 1.67 × 103 (I–C*), 5.15 × 103 (A–Is)

−

14.6 (C*–Cα), 16.4 (CA*–Cγ ), 18.8 (Cα–C*), 288 (Cα–A), 6420 (A–Is)

Density (g/cm3 )

0.994 (C*, 92 ◦ C), 0.985 (A, 100 ◦ C), 0.959 (Is, 120 ◦ C)

−

−

Refractive index n

n e 1.700, n o 1.490 (A, 110 ◦ C, 633 nm)

−

−

Dynamic viscosity η (mPa s)

6.7 (90 ◦ C)

−

−

Spontaneous polarization Ps (nC/cm2 )

+ 4.75 (65 ◦ C)

+260 (45 ◦ C)

+70 (139.5 ◦ C)

N

CH3 O CH 2 5 O

O H15C7

O CH3 O C2H5 Cl

O H17C8

967

O O

O CH 3 O C6H13

968

Part 5

Part 5 1.2

Table 5.1-7 Cholesteryl (cholest-5-ene) substituted mesogens

Special Structures

Number/common name

142 (CC)

Substance

Cl

143

144 H3C

H3C

H3C

Br H3C

I

CH3

H3C

CH3

H3C

Formula

C27 H45 Cl1

C27 H45 Br

C27 H45 I

Molar mass (g/mol)

405.113

449.569

496.564

CAS-RN

910-31-6

516-91-6

2930-80-5

Temperatures of phase

Cr 95.7 (N* 67.3) Is

Cr 100 (N* 69) Is

Cr 106.5 (N* 95) Is

54.4 (Cr–Is), 0.38 (N*–Is)

−

−

transitions

CH3

T tr (◦ C)

Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group

P21

P21

−

Density (g/cm3 )

0.98

−

−

Dielectric constant ε (10 kHz)

3.52 (60 ◦ C), 5.02 (90 ◦ C)

−

−

Dipole moment µ (D)

2.36 (CCl4 ), 2.48 (C6 H6 )

2.68 (CCl4 ), 2.40 (C6 H6 )

−

Number/common name

145

146

147 (CP)

H3C Substance

H

H3C

O O

H3C

CH3

O H3C O

H3C H3C

CH3

O H5C2 O

H3C

Formula

C28 H46 O2

C29 H48 O2

C30 H50 O2

Molar mass (g/mol)

414.678

428.705

442.732

CAS-RN

4351-55-7

604-35-3

633-31-8

Temperatures of phase

Cr 97.5 (N* 60.5) Is

Cr 116.5 (N* 94.5) Is

Cr 101.6 N* 115.2 Is

22.6 (Cr–Is)

20.1 (Cr–Is), 0.3 (N*–Is)

23.0 (Cr–N*), 0.5 (N*–Is) −

CH3

transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group

−

P21

Density (g/cm3 )

−

0.951 (100 ◦ C), 0.898 (130 ◦ C)

−

95 ◦ C)

Refractive index n

n e 1.482, n o 1.499 (N*,

0.919 (110 ◦ C), 0.901 (130 ◦ C) n e 1.472, n o 1.489 (N*, 589 nm, 107.5 ◦ C)

Dielectric constant ε (10 kHz) Viscosity

2.45 (80 ◦ C), 3.40 (100 ◦ C) η 44 25

Surface tension (mN/m)

(71 ◦ C),

(100 ◦ C)

η 53

(mPa s)

28.5 (70 ◦ C) (95 ◦ C),

2.35 (90 ◦ C), 2.90 (130 ◦ C) 17

(105 ◦ C),

(125 ◦ C)

ν 22.1 mm2 /s (117 ◦ C)

(mPa s)

26.6 (110 ◦ C) (100 ◦ C)

2.22 (80 ◦ C), 2.79 (120 ◦ C)

(100 ◦ C),

24.7 (110 ◦ C) (130 ◦ C)

1245 (113 ◦ C), 1228 (120 ◦ C)

Sound velocity v (m/s) (2 MHz)

1030

Pitch p (µm)

−

−

0.289 (110 ◦ C)

Dipole moment µ (D)

2.50 (CCl4 ), 2.55 (C6 H6 )

2.08 (CCl4 ), 1.98 (C6 H6 )

2.30 (CCl4 ), 2.16 (C6 H6 )

990

1107

1042

Liquid Crystals

1.2 Physical Properties of the Most Common Liquid Crystalline Substances

Number/common name

148

149

Substance

O H 7 C3 O

150

H3C

H3C H3C

CH3

Part 5 1.2

Table 5.1-7 Cholesteryl (cholest-5-ene) substituted mesogens, cont.

O H 9 C4 O

H3 C H3C

CH3

O H11C5 O

H3 C

Formula

C31 H52 O2

C32 H54 O2

C33 H56 O2

Molar mass (g/mol)

456.759

470.786

484.813

CAS-RN

521-13-1

7726-03-6

1062-96-0

Temperatures of phase

Cr 102.0 N* 113.0 Is

Cr 93.0 N* 101.5 Is

Cr 99.5 N* 101.5 Is

22.0 (Cr–N*), 0.6 (N*–Is)

22.0 (Cr–N*), 0.6 (N*–Is)

30.0 (Cr–N*), 0.7 (N*–Is)

CH3

transitions T tr (◦ C) Enthalpies of phase transitions ∆H tr (kJ/mol) Crystallographic space group

P21

P21 21 21

P21

Density (g/cm3 )

0.992 (110 ◦ C), 0.984 (120 ◦ C)

0.893 (99 ◦ C), 0.853 (119 ◦ C)

−

Refractive index n (589 nm)

n e 1.4716, n o 1.4865

n e 1.4763, n o 1.4905

n e 1.4735, n o 1.4880

(N*, 589 nm, 107.0 ◦ C)

(N*, 589 nm, 92.5 ◦ C)

(N*, 589 nm, 95 ◦ C)

Kinematic viscosity ν

(mm2 /s)

Surface tension (mN/m)

22.3

(117 ◦ C)

24.6

(110 ◦ C) (109 ◦ C)

39.8

(97.3 ◦ C)

−

24.6

(110 ◦ C)

25.0 (100 ◦ C)

0.2588

(96.2 ◦ C)

0.247 (97 ◦ C)

Pitch p (µm)

0.260

Dipole moment µ (D)

2.21 (CCl4 ), 2.12 (C6 H6 )

2.34 (CCl4 ), 2.48 (C6 H6 )

1.86 (45 ◦ C, C6 H6 )

Number/common name

151

152

153 (CN)

Substance

O H13C6 O

H3C

H3C H3C

CH3

O H15C7 O

H3C H3C

CH3

O H17C8 O

H3C

Formula

C34 H58 O2

C35 H60 O2

C36 H62 O2

Molar mass (g/mol)

498.84

512.867

526.894

CAS-RN

1182-07-6

1182-42-9

1182-66-7

Temperatures of phase

Cr 114.0 (S 200.0 dec

C5 H11 −COO−

Cr 342.2 S 450.0 Is

C4 H9 −COO−

Cr 111.0 D > 200.0 dec

C6 H13 −COO−

Cr 327.0 S 451.0 Is

C5 H11 −COO−

Cr 95.0 D > 200.0 dec

C7 H15 −COO−

Cr 312.0 A 440.0 Is

C6 H13 −COO−

Cr 93.0 D > 200.0 dec

C8 H17 −COO−

Cr 300.0 A 439.0 Is

C7 H15 −COO−

Cr 88.0 D > 200.0 dec

C9 H19 −COO−

Cr 291.0 A 429.0 Is

C8 H17 −COO−

Cr 102.0 D > 200.0 dec

C11 H23 −COO−

Cr 300.0 A 400.0 Is

C9 H19 −COO−

Cr 106.9 D 210.0 dec

C13 H27 −COO−

Cr 212.4 S 217.9 S 240.3 S 277.6

C15 H31 −COO−

Cr 122.0 D 220.0 dec

S 394.0 Is

Table 5.1-9 Liquid crystal salts, cont. L

R

L

R

H−

−C3 H6 −COO−Tl

Cr 58.4 A 62.4 Is

C5 H11 −O−

−COO−Tl

Cr 160.0 S 294.0 A 344.0 Is

H−

−C5 H10 −COO−Tl

Cr 34.0 A 93.0 Is

C6 H13 −O−

−COO−Tl

Cr 27.0 S 114.0 S 284.0

H−

−C7 H14 −COO−Tl

Cr 39.0 A 107.5 Is

C7 H15 −O−

−COO−Tl

A 343.0 Is Cr 36.0 S 57.0 S 121.0 S 274.0 A 334.0 Is H−

−C9 H18 −COO−Tl

Cr 51.0 A 114.0 Is

C8 H17 −O−

−COO−Tl

C6 H13 −

−COO−Tl

Cr 118.0 S 264.0 A 334.0 Is

C9 H19 −O−

−COO−Tl

Cr 30.0 S 43.0 S 131.0 S 269.0 A 330.0 Is Cr 57.0 S 62.0 S 135.0 S 264.0 A 322.0 Is

1.3 Physical Properties of Some Liquid Crystalline Mixtures

Liquid Crystals

Table 5.1-10 Nematic mixtures Mixture

E49 (Merck)

ZLI-2857 (Merck)

ZLI-3086 (Merck)

Components

Cyanobiphenyls

Temperatures of phase

Cr −9 N 100 Is

Cr −19 N 82.3 Is

N 72.0 Is

0.251

0.0776

0.1131

− 1.4

0.1

46.5

20

Mixture

E7 (Merck)

ZLI-1132 (Merck)

ZLI-4792 (Merck)

Components

Cyanobiphenyls

Phenylcyclohexanes

Fluorinated LCs

Temperatures of phase

Cr 300 K, relaxed Relaxed

Mo

bcc

Ni

fcc

(100) (110) (111)

1×1 1×1 1×1

Relaxed (results controversial) Relaxed Unrelaxed

Pb

fcc

(110)

1×1

Relaxed; annealing at T > 340 K gives a c(2 × 4) reconstruction

Pd

fcc

(100) (110) (111)

1×1 1×1 1×1

Essentially unrelaxed Relaxed Unrelaxed

(100)

1×5

Pt

fcc (110)

1×2

(111)

1×1

77 K < T < 1900 K. Reconstruction model: hexagonal layer slightly rotated. Other metastable superstructures, 1 × 1 and 5 × 20, are observed Reconstruction model: missing-row (Fig. 5.2-4 and Table 5.2-4). Reversible transition to 1 × 1 at T = 1100 K Essentially unrelaxed

1×1 1×1 1×1

Essentially unrelaxed Relaxed Relaxed

Rh

fcc

(100) (110) (111)

Ta

bcc

(100)

1×1

Relaxed

Th

fcc

(111)

1×1

After annealing at T ≈ 1000 K becomes 9 × 9

V

bcc

(100) (110)

1×1 1×1

Relaxed Essentially unrelaxed

(100) W

bcc

c(2 × 2) 1×1 1×1

T < 400 K. Reconstruction model: see Fig. 5.2-6 T > 400 K. Relaxed Unrelaxed

(110) 1

Reference to the original papers is given in [2.3]

The Physics of Solid Surfaces

2.2 Surface Reconstruction and Relaxation

989

Table 5.2-3 Vertical relaxation of metals. Data are given as a percentage of the bulk interlayer distance dbulk . The data are average

values from various authors.1 Errors are expressed as standard deviations from the average. The + sign corresponds to expansion. LEIS, low-energy ion scattering; HEIS, high-energy ion scattering; MEIS: medium-energy ion scattering Crystal Ag

Face

dbulk (Å)

(110)

1.445

2.025

Al

Cu

d34 (%)

Technique

−7.5 (13)

+1.6 (6)

−2 (2)

LEED

−8.6 (8)

+5.1 (8)2

−

LEIS, MEIS

0 (5)

−

−

LEED

−2.4 (24)

−

−

HEIS

−1.6

LEED

−

LEED

(110)

1.427

−7 (2)

(111)

2.329

+1.5 (6)

(100)

1.807

−1.1

+5.0 (2) −

1300 K Annealing Annealing T > 1200 K IBA or MBE

p(2 × 2)

Same as above

c(4 × 2)

Same as above

(110)

16 × 2

(111)

32 × 2 2×1

Annealing T > 1300 K Same as above Cleaving

Diamond

Si

7×7

(100) Ge

(111)

p(2 × 2)

Same as above

c(4 × 2) 2×1

Same as above Cleaving at 40 < T < 400 K Annealing T > 400 K IBA T  850 K MBE + annealing T  670 K IBA T  770–850 K Cleaving, IBA

c(2 × 8)

4×6 (110)

Symmetric dimers

5×5 2×1

c(4 × 4)

GaAs

Model

Cleaving + annealing at 550 K or Annealing at 900 K or MBE Same as above IBA or MBE

c(2 × 8) (100)

Preparation

1×1

GaP

(111)Ga 2 × 2 (1¯ 1¯ 1¯ )As 2 × 2 (110) 1×1

IBA or MBE Same as above Cleaving, IBA

GaSb

(110)

Cleaving

1×1

Remarks

Truncated bulk π-bonded chains Symmetric and/or buckled dimers (Fig. 5.2-7) Ordered arrangement of buckled dimers (Fig. 5.2-8) Ordered arrangement of buckled dimers (Fig. 5.2-10) Dimers + adatoms + terraces (?) Same as above π-bonded chains (Fig. 5.2-11, Table 5.2-6) DAS + vacancies (Fig. 5.2-13)

Same as above Symmetric and/or buckled dimers Ordered arrangement of buckled dimers Same as above π-bonded chains

Present locally (∼ 5 %) Present locally (∼ 5 %) Other superstructures (probably stabilized by impurities) are observed: 4 × 5, 5 × 1, 2 × 1 Transforms irreversibly into 7 × 7 at T  550 K Equilibrium reconstruction

Present locally near steps

Present locally

Adatoms (Fig. 5.2-16)

Same as above Transforms irreversibly into c(2 × 8) at T  400 K Equilibrium reconstruction

Ga (or As) dimers (?)

As coverage 0.22–0.52 As coverage 1 –1.25 As coverage 0.27–0.31

Rotation/relaxation (Fig. 5.2-17, Table 5.2-8) Ga vacancies As trimers Rotation/relaxation (Fig. 5.2-17, Table 5.2-8) Same as above

Part 5 2.2

epitaxy; DAS, dimer–adatom–stacking fault. References are given in [2.3]

992

Part 5

Special Structures

Table 5.2-5 Reconstruction and relaxation of semiconductors, cont. Crystal

Face

Reconstruction

Preparation

Model

Remarks

symmetry

Part 5 2.2

InAs

(110)

1×1

Same as above

Same as above

InSb

(110)

1×1

Same as above

Same as above

CdS

(0001)Cd

1×1

IBA

CdSe

(101¯ 0)

1×1

Cleaving

Rotation/relaxation

Results controversial

(Fig. 5.2-17, Table 5.2-8) ZnO

(0001)Zn

1×1

Cleaving, IBA

placements of atoms that conserve the lengths of the bonds but not their relative angles. Figures 5.2-7 – 5.2-17 give the accepted reconstruction models for a selection of covalent and polar semiconductors, together with STM (scanning tunneling microscopy) images of some of the surfaces. Tables 5.2-6, 5.2-7, and 5.2-8 give the positions of the atoms in reconstructed Si(111) 2 × 1 and Si (111)7 × 7 surfaces and the parameters of the rotation/relaxation model of polar semiconductors. A

p (2 × 2)

B b

A – [110] – [100] [010] [110]

B

1A

0>

0 means that the centroid is outside the edge of the jellium. Figure 5.2-31 shows the dispersion curves of surface plasmons for Al(111). For a more detailed discussion see [2.12]. Table 5.2-13 Surface plasmon parameters. The data are

from various authors. References to the original papers are given in [2.12]

Al

energy (eV)

energy (eV)

10.3

15

– Γ

4.3

7.12

0.48

Na

3.98

5.72

0.73

K

2.73

3.72

0.73

– – X'

Ag(110)

B

–– M

– 110

A

001 – Γ

– – X

EF

–2 –4 –6 –– K

– – X'

– – X

–– M

E (eV) Ag(111)

4 2 A

0.82

3.41 2.90

– Γ

E (eV)

2 0

–– M

EF

–– K

– 110

–2

Li

1.99

4

– – X

0

7.38

Cs

d-band

–6

d⊥(ωsp ) (Å)

Mg

Rb

10.4

EF

–4

6

Bulk plasmon

– 011

– – X

–2

k = (2m E kin /~2 )1/2 sin θ ,

Metal Surface plasmon

– Γ

B

0

Part 5 2.3

surface, the determination of the direction of the emitted or incident electron in ARUPS or KRIPES, respectively, and its energy allows the determination of the dispersion curve through the relation

0.88

1001

– Γ

–– M

–– 1 12

–4 –6 – 8 –– K

– Γ

–– M

–– K

– Γ

1002

Part 5

Special Structures

Fig. 5.2-26 Theoretical projected band structure for the

E (eV)

6

unreconstructed Au(110) surface. Note that in the notation  of this figure, X and M correspond to Y and S, respectively, in the SBZ of Fig. 5.2-18 [2.39]

Au(110)

Part 5 2.3

4

B

2

D

E (eV) A Pd (111)

C

0

2

–2 0

–4 –6

EF

–2

–8 – 10 – Γ

– – X'

–– M

E (eV) – Γ 7

– – X

– Γ

–4

– 6–– K

–– Y Au(110)

6 5

– Γ

Fig. 5.2-28 Theoretical projected band structure (shaded

area) for Pd(111), showing an empty surface state (near Γ) and various occupied surface states and resonances [2.42] –– K

4

–– M

– Γ

–– M

5 E (eV)

Pd (111)

3 4 2 1 2 3 4

1 0

3

2

EF

–1 0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6 k⎮⎮ (Å–1)

Fig. 5.2-27 Comparison of experimental results [obtained by KRIPES for the empty states (dots) and by ARUPS for the initial states (triangles)] with the theoretical calculations of Fig. 5.2-26.  Notice the splitting of the state near Y(X ) probably due to the 2 × 1 reconstruction [2.40, 41]

1

EF = 0

Fig. 5.2-29 Comparison of the dispersion of the empty sur-

face state of Fig. 5.2-28 with experimental results obtained by KRIPES [2.43]

The Physics of Solid Surfaces

– Γ – 5.0 E (eV)

–– Σ SH

–– M D

D

0

the ΓM line obtained by ARUPS and comparison with theory [2.44, 45]

5.2.3.2 Semiconductors

– 1.0 – 1.5

Surface Ionization Energies The ionization energy is defined as the distance of the top of the valence band at the surface from the vacuum level. At low impurity concentrations, the ionization energy is independent of doping and should, preferably, be measured in place of the work function. Table 5.2-14 reports the ionization energies for a number of semiconductors.

– 2.0 – 2.5 – 3.0 – 3.5 1 2 3 4

– 4.0 LL

Surface Core Level Shifts In semiconductors, core levels are shifted because of charge transfer between surface atoms. Table 5.2-15 Table 5.2-14 Ionization energies at semiconductor sur-

– 4.5

faces1 0.4

0.8

1.2

1.6

2.0 k⎮⎮ (Å–1)

Crystal

Face

Reconstruction

Ionization energy (eV)

Diamond

(111) (100) (111)

2×1 2×1 2×1 7×7 2×1 c(2 × 8) 1×1 c(2 × 8) c(4 × 4) 4×6 1×1 1×1 1×1 1×1 1×1 1×1 1×1 1×1

6.25 (25) 5.33 5.24 (9) 5.30 4.77 (2) 4.70 5.98 (3) 5.40 (7) 5.34 (5) 5.05 5.48 (6) 4.79 (9) 5.77 (8) 5.37 (6) 4.84 (6) 6.7 (6) 6.62 5.79 (1)

Si

ω/ωp Al(111)

0.92

Ge

0.88

GaP

(111) (110) (100)

0.84 GaAs

0.80 0.76

RPA

0.72 RDA

0.68

0.1

0.2

0.3

0.4

0.5

0.6

0.7 q⎮⎮ (Å–1)

Fig. 5.2-31 Experimental dispersion of the surface plas-

mon in Al(111) as a function of q (squares) and comparison with theoretical results obtained with two different approximations [2.46]

GaSb InP InAs InSb CdS CdSe CdTe 1

(110) (110) (110) (110) (110) (110) (110) (110)

Data are average values from various authors. Errors are standard deviations. References to the original papers and individual errors are given in [2.47]

Part 5 2.3

The data on elemental semiconductors (including diamond) are ordered according to the atomic number. They are followed by data on some of the compound semiconductors. For a more detailed discussion of the various subjects, the reader may consult [2.8, 10, 11] or the books [2.47, 48].

– 0.5

– 5.0 0

1003

Fig. 5.2-30 Dispersion of surface states for W(100) along

–– Σ W(100) D EF

SH

2.3 Electronic Structure of Surfaces

1004

Part 5

Special Structures

Table 5.2-15 Surface core level shifts for elemental semiconductors1 Crystal

Face

Reconstruction

Core level

Surface shifts (eV) S1

Diamond

Part 5 2.3

Si

(111)

2×1

(100)

2×1 c(2 × 4) 2×1 7×7

(111) (100)

Ge

1

(111)

2×1 c(4 × 2) 2×1 c(2 × 8)

S3

S4

0.062 0.062 0.23 (6) 0.30 (6)

0.29 (5) 0.22 0.64 0.52 (3)

1s

−0.8

2p

−0.49 (3) −0.485 −0.46 (9) −0.74 (5)

−0.230 −0.205 −0.14 −0.07 (5)

3d

−0.49 (7) −0.60 −0.49 (8) −0.73 (3)

−0.21 (3) −0.24 0.44 −0.24 (3)

Data are average values from various authors. Errors are standard deviations. References to original papers and individual errors are given in [2.47]

Table 5.2-16 Surface core level shifts at Ga and As sites in

GaAs1 Face

Reconstruction

Surface shift (eV) Ga(3d)

(100)

c(4 × 4) c(2 × 8) 4×6

(110) 1

S2

1×1

+0.49 +0.3 +0.4 −0.21 +0.28 (0)

Table 5.2-17 Surface core level shifts at (110) surfaces of

III–V compounds1 Crystal

Cation

Anion

AlSb

+0.38

−0.38

GaP

+0.31 (2)

−0.41 (0)

GaAs

+0.28 (0)

−0.370 (5)

GaSb

+0.30

−0.36

InP

+0.30 (2)

−0.30 (1)

InAs

+0.27 (1)

−0.30 (0)

InSb

+0.23 (1)

−0.29 (1)

As(3d) −0.285 (5) +0.55 −0.26 (1) +0.55 (0) −0.45 (16) −0.373 (5)

Data are average values from various authors. Errors are standard deviations. References to the original papers and individual errors are given in [2.47]

gives the shifts for the C(1s), Si(2p), and Ge(3d) levels for various faces and reconstructions. The surface shifts of the 3d levels at the Ga and As sites of GaAs (110) and (100) faces are given in Table 5.2-16. The p and d levels are spin–orbit split and give rise to doublets. Nonequivalent atoms increase further the number of surface shifts. Up to four components are observed in Si and Ge and up to two in GaAs. Unresolved surface shifts for various III–V compounds are given in Table 5.2-17. Surface State Bands The origin and nature of surface states have been discussed in the introduction to Sect. 5.2.3. Here the energy versus k along significant directions of the SBZ and/or the density of states are reported for various reconstructed/relaxed surfaces. The experimental data were

Surface shifts (eV)

1

Data are average values from various authors. Errors are standard deviations. References to the original papers and individual errors are given in [2.47]

obtained mainly with ARUPS and KRIPES or by optical, energy loss, and STM techniques. Because of the large amount of available data, only a selection of dispersion curves and surfaces has been given. For more detailed information, the reader is referred to [2.10, 11]. The rearrangement of unsaturated dangling bonds at the surface is considered to be the driving force for reconstruction of semiconductors. An example of DBs is shown in Fig. 5.2-32a,b that give contours of the charge density for the filled (P) and empty (Ga) surface states on the (110) surface of GaP. In Fig. 5.2-32c, a comparison is made with an STM image taken with a bias voltage that allows the observation of filled and empty states. Figures 5.2-33 – 5.2-36 and 5.2-38 – 5.2-40 give the E(k ) curves for selected surfaces of diamond, Si, Ge,

2.3 Electronic Structure of Surfaces

The Physics of Solid Surfaces

b)

a)

Ga

Ga

P

1005

P

Part 5 2.3

Ga

Ga P

P

c)

– [110]

d)

[001] 4Å

Fig. 5.2-32 (a) Theoretical charge density contours for the filled DB states at P sites on the relaxed GaP(110) surface, (b) the same for the Ga site empty states, (c) comparison with constant current STM images for GaAs(110). The two STM

images refer to filled (As) states (left) and empty (Ga) states (right). The two images are obtained with positive (left) and negative (right) bias. The rectangular unit cell is in the same (absolute) position. (d) Schematic representation of the unit cell. As atoms are shown as empty circles; Ga atoms as black circles [2.49, 50]

GaAs, and CdSe. The local density of states for Si(111) 7 × 7 as obtained from ARUPS and STM spectroscopy is shown in Fig. 5.2-37.

E (eV) 8 C(111) 2 × 1

6

Transitions Between Surface States Transitions between surface state levels give rise to optical absorption and electron energy loss. Such transitions have been observed by SDR, RAS, ellipsometry, and EELS. As an example, the arrows in Figs. 5.2-36 and 5.2-38 show the transitions observed in Si and Ge(111)2 × 1. Notice the high joint density of states caused by the quasi-parallelism of the bands along JK.

4

2

0

–2

– 4– Γ

– J

–– K

Fig. 5.2-33 Theoretical surface state bands (full lines) and resonances (dashed lines) for a relaxed π-bonded chain model of diamond(111)2 × 1. Comparison with experimental results (open circles) obtained by ARUPS along the ΓJ line [2.51, 52]

1006

Part 5

Special Structures

Fig. 5.2-35 Dispersion curves of Si(100)2 × 1 observed by ARUPS

Part 5 2.3

at 21.2 eV. Prominent peaks are indicated by open circles, while weak peaks and shoulders by dots. S and B peaks have surface and bulk characters. The experimental bands should be compared with the surface structures of Fig. 5.2-34. No optical transition clearly associated to S1 , S2 (or Ddown , Dup in Fig. 5.2-34) has been observed in spite of the essential parallelism of the two bands (meaning a high JDOS) [2.54, 55] I

EF = 0

Γ

K

W.X

Si(001) 2 × 1 S2

–1

S1

S1

E (eV) B9

–2

S4

–3 Si(001) 2 × 1

B6

B6 B5

E (eV)

4

K

–4

B8 W

B7

–5

B7

2 –6

Ddown

0

Dup

B1

–2

Di

– 8– Γ

B2

B3

k⎮⎮

Theoretical surface band structure of Si (100)2 × 1, obtained with the asymmetric dimer model (see Sect. 5.2.2.3, Fig. 5.2-7). Ddown and Dup refer to the DB bands at the down and up atoms. The bands labeled S1 – S5 and B1 – B5 are back-bond states (modified by the surface) [2.53]

B5 S1

–6

–' J

J Fig. 5.2-34

B4

–4

B10

–7

–8

S2

S3

E (eV) 2.0

Si(111) 2 × 1

RS

S'4

– 10 S5

– J

1.5

–– K

– 12 1.0 – Γ

– 14 – Γ

– J

–– K

– J'

– Γ

– J'

0.5

SS B Ev A

0 RS

Fig. 5.2-36 Surface band structure of Si(111)2 × 1. Comparison be-

tween theoretical structure based on pseudopotential calculations for the π-bonded chain model (see Sect. 5.2.2.3, Fig. 5.2-11) and experimental results from ARUPS. Photoemission from the excited surface states (around the B point in the figure) is obtained by using highly doped samples. Arrows indicate optical transitions observed in SDR and EELS (see Figs. 5.2-41 and 5.2-43) [2.56, 57] I

SS

– 0.5

– 1.0

– 1.5 – Γ

– J

–– K

The Physics of Solid Surfaces

a) PE

IPE Si(111) 7 × 7

2.3 Electronic Structure of Surfaces

E (eV)

2.5

Ge(111) 2 × 1

– J

–– K

2.0

EF

– J'

Part 5 2.3

– Γ

1.5

1.0

0.5

b) STS

IPE

Si(111) 7 × 7

Ev

B

0

Adatoms EF

– 0.5

A

– 1.0

– 1.5 – Γ

1 2 – J

–– K

Fig. 5.2-38 Surface band structure of Ge(111)2 × 1. Com-

c) STS

IPE

Si(111) 7 × 7

Rest atoms

EF

–5

–4

–3

–2

–1

1007

0

1

2

3 E(eV)

Fig. 5.2-37a–c Density of states associated with the dan-

gling bonds (on the adatoms and “rest atoms”) of the Si(111) 7 × 7 surface (see Fig. 5.2-13), obtained (a) by ARUPS (integrated over all atoms), and (b) and (c) by STM spectroscopy. Notice that the gap (if present) occurs at the Fermi energy [2.57–59]

parison between theoretical structure (in the frame of the chain model) and experimental results obtained with KRIPES (open dots and triangles) and ARUPS (black dots). Photoemission from excited states has been reached by using highly doped Ge. Arrows indicate optical transitions observed in SDR and EELS (see Figs. 5.2-42 and 5.2-44) [2.60–62]

In the dielectric theory of the surface response, the transition probability is proportional to –Im εˆ = ε in the optical absorption and to 2 Im[1/1 + εˆ ] = ε /[(1 + ε )2 + ε ] in EELS, εˆ = ε − iε being the dielectric function of the surface layer. The two techniques give essentially the same results, as shown in Fig. 5.2-45. The great anisotropy of some reconstructed surfaces, as shown in Figs. 5.2-41 and 5.2-42, is reflected in second-harmonic generation, which is specially sensitive to the symmetry of the surface, being forbidden for centrosymmetric media (see Fig. 5.2-46 for Si(111)2 × 1). Surface anisotropy has given rise to the technique of reflectance anisotropy spectroscopy (RAS), in which linearly polarized light is modulated between two principal directions (of the surface tensor) and the difference

1008

Part 5

Special Structures

E (eV) – 3.2

∆R/R Si (111) 2 × 1

6

GaAs (110)

× 10 – 2 – 2.4 5

Part 5 2.3

– 1.6 4

– 0.8 3

Ev

0 2

[011]

0.8

-[211]

1

1.6 – Γ

–– X

–– M

–– X'

– Γ k⎮⎮ 0

Fig. 5.2-39 Surface band structure of GaAs(110). Comparison be-

tween theoretical structure (continous brown line) and experimental determinations: KRIPES ( filled and open circles), ARUPS (dashed line), and two-step photoemission (triangles). It can be noticed that the surface states nearly coincide with the band edges of the projected bulk band structure [2.63–67] E (eV) 4

CdTe (110)

2 S1 (ideal)

S1 (relaxed)

0

1

2

3

4 hν (eV)

Fig. 5.2-41 Surface differential reflectivity (SDR) spectra for Si(111)2 × 1, obtained with two polarizations: with the electric vector parallel ([01¯ 1], filled circles) and perpendicular ([2¯ 11], open circles) to the chains of the π-bonded chain model. For the transitions shown by arrows in Fig. 5.2-36 (hν < 1 eV) the change in reflectivity can be observed only with the electric vector parallel to the chains. The spectrum for hν > 1 eV is associated to transitions along ΓJ in the SBZ. The change of anisotropy at 1.2 eV is conform to the “sum rule”: approximately εx ω dω = ε y ω dω [2.70]

in the reflected light is recorded. Figure 5.2-47 gives an example of RAS spectra for GaAs(100).

–2

5.2.3.3 Magnetic Surfaces S2

–4

– 6– Γ

0

–– X

S3

–– M

–– X'

– Γ

Fig. 5.2-40 Electronic band structure of the CdTe(110) surface.

The open circles show experimental points obtained by ARUPS. Theoretical surface states and resonances are shown by solid and dashed lines, respectively [2.68, 69]

The magnetic moments of atoms near the surface plane, pn (n = 1 for the surface), differ from those for the bulk, pb . The total incremental moment at the surface is defined as ∞  ∆ psb = ( pn − pb ) . n=1

Table 5.2-18 gives the values of pb , pn , and ∆ psb for various ferromagnetic surfaces. Temperature is more effective in destroying the magnetic order at the surface than in the bulk. This

2.3 Electronic Structure of Surfaces

The Physics of Solid Surfaces

∆ R / R (%)

I (arb. units) Si (111) 2 × 1

4.0 3.5

300K

3.0

× 100

along [011]

Part 5 2.3

2.5 2.0

-along [211]

1.5 300K

20K

1.0 × 333

0

1009

0.2

0.4

0.4

0.8

1.0

E loss (meV)

0.5 0

0.5

0

1.0

1.5

2.0

2.5

3.0 3.5 Energy (eV)

Fig. 5.2-43 EELS spectra at T = 20 K and 300 K for

Fig. 5.2-42 Surface differential reflectivity versus energy for

Si(111)2 × 1 ( full and dashed lines) compared with the results of SDR of Fig. 5.2-41 (brown dashed line). The peak of EELS is slightly displaced towards higher energies because of the energy of the factor in front of the dependence

loss function Im 1/ˆε + 1 [2.70, 71]

Ge(111)2 × 1 with polarization parallel and perpendicular to the chains of the π-bonded model. The anisotropy for hν < 1 eV is smaller than for Si(111)2 × 1. The same considerations done in the caption of Fig. 5.2-41 hold also here [2.72] εs''d (Å)

I (arb. units)

150 580 meV

× 100

Si(111) 2 ×1

Ge (111) 2 × 1

20 meV

100

×1000

T = 295 K 415 meV

50

Fig. 5.2-44 EELS spectrum of Ge(111)2 × 1 at room temperature. The same considerations done in the caption of Fig. 5.2-43 hold also here [2.73] 0

effect is shown in Fig. 5.2-48, where the ratio of the polarization P at a given temperature to that at absolute zero is plotted versus temperature. The Curie temperature at the surface TCS is approximately equal to that of the bulk (TC ) in most cases. Table 5.2-19 reports the ratio TCS /TC for a number of materials. A more detailed discussion of the magnetic properties of surfaces is given in [2.13].

0

0.5

1

1.5

2

2.5

3.5 3 Energy (eV)

Fig. 5.2-45 Comparison of SDR (dotted line) [2.70,

74], EELS (solid line) [2.75] and ellipsometry (dashed line) [2.76] spectra for Si(111)2 × 1. The qualitative agreement is remarkable [2.70, 74–76]

1010

Part 5

Special Structures

GaAs(001) ∆r /r 0.004

∆ r/ r

[011]

Si (111) 2 × 1

(2 × 4) T = 585 °C

a

0.002

a)

Part 5 2.3

-[211]

0 – 0.002

c(4 × 4) 189 °C

b

0.002 0

0.002

(4 × 2) 609 °C

c

b)

[011]

– 0.002

0

-[211]

– 0.002

(1 × 6) 488 °C

d

0.002 0

0.002

(4 × 6) 220 °C

e

– 0.002

c)

[011]

0 – 0.002 -[211]

– 0.004 1.5

2.5

3.5

4.5

5.5 E (eV)

Fig. 5.2-47 Reflectance anisotropy spectra for GaAs(100) grown

by MBE at different substrate temperatures in an As4 flux of 2.8 × 10−6 torr. The corresponding reconstructions (as determined by RHEED) are also reported [2.78]

Fig. 5.2-46a–c Intensity of the second harmonic (SH) gen-

eration signal as a function of polarization of the incidence pump beam (1.17 eV), for Si(111)2 × 1. (a) total SH signal; (b) SH component polarized along [21¯ 1¯ ]; (c) SH component polarized along [011¯ ] [2.77]

2.3 Electronic Structure of Surfaces

The Physics of Solid Surfaces

1011

Table 5.2-18 Surface magnetizations at given temperatures. The theoretical values are averages from various authors

(obtained with linearized-augmented-plane-wave or tight-binding methods). References to original papers are given in [2.13] Crystal

Ni

Magnetic moment (Bohr magnetons)

Technique

pb

p1

p2

p3

 psb

(100) (110)

0 0 300

2.25 2.22 2.2

2.96 2.60 2.9 (3)

2.34 2.37

2.45 2.28

1.0 0.66 0.7 (3)

Theory Theory SPLEED

(100)

0 300 0 0 300

0.57

0.67

0.59

0.60

0.62 0.58

0.63 0.63

0.64 0.64

0.58 0.58

0.13 0.03 (3) 0.11 0.11 0.06 (12)

Theory SPLEED Theory Theory SPLEED

(110) (111)

ε

P /P0

1.0

Fe (110)

0.8

a

Fig. 5.2-48 Temperature dependence of magnetic order-

ing. Kerr ellipticity (representing bulk magnetization) and normalized polarization P/P0 of scattered electrons in SPLEED (representing surface magnetization) as a function of T/TC . The solid curves are fits to a Bloch law: m 1 (0) − m 1 (T ) = bT 3/2 , m 1 being the magnetization of the first layer [2.79]

0.6

0.4 b

0.2 SPLEED Kerr

0

0

0.2

0.4

0.6

0.8

1.0 T/ TC

Table 5.2-19 Surface Curie temperatures (TCS ). References to original papers are given in [2.13] Crystal

Face

TC (K)

TCS /TC

Technique

Ni

(100) (110) (111)

630 630 630

1 1 1

SPLEED SPLEED ECS

Fe

(100) (110)

1040 1040

1 1

SPARPES Spin-polarized secondary electrons

EuS

(111)

Gd

(0001)

293

1.000 (4)

SPLEED

1.05–1.07

Tb

(0001)

220

SPLEED

1.14

ECS

16.71 (5)

Part 5 2.3

Fe

T (K)

Face

1012

Part 5

Special Structures

5.2.4 Surface Phonons

Part 5 2.4

The lattice dynamics is strongly perturbed by the presence of the surface. The elements of the force constant matrix connecting two atoms at or near the surface differ from those for the bulk. The number of neighbors is also different at the surface. Vibrational frequencies are generally expected to be lower than in the bulk. Phonon bands occur in the SBZ, similarly to the surface states discussed in Sect. 5.2.3. When the frequency of a surface mode corresponds to a gap in the bulk spectrum, the mode is localized at the surface and is called a surface phonon. If degeneracy with bulk modes exists, one speaks of surface resonances. Surface phonon modes are labeled S j ( j = 1, 2, 3, . . . ), and surface resonances by R j ; when strong mixing with bulk modes is present, the phonon is labeled MS j . The lowest mode that is desired from the (bulk) acoustic band is often called the Rayleigh mode, after Lord Rayleigh, who first predicted (in 1887) the existence of surface modes at lower frequencies than in the bulk.

ν– (cm–1) –– X

[ξ ξ]

– Γ

ν (THz) –– M

[ξ 0]

100

Ag(001)

The experimental results have been obtained mainly through atom and electron scattering, HATOF and EELS.

5.2.4.1 Metals Surface phonon bands along symmetry lines of the SBZ are given for fcc metals in Figs. 5.2-49 – 5.2-55 and in Table 5.2-20. In all figures the horizontal axis is the reduced wave vector, expressed as the ratio to its value at the zone boundary. Table 5.2-21 gives the surface Debye temperatures for some fcc and bcc metals, as well as the amplitudes of thermal vibrations of atoms in the first layer: ρ1 as compared with those of the bulk: ρb . In the harmonic approximation, the root mean square displacement of the atoms is proportional to the inverse of the Debye temperature.

h ω (meV) – Γ 18

–– X

[ξ 0] Ag(110)

3.0 15 2.5

80

12 2.0

MS7

60 1.5

9

40 S4

S1

MS0

1.0 6

20

S1

0.5 3

0 0.5 11 22

ξ

0 0 0 0

0.2

0.4

0.6

0.8

0 1.0 1 0 ξ

Fig. 5.2-49 Surface phonon dispersion curves for Ag(100) measured by EELS. The filled and open circles refer to different electron energies. The full and dashed lines are theoretical fits. Energies are given in cm−1 . 1 cm−1 = 0.1240 meV [2.80]

0

0 [00]

0.2

0.4

0.6

0.8

1.0 [10] ξ

Fig. 5.2-50 Surface phonon dispersion curves for Ag(110)

measured by HATOF. The solid curves are theoretical fits [2.81]

2.4 Surface Phonons

The Physics of Solid Surfaces

1013

Table 5.2-20 Surface phonon energies of fcc metals. References to the original articles are given in the figure captions and/or

in [2.14, 15] Face

Ag

(100) (110)

Energy (meV) and mode S1

(111)

Al

(100) (110) (111)

Au

(110) 2 × 1 (111) (100)

S2

(111)

Ni

(100) (110) (111)

Pd Pt

(110) (111)

Technique

Fig. 5.2-49 Fig. 5.2-50

EELS HATOF

Fig. 5.2-51

HATOF

Fig. 5.2-52

EELS HATOF

S4 8.6 (X)

7.7 (Y)

15.1 (X) 14.6 (X) 8.9 (Y) 17 (M) 18.6 (K)

13.5 (Y) HATOF Fig. 5.2-53

EELS HATOF

Fig. 5.2-54

EELS

7.5 (M) 7.5 (K) 16.7 (M)

Cu (110)

S3

10.2 (M) 8.15 (X) 5.0 (Y) 8.7 (M) 9.1 (K)

Figure

∼ = 14 (X) 7.5 (Y) 13.3 (M) 14.0 (K)

20.2 (M) 14.1 (X)

13.6 (X) 13 (Y)

HATOF

26.1 (M)

19.2 (M) 17 (X) 9.9 (Y) 17.2 (M)

32.2 (M)

11 (X) 6.7 (Y)

9 (Y)

EELS, HATOF 16.1 (X)

Fig. 5.2-55

EELS, HATOF EELS

15.8

EELS HATOF

10.8 (M) 11.1 (K)

HATOF

Table 5.2-21 Surface Debye temperatures of metals. References to the original articles are given in [2.4, 6] Crystal

Ag

Al

Bulk ΘD (K)

Face

Surface ΘD (K)

(100) (110)

104 150–190

ρ1 /ρb

1.5 1.65 1.44

225 (111)

⊥ surface 155 surface 226 247

(100)

200

(110) (111)

140 200

LEED LEED LEIS MEIS HEIS LEED HAS

1.25

428

Technique

LEED HEIS LEED LEED

Part 5 2.4

Metal

1014

Part 5

Special Structures

Table 5.2-21 Surface Debye temperatures of metals, cont. Crystal

Au

Bulk ΘD (K)

Face

Surface ΘD (K)

(100) (110) 2 × 1

82 83 127

165

ρ1 /ρb

Part 5 2.4

1.55

Cu

343

Fe

467

(111)

83

(100)

230 260

(110)

260 (150)

(111)

245

(111) (110)

Ir

420

Mo

450

1.18

LEED LEIS MEIS LEIS MEIS HEIS LEED MEIS

(111)

LEED LEIS LEED

(100)

239

LEED

(110)

Pt

LEED LEED LEIS HEIS LEED

150 160 170

(100)

Ni

1.5 1.5 1.55 1.27

Technique

450

1.46 1.35 ⊥ surface 216 surface 344 395

(111)

⊥ surface 208 surface 348

(100) (110)

118 107

(111)

111

240

MEIS HEIS LEED

1.15

MEIS HEIS LEED

1.20

HEIS

1.6

LEED LEED MEIS LEED MEIS

1.3 Rh

480

(111)

197

LEED

V

380

(100)

250

LEED

(100) 1 × 1 (100) c2 × 2

210 400 (200)

(110)

190–235

LEED LEED HEIS LEED HEIS

W

400

1.5 2.6, 1

2.4 Surface Phonons

The Physics of Solid Surfaces

Fig. 5.2-51 Surface phonon dispersion curves for Ag(111)

measured by HATOF. Cirles are experimental points; solid and dashed lines theoretical calculations. The hatched area represents the projected band structure [2.82]. Very similar plots hold for Au(111) and Cu(111). For appropriate energy parameters see Table 5.2-20

175

– Γ

[0 ξ]

[ξ 0]

Au (110) 1 × 2

–– M

ξ

12

–– K

ω (10 13 rad/s) – Γ

ξ

ξ2

24

Ag(111)

3.5

20

3.0

ν (THz) –– X

16

2.5

5.0

12

4.5

8

Part 5 2.4

ν– (cm–1) –– Y

h ω (meV) – ξ 0 Γ

2.0

[110]

[001] 150

1.5 R1 1.0 4.0

S1

4

S1

0.5

125 3.5

100

75

–– Y'

– S'

–– Y

– S

–– Γ

–– X

3.0

0

0 0 0 ξ

0 0 0 0 ξ

1.0 0 0.5 1.0 1.0 1 0 1 12

2.5 2.0

h ω (meV) – Γ

–– –– X Y

[ξ 0]

[0 ξ]

1.0

h ω (meV) – Γ 24

24 Al (110)

1.5

50

Al (110)

20

20

16

16

25 0.5

0 1.0 [0 1] ξ

0 0 [0 0]

0 1.0 [1 0] ξ

12

12

S3

8

8

Fig. 5.2-53 Surface phonon dispersion curves along two

directions of the SBZ for reconstructed Au(110) 2 × 1, measured by EELS. The dashed lines are theoretical results. In the inset, the SBZ shows the folding due to the 2 × 1 reconstruction that introduces the optical bands. Energies are given in cm−1 . 1 cm−1 = 0.1240 meV [2.84]

S1

S1 4

4

0

0 [0 0] ξ

0.2

0.4

0.6

0.8

1015

0 1.0 1.0 0.8 0.6 0.4 0.2 0 [1 0] [0 1] [0 0] ξ

Fig. 5.2-52 Surface phonon dispersion curves for Al(110). The experimental results (circles) were obtained by HATOF. The solid and dashed lines are theoretical fits. The shaded regions represent the projected bulk modes [2.83]

1016

Part 5

Special Structures

ν– (cm–1) –– X

Ni (001) – Γ

ξξ

ν (THz) –– M

ξ0

ν– (cm–1) –– X

ξξ

Cu (001) – Γ

ξ0

ν (THz) –– M

140

320 2nd+2nd

2nd 2

R6

Part 5 2.4

280

4.0

9

2nd

nd

120

3.5

8 2nd

S6

240

R2

Rs

R 1S 2 200

1

2nd

st

100

3.0

6

1st

2.5

80

R3

2nd

160

2

nd

7

2nd

5

R4

2.0 60

1st

4 S4

S1

120

3

1.5

S1

40 1.0

S4

80

2 40

20

0.5

1

0 0.5 11 22

ξ

0.4

0.3

0.2

0.1

0 0 0 0

0.2

0.4

0.6

0.8

0 1.0 10 ξ

Fig. 5.2-55 Surface phonon dispersion curves of Ni(100) obtained

by EELS. S j , surface phonons; R j , surface resonances. Energies are given in cm−1 . 1 cm−1 = 0.1240 meV [2.86]

0 0.5 11 22

ξ

0 0 0 0

0 1.0 10 ξ

Fig. 5.2-54 Surface phonon dispersion curves for Cu(100)

measured by EELS. The solid and dashed lines are theoretical fits. Energies are given in cm−1 . 1 cm−1 = 0.1240 meV [2.85]

The Physics of Solid Surfaces

2.4 Surface Phonons

1017

5.2.4.2 Semiconductors and Insulators

h ω (meV) –– Y 14

[0 ξ]

GaAs (110) – Γ

[ξ ξ]

– S

Table 5.2-23 Surface phonon energies of alkali halides.

References to the original articles are given in [2.14, 15] Crystal

Face

LiF NaF

(100) (100)

NaCl

(100)

NaI

(100)

KCl RbCl

(100) (100)

Energy of mode S1 (meV) 22.9 (M) 16.0 (M) 18.5 (X) 9.9 (M) 11 (X) 4.1 (M) 4.9 (X) 7.2 (M) 4.7 (M) ∼ = 5.7 (X)

Technique HATOF HATOF HATOF HATOF HATOF HATOF

12

10

8

6

4

2

0 1.0 [0 1] ξ

0 0 [0 0]

1.0 [1 1] ξ

Fig. 5.2-56 Surface

phonon dispersion curves for GaAs(110) measured by HATOF (open circles). The energies at symmetry points are: Y, 8.3, 10.2, and 13.0 meV; Γ, 10.0 meV; S, 8.9 meV [2.87] Table 5.2-22 Surface Debye temperatures of semiconductors. References to the original articles are given in [2.4, 6] Crystal

Bulk ΘD (K)

Face

GaSb InAs

265 249

(110) (110) (100)

Si

640

Surface ΘD (K)

ρ1 /ρb

Technique

1.57 1.65

MEIS MEIS HEED HEED, LEED MEIS HEIS

430–475 1.4 1.45, 2.1

(111) 2 × 1 300

Part 5 2.4

Phonon surface bands of some insulators and semiconductors are given in Figs. 5.2-56 – 5.2-58. Surface phonon energies of alkali halide crytals are summarized in Table 5.2-23. Since insulators and semiconductors have in general more than one atom per unit cell, they display both acoustical and optical branches. Surface Debye temperatures of some semiconductors are given in Table 5.2-22.

1018

Part 5

Special Structures

ω (1013 rad/s) – Γ

–– X

ξξ

ξ 1– ξ

–– M

– Γ

ξ0 NaCl (001)

5

Part 5 2.4

4 S2, S5

S3

S2 LM

S6 3

S4 S8

2

S7

S1

1 S1 +

0 00 ξ

11 22

10

00 ξ

Fig. 5.2-57 Surface phonon dispersion curves for NaCl(100). Theoretical projected band structure (hatched) and experimental points (dots) measured by HATOF. Solid and dashed lines represent theoretical surface states and resonances. Ordinates are given in units of 1013 rad/s = 6.586 meV [2.88, 89]

The Physics of Solid Surfaces

h ω (meV) –– X 14

[ξ 0]

Si (111) 2 × 1 – Γ

2.4 Surface Phonons

1019

V (meV) – S

[ξ ξ]

15.0 h pv 12.5

12

10.0

Part 5 2.4

B T

7.5

10

VT V0 VB

5.0 8 –– X

6

2.5 – S

0 – Γ

4

ε1

–2.5

D ε0

–5.0

2

Zm

–7.5 0 1.0 [0 1] ξ

0 0 [0 0]

1.0 [11] ξ

Fig. 5.2-58 Surface phonon dispersion curves for Si(111) 2 × 1 measured by HATOF. Energies at symmetry points: X, 10.2 and 11.1 meV; S, 10.5 and 11.6 meV. The flat phonon mode at 10.5 meV is associated with the 2 × 1 reconstruction. The surface mode couples with transverse bulk phonons near the center of the SBZ, giving rise to considerable broadening. The shaded area corresponds to the width of the 10.5 meV peak [2.90]. The energy of the optical mode (not shown in the figure) is 56.0 meV [2.91]

5.2.4.3 Atom–Surface Potential Many results on surface phonon dispersions are obtained through atomic (mainly He) scattering. The interaction of an incident atom with a surface is described by the atom–surface potential (Fig. 5.2-59), which consists of a hard repulsive part at short distances and a weak van der Waals attraction at larger distances.

–10.0

1

2

3

4

5

6

7 z (Å)

Fig. 5.2-59 Typical atom–surface potential, with defini-

tions of the main interaction parameters. The surface unit cell is shown in the inset. The numbers on the axes refer to He–Ag(110) [2.92]. V0 : surface averaged potential; VT : potential at the top position; VB : potential at the bottom position

The attractive contribution is often assumed in to be the form C3 Vatt = − . (z − z vW )3 In the potential well between the van der Waals potential and the hard repulsive potential, quantized energy levels εn exist (see Fig. 5.2-59). Table 5.2-24 summarizes the parameters of the atom–surface potentials for a number of surfaces and impinging atoms (or molecules). A more extended discussion is given in [2.14, 15].

1020

Part 5

Special Structures

Table 5.2-24 Parameters of the atom–surface potential. Values of εn are given in the order n = 0, 1, 2, 3 . . . . References

to the original papers are given in [2.15] Crystal

Face

Atom/ molecule

D (meV)

z m (Å)

z vW (Å)

C3 (meV Å3 )

εn (meV)

(110)

H2 He H2 He He He He He He Ne He He He He He

31.7 6.0 32.5 5.2 8.0 6.27 (7) 6.1 8.5 13.5 4.2 (theory) 8.05 8.8

3.27

0.755 0.755 0.2 1.71 1.34 1.21 (−0.2) 1.03 0.79

714 249 714 202 274 235 (473) 106 93 (137) 192 218 211 251 174 265

25.3, 16.4, 9.7, 5.3, 2.5, 1.1 4.44, 2.18, 0.92, 0.31, 0.1 25.5, 16.6, 9.9, 5.4, 2.5, 1.1 3.65 5.91 4.52, 2.2, 1.0, 0.3 (4.2) 4.1, 1.5, 0.31 5.9, 2.46, 0.78, 0.21 11.7

Ag

Part 5 2.5

Al Au Cu GaAs NaCl LiF Ni Pd Pt Si W

(111) (110) (111) (110) (110) (100) (100) (100) (110) (110) 2×1 (100) (110)

2.5 4.47 3.98 3.65 (3.5) 3.49 2.98 3.76 (theory) 3.60

6.42 7.4, 5.1, 3.1, 1.5 5.6

5.2.5 The Space Charge Layer at the Surface of a Semiconductor Surface states in the gap of a semiconductor may trap or loose electrons. The localized charge in surface states is neutralized by a macroscopic space charge layer of opposite sign, caused by accumulation or depletion of the bulk carriers. The potential associated with the space charge gives rise to a band bending of the bulk bands at the surface. Band bending alters various properties of semiconductor surfaces and is crucial for many applications, such as chemisorption, catalysis, corrosion, and, most significantly, channel conductivity in MOS field-effect transistors. For this reason, the problem of the surface space charge layer is treated extensively in the following sections.

5.2.5.1 Definitions and Notation Figure 5.2-60 shows the main parameters that characterize the space charge layer. With reference to the figure, the following definitions can be given:

•

E i (z) is the intrinsic level: this level runs parallel to the band edges and coincides, in the bulk, with the intrinsic Fermi level E ib : E ib =

Ec + Ev 1 Nv . + kB T ln 2 2 Nc

•

The following quantities related to band bending: E F − E i (z) , kB T E ib − E i (z) , v(z) = u(z) − u b ≡ kB T

u(z) ≡

(2.1)

where vs , u s , and u b are the values of v(z), and u(z) at the surface and the value of u(z) in the bulk; u b > 0 for n-type semiconductors and u b < 0 for p-type semiconductors. If vs > 0 the band bends downward; if vs < 0 the band bends upward. vs = 0 is the condition for flat bands, and u s = 0 the condition for an intrinsic surface. An accumulation layer exists if vs and u b have the same sign (as in Fig. 5.2-60). An depletion layer exists if vs and u b have opposite signs and u s and u b have the same sign. An inversion layer exists if both of the pairs vs , u b and u s , u b have opposite signs. • Debye length:  ε0 εb kB T LD = (2.2) , q 2 (n b + pb ) where n b and pb are the bulk carrier concentrations and q is the elementary charge. For small

2.5 The Space Charge Layer at the Surface of a Semiconductor

The Physics of Solid Surfaces

1021

Table 5.2-25 Intrinsic Debye lengths for various semiconductors Si Intrinsic Debye length (cm)

Ge

2.9 × 10−3

GaAs

7.0 × 10−5

InP

2.0 × 10−1

InAs

2.7 × 10−2

InSb

8.6 × 10−6

Normalized potential ⏐v⏐= (eV/kT)

Evac

Inversion and depletion layers

⏐ub⏐ⱜ10

Ec

ν(z)kBT

16 ⏐ub⏐= 8

νskBT

12

⏐ub⏐= 6

8

Ecs u(z)kBT

ub kBT

EF

⏐ub⏐= 4

4

⏐ub⏐= 2 ub = 0 ⏐ub⏐ⱜ2

Ei 0

ub = 0

–4 Eis Eν

–8

Accumulation layer

–12 –16 Eνs

Fig. 5.2-60 Schematic behavior of the bands at the surface

of a semiconductor and definition of the main parameters. Notice that band bending v(z) is positive when the band bends downward

bending (< kB T ), the surface barrier decays as v(z) = vs e−z/L D . For larger bending, the shape of the potential cannot be given in analytic form, though the thickness of the space charge layer is still on the order of the Debye length (see Fig. 5.2-61). Values of the intrinsic Debye length for various semiconductors are given in Table 5.2-25. Figures 5.2-62 and 5.2-63 give L D as a function of the carrier density and bulk resistivity for various semiconductors. Q sc is the space charge density (per unit area), Q ss is the charge density (per unit area) in surface states, and Q total = Q sc + Q ss ;

(2.3)

Q total = 0 in the absence of an external electric field. In the presence of an external field, Q total is the charge density on the field electrode (the gate in a MOSFET).

0

0.2 0.4

0.6

0.8

1.0

1.2 1.4 1.6 1.8 2.0 Normalized distance z/LD

Fig. 5.2-61 Profile of the potential |v(z)| as a function of

z/L D plotted for |vs | = 20 and various values of |u b |. The behavior for other values of |vs | can be obtained by drawing the parallel to the abscissa through the new value |vs | and translating the origin of the abscissa at the value of the interception [2.48, p. 329] LD (nm) 10

3

10 2 p-type diamond (εb = 5.7)

Si (εb = 11.9)

10

1 14 10

Ge (εb = 16.2)

1015

1016

1017 Carrier density (cm–3)

Fig. 5.2-62 Debye length as a function of carrier concen-

tration for Si, Ge and p-type diamond

Part 5 2.5

20

•

2.4 × 10−6

1022

Part 5

Special Structures

Space charge function Fs

LD (nm) 10

20

3

u b = 30

u b = 20

u b = 10

15 ub = 0

10 GaAs –n

Part 5 2.5

10 2

5 Ge – n Ge – p

0 Si– n

–5

Si – p

10

–10 – 70

– 60

– 50

– 40

GaAs – p 1

10 –1

1

10 –2

10 –3 Resistivity (Ω cm)

Fig. 5.2-63 Debye length as a function of resistivity for

n-type and p-type Si, Ge, GaAs

The space charge density and surface potential can be obtained by solving Poisson’s equation for the onedimensional problem at the surface [2.93, 94]. For nondegenerate conditions, one obtains (2.4)

(minus sign if vs > 0), where  1/2 √ cosh(u b + v) F(u b , v) = 2 − v tanh u b − 1 . cosh u b (2.5)

The function Fs is plotted in Fig. 5.2-64 as a function of kB Tvs for various values of u b > 0. To obtain values for u b < 0, the following relation can be used: F(u b , −v) = F(−u b , v) .

– 30 – 20 – 10 0 10 Surface band bending in kBT

Fig. 5.2-64 The space charge function Fs (vs , u b ) for n-type semiconductors (u b > 0) plotted versus band bending vs kB T . The function for p-type semiconductors (u b < 0) may be obtained from the relation: F(u b , −vs ) = F(−u b , vs ) [2.47, p. 25]

various values of u b . The profiles are plotted for |vs | = 20. The behavior, however, has a universal character, since

5.2.5.2 Useful Formulas and Numerical Values

Q sc = ∓q(n b + pb )L D Fs (u b , vs )

ub = 0

n-type sample

(2.6)

The profile of the potential barrier v(z) can be obtained from v z dv = (2.7) , LD ∓Fs (u b , v) vs

which can be solved numerically. Figure 5.2-61 shows v(z) as a function of z/L D for accumulation and depletion/inversion layers and

z − z z − = LD LD

v vs

dv + ∓Fs

v v

dv , ∓Fs

(2.8)

so that curves can be scaled for different values of vs simply by translating the origin. The charge Q ss in the surface states can be calculated once their energy in the gap and their donor or acceptor character is known. (A surface state is called a donor if it is neutral when filled with electrons, and an acceptor if it is neutral when empty.) For a discrete distribution of surface states of densities Nid and N aj , where the superscripts “d” and “a” refer to donors and acceptors, respectively,  Q ss = − q N aj (E j ) f(E j − E F ) j

+q



Nid (E i )[1 − f(E i − E F )] ,

(2.9)

i

where f is the Fermi function. A similar expression holds for a continuous distribution of states. If we define a reduced surface state energy uj ≡

E j − E is , kB T

(2.10)

The Physics of Solid Surfaces

Na = 1012 cm–2

Qsc

The excess carrier densities, defined as ∞

Na = 1010 cm–2

– Qss

(n − n b ) dz ,

∆N =

1.5

(2.12)

excess electron density (per unit area) at the surface, and

uj = 0 uj = –2 uj =2

1.0

∞ ( p − pb ) dz ,

∆P =

(2.13)

0

the excess hole density (per unit area) at the surface, can also be obtained from the function Fs :

0.5

•

for majority carriers in accumulation layers: ∆N = n b L D G + (u b , vs ) (u b > 0, vs > 0) ,

0

∆P = pb L D G + (u b , vs ) (u b < 0, vs < 0) ;

• –10

–5

0

5

Q sc + Q ss = 0, for an intrinsic semiconductor (u b = 0) with a single acceptor surface level at reduced energy u j . Two values of acceptor densities N a are shown. In case of u b = 0, the curves −Q ss should be translated rigidly towards the new origin vs = −u b . When, on the other hand, Q total = 0, the Q ss curves should be translated vertically by Q total . The actual band bending is at the intersection of the two sets of curves

where E is is the intrinsic level at the surface, the Fermi function can be written as 1 . eu j −vs −u b + 1

∆N = n b L D G − (u b , vs ) (u b > 0, vs < 0) ,

10 15 Band bending vs

Fig. 5.2-65 Sketch of the graphical solution of the equation

f(E j − E F ) =

for majority carriers in depletion/inversion layers:

(2.11)

It is then possible to solve (2.1) numerically to obtain the band bending vs . A graphical solution (valid in the absence of an external field) is sketched in Fig. 5.2-65 for an intrinsic semiconductor (u b = 0) with a single surface acceptor level and various values of u j and N aj . For extrinsic semiconductors (u b = 0) the procedure is similar, provided the origin is translated to vs = −u b and the appropriate function for Q sc is chosen. The same procedure can also be used in the presence of an external field by translating the origin of the coordinates.

∆P = pb L D G − (u b , vs ) (u b < 0, vs > 0) ;

•

for minority carriers in accumulation layers: ∆N = pb L D g− (u b , vs ) (u b < 0, vs < 0) , ∆P = n b L D g− (u b , vs ) (u b > 0, vs > 0) ;

•

for minority carriers in depletion/inversion layers: ∆N = pb L D g+ (u b , vs ) (u b < 0, vs > 0) , ∆P = n b L D g+ (u b , vs ) (u b > 0, vs < 0) .

The four functions G + , G − , g+ , g− are defined as +

|vs |

G =

G− =

0 |vs |

0 +

ev − 1 dv , F(|u b |, v) e−v − 1 dv , F(−|u b |, v)

−2|u b |

|vs |

g =e

g− = e−2|u b |

0 |vs |

0

(2.14)

ev − 1 dv , F(−|u b |, v) e−v − 1 dv . F(|u b |, v)

(2.15)

Part 5 2.5

0

uj = 0

–0.5 –15

1023

5.2.5.3 Surface Conductivity

Charge density (10 –9 Ccm –2 ) 2.0

2.5 The Space Charge Layer at the Surface of a Semiconductor

1024

Part 5

Special Structures

Inversion and depletion layers

Accumulation layer

102 5

Minority carriers

Majority carriers

g++1

G ++1 ub = 0

2

Part 5 2.5

10

⏐u b⏐= 20

⏐u b⏐= 15

⏐u b⏐= 10

⏐u b⏐= 5

⏐u b⏐= 2

⏐u b⏐ⱜ 2

⏐u b⏐= 0

5 2 ±1

G –– 1

–5 –10 50

⏐u b⏐= 2

Majority carriers

–2

⏐u b⏐= 20

⏐u b⏐= 5

⏐u b⏐= 10

⏐u b⏐= 15

40

⏐u b⏐= 0

⏐u b⏐= 0

⏐u b⏐= 2

Minority carriers g ––1

30

20

10

0

10

⏐vs⏐

Fig. 5.2-66 Dependence of the functions G + , G − , g+ , g− on |vs | for various values of |u b |. The functions defined in

(2.14), (2.15) can be used to obtain the excess carrier densities for majority and minority carriers in accumulation and depletion/inversion layers [2.93, p. 151] Table 5.2-26 Field-effect mobilities of semiconductors. References to original papers are given in [2.47] Semiconductor Si Ge 1

Face

Reconstruction

Field-effect mobility (cm2 V−1 s−1 )

(111)

2×1 7 × 7 (?) 1 2×1 c(2 × 8)

−(1 ± 0.5) −(0.01 ± 0.003) −(100 ± 50) −(200 ± 50)

(111)

Surface prepared in situ by IBA

The superscripts of the functions indicate the signs of the respective integrals. The above functions are plotted in Fig. 5.2-66 as a function of |vs | and, in greater detail, in Fig. 5.2-67 for an inversion layer (as in a MOSFET). Tabulations are given in [2.94]. The surface excess conductivity is defined as ∆σ = q(µns ∆N + µps ∆P) ,

(2.16)

where ∆N and ∆P are given above. The surface mobilities µns and µps are in general different from the mobilities in the bulk, because of excess scattering at the surface. The surface field-effect mobility can be defined as d∆σ µfe (u b , vs ) = . (2.17) dQ total The presence of surface states, which may capture the carriers, decreases the surface field-effect mobil-

ity. Values of µfe for some surfaces are presented in Table 5.2-26. The very low field effect mobilities reported in Table 5.2-26, show that the Fermi level is pinned in the gap because of the large concentration of surface states. Pinning positions of the Fermi level with respect to the top of the valence band at the surface are given in Table 5.2-27 for various semiconductors. In a MOSFET, the surface conductance of the inversion layer channel between the source and the drain (Fig. 5.2-68) is controlled by the gate potential. The above formulas for the surface conductivity are applicable to MOSFETs under equilibrium conditions (low frequency and low voltage). Here the interface states play the role of surface states at the free surface. The density of interface states should be kept to a minimum for optimal performance. Figure 5.2-69 shows the den-

2.5 The Space Charge Layer at the Surface of a Semiconductor

The Physics of Solid Surfaces

Crystal

Face

Reconstruction

EF − EVS (eV)

Diamond

(111) (100) (111)

2×1 2×1 2×1 7×7 2×1 c(2 × 8) c(2 × 8) c(4 × 4) 4×6 1×1 1×1 1×1 1×1

1.5 0.32 (1) 0.38 (2) 0.69 (3) 0.01 (2) 0.12 (2) 0.47 (7) 0.47 (7) 0.49 Flat bands Flat bands Flat bands Flat bands

Si

(111) (100)

GaAs (110) (110) (110) (110)

GaSb GaP InAs

g++1 103 Inversion layer

7 5 3 2

Part 5 2.5

Ge

102 7 5 3 2

⏐ub⏐= 0.5 ⏐ub⏐= 2 ⏐ub⏐= 5

Table 5.2-27 Pinning position of the Fermi level at semi-

conductor surfaces. Data are average values from various authors. Errors are given as standard deviations. References to the original papers and individual errors are given in [2.47]

10 7 5

⏐ub⏐= 10 ⏐ub⏐= 20

3

sity of interface states in the gap of Si for two different orientations. Channel mobilities are generally lower than bulk mobilities. An example is reported for n- and p-type carriers at the silicon–silicon oxide interface in Fig. 5.2-70. A more extended discussion of the space charge layer may be found in [2.47, 48, 93, 94].

⏐ub⏐= 50

2 ±1 –2 ⏐ub⏐= 0.5

–3 –5 –7

⏐ub⏐= 2 ⏐ub⏐= 5 ⏐ub⏐= 10

⏐ub⏐= 20

– 10 –2 –1 G ––1

0

1

2

3

4

5

6

7

8 9 10 ⏐vs⏐– 2⏐u b⏐

Fig. 5.2-67 More detailed plots of the functions G − , g+ for inOxide

Metal electrode

n-channel VG

Source

Source y

x

VD Gate

z

Drain d

+

n

D L

–VBS (Substrate bias)

n+ p-type

1025

z

Fig. 5.2-68 Schematic drawing of a MOSFET. The

n-inversion layer is obtained with a positive bias of the gate with respect to the source [2.48, p. 345]

version layers. Notice the change of the abscissa to |vs | − 2|u b | [2.93, p. 155]

1026

Part 5

Special Structures

a) µ eff (cm2/V s)

Interface trap density Nis (cm–2 eV–1)

103

1013

Electrons

Si

Part 5 2.6

1012 (111)

10 2 10 10

1011

1012

1013 ⏐Qs /q⏐(cm–2)

2

b) µ eff (cm /V s) 103

1011

Holes (100) 10

10 10 2 10 10

1011

1012

1013 ⏐Qs /q⏐(cm–2)

109

Fig. 5.2-70 Effective mobility of electrons and holes in MOSFET’s

inversion channel. Q s = Q total is the charge on the gate electrode. It is seen that mobility decreases at high transverse electric fields. For comparison, bulk mobilities are: µn = 1600, µp = 600 cm2 /V s [2.96]

– 0.6 – 0.4 Ev

– 0.2 0 Energy (eV)

0.2

0.4

0.6 Ec

Fig. 5.2-69 Interface state density in thermally oxidized silicon for two different orientations. Notice the low density around mid-gap [2.95, after [2.48] p. 340]

5.2.6 Most Frequently Used Acronyms Surface physics, like many other fields, is plagued by the use of acronyms. The acronyms used in this chapter, as well as those most frequently found in the literature, are listed below: AES AFM APS ARUPS ARXPS ATR BB BBZ BEP bl BZ CB CBM CCV chan CISS

Auger electron spectroscopy atomic force microscope/microscopy appearance potential spectroscopy angle-resolved ultraviolet photoemission spectroscopy angle-resolved X-ray photoemission spectroscopy attenuated total reflection back bond bulk Brillouin zone beam-equivalent pressure blocking Brillouin zone conduction band conduction band minimum core–core valence Auger transition channeling collision ion scattering spectroscopy

The Physics of Solid Surfaces

current imaging tunneling spectroscopy cylindrical mirror analyzer chemical vapor deposition core valence–valence Auger transition dimer–adatom–stacking fault dangling bond 2-dimensional Brillouin zone density of states differential reflectivity electron capture spectroscopy energy distribution curve electron-energy loss spectroscopy elastic low-energy electron diffraction electrostatic analyzer electron-stimulated desorption extended X-ray absorption fine structure field emission energy distribution field emission microscope/microscopy field ion microscope/microscopy full-potential linearized augmented plane wave helium atom scattering helium atom time-of-flight spectroscopy high-energy electron diffraction high-energy ion scattering/high-energy ion scattering spectroscopy high-resolution electron energy loss spectroscopy high-resolution LEED high-resolution RHEED ion bombardment ion bombardment and annealing impact ion scattering spectroscopy inverse photoemission inverse photoemission spectroscopy image state ion scattering spectroscopy joint density of states K-resolved inverse photoelectron spectroscopy linearized augmented-plane-wave method local-density approximation local density of states low-energy electron diffraction LEED intensity/voltage measurements low-energy ion scattering/low-energy ion scattering spectroscopy low-energy positron diffraction molecular-beam epitaxy

1027

Part 5 2.6

CITS CMA CVD CVV DAS DB 2D BZ DOS DR ECS EDC EELS ELEED ESA ESD EXAFS FEED FEM FIM FLAPW HAS HATOF HEED HEIS HREELS HR-LEED HR-RHEED IB IBA ICISS IPE IPES IS ISS JDOS KRIPES LAPW LDA LDOS LEED LEED-I/V LEIS LEPD MBE

2.6 Most Frequently Used Acronyms

1028

Part 5

Special Structures

Part 5 2.6

MD MEED MEIS ML MOKE MR NICISS PBBS PDS PED PES PLAP 2P-PES RAS REM RHEED RPA SAM SARS SBZ SCLS SDR SEM sh SHG SIMS SPARPES SPIPES SPLEED SPV SS STM STS SXRD TEM TOF TOM TRS UHV UPS VB VBM VLEED XPS

molecular dynamics medium-energy electron diffraction medium-energy ion scattering/medium-energy ion scattering spectroscopy monolayer magneto-optical Kerr effect missing row neutral impact collision ion scattering spectroscopy projected bulk band structure photothermal displacement spectroscopy photoelectron diffraction photoemission spectroscopy, photoelectron spectroscopy pulsed laser atom probe 2-photon photoemission spectroscopy reflectance anisotropy spectroscopy reflection electron microscope/microscopy reflection high-energy electron diffraction random-phase approximation scanning Auger microscope/microscopy scattering and recoiling ion spectroscopy surface Brillouin zone surface core level shift surface differential reflectivity scanning electron microscope shadowing second-harmonic generation secondary-ion mass spectroscopy spin-polarized angle-resolved photoemission spectroscopy spin-polarized inverse photoemission spectroscopy spin-polarized LEED surface photovoltage spectroscopy surface state scanning tunneling microscope/microscopy scanning tunneling spectroscopy surface X-ray diffraction transmission electron microscope/microscopy time of flight torsion oscillation magnetometry truncation rod scattering ultra-high vacuum ultraviolet photoemission spectroscopy valence band valence band maximum very low-energy electron diffraction X-ray photoemission spectroscopy

The Physics of Solid Surfaces

References

1029

References 2.1

2.2

2.4

2.5

2.6

2.7 2.8

2.9

2.10

2.11

2.12

2.13

2.14

2.15

2.16

2.17

2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25

2.26 2.27

2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39

2.40 2.41 2.42 2.43 2.44 2.45 2.46

J. V. Barth, H. Brune, G. Ertl, R. J. Behm: Phys. Rev. B 42, 9307 (1990) M. K. Debe, D. A. King: Phys. Rev. Lett. 39, 708 (1977) R. M. Tromp, R. J. Hamers, J. E. Demuth: Phys. Rev. Lett. 55, 1303 (1985) K. C. Pandey: Phys. Rev. Lett. 47, 1913 (1981) R. M. Feenstra, W. A. Thompson, A. P. Fein: Phys. Rev. Lett. 56, 608 (1986) K. Takayanagi, Y. Tanishiro, M. Takahashi, S. Takahashi: J. Vac. Sci. Technol. A 3, 1502 (1985) H. Huang, S. Y. Tong, W. E. Packard, M. B. Webb: Phys. Lett. A 130, 166 (1988) S. Y. Tong, H. Huang, C. M. Wei, W. E. Packard, F. K. Men, G. Glander, M. B. Webb: J. Vac. Sci. Technol. A 6, 615 (1988) I. K. Robinson, W. K. Waskiewics, P. H. Fuoss, L. J. Norton: Phys. Rev. B 37, 4325 (1988) R. J. Hamers: Scanning Tunneling Microscopy, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1996) p. 363 W. S. Yang, F. Jona: Phys. Rev. B 29, 899 (1984) N. D. Lang, W. Kohn: Phys. Rev. B 1, 4555 (1970) H. Eckardt, L. Fritsche: J. Phys. F 14, 97 (1984) N. Garcia, B. Reihl, K. H. Frank, A. R. Williams: Phys. Rev. Lett. 54, 591 (1985) M. Echenique, J. B. Pendry: Progr. Surf. Sci. 32, 111 (1990) A. Goldmann, V. Dose, G. Borstel: Phys. Rev. B 32, 1971 (1985) D. M. Kolb, W. Boeck, K.-M. Ho, S. H. Liu: Phys. Rev. Lett. 47, 1921 (1981) B. Reihl, K. H. Frank, R. R. Schlittler: Phys. Rev. B 30, 7328 (1984) S. D. Kevan, R. H. Gaylord: Phys. Rev. B 36, 5809 (1987) K. M. Ho, C. L. Liu, D. M. Kolb, G. Piazza: J. Electroanal. Chem. 150, 235 (1983) K. M. Ho, B. N. Harmon, S. H. Liu: Phys. Rev. Lett. 44, 1531 (1980) S. H. Liu, C. Hinnen, C. Nguyen Van Huong, N. R. De Tacconi, K. M. Ho: J. Electroanal. Chem. 176, 325 (1984) R. A. Bartynski, T. Gustafsson: Phys. Rev. B 33, 6588 (1986) P. Heimann, H. Miosga, H. Neddermeyer: Phys. Rev. Lett. 42, 801 (1979) S. G. Louie: Phys. Rev. Lett. 40, 1525 (1978) P. D. Johnson, N. V. Smith: Phys. Rev. Lett. 49, 290 (1982) M. I. Holmes, T. Gustafsson: Phys. Rev. Lett. 47, 443 (1981) M. Posternak, H. Krakauer, A. J. Freeman, D. D. Koelling: Phys. Rev. B 21, 5601 (1980) K. D. Tsuei, E. W. Plummer, A. Liebsch, E. Pehlke, K. Kempa, P. Bakshi: Surf. Sci. 247, 302 (1991)

Part 5 2

2.3

G. Chiarotti (Ed.): The Physics of Solid Surfaces, Landolt–Börnstein, New Series III/24 (Springer, Berlin, Heidelberg 1993 – 1996) J. F. Nicholas: The Structure of Ideal Surfaces, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1993 ) p. 29 A. Fasolino, A. Selloni, A. Shkrebtii: Surface Reconstruction and Relaxation, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1993) p. 125 E. Zanazzi: Elastic Scattering and Diffraction of Electrons and Positrons, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1995) p. 29 R. Colella: X-ray Diffraction of Surface Structures, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1996) p. 312 P. Alkemade: Elastic and Inelastic Scattering of Ions, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1995) p. 176 R. J. Hamers, R. M. Tromp, J. E. Demuth: Phys. Rev. Lett. 56, 1972 (1986) P. Chiaradia: Optical Properties of Surfaces, Landolt– Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1996) p. 29 K. Jacobi: Electronic Structure of Surfaces: Metals, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1994) p. 29 C. Calandra, F. Manghi: Electronic Structure of Surfaces: Semiconductors, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1994) p. 352 A. M. Bradshaw, R. Hemmen, D. E. Ricken, T. SchedelNiedrig: Photoemission and Inverse Photoemission, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1996) p. 70 M. Rocca: Inelastic Scattering of Electrons, Landolt– Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1995) p. 113 U. Gradmann: Magnetic Properties of Single Crystal Surfaces, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1994) p. 506 R. F. Wallis, S. Y. Tong: Surface Phonons, Landolt– Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1994) p. 433 V. Celli: Interaction of Atoms with Surfaces, Landolt– Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1995) p. 278 G. L. Kellog: Field Emission, Field Ionization and Field Desorption, Landolt–Börnstein, New Series III/24, ed. by G. Chiarotti (Springer, Berlin, Heidelberg 1996) p. 342 W. A. Wood: J. Appl. Phys. 35, 1306 (1963)

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2.47 2.48 2.49 2.50

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2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65

2.66 2.67 2.68 2.69 2.70 2.71

W. Mönch: Semiconductor Surfaces and Interfaces (Springer, Berlin, Heidelberg 1995) H. Lüth: Surfaces and Interfaces of Solid Materials (Springer, Berlin, Heidelberg 1995) F. Manghi, C. M. Bertoni, C. Calandra, E. Molinari: Phys. Rev. B 24, 6029 (1981) J. A. Stroscio, R. M. Feenstra, D. M. Newns, A. P. Fein: J. Vac. Sci. Technol. A 6, 499 (1988) V. Vanderbilt, S. G. Louie: Phys. Rev. B 30, 6118 (1984) F. J. Himpsel, D. E. Eastman, P. Heimann, J. F. van der Veen: Phys. Rev. B 24, 7270 (1981) P. Kruger, A. Mazur, G. Wolfgarten: Phys. Rev. Lett. 57, 1468 (1986) P. Koke, A. Goldmann, W. Monch, G. Wolfgarten, J. Polmann: Surf. Sci. 152/153, 1001 (1985) A. Goldmann, P. Koke, W. Monch, G. Wolfgarten, J. Polmann: Surf. Sci. 169, 438 (1986) J. E. Northrup, M. L. Cohen: Phys. Rev. Lett. 49, 1349 (1982) P. Martensson, A. Cricenti, G. V. Hansson: Phys. Rev. B 32, 6959 (1985) F. J. Himpsel, T. Fauster: J. Vac. Sci. Technol. A 2, 815 (1984) R. Wolkov, P. Avouris: Phys. Rev. Lett. 60, 1049 (1988) J. M. Nicholls, B. Reihl: Surf. Sci. 218, 237 (1989) J. M. Nicholls, P. Martensson, G. V. Hansson: Phys. Rev. Lett. 54, 2363 (1985) J. E. Northrup, M. L. Cohen: Phys. Rev. B 27, 6553 (1983) D. Straub, M. Skibowski, F. J. Himpsel: Phys. Rev. B 32, 5237 (1985) B. Reihl, T. Riesterer, M. Tschudy, P. Perfetti: Phys. Rev. B 38, 13456 (1988) J. Henk, W. Shattke, H. P. Hannescheidt, C. Janowitz, R. Manzke, M. Skibowski: Phys. Rev. B 39, 13286 (1989) A. Huijser, J. van Laar, T. L. van Roy: Phys. Lett. A 65, 337 (1978) Zhu, S. B. Zhang, S. G. Louie, M. L. Cohen: Phys. Rev. Lett. 63, 2112 (1989) K. O. Magnusson, S. A. Flodstrom, P. E. S. Persson: Phys. Rev. B 38, 5384 (1988) Y. R. Wang, C. B. Duke, K. O. Magnusson, S. A. Flodström: Surf. Sci., 205, 2760 (1988) S. Selci, P. Chiaradia, F. Ciccacci, A. Cricenti, N. Sparvieri, G. Chiarotti: Phys. Rev. B 31, 4096 (1985) N. J. DiNardo, J. E. Demuth, W. A. Thompson, P. Avouris: Phys. Rev. B 31, 4077 (1985)

2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96

G. Chiarotti, P. Chiaradia, E. Faiella, C. Goletti: Surf. Sci. 453, 112 (2000) J. E. Demuth, R. Imbihl, W. A. Thompson: Phys. Rev. B 34, 1330 (1986) G. Chiarotti, S. Nannarone, R. Pastore, P. Chiaradia: Phys. Rev. B 4, 3398 (1971) H. Froitzheim, H. Ibach, D. L. Mills: Phys. Rev. B 11, 4980 (1975) M. K. Kelly, S. Zollner, M. Cardona: Surf. Sci. 285, 282 (1993) T. F. Heinz, M. M. T. Loy, W. A. Thompson: Phys. Rev. Lett. 54, 63 (1985) I. Kamiya, D. E. Aspness, L. J. Florez, J. P. Harbison: Phys. Rev. B 46, 15894 (1992) M. Taborelli, O. Paul, O. Zuger, M. Landolt: J. Phys. (Paris) Colloq. 8, 1659 (1988) P. Moretto, M. Rocca, U. Valbusa, J. E. Black: Phys. Rev. B 41, 12905 (1990) G. Bracco, R. Tatarek, F. Tommasini, U. Linke, M. Persson: Phys. Rev. B 36, 2928 (1987) U. Harten, J. P. Toennies, Ch. Woll: Faraday Discuss. Chem. Soc. 80, 137 (1985) J. P. Toennies, C. Wöll: Phys. Rev. B 36, 4475 (1987) B. Voigtlander, S. Lehwald, H. Ibach, K. P. Bohnen, K. M. Ho: Phys. Rev. B 40, 8068 (1989) M. Wuttig, R. Franchy, H. Ibach: Z. Phys. B 65, 71 (1986) M. Rocca, S. Lehwald, H. Ibach, T. S. Rahman: Surf. Sci. 171, 632 (1986) U. Harten, J. P. Toennies: Europhys. Lett. 4(7), 833 (1987) A. Safron, W. P. Brug, G. Chern, J. Duan, J. G. Skofronick: J. Vac. Sci. Technol. A 8, 2627 (1990) G. Benedek, G. Brusdeylins, R. B. Doak, J. G. Skofronick, J. P. Toennies: Phys. Rev. B 28, 2104 (1983) U. Harten, J. P. Toennies, C. Woll: Phys. Rev. Lett. 57, 2947 (1986) H. Ibach: Phys. Rev. Lett. 27, 253 (1971) D. Eichenauer, U. Harten, J. P. Toennies, V. Celli: J. Chem. Phys. 86, 3693 (1987) A. Many, Y. Goldstein, N. B. Grove: Semiconductor Surfaces (North-Holland, Amsterdam 1965) D. R. Frankl: Electrical Properties of Semiconductor Surfaces (Pergamon, Oxford 1967) M. H. White, J. R. Cricchi: IEEE Trans. Electron Dev. 19, 1280 (1972) O. Leistiko, A. S. Grove, C. T. Sah: IEEE Trans. Electron Dev. 12, 248 (1965)

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Mesoscopic an

5.3. Mesoscopic and Nanostructured Materials

5.3.1 Introduction and Survey...................... 5.3.1.1 Historical Review..................... 5.3.1.2 Definitions ............................. 5.3.1.3 Specific Properties ................... 5.3.1.4 Organization of this Chapter .....

1031 1031 1032 1034 1034

5.3.2 Electronic Structure and Spectroscopy... 5.3.2.1 Electronic Quantum Size Effects . 5.3.2.2 Breakdown of the Momentum Conservation Rule ................... 5.3.2.3 Excitons in Quantum-Confined Systems.. 5.3.2.4 Vibrational Modes and Electron–Phonon Coupling. 5.3.2.5 Electron Transport Phenomena .

1035 1035 1036 1036 1040 1042

5.3.3 Electromagnetic Confinement .............. 1044 5.3.3.1 Nanoparticle-Doped Materials .. 1044 5.3.3.2 Periodic Electromagnetic Lattices........... 1048 5.3.4 Magnetic Nanostructures..................... 1048 5.3.4.1 Spin Electronics....................... 1049 5.3.4.2 Ultrahigh-Density Storage Media in Hard Disk Drives......... 1060 5.3.5 Preparation Techniques ...................... 5.3.5.1 Molecular-Beam Epitaxy .......... 5.3.5.2 Metal-Organic Chemical Vapor Deposition (MOCVD) ................. 5.3.5.3 Lithography ............................ 5.3.5.4 Nanocrystals in Matrices........... 5.3.5.5 Ex Situ Synthesis of Clusters ......

1063 1063 1064 1064 1064 1065

References .................................................. 1066

5.3.1 Introduction and Survey 5.3.1.1 Historical Review Except in the life sciences, there are only a few examples of materials that are naturally structured on scales of the order of a few to a few hundred nanometers. One

can cite, however, the natural zeolites, which constitute a group of hydrated crystalline aluminosilicates containing regularly shaped pores with sizes from 1 nm to several nanometers. This provides them the ability to reversibly adsorb and desorb specific molecules.

Part 5 3

This chapter addresses the properties of nanostructured materials considered as statistical ensembles of nanostructures. Emphasis is put on size and confinement effects, although enhancements in surface and interface properties are mentioned. After a survey and a summary of basic definitions and concepts in the introductory Sect. 5.3.1, the properties associated with electronic confinement are addressed in Sect. 5.3.2. Electronic confinement affects the spectral properties, i. e. light absorption and luminescence, mainly through quantum size effects, and the electrical conduction properties through the Coulomb blockade. Both two-dimensional systems (quantum wells) and zero-dimensional systems (quantum dots) are reviewed. Particular attention is drawn to semiconductor-doped matrices. The effects associated with confinement of electromagnetic fields are treated in Sect. 5.3.3. Numerical relationships and data for plasmon excitations of various metal nanoparticles can be found in this section. Magnetic nanostructures are addressed in Sect. 5.3.4. The two main applications of nanostructured magnetic materials, namely spin electronics, or spintronics, and ultrahigh-density data storage media, are treated. Finally, we list and briefly describe in Sect. 5.3.5 some generic techniques for the preparation of nanostructured materials, organized into the following groups of methods: molecular-beam epitaxy (MBE), metal-organic chemical vapor deposition (MOCVD), nanolithography, nanocrystal growth in matrices, and ex-situ synthesis of clusters.

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Part 5 3.1

They were named “zeolite” (“boiling stone”) in 1756 by Cronstedt, a Swedish mineralogist, who observed their emission of water vapor when heated. At the other size limit, opals constitute another example of a naturally occurring nanostructured material. These gems are made up mainly of spheres of amorphous silica with sizes ranging from 150 nm to 300 nm. In precious opals, these spheres are of approximately equal size and can thus be arranged in a three-dimensional periodic lattice. The optical interferences produced by this periodic index modulation are the origin of the characteristic iridescent colors (opalescence). Apart from these few examples, most nanostructured materials are synthetic. Empirical methods for the manufacture of stained glasses have been known for centuries. It is now well established that these methods make use of the diffusion-controlled growth of metal nanoparticles. The geometrical constraints on the electron motion and the electromagnetic field distribution in noble-metal nanoparticles lead to the existence of a particular collective oscillation mode, called the plasmon oscillation, which is responsible for the coloration of the material. It has been noticed recently that the beautiful tone of Maya blue, a paint often used in Mesoamerica, involves simultaneously metal nanoparticles and a superlattice organization [3.1]. The chemistry and color changes of colloidal gold solutions were observed by Faraday during the 19th century [3.2]. These properties were due to highly sizedispersed gold nanoparticles. Improvements in the diffusion-controlled growth technique opened up the possibility of growing nanocrystallites with better-controlled sizes and densities and permitted its extension to various semiconductors. The fabrication of colored long-wavelength-pass glasses and of photochromic glasses provides wellknown examples of commercial technologies based on such methods developed decades ago. Various techniques for the production and assembly of cluster- and nanoparticle-based materials are currently under intense study. More recently, important technological efforts have been made, driven by the increasing needs of the electronics industry, in order to understand and control the growth of semiconductors at the atomic level. The development of molecular-beam epitaxy (MBE) permitted the control of atomic-layer-by-atomic-layer growth of semiconductors. It has become possible to create structures made up of an alternation of different layers, each of which is only a few atomic layers thick. The first observation of the quantization of energy levels in

a quantum well in 1974 [3.3] opened the way to the tailoring of the electronic wave function in one dimension on the nanometer scale, leading to the production of new electronic and also magnetic materials. A new trend in surface science is work aimed at the control of in-plane nanostructuring, such as the formation of wire or dot shapes, through self-organization. In parallel to developments in the field of electronics, nanostructured materials have been developed by materials scientists and chemists also. The concept of nanocrystalline structures emerged in the field of materials science, and polycrystals with ultrafine grain sizes in the nanometer range have been produced. These “nanophase materials” have been shown to have significant modifications of their mechanical properties compared with the coarse-grain equivalent materials. The huge surface area of nanoporous materials has attracted much attention for applications in chemistry such as molecular sieves, catalysis, and gas sensing. This has motivated intense research aimed at the fabrication of materials with a well-controlled composition and nanoscale structure, such as synthetic zeolites. The scientific and technological domains of research on nanostructured materials cover a range of disciplines, from biology to physics and chemistry. However, their convergent aspects, as well as, to some extent, a common type of approach, have been recognized recently in the realm of nanoscience and nanotechnology, under the term “nanostructured materials”, or simply “nanomaterials”. For an extended review on nanotechnology see the recently published Handbook of Nanotechnology [3.4].

5.3.1.2 Definitions In their broadest definition, nanostructured materials show structural features with sizes in the range from 1 nm to a few hundred nanometers in at least one dimension. This very general criterion actually includes very diverse physical situations. First, as is apparent from the previous section, each nanostructured material is associated with a specific novel property or a significant improvement in a specific property resulting from the nanoscale structuring. As a consequence, the type of nanostructuring used must be based on a spatial dependence of some parameter related to the property under consideration. This parameter could be, for example, the material density, transport parameters, or the dielectric constant. Another consequence is that the upper size limit of the structural features varies depending on the property considered,

Mesoscopic and Nanostructured Materials

•

The top-down manufacturing paradigm consists in downscaling the patterning of materials to nanometer sizes. This allows the generation of materials

•

1033

which are coherently and continuously ordered from macroscopic down to nanoscopic sizes. The bottom-up paradigm is based on the atomically precise fabrication of entities of increasing size. It is the domain of macromolecular and supramolecular chemistry (dendrimers, engineered DNA, etc.) and of cluster and surface physics (epitaxy, selfassembly, etc.).

Mesoscopic materials form the subset of nanostructured materials for which the nanoscopic scale is large compared with the elementary constituents of the material, i. e. atoms, molecules, or the crystal lattice. For the specific property under consideration, these materials can be described in terms of continuous, homogeneous media on scales less than that of the nanostructure. The term “mesoscopic” is often reserved for electronic transport phenomena in systems structured on scales below the phase-coherence length ΛΦ of the carriers. Most of the common nanomaterials can be classified in terms of dimensionality, according to the number of orthogonal directions X, Y, Z in which the structural patterns referred to above have dimensions L X,Y,Z smaller than the nanoscopic limit L 0 . This leads to the classical definitions of dimensionality summarized in Table 5.3-1. However, it should be noted that experimental situations

Table 5.3-1 Examples of reduced-dimensional material geometries, and definitions of their dimensionality and of the associated

type of confinement

L X,Y,Z > L 0

No nanostructures

No confinement

Bulk material

L X,Y > L 0 > L Z

Two-dimensional (2-D) nanostructures

One-dimensional (1-D) confinement

Wells

L X > L 0 > L Y,Z

One-dimensional (1-D) nanostructures

Two-dimensional (2-D) confinement

Wires

L 0 > L X,Y,Z

Zero-dimensional (0-D) nanostructures

Three-dimensional (3-D) confinement

Dots

Part 5 3.1

from a molecular size for molecular-sieve properties up to the wavelength of light for the optical properties. Second, in addition to the nanometer-scale structuring, a larger-scale ordering of the unit patterns may be necessary for the existence of the property sought. For example, the particular optical properties of opals mentioned above require the silica nanospheres to show a long-range order with a coherence length well beyond a micron. The same considerations hold for quantum-well superlattices, for example. In other cases, the nanosized building blocks do not need long-range order to provide a specific property, but still require some degree of short-range organization. For example, an electrical conductivity appears only above a critical percolation density of conducting particles. Finally, some properties of nanostructured materials simply reflect a corresponding intrinsic property of their individual building blocks. This is the case, for instance, in nanoparticles embedded in glass or polymer matrices for optical-filtering applications. Two main technological approaches may be defined:

3.1 Introduction and Survey

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Part 5 3.1

can be encountered in which the dimensionality may not be so obviously defined. For instance, the structural patterns may be formed by nonrectilinear wires which occupy a surface or a volume or may be branched. The structure of the density of states (DOS) in nanostructures is strongly dependent on the dimensionality. A free 3-D motion yields a band characterized by three wave vectors k x , k y , kz . The corresponding DOS depends smoothly on the energy E, as (E − E 0 )1/2 , where E 0 is the energy of the bottom of the band. Confinement into a 2-D system splits the band into subbands, and leaves only two continuously varying wave vectors k x , k y in each subband. The DOS for each subband is then constant above the energy E 0N of its bottom state. The overall DOS is discontinuous, with a stepwise structure that is characteristic of quantum wells (Fig. 5.3-1). Confinement in one additional dimension splits each 2-D subband further into a set of 1-D subbands. Each 1-D subband is characterized by only one continuously varying wave vector k x , and two quantum numbers N, M. The DOS corresponding to the subband N, M has a variation of the form (E − E 0N,M )−1/2 , with a divergence at the bottom of the subband E 0N,M . The DOS of a quantum wire thus has a more pronounced structure than does a 2-D well, with a larger number of subbands, each one starting as a peak (Fig. 5.3-1). Finally, confinement in all three dimensions creates a completely discrete, atom-like set of states. The DOS of a quan-

tum dot thus consists of a series of δ-functions (not represented in Fig. 5.3-1). The sharpening of the DOS at specific energies induced by quantum confinement is the origin of many improvements in the properties of nanostructured materials compared with bulk materials. This spectral concentration enhances all resonant effects and increases the energy selectivity. The preservation of these effects when one is dealing with an ensemble of quantum-confined systems requires a high homogeneity.

5.3.1.3 Specific Properties The specific properties of nanostructured materials can have two different possible origins:

•

•

Size effects, which result from the spatial confinement of a physical entity inside an element of the nanoscale structural pattern. Such an element is called a low-dimensional system. An example is the confinement of electron wave functions inside a region whose size is smaller than the electron mean free path. This class of effects may give birth to completely new properties. Boundary effects, which are a consequence of the significant volume fraction of matter located near surfaces, interfaces, or domain walls. Processes that take place only at such locations may be highly favored, and properties specific to structural boundaries may also be greatly enhanced.

For a recent comprehensive review of the basic principles of the origin of the properties of nanostructured materials, see [3.5].

DOS

5.3.1.4 Organization of this Chapter

E

Fig. 5.3-1 Schematic illustration of the density of states for

3-D motion of a free electron (dashed line), a 2-D quantum well (solid line), and a 1-D quantum wire (shaded area) as a function of energy

Many classification schemes for nanostructured materials exist. These may be based on their chemical composition, on the technique for their manufacture, or on their dimensionality. These schemes, however, are often suitable only for a subset of materials. Moreover, they generally address only one particular scientific or technological approach and its associated community of specialists. Since, as noted above, most nanostructured materials are associated with a specific property, we have chosen a presentation based on properties. This scheme allows us to include all nanostructured materials and is accessible to the largest possible readership. Consistently with the materials approach of this chapter and with its limited size, only the properties of statistical ensembles of nanostructures will be considered. The specific behaviors of individual nano-

Mesoscopic and Nanostructured Materials

sized objects or devices are not included. Since surface and interface properties are treated in another section, emphasis will be put here on size effects. Properties related to electronic confinement and its consequences for spectral properties are addressed in Sect. 5.3.2. Ef-

3.2 Electronic Structure and Spectroscopy

1035

fects of the confinement of electromagnetic fields are treated in Sect. 5.3.3. Magnetic size effects are addressed in Sect. 5.3.4. Finally, we list and briefly describe in Sect. 5.3.5 some generic methods for preparation of nanostructured materials.

5.3.2 Electronic Structure and Spectroscopy 5.3.2.1 Electronic Quantum Size Effects

where m is the effective mass of the carrier, d is the confinement dimension, and N is a quantum number. The first term appears because of the quantized motion in the z direction, whereas the second term represents the energy of the free x, y motion, characterized by wave vectors k x , k y . Each value of N defines a semiinfinite subband of energy levels. Although the “particle in a box” model is simplistic compared with real systems, this limiting case is often successful in describing the essential features of quantum size effects [3.6]. The importance of the quantum size effect is mainly determined by the energy differences E N+1 − E N . Quantum size effects become observable when this separation exceeds the thermal energy of the carriers, so that adjacent subbands are differently populated. Since the energy difference E N+1 − E N increases with N, it could be anticipated that quantization effects would

Part 5 3.2

Confined electronic systems are quantum systems in which carriers, either electron or holes, are free to move only in a restricted number of dimensions. In the confined dimension, the sizes of the structural elements are of the order of a few de Broglie wavelengths of the carriers or less. Depending on their dimensionality, these structures can be quantum dots (0-D), quantum wires (1-D), or quantum wells (2-D). Quantum wells are typically produced by the alternate epitaxial growth of two or more different semiconductors. Quantum wires are less commonly encountered, since their fabrication procedures are much more complicated (Sect. 5.3.4). One of the most dramatic effects, called the quantum size effect, consists in a redistribution of the energy spectrum of the system, the density of states becoming discrete along the confinement direction. In the most simple “particle in a box” model of a quantum well, the energies of the corresponding eigenstates are  ~2 π 2 ~2  2 E N,kx ,k y = N 2 + k x + k2y (3.1) , 2 2m 2md

be more important for processes involving higher subbands. However, the practical observation of such effects in systems with a large Fermi energy (E F  E 1 ), i. e. in metals, is often made difficult because of contributions from many levels and the appearance of collective phenomena such as plasmon oscillations, which wash out quantization effects. Most of the spectral data revealing quantum well states in metal films a few monolayers thick have been obtained by angleresolved photoemission for Cs on Cu(111) [3.7] and for Ag on Au(111) [3.8]. The Fabry–Perot-like regularlyspaced spectrum of energy levels appears particularly clearly in a study of Ag films on Fe(100) for thicknesses up to more than 100 monolayers (Fig. 5.3-2). The superposition at half-integer coverages (27.5 and 42.5 monolayers) of two sets of peaks corresponding to the two closest integer thicknesses emphasizes the extreme sensitivity to surface homogeneity. Quantitatively, the characteristic roughness of well barriers must be much below the de Broglie wavelength of the quantum states observed. This is another reason why quantum size effects have been observed mainly in semiconductor nanostructures, which have large Fermi wavelengths, rather than in metals, which have Fermi wavelengths comparable to a few crystal lattice periods. The existence of discrete electronic states of electrons confined in a small metal cluster has been observed to influence the thermodynamic stability of the system, in particular during the production of sodium clusters in supersonic beams composed of the metal vapor and an inert gas. The statistics of the relative abundances of different particle sizes reveal the existence of “magic numbers” for the number of atoms in the cluster, N = 8, 20, 40, 58, 92, . . . [3.9]. This has been interpreted in terms of the existence of degenerate energy levels in a spherical well with infinite-potential walls. Particularly stable structures are obtained when the number of valence electrons is such that it leads to a closed-shell electronic structure, i. e. a structure with a completely filled energy level and an empty up-

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Part 5

Special Structures

5.3.2.2 Breakdown of the Momentum Conservation Rule

Photoemission intensity (arb. units) Thickness (ML)

Ag / Fe (100) h ν = 16 eV

119 95 71

Part 5 3.2

57 42.5 42

28

27.5

14

12

2

1

0 Binding energy (eV)

Fig. 5.3-2 Dots: experimental normal photoemission spec-

tra for Ag quantum wells deposited on Fe(100), with various thicknesses. Solid curves: fits and background functions. (After [3.12])

per level. The electronic shell structure induces similar size dependences in the work function and the electron density, through Friedel-like oscillations [3.10]. The series of “magic numbers” is discernible up to N = 1430. For larger particles, the relative abundance of different sizes is controlled instead by the stability and relative sizes of the various facets of the surface of the particle. It is noteworthy that 2-D quantum well states are also predicted to produce oscillatory variations of the energetics of a film as a function of thickness, with similar “magic numbers” for the number of deposited monolayers [3.11].

As a result of the Heisenberg uncertainty principle, localization of carriers in a confinement volume spreads their wave functions in reciprocal space. The possible overlap in k space of electron and hole wave functions breaks the rule of conservation of crystal momentum. In other words, the momentum needed for a transition at a different k may be provided by scattering from the boundaries. This consequence of quantum confinement is particularly meaningful for nanostructures based on indirect-band-gap semiconductors, for which luminescence from recombination of the lowestenergy electrons and holes is forbidden in the bulk material, but becomes increasingly possible for systems of decreasing size, with a scaling law of d −6 for dots [3.13]. The observation of bright luminescence from nanoporous silicon samples [3.14] was, from the start, interpreted in terms of quantum confinement into silicon nanowires [3.14, 15]. This observation triggered an important research activity motivated by the industrial prospect of being able to incorporate silicon photonic elements into the current silicon technology. Although it has been shown that other phenomena such as surface effects and phonon modes (discussed later) come into the play, and that more complicated geometries including both quantum dots and quantum wires have to be considered, the role of quantum confinement in the luminescence of porous silicon is generally considered to be central, at least for the “red” part of the luminescence. The studies of nanostructure-induced luminescence have been extended to porous GaP [3.16,17] and SiC [3.18], two other semiconductors with an indirect band gap, and the results parallel those for porous silicon. Quantum-confined luminescence has been observed in indirect-gap semiconductor nanostructures with well-controlled geometries such as silicon and germanium 2-D wells [3.19] and quantum dots (see e.g. [3.20]), which may possibly be integrated into lightemitting devices [3.21]. The observation of optical gain in silicon nanocrystals [3.22] opens up new prospects for the creation of silicon-based lasers [3.23].

5.3.2.3 Excitons in Quantum-Confined Systems A very general effect of quantum confinement in semiconductors is a widening of their optical band gap. For the model system of an infinite-barrier 2-D quantum well, (3.1) shows that the lowest energy (N = 1) of a con-

Mesoscopic and Nanostructured Materials

∆E Weak =

sequence, in the weak-confinement regime, the exciton energy is not affected by the band gap increase which results from the increase in the energy levels of the lowest electron and hole states discussed above. The weak-confinement model is very suitable for describing spectral variations in nanoparticles of semiconductors with low exciton Bohr radii, such as CuCl (Table 5.3-2), as shown in Fig. 5.3-3. The strong-confinement regime corresponds to the opposite limit, d ≤ 2a0∗ . In that case the relative electron– hole motion is strongly affected by the barriers. In the direction of restricted motion, the kinetic energies of the lowest-energy electron and hole states determined by the quantum confinement are larger than the Coulomb Energy shift (E *Ry)

10 5 1.0 0.5 0.1 0.05 σ= ∞ 0.01 0.005

σ= 1 σ= 5 σ = 10

π 2 ~2

. (3.2) 2MEx d 2 Like that for electron states, this shift has comparable magnitudes for various dimentionalities. In the weakconfinement regime, the exciton wave function still involves combinations of several conduction-band electron states and valence-band hole states, and not only the lowest-energy states. The quantization of carrier states does not change significantly the average energy of all of the states involved in exciton formation. As a con-

0

2

4

6

8

10

12

14 R/a*B

Fig. 5.3-3 Observed values of energy shifts in the lu-

minescence peak of CuCl nanocrystals in NaCl (circles) and in the absorption peak of CdS nanocrystals in silicate glass (triangles), compared with theoretical models: weak-confinement model (dashed-dotted lines), strong confinement model (short-dashed line); σ = m ∗h /m ∗e is considered as a fixed parameter. (After [3.25])

Table 5.3-2 1s exciton Bohr radius for various semiconductors

Direct-band-gap semiconductors Semiconductor CuCl Diamond 0.7 0.85 aB∗ (nm)

CdTe 2.8

CdS 2.9

Indirect-band-gap semiconductors Semiconductor GaP SiC 1.17 2.7 aB∗ (nm)

Si 4.9

Ge 17.7

GaN 3.6

CdSe 5.6

GaAs 12

1037

Part 5 3.2

duction electron is increased compared with the bottom of the conduction band. A similar consideration applies to the lowest energy of a hole in the valence band. Both effects contribute to an increase in the minimum excitation energy of the system compared with the bulk band gap. This blueshift has a comparable magnitude in 2-D and 0-D structures [3.24]. This constitutes the leading contribution to the characteristic blueshifts in the optical spectra of strongly quantum-confined semiconductor systems. However, the confinement of oppositely charged carriers at reduced separations also has dramatic effects on the electron–hole Coulomb energy and thus on exciton formation. Two regimes of exciton confinement must be distinguished, depending on the confinement size d compared with the Bohr radius a0∗ of the Mott–Wannier exciton in the bulk semiconductor [3.25]. The weak-confinement regime corresponds to sizes such that d ≥ 4a0∗ . In this regime, the relative electron–hole motion, and in particular its binding energy, is essentially left unchanged. The exciton can still be considered as a quasiparticle, but its center-of-mass translational motion becomes quantized. A simple model [3.26] of a single-point quasiparticle with mass MEx equal to the total mass of the exciton, MEx = m ∗e + m ∗h , explains the observed frequency shifts. The translational state with the lowest energy, N = 1, which is the only optically allowed state, has a nonzero kinetic energy. Compared with an infinite-sized system, the lowest excitation energy in the weak-confinement regime is thus increased by

3.2 Electronic Structure and Spectroscopy

1038

Part 5

Special Structures

Part 5 3.2

attraction. The exciton states are thus formed from uncorrelated electron and hole states of the “particle in a box” model in the confinement direction, whereas spatially correlated electron–hole bound states can still be formed in the unrestricted directions. This yields 2-D, 1-D, and 0-D excitons in quantum wells, quantum wires, and quantum dots, respectively. The binding energy of a 2-D exciton can be deduced from the two-dimensional hydrogen atom problem [3.27]. The exciton Rydberg ∗ = −R∗ /n 2 in the 3-D case series changes from E 3-D ∗ = −R∗ /(n − 1/2)2 in the 2-D case, where R∗ to E 3-D is the Rydberg constant for the exciton. This effect is opposed by the increased energy required for the creation of an electron–hole pair owing to the confinement of the carrier motion. The variation of the excitation energy of the first 1s-like exciton state in the regime of strong 1-D confinement is then 2-D ∆E Strong =

π 2 ~2 − 3R∗ , 2µd 2

(3.3)

where µ is the electron–hole reduced mass, such that µ−1 = m ∗e −1 + m ∗h −1 . The first term is larger than the term due to the weak confinement of exciton motion (3.2) because of the difference between µ and MEx . The 0-D case is treated in detail in [3.25]. The variation of the minimum excitation energy in the regime of strong 3-D confinement is 0-D ∆E Strong =

π 2 ~2 e2 − 1.786 − 0.248R∗ . (3.4) 4πεd 2µd 2

The divergence as d −1 of the second term for small sizes results from the increased Coulomb interaction in this restricted geometry compared with the 2-D case. As could be expected, the case of a 1-D exciton in a quantum wire is intermediate between 0-D and 2-D, with a divergent Coulomb interaction which is sublinear in d −1 [3.28]. For all dimensionalities, in the strong-confinement regime, the increased kinetic energy of quantumconfined carriers is dominant, and a blueshift of the optical gap is observed that varies continuously between the weak- and the strong-confinement regimes. However, the considerably increased exciton binding energy in strongly confined systems yields more pronounced exciton effects. For the most widely used semiconductors, excitonic effects are not discernible in room temperature spectra without quantum-confinement. However, in strongly confined geometries of any dimensionality, many semiconductors exhibit well-resolved excitonic peaks since the exciton binding energy can then exceed the thermal excitation energy kB T . Both the blueshift of the spectra and the increasingly pronounced

excitonic absorption are very evident in II–VI semiconductor nanoparticles, as exemplified in Fig. 5.3-4 for CdSe [3.29]. Semiconductor-doped glasses, formed from a dispersion of II–VI semiconductor crystallites in a silicate glass matrix, are the basis for some commercially available yellow-to-red long-wavelength-pass optical filters [3.30]. The glasses with a cutoff wavelength in the visible contain CdS1−x Sex nanocrystallites, and the glasses used in the infrared filters contain essentially CdTe nanocrystallites. Their abrupt absorption band edge can be tuned by adjusting the composition, the size [3.31], and, as will be discussed later, the concentration of the particles. In other widely used semiconductors, such as Si, Ge, and III–V compounds, the valence bands may have complex features and contain light- and heavy-hole branches. The two corresponding types of excitons will have different characteristics, such as different binding energies. The second important consequence of the squeezing of excitons in the strong-confinement regime is an increase in the optical matrix element associated with their excitation. A detailed discussion of this effect can be found in [3.32]. Its origin is the stronger overlap of electron and hole wave functions in reduceddimensional excitons. This effect, associated with the concentration of oscillator strength into a few discrete transitions, has found many applications in optoelectronic devices. Certainly the most important is the fabrication of electrically powered multiple-quantumwell (MQW) lasers in Inx Ga1−x As and Alx Ga1−x As (infrared), and Alx Ga y In1−x−y P (red). These systems are widely used today in data storage systems, bar code scanners, laser pointers, and printers. The physics and technology of MQW lasers are far beyond the scope of this section. Details may be found in [3.33], for example. 1-D and 0-D systems are also of interests for laser systems [3.34]. Laser applications of quantum-confined systems exploit the enhanced stimulated-emission coefficients that result from the increased transition matrix elements and spectral sharpening in quantum-confined systems. Besides MBE-grown devices, optical gain in chemically synthesized CdSe nanocrystal quantum dots has been achieved [3.35]. The operation of an optically pumped solid-state distributed-feedback (DFB) laser based on a CdSe-doped titania matrix gain medium has been demonstrated [3.36]. The output color of this laser can be selected by choosing appropriately sized nanocrystals and tuning the DFB period accordingly (see Fig. 5.3-5). Another consequence of the large oscillator strengths associated with confined-exciton transitions is the

3.2 Electronic Structure and Spectroscopy

Mesoscopic and Nanostructured Materials

Absorbance (arbitrary units) 700 600 500

Wavelength (nm) 400

a)

10 K

D (Å) 115 67 51 46 38

Fig. 5.3-4 (a) Low-temperature (10 K) absorption spectra

of CdSe dots dispersed in a polymer matrix, for various mean diameters. (b) Nanosecond saturated-absorption spectra for 67 Å dots. The pump beam had a 7 ns FWHM. The excitation photon energy, 1.984 eV, is prolonged as a dashed vertical line from (a) for easier comparison. The horizontal dashed line corresponds to ∆OD = 0. (c),(d) Photoluminescence(PL) and photoluminescenceexcitation(PLE, observed at 2.022 eV) spectra for 67 Å dots (c) and for 62 Å dots (d). (After [3.29])

600

550

500

30 28

a

b

c

d

2.1

2.2

26 19 1.8 –∆OD

2.0

2.2

2.4

2.6

2.8

3.0

3.2 Energy (eV)

b)

10 K

67 Å 1.8

2.0

2.2

2.4

2.6

2.8

3.0

Intensity

3.2 Energy (eV)

c) 1.8

PL

PLE 10 K

67 Å 1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2 Energy (eV)

2.6

2.8

3.0

3.2 Energy (eV)

Intensity

d) PLE

PL

2.0

2.3

2.4 Energy (eV)

Fig. 5.3-5 The photoluminescence emission spectra of CdSe nanocrystals with different radii (dashed and dotted lines, for radii of 2.7 nm, 2.4 nm, and 2.1 nm) and of 1.7 nm CdSe/ZnS core–shell nanocrystals (the radii are given in order of increasing photon energy) at low pump power, and at a pump power above the laser threshold (solid lines). The nanocrystals were dispersed in a titania film used in a distributed-feedback laser configuration at 80 K. (After [3.36])

10 K

62 Å 1.8

1.9

2.0

2.2

2.4

enhancement of nonlinear optical and electrooptical coefficients. Nonlinear absorption and electroabsorption correspond to changes in absorption coefficients induced by high-intensity optical fields and large DC

electric fields, respectively. Exciton–exciton interactions increase the energy of doubly excited states in quantum dots, which results in large saturable absorption effects (see Fig. 5.3-4b). The absorption saturation intensities may be as low as those of saturable dye solutions, but these systems have an increased robustness and the possibility of including them in solid-state media.

Part 5 3.2

Wavelength (nm) 700 650

32

1039

1040

Part 5

Special Structures

Part 5 3.2

PbS-nanocrystal-doped glasses with an absorption saturation intensity of 0.2 MW/cm have been realized [3.37] and used as intracavity passive Q-switches in picosecond [3.37] and femtosecond [3.38] pulsed near-infrared lasers. The Frantz–Keldysh effect is also strongly enhanced in quantum-confined systems [3.39]. Moreover, the well-resolved excitonic transition shows quantumconfined Stark effects (QCSEs) with particularly large magnitudes. In quantum wells, this effect usually consists of a redshift of the absorption and a strong decrease of its oscillator strength, and has been exploited for the realization of fast, low-drive-voltage electrooptic modulators [3.40], which could possibly be integrated with semiconductor lasers [3.41].

5.3.2.4 Vibrational Modes and Electron–Phonon Coupling The description in terms of phonons of the vibrational properties of solids assumes a translational invariance. It can be used only inside domains of homogeneous mechanical properties with sizes larger than the spatial extension of the phonon considered, typically given by its wavelength λph . Similarly to the case of vibrational modes of impurities in crystals [3.43], the confinement of phonons in structures smaller than λph leads to the localization and the quantization of the vibrational modes. For typical solids, the phonon frequencies affected by confinement sizes on the 1–100 nm scale have frequencies on the order of 0.1–10 THz, i. e. thermal phonon energies and higher, and both acoustic and optical phonons are affected. The frequencies of the quantized modes, as well as their damping rates, depend on the size, shape, and nature of the environment of the nanostructure and its interfaces. The electron–phonon coupling may be strongly modified by phonon confinement, with manifestations in the transport properties and in the optical absorption and luminescence. In 2-D systems, two-dimensional phonons appear, with properties and consequences similar to those of surface phonons. The role of in-plane propagating phonons in electron–phonon scattering rates has been demonstrated in metal films [3.44] and in Si/Ge quantum wells [3.45]. Phonon propagation perpendicular to a quantum-well superlattice produces Bragg-like selective transmission [3.46]. The formation of phonon band gaps results from the zone folding of the LA and TA phonons propagating perpendicular to the layers, and is well described by a mesoscopic model of a periodic series of homogeneous layers [3.47].

When we move to 0-D systems, the phonon spectrum changes to a set of size-dependent discrete lines. As in the case of 2-D systems, most data on the various vibrational modes of metal nanoparticles [3.48] and semiconductor nanocrystals (see e.g. [3.49] and references therein) embedded in solid matrices have been obtained by spontaneous-Raman-scattering spectroscopy. The lowest frequencies are well described by the simple Lamb theory [3.50] of the vibration of a homogeneous, elastic sphere. The breathing mode, the mode of lowest energy, is usually the best resolved one. A detailed calculation of the mesoscopic acoustic modes in quantum dots of various compositions embedded in various matrices can be found in [3.51]. The availability of ultrafast pulsed lasers, with a pulse duration shorter than the period of an acoustic vibration mode, offers the possibility to monitor the vibrations in the time domain rather than the frequency domain, as shown in Fig. 5.3-6 for 3 nm PbS quantum dots in a polymer matrix. Similar experiments have been performed on Ag particles of various sizes in a glass matrix [3.52]. These experiments offer a unique opportunity to analyze the damping of these vibrations, which is generally attributed to radiation of acoustic waves into the matrix. The modes excited by ultrafast laser pulses are usually not the same as those detected by spontaneousRaman spectroscopy, mainly for symmetry reasons [3.53] (see Fig. 5.3-7). Moreover, the symmetry selection rules depend on the mechanism of excitation by the laser pulse. A thermal mechanism provokes

0.04

∆ T/T

0.035 0.03 0.025 0.02 0.015 0.01 0.005 0 0

1

2

3

4 5 Delay (ps)

Fig. 5.3-6 Time-domain breathing-mode acoustic oscillations in 3 nm PbS quantum dots embedded in a polymer matrix, observed by transient saturated absorption. (After [3.42])

Mesoscopic and Nanostructured Materials

Frequency (THz) 5 4 2

3

2

S01'

R (nm) 1 S01

S01

S21

1

phonon coupling results not from phonon quantization but rather from an increased overlap factor [3.57]. In metal particles, the main consequence of changes in the electron–phonon couplings is a variation of the electron relaxation rates. This effect depends strongly on the intensity regime of the excitation, but experiments carried out at weak excitation on Ag and Au nanoparticles in various matrices show a strong increase of the relaxation rate, i. e. a decrease of the electron– lattice energy exchange time, with quantum confinement (see Fig. 5.3-8) [3.54]. In this case also, the increased a) τ (ps) 0.9 0.8

0

0

0.5

1 1/ radius (nm–1)

Fig. 5.3-7 Frequency of the coherent-phonon and Raman peaks as function of PbSe dot size. The solid lines represent the calculation on the assumption that the stress at the dot boundary is zero, and the dashed line represents the calculation with a rigid boundary condition. The matrix was a phosphate glass. The inset represents the displacement in the S01 and S21 spheroidal modes. The coherent-phonon and Raman frequencies are assigned to the S01 and S21 modes, respectively. (After [3.53])

breathing-mode (S01 ) oscillations, whereas electrostrictive excitation excites the elongation mode (S12 ). Figure 5.3-7 also illustrates the parallel dependences of the modes excited by Raman scattering and by ultrafast laser-pulse on particle size. These dependences are consistent with a Lamb model with boundary conditions corresponding to the absence of stress. The confinement also influences the electron– phonon coupling. For example, in GaAs, each quantized optical-phonon mode produces a Huang–Rhys ladder in the phonon sidebands in the spectrum of the exciton transition [3.55]. A scaling law in d −3 is predicted for the effective coupling strength [3.55]. It has been shown that the luminescence spectra of silicon nanocrystals exhibit not only a no-phonon peak but also TO- and TA-phonon-assisted peaks. Hence, besides the breakdown of the momentum conservation rule discussed above, an increased electron–phonon interaction also favors luminescence in this indirect-band-gap semiconductor. This coupling prevails for moderate confinement energies, below 0.7 eV [3.56]. The enhanced electron–

1041

Part 5 3.2

S21

3.2 Electronic Structure and Spectroscopy

0.7 0.6 0.5

Ag 0

5

10

15

b) τ (ps)

20 25 30 Nanoparticle diameter (nm)

1.2

1.0

0.8

0.6 Au 0.4

0

5

10

15

20 25 30 Nanoparticle diameter (nm)

Fig. 5.3-8 (a) Size dependence of the measured electron-

lattice energy exchange time τe–ph for silver clusters in BaO−P2 O5 (circles), in Al2 O3 (open squares), in MgF2 (diamond), in a polymer (up triangles), and deposited on a glass substrate (down triangle). The solid line is the result of the theoretical model proposed by the authors of [3.54]. The dashed line is a guide to the eye. (b) As (a), for gold clusters in Al2 O3 (squares), in colloidal solutions prepared using a radiolysis technique (triangles), and in commercially available colloidal solutions (circles). (After [3.54])

1042

Part 5

Special Structures

electron–phonon coupling is attributed not to phonon confinement but to a reduction of the screening of the electron–ion interaction following electron confinement.

5.3.2.5 Electron Transport Phenomena

Part 5 3.2

The charge transport properties in the direction of freecarrier motion in a restricted-dimensional system have important consequences for the magnetotransport effects. This is treated in Sect. 5.3.4. For disordered systems, when the Mott variable-range hopping mechanism [3.58] dominates the conductivity, the temperature scaling law depends on the dimensionality: the 3-D conductivity σ3-D varies with temperature following the law log σ3-D ∝ T −4 , whereas the 2-D conductivity varies as log σ2-D ∝ T −3 . The transition from 3-D to 2-D behavior has been demonstrated for films of amorphous Ge at a thickness d of 50 nm, as illustrated in Fig. 5.3-9 [3.54]. A vertical conductance, i. e. perpendicular to the free-motion direction, is necessary in quantum wells in many device applications. This requires a finite barrier in order for one to have a continuum of unbound states, in addition to one or a few bound states, as illustrated in Fig. 5.3-10. Practical realizations of such structures are formed from an n-type low-band-gap well, usually GaAs, sandwiched between barrier layers of an intrinsic semiconductor with larger band gap, such as Alx Ga1−x Al. The conduction electron states form a structure of the type shown in Fig. 5.3-10. The choice of the well width and barrier height (through the composSlope 1000 T1/3 slope

100

10 10

T1/4 slope

d –1/3

100

1000

d (Å)

Fig. 5.3-9 Plot of the experimental power-law dependence

of the conductivity on temperature for films of amorphous Ge of various thicknesses d. The transition from a 3-D (T −1/4 ) behavior (region marked as T 1/4 slope) to a 2-D (T −1/3 ) behavior (region marked as T 1/3 slope), as expected for the variable-range hopping mechanism, is clearly observed d = 500 Å (vertical bar). (After [3.54])

E2

E1

Fig. 5.3-10 Schematic view of the electron states in a finitebarrier quantum well. States with energies below the barrier are bound to the well, and states with energies above the barrier are extended outside the well and form a continuum of conduction states

ition x of the barrier) permits one to adjust the number and energy of bound states, and the n-type doping of the well controls their population. An important example of a device based on such a structure is the quantum-well infrared photodetector (QWIP) [3.59]. The energy difference E 1 − E 2 between the subbands matches the energy of the photons to be detected. E 2 is close to the top of the barrier. Excitation of the intersubband transition by absorption of an IR photon results in the population of the second subband. If an electric field is applied, the excited electron can tunnel through the small remaining barrier towards the continuum and move away from the well under the influence of the electric field. This gives rise to a photocurrent, which can either constitute the signal of the detector or feed a visible-light-emitting junction in order to achieve IR-to-visible conversion. To increase the collection efficiency in practical devices, several quantum wells are associated in a periodic stack. For a large enough bias, once an electron has reached the continuum it is accelerated by the electric field and has a high probability of crossing subsequent wells without being trapped in a bound state. In applications such as IR detection, the conductivity is obtained by populating the continuum. In that case, the interwell spacing is large enough to prevent direct coupling between neighboring wells, and each well can be considered as isolated. Such systems are usually called multiple quantum wells. A nonzero conductivity in the ground state can be obtained by reducing the width of the barriers, as originally proposed in [3.60]. Then, the subband states of neighboring wells interact through the evanescent parts

Mesoscopic and Nanostructured Materials

transport, these materials can often be modeled as a dense assembly of metal or semiconductor quantum dots dispersed in an insulating matrix. As in noncrystalline materials [3.63], the elementary mechanism of conduction is phonon-assisted electron tunneling from one dot to another, or hopping. Above a threshold temperature, the limiting factor for the hopping probability is the spatial proximity of two dots. Below this threshold, the weak thermal energy available imposes a strong selection of sites with a low energy difference, tunneling to such sites at larger distances becomes dominant, and the variable-range hopping regime is obtained [3.58]. The temperature dependence of the conductance σ changes from − log(σ) ∝ T −α with 1/2 < α < 1 for nearest-neighbor hopping to − log(σ) ∝ T −1/4 for variable-range hopping [3.64]. However, in contrast to noncrystalline semiconductors, the sites in such granular materials are spatially expanded to the particle size, and the tunnel gap between neighboring particles is usually much smaller than this size. As a consequence, the threshold temperature is very low and a T α law with α ≈ 1/2 is observed over a wide temperature range. Another important factor comes into play in nanoparticle-based conductors compared with 2-D well systems. The addition of an electron to an initially electrically neutral nanoparticle requires an energy e2 /2C, where C is the capacitance between the nanoparticle

Conductance (mS)

a)

8

E2 E1

6

E2

b)

4 2

E1 E2

c)

0 –2

E1 E2

d)

–4

E1

–6 –8

0

1

2

3

4 5 Bias voltage (V)

Fig. 5.3-11 Left: differential conductance as a function of the applied voltage for a 49-period superlattice at 20 K. Right: schematic model to explain the 48 negative peaks in the differential conductance. (a) Zero bias; (b) ground-state resonanttunneling conduction; (c) first field localization, where resonant tunneling between the ground state and an adjacent excited state takes place; (d) expansion of the high-field region by one additional quantum well. (After [3.62])

1043

Part 5 3.2

of their wave functions in the barrier. The ensemble of bound states consisting of the subband levels from all of the coupled quantum wells forms a band in the confinement direction called a miniband. The periodic set of coupled quantum wells is called a superlattice. At very low applied voltages, a band-type conduction governs the electron transport. However, above a threshold voltage, the conduction mechanism becomes highly complicated. This results in highly nonlinear behaviors, with the appearance of negative differential resistance and oscillations at low temperatures [3.61]. These effects are attributed to the localization of the electron states when the voltage drop between neighboring wells induces an energy difference larger than the coupling energy between them. At even higher fields, the voltage drop spontaneously localizes on one single well [3.61]. A particularly spectacular manifestation of this effect has been observed in weakly coupled wells at low temperature, as shown in Fig. 5.3-11 [3.62]. Electrical conduction is also very important for many devices that exploit the huge area of surface or interface per unit volume in zero-dimensional nanostructured materials such as nanoporous materials, granular materials, nanocomposites, and nanoparticle assemblies. Examples of such devices are chemiresistor-type sensors, solar cells, light-emitting diodes, and energystorage cells. From the point of view of electron

3.2 Electronic Structure and Spectroscopy

1044

Part 5

Special Structures

a) Current

b) Current Au – SiO2

Ag –SiO2

10 pA

1 nA

78.6 K

29.3 K 14.3 K

44.4 K

3.9 K

15.0 K

Part 5 3.3

3.1 K

dI/dV (nS)

2.9 K

dI/dV (nS) 0.6

2.9 K

0.4 0.2

3.1 K –0.2

–0.1

0.0

0.0 0.1 0.2 Voltage (V)

–0.4

–0.2

0.0

0.2

0.4 Voltage (V)

20 15 10 5 0

Fig. 5.3-12a,b Temperature dependence of I/V characteristics of films of (a) Ag nanoparticles dispersed in SiO2 (sizes 3.8 ± 1.0 nm, volume fraction 1.5%, film thickness 12 nm) and (b) Au nanoparticles dispersed in SiO2 (sizes 2.9 nm, film thickness 9 nm). In both cases the electrode area was 100 × 100 µm2 . (After [3.68])

and its surroundings. Typical values of C can be in the region of 10−17 F or less, so that the charging energy approaches or is larger than the thermal energy at room temperature. This produces the Coulomb blockade effect: conduction through a single nanoparticle requires a minimum voltage to overcome the cost in charging energy. The conduction may even show a stepwise dependence on the bias, called a Coulomb staircase, which has been observed for a single nanoparticle at room temperature [3.65]. Extension to three-terminal devices has led to the realization of mesoscopic devices such as single-electron transistors, where the charge state of a confined electron pool is controlled by a gate volt-

age [3.66]. The influence of the single-electron charging energy on the conductivity of a mesoscopic material made of an assembly of dots has not yet been completely elucidated. It is predicted to reinforce the T α law with α ≈ 1/2 for the conductivity [3.67]. However, the most prominent experimental effect is the appearance of remnants of the single-particle blockade effect when the conducting path involves only a few particles, which occurs mainly for the perpendicular conductivity in very thin films with a low particle volume fraction (see Fig. 5.3-12) [3.68, 69]. There are some indications that a regular ordering also favors Coulomb blockade effects [3.70].

5.3.3 Electromagnetic Confinement 5.3.3.1 Nanoparticle-Doped Materials The polarizability α(ω) of a spherical inclusion of volume V with a dielectric constant ε(ω) at an optical frequency ω, in a matrix with a dielectric constant εM (ω), is given by α = 9ε0 V

ε − εM , ε + 2εM

(3.5)

where the explicit frequency dependence of α, ε, and εM has been dropped in the notation. When the medium is subjected to a propagating optical field, the polarizability of the particle will produce both absorption and elastic scattering of light. The corresponding cross sections, σA and σS , respectively, are σA =

ε0 ε 18πV λM (ε + 2εM )2 + ε 2

(3.6)

Mesoscopic and Nanostructured Materials

and σS =

6ε20 V 2 (ε − εM )2 + ε 2 ε2M λ30 λM (ε + 2εM )2 + ε 2

,

(3.7)

where λ0 and λM are the wavelengths of the light in vacuum and in the matrix, respectively, and ε = ε + iε , with ε and ε real. The dependence of σA and σS on the volume shows that for nanoparticles with diameters much smaller than the optical wavelength, absorption effects, when present, are preponderant over scattering.

Waveguide losses (dB / cm) 101

Refractive index 2.8

0

10

2.6 1064 nm 10–1

1295 nm

2.4

10–2 2.2 10–3 2 10–4

0

2

4

6 8 10 Mean particle diameter (nm)

Fig. 5.3-13 Scattering losses of a 5% PbS nanoparticle-

doped silica–titania waveguide as a function of the nanoparticle diameter at wavelengths of 1064 nm and 1295 nm (After [3.71])

matrix-dependent spectra for various metals, see [3.72]. Higher-multipolar-order plasmon modes exist [3.73] but cannot be excited optically in the quasi-static regime. However, they have a nonnegligible influence on the optical absorption spectra of larger particles, as shown in Fig. 5.3-15, and can be excited by, for example, electron beams. From the Mie theory, the frequency of the Lth-order plasmon mode of a small particle of a Drudemodel metal, with ε(ω) = ε0 (1 − ω2p /ω2 ), where ωp is the plasma frequency, is given by [3.73] " ωp ωL = (3.8) . 1 + (εM /ε0 )(1 + 1/L) A continuous tuning of the positions of the plasmon absorption peak by alloy formation has been demonstrated. The dependence of the absorption spectra of Au−Ag alloy nanoparticles on the composition is reproduced in Fig. 5.3-16 [3.74]. Local-Field Effects In the quasi-static approximation, the electric field inside a nanoparticle is changed compared with the field outside by a local-field factor f , given by 3εM (ω) (3.9) f(ω) = . ε(ω) + 2εM (ω) This factor is taken into account in (3.5) – (3.8) above, but it can have an even greater importance in nonlinear effects, since the second-order and third-order nonlinear optical coefficients, χ (2) and χ (3) , respectively, are affected by factors f 2 and f 3 , respectively, as compared with the bulk material of the nanoparticle. Hence, for large f , a nanostructured material can have a larger optical nonlinearity than its bulk constituents. For typical semiconductor-doped matrices, ε > εM and f < 1. However, particularly strong local-field enhancements are observed for metal nanoparticles in the vicinity of the plasmon resonance [3.75]. Electromagnetic Concentration Effects For larger particle concentrations, the interactions between particles influence the electromagnetic properties. For interparticle distances much smaller than the wavelength, the Maxwell–Garnett model applies and leads to the Lorentz–Lorenz relation for the effective dielectric constant εeff of the composite medium, which takes the form ε(ω)(1 + 2 p) + 2ε0 (1 − p) (3.10) , εeff = εM ε(ω)(1 − p) + ε0 (2 + p) where p is the volume fraction. This usually leads to a redshift of absorption peaks. In particular, the frequency of the dipole (L = 1) plasmon mode of a particle

1045

Part 5 3.3

Low-Concentration Systems For semiconductor particles, the absorption spectrum is changed only slightly compared with the bulk. The scattering losses, present even in the nonabsorbing region, have been studied in detail, in view of their waveguiding applications and account has been taken of the size dependence of the refractive index [3.71]. Some results are reproduced in Fig. 5.3-13. In contrast, metals often show negative values of ε . In that case both the absorption and the scattering show resonances when ε + 2εM = 0, which corresponds to the dipolar plasmon oscillation mode, and a peak appears in the absorption spectrum; this is observed especially clearly with alkali and noble metals (Fig. 5.3-14). For most metals, the plasmon peak shifts towards longer wavelengths and becomes sharper for matrices with a larger refractive index. This is clearly observed for the alkali metals in Fig. 5.3-14; for a computation of

3.3 Electromagnetic Confinement

1046

Part 5

Special Structures

200

600

800

200

Li

Na

Mg

150

150

600

100

100

400

50

50

200

K 400

200

0 200 300 400 500 600 700 800 900

0 0 200 300 400 500 600 700 800 900 200 300 400 500 600 700 800 900 80

160

Ca

Cu

Part 5 3.3

120

60

90

40

0 200 300 400 500 600 700 800 900 240

100

Pd

80

Ag 180

60 120 40 40

20

0 200 300 400 500 600 700 800 900

0 0 200 300 400 500 600 700 800 900 200 300 400 500 600 700 800 900 60

80

60

20

Eu

200

100

Cs

Au 80

60 40

Hg 150

60 100

40 20 20 0 200 300 400 500 600 700 800 900

0 200 300 400 500 600 700 800 900

40 50

20 0 0 200 300 400 500 600 700 800 900 200 300 400 500 600 700 800 900

0 200 300 400 500 600 700 800 900

Fig. 5.3-14 Absorption spectra, represented by the dimensionless function Cλ/V where C is the cross section, λ the wavelength, and V the particle volume, of 10 nm diameter spherical particles of selected metallic elements, as calculated from their frequency-dependent dielectric constant, in vacuum (dashed lines) and in a matrix with a refractive index equal to that of water, 1.33 (solid lines). Horizontal scale: λ (nm). (After [3.77]) Fig. 5.3-15 Absorption spectra of spherical particles of various materials, as calculated from their frequency-dependent

dielectric constant, in vacuum for various particle radii. (After [3.72]) I

Fig. 5.3-16 Effect of formation of a gold–silver alloy on the surface plasmon absorption: measured UV–VIS absorption spectra of spherical Au−Ag alloy nanoparticles of various compositions. The gold mole fraction xAu varies between 1 and 0.27. The plasmon absorption maximum is blueshifted with decreasing xAu . (After [3.74])

Absorbance x Au = 1 x Au = 0.8 x Au = 0.54 x Au = 0.27

1.0 0.8 0.6

√ in the √ Drude model is ω L=1 = (1 − p)/3ωp instead of ωp / 3, the value in the low-concentration limit ( p ≈ 0). This effect has found applications in sensing, in particular the selective colorimetric detection of nucleotides based on aggregation of gold nanoparticles [3.76]. The electromagnetic concentration effect is also used,

0.4 0.2 350

400

450

500

550

600 650 Wavelength λ (nm)

Mesoscopic and Nanostructured Materials

Extinction constant

Extinction constant 2R (nm): 100 90 80 70 60 50 40 30 20 10 5

a) Gold

3

hω (eV)

Extinction constant

b) Silver

2 R (nm): 100 90 80 70 60 50 40 30 20 10 5

2

3

e) Sodium

2 R (nm):

40

3

5

7

40

20

30 20 10

10

5 2

3

hω (eV)

Extinction constant

h) MgO

2 R (µm):

2 R (nm): 100 70 50 30 10 5

9 7 5 3 2 1 0.5

4

6

8

hω (eV)

2 R (nm): 100 90 80 70 60 50 40 30 20 10 5

50

30

g) Silicon

50

3 hω (eV)

f ) Potassium

100 90 80 70 60

5 hω (eV)

2 R (nm): 100 90 80 70 60 50 40 30 20 10 5

Extinction constant

2R (nm): 100 90 80 70 60 50

Extinction constant

2

hω (eV)

Extinction constant

d) Aluminium

c) Copper

70

hω (meV)

2

1047

3 hω (eV)

Part 5 3.3

2 Extinction constant

3.3 Electromagnetic Confinement

1048

Part 5

Special Structures

in addition to quantum size effects (Sect. 5.3.2), to tune the absorption band edge of semiconductor-doped glasses.

5.3.3.2 Periodic Electromagnetic Lattices

Part 5 3.4

Coupled Plasmon Modes The coupling between the plasmon modes of several closely packed nanoparticles yields new electromagnetic eigenmodes and spectroscopic properties. The electromagnetic eigenmodes of some few-particle systems, such as Ag and Au pairs and triplets with various geometries, have been computed, for instance in [3.72, Sect. 2.3.4], and have been observed directly by e-beam excitation [3.78]. For the lowest eigenmodes, a large field enhancement is observed in the small gap between the particles. Coupled plasmon modes have been observed experimentally in regularly spaced linear chains of gold nanoparticles [3.79] and in 2-D hexagonal arrays of silver nanoparticles [3.80]. The controlled propagation of plasmon excitations in tailored metal nanoparticle struc-

tures is a new domain of application, sometimes called “plasmonics” [3.81]. Opals and Photonic-Band-Gap Materials 3-D ordered arrays of nanostructures with periods of the order of a fraction of the optical wavelength may show intense Bragg diffraction for specific wavelengths and diffraction angles. This phenomenon is the origin of the iridescent colors (opalescence) of opals. Opals consist of an fcc-like array of silica nanoparticles with sizes in the range 150–900 nm [3.82], with a size dispersion below 5% [3.83]. For nanoscale objects with large scattering strengths and particular geometries, spectral intervals where no propagating mode is allowed in any direction appear, thus forming “photonic band gaps”. The idea of exploiting this phenomenon in optoelectronic devices has been suggested [3.84,85]. However, up to now, this phenomenon has been realized only in the infrared and microwave regions. Application in the visible, which would require 3-D nanostructured materials, is still under active development.

5.3.4 Magnetic Nanostructures The driving force for the research on magnetic nanostructures is the possibility of their incorporation into future generations of information storage devices. This could lead to a real technological breakthrough, and a huge economic impact is foreseen. As always, the key question is whether any potential benefit of such technology will be worth the production costs. Overall, the current effort in this research field is considerable. The study of the magnetism of nanoscale objects is characterized by the closeness between fundamental research and applications. What is more, a number of magnetic devices are currently in commercial use without a full understanding of the basic magnetic phenomena underlying them. An instructive example is the following: spin electronic phenomena have been applied rapidly since the first observation of giant magnetoresistance (GMR) was reported in 1988, and magnetic sensors and read heads based on this effect have been available since 1994 and 1997, respectively. Most digital information is stored in the form of tiny magnetized regions or “bits” within thin magnetic layers on disks. The size of a magnetic bit determines the information storage capacity of a magnetic disk drive. The magnetic storage media used in today’s commercial hard disks consist of homogeneous

polycrystalline magnetic films. Owing to continuous improvements in both the magnetic properties of the media and the read/write heads, the storage density of hard disk drives has increased considerably during recent years, as shown in Fig. 5.3-17. Since 1990, the storage capacity of disk drives has increased at a 60% Areal density (Gb / in2) 1 Magnetoresistive read head 57 % / year 0.1

Inductive read / write head 21 % / year

0.01

10–3 1975

1980

1985

1990 1995 2000 Date of general availability

Fig. 5.3-17 Evolution of areal storage density of hard disk

drives (data from IBM, Almaden)

Mesoscopic and Nanostructured Materials

5.3.4.1 Spin Electronics Conventional electronic devices are based on charge transport, and their performance is limited by the speed of the carriers (electrons) and the dissipation of their energy. Conventional electronics has ignored the spin of the electron. Nevertheless, in every wire or device, approximately 50% of the conducting electrons are generally spin-up and the remainder spin-down (where “up” or “down” relate to some locally induced quantization axis). Spin electronics, or spintronics, is a new field of electronics which relies on the different transport properties of majority-spin and minority-spin electrons. Mott postulated the basis of spin electronics in the mid-1930s: he attributed certain anomalies in the electrical transport behavior of metallic ferromagnets to the fact that the spin-up and spin-down conduction electrons are two independent families of charge carriers, each with its own distinct transport properties [3.89].

The Concepts of Spin Accumulation and Spin Diffusion Length The other necessary ingredient of this model is that the two families contribute very differently to the electrical transport processes. This may be because the number densities of the carrier types are different, or it may because they have different mobilities. In either case, the asymmetry which makes spin-up electrons behave differently from spin-down ones arises because the ferromagnetic exchange field causes a splitting between the spin-up and spin-down conduction bands, leaving different band structures evident at the Fermi surface. In nonmagnetic materials, the two spin channels are equivalent because they have the same density of states (DOS) at the Fermi energy. In a magnetic material, the spin polarization is defined as the ratio of the difference between the populations in the up and down spin channels to the total number of carriers at the Fermi level,

SP =

N↑ − N↓ . N↑ + N↓

(3.11)

Clearly, if there is a nonzero spin polarization, the numbers of electrons participating in the conduction process are different for the two spin channels. More subtly, this implies that the susceptibilities to scattering of the two spin types are different, and this in turn leads to different mobilities [3.90]. Let us consider two spin channels of different mobility. When an electric field is applied to the metal, there is a shift in momentum space ∆k of the spin-up and spin-down Fermi surfaces in accordance with the equation dk ∆k (3.12) =~ , dt τ where F is the force on the carrier, E is the electric field, e is the electronic charge, and τ is the electron scattering time. Since the channels have different mobilities, this shift is different for the spin-up and spin-down Fermi surfaces, as illustrated in Fig. 5.3-18. As a consequence, if a current is passed from such a spin-asymmetric material, for example cobalt, into a paramagnetic material such as silver (which has no spin asymmetry between spin channels), there is a net influx into the silver of up-spins over down-spins. Thus, a surplus of up-spins appears in the silver, and with it a small associated magnetic moment per unit volume. This surplus is known as a spin accumulation. Evidently, for a constant current flow, the spin accumulation cannot increase indefinitely. The spin-up electrons injected across F = eE = ~

1049

Part 5 3.4

annual compound growth rate. The changes of the head technology first from thin-film heads to magnetoresistive heads and then to read heads based on the GMR effect [3.86, 87] have enabled enormous increases in volumetric storage capacity. The overall gain in areal density has been achieved by scaling the complete disk drive system. The medium has to accommodate smaller bit dimensions and smaller transition widths between written bits. However, the optimization also includes more sensitive read/write heads, improving the signal processing and coding, and improving the head–disk tribology. A good discussion of these aspects can be found in [3.88]. Progress in this field would not be possible without the maturity of growth techniques such as electron- or ion-beam lithography, and molecular-beam epitaxy and the ability to manufacture devices on a nanometric scale by nanoimprinting lithography. Another essential point has been the addition of magnetic contrast to near-field microscopy and electron microscopy (magnetic-force and Lorentz microscopy, respectively). These new tools permit us to establish a link between magnetism and structure on the atomic scale. We have selected here some examples to illustrate the state of the art in nanometric nanostructures, keeping as the main idea the impact of the underlying technological breakthrough. We focus our attention on two very active fields: magnetoresistive nanometric multilayers for spin electronics, and magnetic dots for ultrahighdensity storage media.

3.4 Magnetic Nanostructures

1050

Part 5

Special Structures

Displaced Fermi spheres

∆k Electric field

+ k=0

Part 5 3.4

Brillouin zone

Fig. 5.3-18 Schematic illustration of the shift in the Fermi

surface when an electric field is applied to a ferromagnet. The solid circles represent the Fermi spheres of upand down-spin electrons in the field, and the dashed circle represents the Fermi sphere in zero external field. (After [3.90])

the cobalt–silver interface are converted into spin-down electrons by spin-flip process, which we have hitherto ignored. So now we have a dynamic equilibrium between an influx of up-spins and their destruction by spin-flipping. This in turn defines a characteristic length scale that describes how far the spin accumulation extends into the silver. In the present description, we have assumed that both the spin-up and spin-down electrons are present in the ferromagnetic material in equal numbers but that their mobilities are different. Nevertheless, we can produce spin accumulation either as a direct consequence of an asymmetric density of states or as an indirect consequence via asymmetry in the electron mobility. It follows from the above discussion that the spin accumulation decays exponentially away from the interface, on a length scale called the spin diffusion length (λsd ). This concept is crucial for realizing a link between spin electronics and magnetic nanostructures. In this section, we shall not go further into this concept, but we shall do a rough calculation to see how large λsd is and on what parameters it depends. We use the following expression from [3.90]: " λvF τ↑↓ λsd = (3.13) , 3 where vF is the Fermi velocity, τ↑↓ is the spin-flip time, and λ is the mean free path. This relationship highlights the critical role of the impurity concentration in determining the spin diffusion length. If the impurity

level is increased in the nonmagnetic material, λsd drops because λ is shortened. This relation also allows us to estimate values for the spin diffusion length. Taking silver as an example, λsd can vary between several microns for very pure silver to the order of 10 nm for silver with 1% gold impurity. In a realistic material, λsd is of the order of 10–100 nm. This is the reason why the experimental observation of spin-dependent transport phenomena has been possible when researchers have controlled the growth of nanometric multilayers. It is obvious that the layer thickness has to be small on the scale of the spin diffusion length. The Discovery of Giant Magnetoresistance The era of spin electronics began with the discovery of a magnetoresistance effect in a magnetic multilayer consisting of a sequence of thin magnetic layers separated by equally thin nonmagnetic metallic layers: the electric current is strongly influenced by the relative orientation of the magnetizations of the magnetic layers. This experimental observation was made almost simultaneously by two research groups: Albert Fert’s group in Orsay [3.86] and Peter Grünberg’s group in Jülich [3.87, 91]. In fact, it was found that the resistance of the overall multilayer is low when the magnetizations of all the magnetic layers are parallel (ferromagnetic coupling), but it becomes much higher when the magnetizations of neighboring magnetic layers are antiparallel (antiferromagnetic coupling). Figure 5.3-19 shows the magnetoresistance curves at 4.2 K of Fe/Cr (magnetic/nonmagnetic) multilayers with thicknesses of the individual layers of the order of 1 nm (from [3.86]). In these multilayers, for certain thicknesses of the Cr interlayer, the magnetizations of adjacent Fe layers are oriented antiparallel by an antiferromagnetic interlayer exchange coupling [3.87]. When a magnetic field is applied, the resistance of the multilayer decreases drastically as the magnetizations of the two layers progressively align in the direction of the field. The GMR ratio is usually defined as

GMR =

RAP − RP , RP

(3.14)

where RP and RAP are the resistances in the parallel and the antiparallel state, respectively. In the case of Fe/Cr multilayers, the GMR is 80% at liquid-helium temperature and 20% at room temperature when the thickness of the Cr is 9 Å. The relative change of the resistance can be larger than 200% [3.92], and that is the reason why the effect is called “giant” magnetoresistance. GMR effects

Mesoscopic and Nanostructured Materials

3.4 Magnetic Nanostructures

1051

GMR (%) 1

R/ R (H = 0) 30 (Fe 30 Å / Cr 18 Å)30

≈ 80%

H3

0.8 0.7 0.6

20

(Fe 30 Å / Cr 12 Å)35 10

H3 (Fe 30 Å / Cr 9 Å)40

0.5

10

0 0

1

2

20 30 40 Magnetic field (kG)

3 4 5 Chromium thickness (nm)

Fig. 5.3-20 Dependence of the GMR ratio of an Fe/Cr Fe Cr Fe

Fig. 5.3-19 Magnetoresistance curves at 4.2 K of Fe/Cr

multilayers. (After [3.86])

have been reported in a large number of systems combining ferromagnetic transition metals or alloys with nonmagnetic metals (for a review, see [3.93]). The most commonly used combinations of magnetic and nonmagnetic layers are Co/Cu and Fe/Cr, but multilayers based on permalloy as the magnetic component are also frequently used. The second key ingredient was discovered by Parkin and Mauri [3.94]. These authors discovered that the orientation of the magnetic moments of two neighboring magnetic layers depends on the thickness of the intervening nonmagnetic layer. In fact, the orientation of the magnetic moments oscillates between parallel and antiparallel as a function of the thickness of the nonmagnetic layer [3.96]. This phenomenon is referred to as an oscillatory exchange coupling. Figure 5.3-20 shows the results of the original experiment of Parkin and Mauri. Oscillations of the GMR as a function of the Cr thickness occur because the magnetoresistive effect is only measurable for those thicknesses of Cr for which the interlayer coupling aligns the magnetic moments of all the Fe layers so that they are antiparallel. GMR effects have been obtained in two geometries. In the first one, the current is applied in the plane of the layer (hereafter denoted by CIP), as in the experiments for which results are shown in Figs. 5.3-19 and 5.3-20, while in the second one, the current flows perpendicular to the plane of the layers (hereafter denoted by CPP). The first measurements in the CPP configuration were

multilayer on Cr thickness. (After [3.94])

obtained by sandwiching the multilayer between two superconducting Nb layers [3.97]. A CPP-GMR configuration has also been obtained in nanowires, namely multilayers electrodeposited in the pores of a nucleartrack-etched polycarbonate membrane [3.98], and by oblique deposition on a prestructured substrate [3.99]. The CPP-GMR effect is definitely larger than the CIPGMR effect and occurs at much larger thicknesses. The mechanism of the GMR effect is illustrated in Fig. 5.3-21 for α = (ρ↓ /ρ↑ ) > 1, where ρ↓ and ρ↑ are Parallel configuration M NM M

+

Antiparallel configuration M NM M

+

–

– R += 1

R+= (1 + R) / 2

1

1

1

R

R

R

R

1

R– = R

R–= (R+1) / 2

Fig. 5.3-21 Schematic picture of the GMR mechanism.

The electron trajectories between two scatterings are represented by straight lines and the scatterings by abrupt changes in the direction. The signs + and − are for spins Sz = 1/2 and Sz = −1/2, respectively. The arrows represent the majority-spin direction in the magnetic layers. M = magnetic, NM = nonmagnetic. (After [3.95])

Part 5 3.4

–40 –30 –20 –10 0

H3

1052

Part 5

Special Structures

Part 5 3.4

the resistivities for spins parallel and antiparallel, respectively, to the magnetization direction; α > 1 means that the resistivity is smaller for the majority spins. In the parallel configuration, the spin+ (up) electrons are always the majority-spin electrons and are always weakly scattered in all layers, resulting in a resistance r for this channel that is smaller than the resistance R for the spin− (down) channel. The shorting of the current by this fast electron channel makes the resistivity low in the parallel state (RP = r). In the antiparallel configuration, each of the spin directions is alternately the majority and the minority one. The resistance is averaged for each channel, and the overall resistance RAP = (r + R)/4 is larger than in the parallel state. The GMR ratio is then (r − R)2 RAP − RP = (3.15) . RP 4r R This picture holds in both the CIP and the CPP geometries. An antiparallel configuration can also be obtained in multilayers in which consecutive magnetic layers have GMR =

a)

different coercivities [3.101], or by combining hard and soft magnetic layers. Spin Valves The best known structure for obtaining an antiparallel arrangement is the spin valve structure, originally proposed by Dieny et al. [3.100] (Fig. 5.3-22). A spin valve has two ferromagnetic layers (alloys of Ni, Fe, and Co) sandwiching a thin nonmagnetic metal (usually Cu), with one of the two magnetic layers being “pinned”, i. e. the magnetization in this layer is relatively insensitive to moderate magnetic fields. The other magnetic layer is called the “free layer” and its magnetization can be changed by application of a relatively small magnetic field. As the alignment of the magnetizations in the two layers changes from parallel to antiparallel, the resistance of the spin valve typically rises by 5–10%. The goal is to obtain the result that the magnetization of the free layer reverses in a very small field (a few oersteds), while the magnetization of the pinned layer remains M (10–3 emu)

b)

FeMn 10 nm

Antiferromagnetic

NiFe 15 nm

Ferromagnetic pinned

Cu 2.6 nm

Nonmagnetic

2

RT H in plane || EA

0

–2 –200

0

200

0

200 H (Oe)

c) 2.5 ∆R/R (%) NiFe 15 nm

Ferromagnetic free

2.0

H (Oe)

RT H in plane || EA

1.5 1.0 Substrate

0.5 0 –200

Fig. 5.3-22 (a) Schematic illustration of the spin valve multilayer originally proposed by Dieny et al. (15 nm NiFe/2.6 nm Cu/15 nm NiFe/10 nm FeMn). (b) Magnetization curve, and (c) relative change in resistance. The magnetic field is applied

parallel to the exchange anisotropy (EA) field created by the FeMn layer. The current flows perpendicular to this direction. (After [3.100])

Mesoscopic and Nanostructured Materials

Magnetic Tunnel Junctions Tunneling belongs to a class of electron transport phenomena known as quantum transport, “quantum” because they cannot be explained unless the wave nature of electrons is invoked. In the quantum mechanical picture, an electron is associated with a wave function ψ related to the probability Ψ that the electron can be found in a volume dv: by Ψ = ψψ ∗ dv. Quantum theory predicts that a particle has a nonzero probability of penetrating through a classically forbidden region separating two classically allowed regions of configuration space, by the process of tunneling. The concept of tunneling has found applications in a vast number of domains in modern physics and chemistry; the particular case of interest here is tuneling in heterostructures consisting of metallic and insulator films, leading to innovative electronic devices. In a metal–insulator–metal (M–I–M) heterostructure, the potential barrier arises from the microscopic interactions between the metals and the insulator layer. By means of tunneling, an electron with an energy lower than the potential barrier can be transferred from one metal to the other, under the condition that the thickness of the potential barrier is not too large compared with the electron’s wavelength (Fig. 5.3-24). For a long period, up to the 1970s, the spin of the electron was neglected in tunnel transport. In 1971, Tedrow and Meservey [3.104] conducted tunneling measurements on junctions between a very thin superconducting Al film and a ferromagnetic Ni film, through an Al2 O3 barrier, in a high magnetic field. They showed F1

Exchange layer

yˆ

Insulating layer

xˆ Spacer Lead

M1 θ1

M2 θ2

F2 Lead EF

eV EF

Free layer

Pinned layer

Fig. 5.3-23 Schematic illustration of an IBM GMR spin

valve sensor used in read heads. M1 and M2 are magnetizations,and θ1 and θ2 are angles from the longitudinal direction. The read head moves perpendicular to the xy plane. (After [3.102])

0

Fig. 5.3-24 One-electron energy diagram for a metal– insulator–metal tunnel junction

1053

Part 5 3.4

fixed. Pinning is usually accomplished by using an antiferromagnetic layer, such as FeMn, that is in close contact with the pinned magnetic layer. The resultant spin valve response is given by ∆R ∝ cos(θ1 − θ2 ), where θ1 and θ2 are the angles of the magnetization directions respectively of the free layer and of the pinned layer with respect to the direction parallel to the plane of the magnetization of the medium whose magnetization is being sensed, as shown in Fig. 5.3-23. The discovery of the GMR effect has created great expectations, since this effect has important applications, particularly in magnetic information storage technology. The use of spin valve multilayers in hard-disk read heads was first proposed by IBM in 1994 [3.102]. The principle of operation of a magnetic read head will be detailed in the section on ‘Applications’ below. Because the GMR effect is so important for industrial applications, there have been many improvements in recent years. The simplest type of pinned layer has been replaced by a synthetic antiferromagnet (two magnetic layers separated by a very thin (1 nm) nonmagnetic conductor, usually ruthenium) [3.94]. The magnetizations in the two magnetic layers are strongly coupled so as to make them antiparallel, and are thus effectively immune to outside magnetic fields. The second innovation is the nano-oxide layer (NOL), which is formed on the outside surface of the soft magnetic layer. This NOL reduces the resistance due to surface scattering, thus reducing the background resistance and thereby increasing the percentage change in the magnetoresistance of the structure [3.103].

3.4 Magnetic Nanostructures

1054

Part 5

Special Structures

that the tunneling current was spin-dependent. The spin splitting of the quasiparticle density of states of the superconductor caused by the application of the magnetic field was used to analyze the spin polarization of the tunneling current for Ni. The same method was used by the same authors to measure the spin polarization of electrons tunneling from a variety of ferromagnetic films: Fe, Co, Ni, and Gd [3.105]. A positive spin polarization was obtained in all cases; +44% was found for Fe, +34% for Co, +11% for Ni, and + 4.3% for Gd. These results demonstrated that the tunneling process preserves the character of the electronic spin and inaugurated the exciting research field of spin-dependent

Part 5 3.4

a) Soft electrode (HC,1)

M1

Tunnel barrier Hard electrode (HC,2)

GMR (%) = 100

(RAP – RP) RP

M2 M

b)

–HC,2

–HC,1

c)

HC,1

HC,2

H

R AP

R

RP –HC,2

–HC,1

HC,1

HC,2

H

Fig. 5.3-25a–c Schematic representation of a magnetic tunnel junction (a) and its magnetization loop (b). The resistance of the MTJ

is determined by the relative orientation of the magnetizations of the ferromagnetic electrodes of the junction, giving rise to lowand high-resistance states for parallel and antiparallel alignments, respectively (c). (After [3.106])

tunnel transport. The large amount of progress in recent years in this particular domain has led to the construction of innovative spintronic devices, at the heart of which we find the magnetic tunnel junction (MTJ). An MTJ behaves as a spin valve. However, it is a hybrid system comprising at least two ferromagnetic metals of different coercivities HC,1 and HC,2 (HC,1 < HC,2 ), separated by a thin insulator (Fig. 5.3-25a) instead of a nonmagnetic metallic spacer as in classic spin valves. In Fig. 5.3-25b, the magnetization loop of a magnetic tunnel junction is schematically shown. In such a device, the current flowing perpendicular to the film plane (CPP geometry) depends on the relative orientation of the magnetizations M1 and M2 of the two ferromagnetic electrodes of the junction, reaching extreme values for parallel and antiparallel alignment (we assume that the magnetization lies in the plane of the ferromagnetic layers). For an applied magnetic field parallel to the plane of the films with a value H ≥ |HC,2 |, the magnetizations of the two electrodes are aligned parallel to each other, giving rise to a lowresistance state (RP ) for the junction (Fig. 5.3-25c). In the magnetic-field window |HC,1 | < H < |HC,2 |, the electrodes’ magnetizations are aligned antiparallel to each other, corresponding to a high-resistance state (RAP ) for the junction. High tunnel magnetoresistance (TMR) at room temperature was discovered in magnetic tunnel junctions in the mid-1990s in Fe/Al2 O3 /Fe junctions [3.107], Fe/Al2 O3 /Ni1−x Fex junctions [3.108], and CoFe/ α-Al2 O3 /Co and NiFe [3.109] junctions, although the first measurements at low temperature were performed in 1975 [3.110]. The tunneling resistance is modulated by the magnetic field in the same way as in a spin valve, but the advantage over a “classical” spin valve is that it has been shown to exhibit a significantly higher GMR ratio (50% or more), while requiring a saturation magnetic field equal to or somewhat less than that required for a spin valve. It was proposed that these MTJs would have potential uses as low-power field sensors and memory elements. Because the tunneling current density is usually small, MTJ devices tend to have high resistances. The resistance of an MTJ depends exponentially on the thickness of the insulating layer. Uniformity over the insulating layer is crucial to device operation. In addition, reproducibility from MTJ element to MTJ element is important for the proper working of arrays of such devices. An example of such an effect is shown in Fig. 5.3-26, for a Co/Al2 O3 /NiFe junction. When the magnetizations of the Co and NiFe layers go from an antiparallel

3.4 Magnetic Nanostructures

Mesoscopic and Nanostructured Materials

Spin Spin

NiFe Co

TMR (%)

Spin Spin

Spin Spin

1055

Spin Spin

16 12 8 F1

4

I

F2

–200

0

200 H (Oe)

Fig. 5.3-26 Tunnel magnetoresistance curve at room tem-

perature of a Co/AL2 O3 /NiFe junction. (After [3.111])

to a parallel arrangement, the resistance of the junction decreases. In this example, the effect is 16% at room temperature [3.111]. Most of the measurements reported in the literature have been performed using an alumina (oxidized aluminium) barrier. In Jullière’s model [3.110], the TMR ratio is expressed as a function of the spin polarizations SP1 and SP2 of the two magnetic electrodes by 2SP1 SP2 RAP − RP = , P R 1 + SP1 SP2 N↑ (E F ) − N↓ (E F ) where SPi = (3.16) . N↑ (E F ) + N↓ (E F ) A structure analogous to the spin valve described above may be made by making the two metallic electrodes from a half-metallic ferromagnet (HMF, SP = 100%) and separating them with a thin layer of insulator. Now, if the magnetizations of the electrodes are opposite, no current can flow across the junction, since the electrons which might tunnel have no density of final states on the far side to receive them. However, if the electrode magnetizations are parallel, a tunneling current may flow as usual. This can be explained simply by the schematic picture in Fig. 5.3-27, which represents the case of two half-metals (with only one spin direction at the Fermi level) separated by a thin insulating barrier. We thus have a spin-electronic switch whose operation mirrors that of a pair of crossed optical polarizers, and which may be switched “on” and “off” by the application of an external magnetic field. If the electrodes are not ideal HMFs, then the on/off conductance ratio GMR =

I

F2

Antiparallel configuration, R infinite

Fig. 5.3-27 Schematic picture of the TMR effect in the case of two half-metallic electrodes. The transmission of the electrons from one layer to the other is only possible in the parallel state, resulting in a 100% TMR effect. (Courtesy of A. Bartélémy)

is finite and reflects the majority and minority densities of states of the ferromagnet concerned. In the case of an ideal HMF, in the antiparallel configuration, transmission from one electrode to the other is not allowed, and the resistance of the junction is infinite. In contrast, in the parallel state, transmission occurs, and the resistance is finite. This gives, for half-metallic electrodes, a spin polarization equal to 1 and a maximum TMR effect of 100%. In the case of a transition metal, the effect is more complex to analyze owing to the presence of s and d bands at the Fermi level with majority and minority spin directions. For transition metals, the TMR ratio is limited to 40% at liquid-helium temperature and 29% at room temperature. This is a demonstration of how the properties of metallic systems are controlled exclusively by the “mafia” of electrons at or very near the Fermi surface, whose band-structure properties the metal reflects. The spin tunnel junctions described above depend for their operation only on the density of states, and not on the carrier mobility. Unlike fully metallic systems, they have a lower conductance per unit area of device, and hence larger signal voltages (of the order of millivolts or more) are realizable for practical values of the operating current. Moreover, the device characteristics, such as the size of the “on” resistance, the current density, the operating voltage, and the total current, may be tuned by varying with device cross section, the barrier height, and the barrier width. This is just one reason why spin tunnel junctions are very promising candidates for the spin injector stages of future spin-

Part 5 3.4

Parallel configuration, R low

0

F1

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Special Structures

electronic devices. They will also be the basis of the next generation of MRAMs, as illustrated later in this section. Large TMR effects have been obtained using HMFs as electrodes, as can be seen in Fig. 5.3-28 in the case of a junction with La0.7 Sr0.3 MnO3 (LSMO) electrodes and a SrTiO3 (STO) barrier [3.112, 113]. The spin polarization deduced from this measurement is 83% if one assumes the same polarization for the two magnetic electrodes. With a polarization of 100%, half-metallic compounds would allow true on/off operations, and would be appropriate for gates of nonvolatile logic devices.

Part 5 3.4

LSMO / SrTiO3 / LSMO

a)

R (Ω)

6 ×105

SP = 83%

T = 4.2 K

5 ×105 4 ×105 TMR = 80%

Recently, Bowen et al. [3.114] reported a TMR ratio of more than 1800% at T = 4.2 K in LSMO/ SrTiO3 /LSMO fully epitaxial MTJs, from which they deduce a spin polarization of least 95% for the LSMO layer. This large TMR value arises both from preserving the quality of the LSMO/STO interfaces during the upgraded patterning process and from the use of junctions of small size (5.6 × 5.6 µm2 ) (Fig. 5.3-29). The TMR extends to temperatures of about 280 K, an improvement compared with previous results in the literature [3.115]. The temperature dependence of the TMR is plotted in Fig. 5.3-30a,b for two junctions using R(H ) loops measured at Vdc = 10 mV. The TMR decreases rather quickly with increasing T , but vanishes only at temperatures of about 280 K for the 2 × 6 µm2 junction. TMR ratios of 30% (Fig. 5.3-30c) and 12% are obtained at 250 and 270 K, respectively. This represents a sizable improvement with respect to previous results [3.112, 113] obtained from heterostructures grown under identia)

50 µm

3 ×10

5

2 ×105

1 mm

1 ×105 0 –1000

–500

0

500

1000 B0ˆ (G)

b)

b) R (kΩ)

TMR (%) 2000

400

LSMO

350 1500

300 SrTiO3

250 1000

200 2.5 nm LSMO

150 500

100 50 0

Fig. 5.3-28 (a) TMR curve of an LSMO/STO/LSMO

junction at 4.2 K. The spin polarization of the LSMO layer is 83%. After [3.112, 113]. (b) High-resolution transmission electron microscopy (HRTEM) image of an LSMO/STO/LSMO junction (courtesy of J. L. Maurice)

–400

–200

0

200

0 400 H (Oe)

Fig. 5.3-29 (a) Optical images of a processed sample of

small-size LSMO/STO/LSMO magnetic tunnel junctions. (b) R(H ) loop for a 5.6 × 5.6 µm2 junction measured at 4.2 K. (After [3.114])

Mesoscopic and Nanostructured Materials

a)

3.4 Magnetic Nanostructures

1057

c) TMR (%)

TMR (%)

800 30

600

T = 250 K

400 200 0

b)

20 0

50

100

150

200

250

TMR (%)

T (K)

800

Part 5 3.4

10 600 400 0

200 0

0

50

100

150

200

250

T (K)

–500

–250

0

250

500

H (Oe)

Fig. 5.3-30a–c Temperature dependence of the TMR measured with Vdc = 510 mV for two junctions: 2 × 6 µm2 (a) and 1.4 × 4.2 µm2 (b) (the dashed lines are guides to the eye). (c) R(H ) loop at T = 250 K and Vdc = 10 mV, showing 30%

TMR. (After [3.114])

cal conditions. Since the results shown in Fig. 5.3-30 were obtained from LSMO/STO/LSMO junctions with a fully strained crystallographic structure, these measurements prove that strain is not a limiting factor in the potential production of manganite-based MTJs with sizable TMR values at relatively high temperatures. High-quality interfaces that limit the disruption of the properties of the manganite are a more important requirement. This example illustrates fairly well that progress in spin electronics would not be possible without the improvement in the manufacturing of devices on the nanometric scale. Another promising HMF is Fe3 O4 , because this oxide exhibits the highest Curie temperature (Tc = 858 K). Consequently, one can expect that its HMF character will remain significant at room temperature. Figure 5.3-31 shows a cross-sectional high-

Fe3O4

γ –Al2O3

Fe3O

Fig. 5.3-31 HRTEM image of a fully epitaxial Fe3 O4 /

Al2 O3 /Fe3 O4 MTJ grown by MBE. The Fourier transform of the barrier region of the micrograph shows the high crystalline quality of this region. (Courtesy of P. Bayle Guillemaud and P. Warin)

5 nm

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Special Structures

Part 5 3.4

resolution transmission electron micrograph of a fully epitaxial Fe3 O4 /Al2 O3 /Fe3 O4 MJT, grown by MBE assisted by atomic oxygen [3.116]. The interest in this result is that the growth of the interfaces was performed without exposing the surface layers to air, limiting the disruption of the bulk properties. The Fourier transform of the barrier region of the micrograph shows the high crystalline quality of this region. The use of crystalline barriers in MTJs opens the way to investigation of tunnel transport in periodic barriers, which will permit a better understanding of the underlying fundamental physics. The record for magnetoresistance values has recently been obtained by Van Dijken et al. [3.117]. These authors report a large magnetic-field sensitivity of the collector current in a three-terminal magnetic tunnel transistor device with spin-valve metallic base layers. Giant magnetocurrents exceeding 3400% result from strong spin-dependent filtering of electrons traversing perpendicular to the spin-valve layers at energies well above the Fermi energy. With its giant magnetocurrent and reasonable output current, the magnetic tunnel transistor is a promising candidate for future magnetoelectronic devices. Applications Magnetic Read Heads and Sensors. Information is

stored on a magnetic disk in small magnetic domains arranged in concentric tracks. The conventional read head used to be an induction coil, which sensed the rate of change of the magnetic field as the disk rotated. The signal and hence the density of magnetized bits were thus limited by the speed of rotation of the disk. Magnetoresistive sensors do not suffer from this defect, since they sense the strength of the field rather than its rate of change. They are, therefore, capable of reading disks with a much higher density of magnetic bits. Magnetoresistive read heads are commercially available and will be the leading technology beyond the year 2004. When two oppositely magnetized domains meet, a domain wall appears, with a characteristic width of 100–1000 Å, depending on the magnetic properties of the material. Although there is no magnetic field emanating from the uniformly magnetized domains themselves, uncompensated magnetic poles at the domain walls emanate stray fields that extend out of the medium. Magnetic read heads contain a GMR or MTJ sensor element, which is sensitive to these domain wall stray fields. A schematic illustration of a GMR read head is shown in Fig. 5.3-32. The element is fabricated in such a way that the magnetization of the free layer is paral-

Iin

Support

Iout

Heads

MTJ sensor

Domain wall stray fields

Recording-medium track

Fig. 5.3-32 Schematic illustration of an MR read head.

A spin valve (“all-metal” or MTJ) is used as an ultrasensitive sensor for the very low magnetic field strength generated by the small magnetic domains (bits). When a weak magnetic field, such as from a bit on a hard disk, passes beneath the read head, the magnetic orientation of the free layer changes its direction relative to the pinned layer, generating a change in electrical resistance due to the GMR effect. (After [3.106])

lel to the plane of the medium. Every time the magnetic head passes over a domain wall, the magnetic field emanating from the wall pushes the magnetization of the free layer upwards or downwards, resulting in a change in the resistance of the MTJ device (the magnetization of the pinned layer is fixed). The design goal is to obtain the maximum rate of change in the resistance for a change in the magnetic field. The concept used in read heads is also applied in another type of magnetic sensors, with which we can sense the operation of a piece of machinery when a magnetic field is applied, as illustrated in Fig. 5.3-33. A gear made of ferrous metal can be arranged so that it perturbs the magnetic fringing field originating from a permanent magnet close to the rotating gear and the sensor MTJ element. The MTJ element is sensitive to the changing orientation of the magnetic flux as gear teeth pass by the magnet. Thus, the readout resistance is related to the angular position of the rotating gear. Such an arrangement is used to monitor the engine speed in an automobile. Magnetic Random Access Memories (MRAMs). Anisotropic-magnetoresistance elements were the first to be used for MRAM applications, approximately ten years ago. However, they provided a very small mag-

3.4 Magnetic Nanostructures

Mesoscopic and Nanostructured Materials

Soft electrode

Rotating wheel M1

Sensor element (MTJ) N

1059

R RAP

θ Insulator M3

S

RP

Permanent magnet

0

60 120 180 240 300 360

Angle θ (deg)

Hard electrode

Fig. 5.3-33 Principle of operation of a magnetic sensor using an MTJ element

a)

b) Blocking diode

Logical “0”

Logical “l”

Free layer Insulator Pinned layer

RP

RAP in

c)

I

ik

k

kn m

d)

n

I V k kn m

n i

V+

Fig. 5.3-34 (a) Schematic representation of an MRAM cell containing a single MTJ and a blocking diode (CMOS transistor), allowing current flow in only one direction, in series. (b) Representation of a logical “0” by the low-resistance state RP and of a logical “1” by the high-resistance state RAP . (c) The process of writing information on bit kn situated at the crossing of word lines k and n. The existence of the two currents i n and i k is necessary to switch the magnetization of the free layer. For example, in the memory cell km, which is influenced by a single current i k , no information is stored. (d) The process of reading information from cell kn. A bias is applied between the word lines k and n and the current through the bit cell is measured and compared with a reference value. The determination of the magnetic state of the junction, which can then be related to logical “0” or “1”, is thus possible

Part 5 3.4

netoresistive effect of about 2%, making their use disadvantageous in comparison with semiconductor memories in terms of read access time (> 250 ns). The density and cost of this kind of MRAMs were also not competitive with standard semiconductor memories. A major breakthrough in MRAM technology came with the use of GMR multilayers. The magnetoresistive signal is much higher – rising up to 18% – but the resistance of the all-metal GMR element is too small compared with the complementary metal–oxide– semiconductor (CMOS) transistor serving as the diode in an integrated structure. For this reason, a number of GMR cells have to be connected in series with the CMOS transistor, thereby decreasing the effective magnetoresistive signal. This is a serious drawback in the design of a fast-access memory. MTJs are the best candidates for MRAMs, as they provide a high magnetoresistive effect of 20–50% depending on the spin polarization of the magnetic electrodes, combined with a modifiable resistance, which depends on the thickness of the insulator and its degree of oxidation. This permits the utilisation of a single MTJ cell in series with a CMOS transistor (Fig. 5.3-34). This high-density architecture is suitable for fast-memory applications. The idea of the MRAM is to use the magnetization direction of the free magnetic layer for information storage, and the resulting resistance for readout. The resistance of the memory bit is either low or high, depending on the relative orientation (parallel or antiparallel) of the magnetization of the free layer with respect to the pinned layer. An applied magnetic field can switch the free layer between the two states. In an MRAM array, orthogonal lines pass under and over each memory bit, carrying the current which produces the switching magnetic field. The idea is that the current in one line is not sufficient to switch the memory cell; the bit will switch only if current is flowing through both of the lines that cross at the selected

1060

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Special Structures

Part 5 3.4

bit. The readout of the stored information in the selected bit is done by applying a bias between the lines that cross it and measuring the current that flows through it. For the successful realization of MRAM devices using MTJs, two very critical components – the tunnel barrier and the free layer – have to be optimized. The tunnel barrier needs to show large-scale uniformity over the wafer, in addition to the more or less obvious prerequisites of being pinhole-free and extremely smooth. This is because the tunnel resistance depends exponentially on the barrier thickness and the absolute value of the MTJ resistance is compared with a reference cell during the read operation. As far as the free layer is concerned, its thickness is directly related to the value of the magnetic field or current required for switching a bit. A free layer less than 5 nm thick is desirable, since it results in a low switching field and, as a consequence, low power consumption. A number of difficulties have to be resolved to create successful devices. These include efficient spin injection into semiconductors and heterostructures, and a search for new spin-polarized materials. Other effects potentially important for spintronic devices include optical and electrical manipulation of ferromagnetism, currentinduced switching and precessing of magnetization, and the possibility of a long coherence time for optically excited spins in semiconductors. For a good overview of the issues in spin electronics, including the prospects for spintronic quantum devices, see [3.118].

5.3.4.2 Ultrahigh-Density Storage Media in Hard Disk Drives The Limits of the Present Technology In the current storage technology, which uses continuous polycrystalline thin-film media, the signal-to-noise ratio (SNR) of the medium is directly related to the number of grains per bit. At storage densities on the order of 80 Gb/in2 , the grain size of the CoCrPtX alloys (X = Ta, P, etc.) used in the current media is on the order of 8 nm, the number of grains per bit is about 100, and the bit size is on the order of 250 nm × 30 nm. A further reduction in the number of grains per bit below 100 would lead to a strong decrease in the SNR. To continue decreasing the bit cell size in continuous media (while keeping the SNR constant), it is necessary to reduce the grain size further. However, there is a physical limit to how small the grain size can be before thermal variations can affect the stability of the magnetization. This is known as the superparamagnetic limit. In CoCrPt al-

loys, the minimum grain size for which the criterion for magnetic stability can be satisfied is about 8 nm, which is the grain size used in today’s media. Further reducing the grain size requires the use of other materials as FePt, SmCo, and FeNdB alloys. However, this implies that larger write fields will be needed to switch the magnetization of the grains. This would necessitate the development of new materials which are not yet known. In the short term, the use of antiferromagnetically coupled media has allowed the superparamagnetic limit to be extended in combination with GMR read heads [3.119]. The Promise of Perpendicular Media It is foreseen that within two or three years, magnetic recording will switch to perpendicular discontinuous media for several reasons. In perpendicular media, as opposed to longitudinal granular media, the smaller the bit size, the smaller the effect of the demagnetizing field on each bit is. In addition, the efficiency of the writer can be greatly improved, and higher-anisotropy materials can be used. Both effects contribute to a better thermal stability at small size grain size as compared with longitudinal media. This should help us to reach densities of the order of 200–400 Gb/in2 . However, to progress beyond these densities, a totally different approach will be required, which may consist of using patterned media, i. e. media made of arrays of nanometer-scale individual dots, in which each dot carries a bit of information. The significant advantage of this type of medium is that the shape and edge of each bit are not determined by the grain size as in continuous media, but are determined by the patterning process used to make the dots. Consequently, each dot can be made of a single magnetic domain (1 grain per bit instead of the 100 grains per bit in a continuous medium). The volume of a grain can therefore be much larger in a patterned medium so that the superparamagnetic limit is no longer a problem, at least up to several terabits per square inch. Of course, the use of patterned media raises other questions such as fabrication at low cost, tracking, and reproducibility. Various techniques have been developed to prepare arrays of submicrometer magnetic dots: optical, electron-beam, or X-ray lithography followed by etching of the magnetic material; patterning using a focused beam [3.120]; and self-organization of nanoparticles [3.121]. So far, however, none of these techniques seems to be able to combine the criteria of low cost, and rapid patterning of large areas (several square inches) down to 25 nm pitch.

Mesoscopic and Nanostructured Materials

Nanoimprinting. Nanoimprinting is a promising

represents a density of 200 Gb/in2 . After the nanoimprinting of the Si substrate, a magnetic material was deposited on the prepatterned wafer by sputtering or by some other relatively directional physical deposition process. The magnetic material then covered the top of the dots, the bottom of the trenches separating the dots, and, to a lesser extent, the sidewalls of the dots [3.122]. Corresponding atomic and magnetic images are shown in Fig. 5.3-36. a)

b)

Fig. 5.3-36 Structural (a) and magnetic (b) images of an array of single-domain dots with a 60 nm pitch prepared by nanoimprinting and coating with a (Pt/Co) multilayer. Images obtained by atomic and magnetic force microscopy

Influence of the Angle of Deposition. In order for one to be able to use these arrays of magnetic dots as recording media, the dots should be weakly coupled so that the magnetization of one dot can be switched without affecting the magnetization of the neighboring dots. In the present example, the sputtered species

a)

b)

1. Imprint. Press mold

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Part 5 3.4

method of nanopatterning proposed recently for solving the above-mentioned drawbacks. Nanoimprint lithography is a major breakthrough in nanopatterning because it can produce sub-10 nm feature sizes over a large area with a high throughput and low cost, a feat impossible with current, conventional lithography. Basically, the process of nanoimprinting starts by first making a mold by electron-beam lithography. This may take a long time, but this mold can be subsequently used a large number of times to imprint layers of resists on almost any kind of flat substrate. The patterned layer of resist is next used as an etching mask to transfer the pattern to the substrate by direct reactive ion etching (RIE) (Fig. 5.3-35a). The original approach to preparing arrays of magnetic dots starts from prepatterned wafers, on top of which a ferromagnetic material is deposited. In that case the nanopatterning of the magnetic material results directly from its deposition on a prepatterned wafer (Fig. 5.3-35b). Moritz and coworkers have studied the coupling between the dots obtained by deposition of Co/Pt multilayers on prepatterned Si substrates [3.122, 123]. Two patterning process were compared: (a) electronbeam lithography followed by direct RIE [3.124], and (b) nanoimprint lithography followed by lift-off and dry RIE of silicon [3.125, 126]. Subsequent deposition of a magnetic material (Co−Pt) leads to arrays of singledomain dots with a perpendicular magnetization. By nanoimprinting, a dot size down to 30 nm in diameter with a pitch of 60 nm has been obtained. This

3.4 Magnetic Nanostructures

Mold Resist Substrate

Remove mold

2. Pattern by transfer RIE

Fig. 5.3-35a,b Schematic principle of (a) the successive technological steps of pattern transfer by imprinting, and (b) the deposition of a magnetic material on a prepatterned substrate. The magnetic deposit covers the top of the dots, the bottom of the trenches, and, to a lesser extent, the sidewalls of the dots

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Special Structures

Part 5 3.4

(Co and Pt) were directed onto the substrate at either normal or oblique (37◦ from the normal) incidence (Fig. 5.3-37) [3.123]. When the substrate consists of an array of silicon pillars, the structural and magnetic properties obtained with the two deposition modes are quite different, as illustrated in Figs. 5.3-37 and 5.3-38 [3.123]. With normal deposition, a rough deposit made of Co, Pt, and CoPt alloy grains is observed (Fig. 5.3-37a), which induces a ferromagnetic coupling between adjacent dots (Fig. 5.3-38a) via the sidewalls and the magnetic deposit in the bottom of the trenches [3.122]. In contrast, when the Pt is deposited at oblique incidence, one sidewall of the dots is coated with antiferromagnetic CoO, whereas the other side consists of a Pt-rich PtCo alloy, which is nonmagnetic (Fig. 5.3-37b). In this latter case, no direct coupling bea)

Co

Pt

b)

Co

Pt

75 nm

Fig. 5.3-37a,b Cross-sectional TEM views of dots prepared by electron-beam lithography followed by Si RIE and covering by (Pt/Co) multilayers. In (a), both Co and Pt were deposited at normal incidence. In (b), Co was deposited at normal incidence, whereas Pt was deposited at oblique incidence. The width of the dots in both cases is 75 nm. (From [3.123])

tween the top of the dots and the bottom of the trenches takes place, resulting on no direct ferromagnetic coupling between adjacent dots. A checkerboard-like pattern of single-domain dots with a perpendicular magnetization is observed (Fig. 5.3-38b) [3.122, 123, 126]. This second situation is favorable if one wishes to use this type of array of dots as a discrete recording medium. Storing the Information on the Sidewalls of the Dots.

So far, the magnetic deposit on the top of the dots carries the recorded information. An alternative method would be to deposite the material on the sidewalls of the dots. This can be achieved by performing a codeposition of Cr at normal incidence and Co at oblique incidence. Thereby, a nonmagnetic Cr-rich CoCr alloy forms on top of the dots, whereas the sidewalls are coated with almost pure magnetic Co. The information can be stored by setting the magnetization of these “vertical nanomagnets” to be up or down on the sidewalls. Figure 5.3-39 compares the magnetic contrast measured by magnetic force microscopy (MFM) in two arrays of dots of the same geometry, one coated on the top of the dots with a (Pt/Co) multilayer, the other coated on the sidewalls with Co. Clearly the stray fields are much more localized and intense in the second case. It should be pointed out that the sidewalls are not single-domain here, but this can be fixed by using materials with higher coercivity (Co80 Cr20 alloys for instance). Another advantage of this approach is that two opposite sidewalls can be used per dot, which allows one to double the areal density for the same geometry. Manipulating the Magnetization of Individual Dots.

Two techniques have been developed to manipulate the magnetization of each dot individually. The first one is a thermomagnetic technique, which consists of usa)

a)

b)

b)

Fig. 5.3-38a,b 8 µm MFM images of domain patterns in arrays of (Pt/Co) dots deposited at normal incidence (a), and oblique incidence (b). (Courtesy of B. Dieny)

Fig. 5.3-39a,b MFM domain patterns in as-deposited arrays of 400 × 400 nm dots (a) coated on the top by a (Pt/Co) multilayer and (b) coated on the sidewall by 5 nm thick Co deposit. (Courtesy of B. Dieny)

Mesoscopic and Nanostructured Materials

Fig. 5.3-40 MFM images of an array of dots covered by a multilayer of composition Pt 20 nm/(Co 0.5 nm/Pt 1.8 nm). The dots are 400 nm in size, with an edge-to-edge spacing of 100 nm. A controlled switching of individual dots has been achieved by passing a pulse of current from a metallic AFM tip to the dot and simultaneously applying a uniform field of −200 Oe over the whole sample. (From [3.123])

Fig. 5.3-41 4 µm × 4 µm MFM image of a line written on an array of rectangular dots 100 nm × 200 nm in size with an edge-to-edge spacing of 100 nm. The writing was performed using a commercial inductive write head provided by Headway Inc. (From [3.123])

5.3.5 Preparation Techniques Various strategies have been developed for the manufacture of nanostructured materials. They follow essentially two approaches:

• •

The top-down manufacturing paradigm is that of the existing electronic technologies. It consists in downscaling the pattern size in lithographically structured materials. The bottom-up paradigm of nanosciences consists in the fabrication of atomically precise structures of increasing size, up to the mesoscopic scale.

Many preparation techniques are very specific to one particular type of material: for instance, many different chemical and physical techniques are used to produce porous silicon. Hence, we list and briefly describe below only the most common and generic methods for the

synthesis and fabrication of nanostructured materials. For a more detailed, recent, comprehensive description and discussion of the following production techniques, see [3.5, 128].

5.3.5.1 Molecular-Beam Epitaxy 2-D Structures An atomic or molecular beam of Ga, As, Al, and/or other elements is created thermally in a ultrahigh-vacuum chamber and directed at a specific, well-defined, atomically flat facet of a single-crystal substrate. A very low deposition rate, associated with a precisely controlled substrate temperature and various real-time techniques for monitoring the state of the surface, permit one to find growth conditions that preserve a coherent crystalline order or minimize the density of structural

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Part 5 3.5

ing a conductive atomic force microscope (AFM) tip to locally heat a given dot by passing a pulse of current between the tip and the dot [3.127]. The temperature rise leads to a decrease in the switching field of the magnetization of the addressed dot. Simultaneously, a static field of −200 Oe is applied to the whole sample. This field is large enough to switch the magnetization of the heated dot in the desired direction but low enough not to switch the magnetization of the other dots [3.123]. This is illustrated in Fig. 5.3-40. These experiments are preliminary, but impressive and highly encouraging. The main difficulty was irreproducibility in the contact resistance. A second technique has also been developed to manipulate the magnetization of individual dots; this technique is based on the use of write heads developed by Headway Inc. The array of dots is mounted on a piezoelectric stage, which allows displacement of the sample over an area of 120 µm × 120 µm. The head is in contact with the surface of the sample. A write current of 30 mA was used in the writer. An example of controlled writing of a line of dots is shown in Fig. 5.3-41 [3.123].

3.5 Preparation Techniques

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Part 5

Special Structures

defects. Because of the atomic layer-by-layer deposition, MBE is the technique that allows the best control over the thickness of a 2-D film down to the subatomic level. This has motivated a huge number of research studies on the mechanism of MBE growth. MBE is used when the highest thickness accuracy, abrupt interfaces, the highest purity, and/or the lowest density of surface defects is needed. Its main applications are for semiconductor quantum wells, since the band gap of Alx Ga1−x As can be tuned continuously through the composition x of the ternary alloy without inducing too large a lattice mismatch (see e.g. [3.32]).

Part 5 3.5

1-D Structures Quantum wires are less commonly encountered, since their fabrication procedures are even more complicated: one method exploits the step-flow growth of vicinal surfaces [3.129]. Self-assembly in specific MBE-type situations leads to the formation of wire structures. Thus, straight atomic lines of Si have been grown on a β-SiC(100) surface [3.130]. 0-D Structures MBE was primarily designed for the growth of 2-D nanostructures. However, it has been observed that the combination of two lattice-mismatched materials can lead to the formation of self-assembled sizemonodispersed clusters or dots during growth in the Stranski–Krastanov (SK) mode. The most studied system is that of InAs deposited on a GaAs(100) substrate [3.131]. In that case, the lattice mismatch is 7%, and the nanocluster size is 20 nm ± 10%. The average nanocluster size and density are tunable over a narrow range through the choice of growth parameters. Moreover, various cluster shapes are obtained with different substrate faces. More complicated systems have been produced, such as 2-D core–shell magnetic dots [3.132]. Finally, the use of a high-index substrate (such as GaAs(311)) can lead to a lateral ordering of the nanocluster distribution [3.133]. Clusters of various metals can be formed by use of a dewetting (Vollmer–Weber) type of epitaxial growth; this has been done mainly on highly oriented pyrolytic graphite (HOPG). Formation of 3-D islands has been reported for Cu, Ag, Au [3.134], Pt [3.135], Co [3.136], Mo, [3.137], and Pd [3.138]. In some specific situations, a 3-D stacking of quantum dot layers has been achieved [3.139].

5.3.5.2 Metal-Organic Chemical Vapor Deposition (MOCVD) This type of growth takes place in a reaction chamber in which the substrate is heated to a very high temperature (500 ◦ C to 1000 ◦ C). A combination of metal-organic and metal hydride vapors (e.g. triethylgallium, Ga(C2 H5 )3 , and arsine, AsH3 , for GaAs formation) is then brought into contact with the substrate by use of a laminar flow of a carrier gas (typically N2 or H2 ). The desired atoms are deposited layer by layer through a chemical reaction taking place at the substrate surface. MOCVD can be adapted to large-scale, long, continuous runs. Today, it is thus the most conventional industrial manufacturing technique for semiconductor heterostructures.

5.3.5.3 Lithography The lateral patterning in large-scale integrated electronic circuits is produced by projection photolithography. The resolution is limited not by the resists themselves but by optical diffraction during exposure, the minimum line spacing being of the order of λ/NA, where λ is the wavelength and NA the numerical aperture of the projection system. Today, the deep-UV technology is used; this is based on ArF excimer laser sources (λ = 193 nm), the numerical aperture is of the order of 0.8, and image enhancement techniques such as phase-shift masks are used [3.140]. This technique achieves typical line spacings close to 100 nm. To achieve higher resolution, alternative radiation sources and/or exposure techniques have been used and are summarized in Table 5.3-3.

5.3.5.4 Nanocrystals in Matrices Diffusion-Controlled Growth The growth of clusters from ions dissolved in a glass can be kinetically controlled by tuning the temperature between the glass transition temperature and the melting temperature. Empirical methods for the growth of metal clusters for use in stainedglass windows have been known for centuries. This technique is now mainly used for the fabrication of color cutoff filters using II–VI compounds. The main compound used is CdSx Se1−x , and such filters are made by Schott in Germany, Corning in the USA, and Hoya in Japan. It is also used for photochromic glasses based on I–VII compounds (mainly AgBr).

Mesoscopic and Nanostructured Materials

3.5 Preparation Techniques

1065

Table 5.3-3 Radiation sources and exposure techniques for higher resolution

Radiation source

Energy

Deep UV X-rays Electrons Ions

6.4 eV 2 keV 20 keV 100 keV Comments

Contact printing Proximity printing

The resolution is the limited by the optical skin depth of the mask material. √ The resolution is limited by diffraction, with a minimum line spacing of gλ, where g is the mask–surface distance. Proximity printing techniques have been used mainly in conjunction with X-ray radiation sources. A master stamp is used directly for hot embossing of a substrate, usually made of a polymer. This allows the stamp to produce many patterned substrates. Although there is no diffraction limit here, hot embossing has been applied mainly for low-resolution applications, in various fields such as miniaturized total-analysis Systems (µTAS), microfluidics, and microoptics. UV–nanoimprint lithography corresponds to contact printing with UV exposure.

Nanoimprinting

Scanned-source techniques Electron and ion beams

Near-field scanning optical microscope (NSOM) Scanning tunneling microscope (STM)

Scanning electron beam lithography is the most widely used technique for nanostructuring surfaces beyond the optical resolution limit. The resist used is polymethylmethacrylate (PMMA). This is the scanned-source equivalent of contact and proximity printing. In contrast to electron-beam lithography, the mechanism of STM lithography is generally an inelastic electron tunneling process, with energy quanta of an electron volt. STM can also be used for single-atom or single-molecule manipulations for the fabrication of individual nanostructures.

Sol–Gel Synthesis Cold chemical synthesis of nanoporous glasses by the sol–gel technique allows the embedding of temperaturesensitive clusters such as organic nanocrystals. Moreover, it often permits one to achieve larger densities of semiconductor nanocrystals than in diffusion-controlled growth. Zeolites Zeolites constitute a group of hydrated crystalline aluminosilicates containing regularly shaped pores with sizes from 1 nm to several nanometers. This provides them with the ability to reversibly adsorb and desorb specific molecules. Chemical synthesis of semiconductors inside such pores permits the fabrication of regularly distributed, highly size-monodispersed nanocrystal arrays. This has been applied to CdS, PbI2 , and Ge.

5.3.5.5 Ex Situ Synthesis of Clusters As an alternative to in situ growth, nanocrystals can be synthesized either in solution (e.g. by colloidal synthesis) or in the gas phase, prior to dispersion in a matrix or deposition or self-assembly onto a substrate. Colloidal Synthesis Although gold colloids were known and studied very early [3.2], the synthesis technique has been much studied and greatly improved during the past few decades. The two-phase approach permits the fabrication of thiolcovered noble-metal nanoparticles [3.141]. The thiol layer prevents coalescence of the metal particles, thus stabilizing the colloid and preserving the size distribution. Motivated by the self-ordering properties of layers of nanoparticles with a narrow size distribution,

Part 5 3.5

Exposure techniques

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Part 5

Special Structures

q

p

Part 5 3

50 nm

Fig. 5.3-42 TEM image showing a superlattice of

thiol-passivated Au clusters with a bimodal size distribution (∼ 4.5 and 7.8 nm diameter). The 2-D supracrystallization shows a regular self-organized bimodal packing. (After 3.144)

researchers have developed various size-selection techniques [3.142, 143]. As shown in Fig. 5.3-42, relatively complex self-organized structures are now achievable through self-assembly of size-selected thiol-capped nanoparticles obtained from colloidal synthesis [3.144], including mixtures of particles of different chemical nature (Au and Ag, [3.145]). This technique has been extended to transition metals. 6 nm trioctylphosphine-coated Co particles have

been synthesized using a reverse-micelle approach and assembled as a hexagonal self-organized superlattice [3.146]. 3-D self-assembled superlattices of FePt nanoparticles have also been produced [3.121]. Ligand-stabilization techniques have led to macromolecular complexes consisting of a metal core containing a fixed number of atoms surrounded by a precise number of organic ligand molecules. Following the synthesis of Au55 (P(C6 H5 )3 )12 Cl3 clusters [3.147], a number of such macromolecules of various sizes and compositions have been studied, such as giant ligand-stabilized clusters containing 561 Pd atoms [3.148]. Variations of the colloidal-synthesis and size selection techniques have also been developed in parallel for the preparation of semiconductor nanoparticles, particularly II–VI compounds such as CdSe [3.149], from which self-assembled superlattices can be grown [3.150]. GaAs nanocrystals have been produced similarly [3.151]. Gas-Phase Production Several techniques have been applied for the production of “preformed” clusters in the gas phase, prior to their deposition onto a substrate. The low-energy cluster beam deposition technique was developed especially for the deposition of small clusters of transition metals (Ni, Fe, Co, etc.) [3.152]. An extensive review of this vast subject can be found in [3.153].

References 3.1

3.2

3.3

3.4 3.5 3.6

3.7

M. Jos´ e-Yacaman, L. Rendon, J. Arenas, M. C. S. Puche: Maya blue paint: An ancient nanostructured material, Science 273, 223–225 (1996) M. Faraday: Experimental relations of gold (and other metals) to light, Phil. Trans. R. Soc. 147, 145–181 (1857) R. Dingle, W. Wiegmann, C. H. Henry: Quantum states of confined carriers in very thin Alx Ga1−x As−GaAs−Alx Ga1−x As heterostructures, Phys. Rev. Lett. 33, 827–830 (1974) B. Bhushan (Ed.): Springer Handbook of Nanotechnology (Springer, Berlin, Heidelberg 2004) P. Moriarty: Nanostructured materials, Rep. Prog. Phys. 64, 297–381 (2001) M. Milun, P. Pervan, D. P. Woodruff: Quantum well structures in thin metal films: Simple model physics in reality?, Rep. Prog. Phys. 65, 99–141 (2002) S. A. Lindgren, S. Valden: Electron-energy-band determination by photoemission from overlayer states, Phys. Rev. Lett. 61, 2894–2897 (1988)

3.8

3.9

3.10

3.11

3.12

3.13

T. Miller, A. Samsavar, G. E. Franklin, T.-C. Chiang: Quantum-well states in a metallic system: Ag on Au(111), Phys. Rev. Lett. 61, 1404–1407 (1988) S. Bjornholm, J. Borggren, O. Echt, K. Hansen, J. Pedersen, H. D. Rasmussen: The influence of shells, electron thermodynamics, and evaporation on the abundance spectra of large sodium metal clusters, Z. Phys. D 19, 47 (1991) W. Ekardt: Work function of small metal particles: Self-consistent spherical jellium-background model, Phys. Rev. B 29, 1558–1564 (1984) J. H. Cho, K. S. Kim, C. T. Chan, Z. Y. Zhang: Oscillatory energetics of flat Ag films on MgO(001), Phys. Rev. B 63, 113408 (2001) J. J. Paggel, T. Miller, T. C. Chiang: Quantum-well states as Fabry-Perot modes in a thin-film electron interferometer, Science 283, 1709–1711 (1999) M. S. Hybertsen: Mechanism for light emission from nanoscale silicon. In: Porous Silicon Science and Technology, ed. by J.-C. Vial, J. Derrien (Les éditions de physique, Les Ulis 1995) p. 67

Mesoscopic and Nanostructured Materials

3.14

3.15

3.16

3.17

3.19

3.20

3.21

3.22

3.23 3.24

3.25

3.26

3.27

3.28

3.29

3.30

3.31

3.32 3.33

3.34

3.35

3.36

3.37

3.38

3.39

3.40

3.41

3.42

3.43 3.44

3.45

M. H. Yukselici: Growth kinetics of CdSe nanoparticles in glass, J. Phys.: Condens. Matter 14, 1153–1162 (2002) C. Weisbuch, B. Vinter: Quantum Semiconductor Structures (Academic Press, Boston 1991) Chap. 3 B. Zhao, A. Yariv: Quantum well semiconductor lasers. In: Semiconductor Lasers I: Fundamentals, ed. by E. Kapon, P. L. Kelley (Academic Press, San Diego 1999) Chap. 1 E. Kapon: Quantum wire and quantum dot lasers. In: Semiconductor Lasers I: Fundamentals, ed. by E. Kapon, P. L. Kelley (Academic Press, San Diego 1999) Chap. 4 V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi: Optical gain and stimulated emission in nanocrystal quantum dots, Science 290, 314–317 (2000) H. J. Eisler, V. C. Sundar, M. G. Bawendi, M. Walsh, H. I. Smith, V. Klimov: Color-selective semiconductor nanocrystal laser, Appl. Phys. Lett. 80, 4614–4616 (2002) P. T. Guerreiro, S. Ten, N. F. Borrelli, J. Butty, G. E. Jabbour, N. Peyghambarian: PbS quantum-dot doped glasses as saturable absorbers for mode locking of a Cr:forsterite laser, Appl. Phys. Lett. 71, 1595–1597 (1997) K. Wundke, S. Potting, J. Auxier, A. Schulzgen, N. Peyghambarian, N. F. Borrelli: PbS quantum-dotdoped glasses for ultrashort-pulse generation, Appl. Phys. Lett. 76, 10–12 (2000) S. Schmitt-Rink, D. S. Chemla, D. A. B. Miller: Linear and nonlinear optical properties of semiconductor quantum wells, Adv. Phys. 38, 89–188 (1989) F. Devaux, F. Dorgeuille, A. Ougazzaden, F. Huet, M. Carre, A. Carenco, M. Henry, Y. Sorel, J.-F. Kerdiles, E. Jeanney: 20 Gbit/s operation of a high-efficiency InGaAsP/InGaAsP MQW electroabsorption modulator with 1.2-V drive voltage, IEEE Photonics Tech. Lett. 5, 1288–1990 (1993) D. Delprat, A. Ramdane, A. Ougazzaden, H. Nakajima, M. Carre: Integrated multiquantum well distributed feedback laser-electroabsorption modulator with a negative chirp for zero bias voltage, Electron. Lett. 33, 53–55 (1997) T. D. Krauss, F. W. Wise: Coherent acoustic phonons in a semiconductor quantum dot, Phys. Rev. Lett. 79, 5102–5105 (1997) D. Donovan, J. F. Andress: Lattice Vibrations (Chapman and Hall, London 1971) J. F. DiTusa, K. Lin, M. Park, M. S. Isaacson, J. M. Parpia: Role of phonon dimensionality on electron–phonon scattering rates, Phys. Rev. Lett. 68, 1156–1159 (1992) S. H. Song, W. Pan, D. C. Tsui, Y. H. Xie, D. Monroe: Energy relaxation of two-dimensional carriers in strained Ge/Si0.4 Ge0.6 and Si/Si0.7 Ge0.3 quan-

1067

Part 5 3

3.18

L. T. Canham: Silicon quantum wire array fabrication by electrochemical and chemical dissolution of wafers, Appl. Phys. Lett. 57, 1046–1048 (1990) V. Lehmann, U. Gösele: Porous silicon formation: A quantum wire effect, Appl. Phys. Lett. 58, 856– 858 (1990) A. I. Belogorokhov, V. A. Karavanskii, A. N. Obraztsov, V. Y. Timoshenko: Intense photoluminescence in porous gallium-phosphide, JETP Lett. 60, 274–279 (1994) A. Anedda, A. Serpi, V. A. Karavanski, I. M. Tiginyanu, V. M. Ichizli: Time-resolved blue and ultraviolet photoluminescence in porous GaP, Appl. Phys. Lett. 67, 3316–3318 (1995) J. S. Shor, L. Bemis, A. D. Kurtz, I. Grimberg, B. Z. Weiss, M. F. Macmillian, W. J. Choyke: Characterization of nanocrystallites in porous p-type 6H-SiC, J. Appl. Phys. 76, 4045–4049 (1994) D. J. Lockwood, Z. H. Lu, J.-M. Baribeau: Quantum confined luminescence in Si/SiO2 superlattices, Phys. Rev. Lett. 76, 539–541 (1996) R. W. Collins, P. M. Fauchet, I. Shimizu, J.-C. Vial, T. Shimada, A. P. Alivisatos (Eds.): Advances in Microcrystalline and Nanocrystalline Semiconductors, Vol. 452 (Materials Research Society, Pittsburgh 1997) N. M. Park, T. S. Kim, S. J. Park: Band gap engineering of amorphous silicon quantum dots for light-emitting diodes, Appl. Phys. Lett. 78, 2575– 2577 (2001) L. Pavesi, L. Dal Negro, C. Mazzoleni, G. Franzo, F. Priolo: Optical gain in silicon nanocrystals, Nature 408, 440–444 (2000) P. Ball: Let there be light, Nature 409, 974–976 (2001) L. E. Brus: Electron–electron and electron–hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state, J. Chem. Phys. 80, 4403–4409 (1984) Y. Kayanuma: Quantum-size effects of interacting electrons and holes in semiconductor microcrystals with spherical shape, Phys. Rev. B 38, 9797–9805 (1988) Al. L. Efros, A. L. Efros: Interband absorption of light in a semiconductor sphere, Sov. Phys. Semicond. 16, 772–775 (1982) A. Shik: Quantum Wells, Physics and Electronics of Two-Dimensional Systems (World Scientific, Singapore 1997) Chap. 4.4 S. Glutsch, D. S. Chemla: Transition to onedimensional behavior in the optical absorption of quantum-well wires, Phys. Rev. B 53, 15902–15908 (1996) D. J. Norris, A. Sacra, C. B. Murray, M. G. Bawendi: Measurement of the size-dependent hole spectrum in CdSe quantum dots, Phys. Rev. Lett. 72, 2612–2615 (1994) G. Banfi, V. Degiorgio: Neutron scattering investigation of the structure of semiconductor-doped glasses, J. Appl. Phys. 74, 6925–6935 (1993)

References

1068

Part 5

Special Structures

3.46

3.47

3.48

Part 5 3

3.49

3.50 3.51

3.52

3.53

3.54

3.55

3.56

3.57

3.58

3.59 3.60

tum wells: Evidence for two-dimensional acoustic phonons, Appl. Phys. Lett. 70, 3422–3424 (1997) V. Narayanamurti, H. L. Störmer, M. A. Chin, A. C. Gossard, W. Wiegmann: Selective transmission of high-frequency phonons by a superlattice: The dielectric phonon filter, Phys. Rev. Lett. 43, 2012– 2016 (1979) P. V. Santos, L. Ley, J. Mebert, O. Koblinger: Frequency gaps for acoustic phonons in a-Si:H/a-SiNx :H superlattices, Phys. Rev. B 36, 4858–4867 (1987) M. Fujii, T. Nagareda, S. Hayashi, K. Yamamoto: Low-frequency Raman scattering from small silver particles embedded in SiO2 thin films, Phys. Rev. B 44, 6243–6248 (1991) L. Saviot, B. Champagnon, E. Duval, A. I. Ekimov: Size-selective resonant Raman scattering in CdS doped glasses, Phys. Rev. B 57, 341–346 (1998) H. Lamb: On the vibrations of an elastic sphere, Proc. Math. Soc. London 13, 187 (1882) S. Rufo, M. Dutta, M. A. Stroscio: Acoustic modes in free and embedded quantum dots, J. Appl. Phys. 93, 2900–2905 (2003) N. Del Fatti, C. Voisin, F. Chevy, F. Vallee, C. Flytzanis: Coherent acoustic mode oscillation and damping in silver nanoparticles, J. Chem. Phys. 110, 11484–11487 (1999) M. Ikezawa, T. Okuno, Y. Masumoto, A. A. Lipovskii: Complementary detection of confined acoustic phonons in quantum dots by coherent phonon measurement and Raman scattering, Phys. Rev. B 64, 201315 (2001) A. Arbouet, C. Voisin, D. Christofilos, P. Langot, N. Del Fatti, F. Vallee, J. Lerme, G. Celep, E. Cottancin, M. Gaudry, M. Pellarin, M. Broyer, M. Maillard, M.-P. Pileni, M. A. Treguer: Electron–phonon scattering in metal clusters, Phys. Rev. Lett. 90, 177401 (2003) S. Schmitt-Rink, D. A. B. Miller, D. S. Chemla: Theory of the linear and nonlinear optical properties of semiconductor microcrystallites, Phys. Rev. B 35, 8113–8125 (1987) D. Kovalev, H. Heckler, M. Ben-Chorin, G. Polisski, M. Schwartzkopff, F. Koch: Breakdown of the k-conservation rule in Si nanocrystals, Phys. Rev. Lett. 81, 2803–2806 (1998) M. S. Hybertsen: Absorption and emission of light in nanoscale silicon structures, Phys. Rev. Lett. 72, 1514–1517 (1994) N. F. Mott: Conduction in non-crystalline materials III. Localized states in a pseudogap and near extremities of conduction and valence bands, Philos. Mag. 19, 835–852 (1969) B. F. Levine: Quantum-well infrared photodetectors, J. Appl. Phys. 74, R1–81 (1993) L. Esaki, R. Tsu: Superlattice and negative differential conductivity in semiconductors, IBM J. Res. Devel. 14, 61–65 (1970)

3.61

3.62

3.63

3.64

3.65

3.66 3.67

3.68

3.69

3.70

3.71

3.72 3.73

3.74

3.75

3.76

L. Esaki, L. L. Chang: New transport phenomenon in a semiconductor superlattice, Phys. Rev. Lett. 33, 495–498 (1974) K. K. Choi, B. F. Levine, R. J. Malik, J. Walker, C. G. Bethea: Periodic negative conductance by sequential resonant tunneling through an expanding high-field superlattice domain, Phys. Rev. B 35, 4172–4175 (1987) N. F. Mott: Conduction in Non-Crystalline Materials, Oxford Science Publications, 2nd edn. (Clarendon, Oxford 1993) P. Sheng, J. Klafter: Hopping conductivity in granular disordered systems, Phys. Rev. B 27, 2583–2586 (1983) R. P. Andres, T. Bein, M. Dorogi, S. Feng, J. I. Henderson, C. P. Kubiak, W. Mahoney, R. G. Osifchin, R. Reifenberger: Coulomb staircase at room temperature in a self-assembled molecular nanostructure, Science 272, 1323–1325 (1996) M. A. Kastner: The single-electron transistor, Rev. Mod. Phys. 64, 849–858 (1992) A. L. Efros, B. I. Shklovskii: Coulomb gap and lowtemperature conductivity of disordered systems, J. Phys. C: Solid State Phys. 8, L49–51 (1975) M. Fujii, T. Kita, S. Hayashi, K. Yamamoto: Currenttransport properties of Ag−SiO2 and Au−SiO2 composite films: Observation of single-electron tunnelling and random telegraph signals, J. Phys.: Condens. Matter 9, 8669–8677 (1997) P. E. Trudeau, A. Escorcia, A. A. Dhirani: Variable single electron charging energies and percolation effects in molecularly linked nanoparticle films, J. Chem. Phys. 119, 5267–5273 (2003) A. Taleb, F. Silly, A. O. Gusev, F. Charra, M.-P. Pileni: Electron transport properties of nanocrystals: Isolated, and “supra”-crystalline phases, Adv. Mater. 12, 633–637 (2000) J. Fick, A. Martucci, M. Guglielmi, J. Shell: Nonlinear optical properties of semiconductor-doped sol–gel waveguides, Fiber Integrated Opt. 19, 43–56 (2000) U. Kreibig, M. Vollmer: Optical Properties of Metal Clusters (Springer, Berlin, Heidelberg 1995) p. 50 K. Kolwas, S. Demianiuk, M. Kolwas: Optical excitation of radius-dependent plamon resonances in large metal clusters, J. Phys. B 29, 4761–4770 (1996) S. Link, Z. L. Wang, M. A. El-Sayed: Alloy formation on gold–silver nanoparticles and the dependence of the plasmon absorption on their composition, J. Phys. Chem. B 103, 3529–3533 (1999) F. Hache, D. Ricard, C. Flytzanis: Optical nonlinearities of small metal nanoperticles: Surface-mediated resonance and quantum size effects, J. Opt. Soc. Am. B 3, 1647–1655 (1986) R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, C. A. Mirkin: Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles, Science 277, 1078–1081 (1997)

Mesoscopic and Nanostructured Materials

3.77

3.78 3.79

3.80

3.82

3.83 3.84

3.85

3.86

3.87

3.88 3.89 3.90

3.91

3.92

3.93

3.94

3.95

3.96

3.97

3.98 3.99

3.100

3.101

3.102

3.103

3.104

3.105

3.106

A. Bartélémy, A. Fert, F. Petroff: Giant magnetoresistance in magnetic multilayers. In: Handbook of Magnetic Materials, Vol. 12, ed. by K. H. J. Buschow (Elsevier, Amsterdam 1999) Chap. 1, pp. 1–96 S. S. P. Parkin, D. Mauri: Spin engineering: Direct determination of the Ruderman–Kittel–Kasuya– Yosida far-field range function in ruthenium, Phys. Rev. B 44, 7131 (1991) A. Barthélémy, A. Fert, J-P. Contour, M. Bowen, V. Cros, J. M. De Teresa, A. Hamzic, J. C. Faini, J. M. George, J. Grollier, F. Montaigne, F. Pailloux, F. Petroff, C. Vouille: Magnetoresistance and spin electronics, J. Magn. Magn. Mater. 242–245, 68 (2002) D. H. Mosca, F. Petroff, A. Fert, P. A. Schroeder, W. P. Pratt, R. Loloee: Oscillatory interlayer coupling and giant magnetoresistance in Co/Cu multilayers, J. Magn. Magn. Mater. 94, L1 (1991) W. P. Pratt, S. F. Lee, J. M. Slaughter, R. Loloee, P. A. Schroeder, J. Bass: Perpendicular giant magnetoresistances of Ag/Co multilayers, Phys. Rev. Lett. 66, 3060 (1991) A. Fert, L. Piraux: Magnetic nanowires, J. Magn. Magn. Mater. 200, 338 (1999) (Special issue) M. A. M. Gijs, M. T. Johnson, A. Reinders, P. E. Huisman, R. J. M. van de Veerdonk, S. K. J. Lenczowski, R. M. Gansewinkel: Perpendicular giant magnetoresistance of Co/Cu multilayers deposited under an angle on grooved substrates, Appl. Phys. Lett. 66, 1839 (1995) B. Dieny, V. S. Speriosu, S. S. Parkin, B. A. Gurney, D. R. Wilhoit, D. Mauri: Giant magnetoresistance in soft ferromagnetic multilayers, Phys. Rev. B 43, 1297 (1991) J. Barnas, A. Fuss, R. E. Camley, P. Grünberg, W. Zinn: Novel magnetoresistance effect in layered magnetic structures: Theory and experiment, Phys. Rev. B 42, 8110 (1990) C. Tsang, D. E. Heim, R. E. Fontana, V. S. Speriosu, B. A. Gurney, M. L. Williams: Design, fabrication and testing of spin-valve read heads for high density recording, IEEE Trans. Magn. 30, 3801 (1994) W. F. Egelhoff Jr, P. J. Chen, C. J. Powell, D. Parks, G. Serpa, R. D. McMichael, D. Martien, A. E. Berkowitz: Specular electron scattering in metallic thin films, J. Vac. Sci. Technol. B 17, 1702 (1999) P. M. Tedrow, R. Meservey: Spin-dependent tunneling into ferromagnetic nickel, Phys. Rev. Lett. 26, 192 (1971) P. M. Tedrow, R. Meservey: Spin polarization of electrons tunneling from films of Fe, Co, Ni, and Gd, Phys. Rev. B 7, 318 (1973) T. Dimopoulos: Spin polarised tunnel transport in magnetic tunnel junctions: The role of metal/oxide interfaces in the tunnel process. Ph.D. Thesis (University Louis Pasteur, Strasbourg 2002)

1069

Part 5 3

3.81

J. A. Creighton, D. G. Eadon: Ultraviolet-visible spectra of the colloidal metallic elements, J. Chem. Soc. Faraday Trans. 87, 3881–3891 (1991) P. E. Batson: Surface plasmon coupling in clusters of small spheres, Phys. Rev. Lett. 49, 936–940 (1982) J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet, G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, C. Girard: Squeezing the optical near-field zone by plasmon coupling of metallic nanoparticles, Phys. Rev. Lett. 82, 2590– 2593 (1999) F. Silly, A. O. Gusev, A. Taleb, F. Charra, M. P. Pileni: Coupled plasmon modes in an ordered hexagonal monolayer of metal nanoparticles: A direct observation, Phys. Rev. Lett. 84, 5840–5843 (2000) S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, H. A. Atwater: Plasmonics – a route to nanoscale optical devices, Adv. Mater. 13, 15 (2001) R. Mayoral, J. Requena, J. S. Moya, C. Lopez, A. Cintas, H. Miguez, F. Meseguer, L. Vazquez, M. Holgado, A. Blanco: 3D long-range ordering in an SiO2 submicrometer-sphere sintered superstructure, Adv. Mater. 9, 257–260 (1997) J. V. Sanders: Colour of precious opal, Nature 204, 1151–1153 (1964) E. Yablonovitch: Inhibited spontaneous emission in solid-state physics and electronics, Phys. Rev. Lett. 58, 2059–2062 (1987) S. John: Strong localization of photons in certain disordered dielectric superlattices, Phys. Rev. Lett. 58, 2486–2489 (1987) M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, J. Chazelas: Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices, Phys. Rev. Lett. 61, 2472 (1988) P. Grünberg, R. Shreiber, Y. Pang, M. B. Brodsky, H. Sowers: Layered magnetic structures: Evidence for antiferromagnetic coupling of Fe layers across Cr interlayers, Phys. Rev. Lett. 57, 2442 (1986) R. L. Comstock: Introduction to Magnetism and Magnetic Recording (Wiley, New York 1999) N. F. Mott: The electrical conductivity of transition metals, Proc. R. Soc. 153, 699 (1935) J. F. Gregg: Introduction to spin electronics. In: Spin Electronics, Lecture Notes in Physics, No. 569, ed. by M. Ziese, M. J. Thornton (Springer, Berlin, Heidelberg 2001) Chap. 1 G. Binasch, P. Grünberg, F. Saurenbach, W. Zinn: Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange, Phys. Rev. B 39, 4828 (1989) R. Schad, C. D. Potter, P. Beliën, G. Verbanck, V. V. Moshchalkov, Y. Bruynseraede: Giant magnetoresistance in Fe/Cr superlattices with very thin Fe layers, Appl. Phys. Lett. 64, 3500 (1994)

References

1070

Part 5

Special Structures

Part 5 3

3.107 T. Miyazaki, N. Tezuka: Giant magnetic tunneling effect in Fe/Al2 O3 /Fe junction, J. Magn. Magn. Mater. 139, L231 (1995) 3.108 N. Tezuka, T. Miyazaki: Magnetic tunneling effect in Fe/Al2 O3 /Ni1−x Fex junctions, J. Appl. Phys. 79, 6262 (1996) 3.109 J. S. Moodera, L. R. Kinder, T. M. Wong, R. Meservey: Large magnetoresistance at room temperature in ferromagnetic thin film tunnel junctions, Phys. Rev. Lett. 74, 3273 (1995) 3.110 M. Julli` ere: Tunneling between ferromagnetic films, Phys. Lett. 54, 225 (1975) 3.111 J. Nassar, M. Hehn, A. Vaures, F. Petroff, A. Fert: Magnetoresistance of ferromagnetic tunnel junctions with Al2 O3 barriers formed by rf sputter etching in Ar/O2 plasma, Appl. Phys. Lett. 73, 698 (1998) 3.112 M. Viret, M. Drouet, J. Nassar, J. P. Contour, C. Fermon, A. Fert: Low-field colossal magnetoresistance in manganite tunnel spin valves, Europhys. Lett. 39, 545 (1997) 3.113 J. Nassar, M. Viret, M. Drouet, J. P. Contour, C. Fermon, A. Fert: Low-field colossal magnetoresistance in manganite tunnel junctions, Mater. Res. Soc. Symp. Proc. 494, 231 (1998) 3.114 M. Bowen, M. Bibes, A. Barthélémy, J.-P. Contour, A. Anane, Y. Lemaître, A. Fert: Nearly total spin polarization in La2 O3 Sr1 O3 MnO3 from tunneling experiments, Appl. Phys. Lett. 82, 233 (2003) 3.115 T. Obata, T. Manako, Y. Shimakawa, Y. Kubo: Tunneling magnetoresistance at up to 270 K in La0.8 Sr0.2 MnO3 /SrTiO3 /La0.8 Sr0.2 MnO3 junctions with 1.6-nm-thick barriers, Appl. Phys. Lett. 74, 290 (1999) 3.116 S. Gota, J. B. Moussy, M. Henriot, M. J. Guittet, M. Gautier-Soyer: Atomic-oxygen-assisted MBE growth of Fe2 O4 (111) on α-Al2 O3 (0001), Surf. Sci. 482– 485, 809–816 (2001) 3.117 S. Van Dijken, X. Jiang, S. S. P. Parkin: Giant magnetocurrent exceeding 3400% in magnetic tunnel transistors with spin-valve base layers, Appl. Phys. Lett. 83, 951 (2003) 3.118 S. A. Wolf, A. Y. Chtchenlkanova, D. M. Treger: Spintronics: Spin based electronics. In: Handbook of Nanoscience, Engineering and Technology, Electrical Engineering Textbook Series, Vol. 27, ed. by W. A. Goddard III, D. W. Brenner, S. E. Lyshevski, G. J. Iafrate (CRC, Boca Raton 2003) Chap. 8 3.119 E. E. Fullerton, D. T. Margulies, M. E. Schabes, M. Carey, B. Gurney, A. Moser, M. Best, G. Zeltzer, K. Rubin, H. Rosen, M. Doerner: Antiferromagnetically coupled magnetic media layers for thermally stable high-density recording, Appl. Phys. Lett. 77, 3806 (2000) 3.120 C. Fermon: Micro- and nanofabrication techniques. In: Spin Electronics, Lecture Notes in Physics, No. 569, ed. by M. Ziese, M. J. Thornton (Spinger, Berlin, Heidelberg 2001) Chap. 16

3.121 S. H. Sun, C. B. Murray, D. Weller, L. Folks, A. Moser: Monodisperse FePt nanoparticles and ferromagnetic FePt nanocrystal superlattices, Science 287, 1989– 1992 (2000) 3.122 J. Moritz, B. Dieny, J. P. Nozières, S. Landis, A. Lebib, Y. Chen: Domain structure in magnetic dots prepared by nanoimprinting and E-beam lithography, J. Appl. Phys. 91, 7314 (2002) 3.123 J. Moritz, S. Landis, J. C. Toussaint, P. BayleGuillemaud, B. Rodmacq, G. Casali, A. Lebib, Y. Chen, J. P. Nozières, B. Dieny: Patterned media made from pre-etched wafers: A promising route toward ultrahigh-density magnetic recording, IEEE Trans. Magn. 38, 1731 (2002) 3.124 S. Landis, B. Rodmacq, B. Dieny, B. Dal’Zotto, S. Tedesco, M. Heitzmann: Domain structure of magnetic layers deposited on patterned silicon, Appl. Phys. Lett. 75, 2473 (1999) 3.125 A. Lebib, Y. Chen, F. Carcenac, E. Cambril, L. Manin, L. Couraud, H. Launois: Tri-layer systems for nanoimprint lithography with an improved process latitude, Microelectron. Eng. 53, 175 (2000) 3.126 S. Landis, B. Rodmacq, B. Dieny: Magnetic properties of Co/Pt multilayers deposited on silicon dot arrays, Phys. Rev. B 62, 12271 (2000) 3.127 X. G. Binning, M. Despont, U. Drechsler, W. Häberle, M. Lutwyche, P. Vettiger, H. J. Mamin, B. W. Chui, T. W. Kenny: Ultrahigh-density atomic force microscopy data storage with erase capability, Appl. Phys. Lett. 74, 1329 (1999) 3.128 J. L. Marin, R. Riera, R. A. Rosas: Confined systems and nanostructured materials. In: Nanomaterials, Handbook of Advanced Electronic and Photonic Materials and Devices, Vol. 9, ed. by H. S. Nalwa (Elsevier, Amsterdam 2000) p. 55 3.129 J. M. Hartmann, M. Charleux, J. L. Rouviere, H. Mariette: Growth of CdTe/MnTe tilted and serpentine lattices on vicinal surfaces, Appl. Phys. Lett. 70, 1113–1115 (1997) 3.130 P. Soukiassian, F. Semond, A. Mayne, G. Dujardin: Highly stable Si atomic line formation on the betaSiC(100) surface, Phys. Rev. Lett. 79, 2498–2501 (1997) 3.131 D. Leonard, K. Pond, P. M. Petroff: Critical layer thickness for self-assembled InAs islands on GaAs, Phys. Rev. B 50, 11687–11692 (1994) 3.132 S. Rusponi, T. Cren, N. Weiss, M. Epple, P. Buluschek, L. Claude, H. Brune: The remarkable difference between surface and step atoms in the magnetic anisotropy of two-dimensional nanostructures, Nature Mater. 2, 546–551 (2003) 3.133 R. Nötzel, T. Fukui, H. Hasegawa, J. Temmyo, T. Tamamura: Atomic-force microscopy study of strained InGaAs quantum disks self-organizing on GaAs(n11) substrates, Appl. Phys. Lett. 65, 2854–2856 (1994)

Mesoscopic and Nanostructured Materials

3.143 A. Taleb, C. Petit, M. P. Pileni: Synthesis of highly monodisperse silver nanoparticles from AOT reverse micelles: A way to 2D and 3D self-organization, Chem. Mater. 9, 950–959 (1997) 3.144 C. J. Kiely, J. Fink, M. Brust, D. Bethell, D. J. Schiffrin: Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters, Nature 396, 444–446 (1998) 3.145 C. J. Kiely, J. Fink, J. G. Zheng, M. Brust, D. Bethell, D. J. Schiffrin: Ordered colloidal nanoalloys, Adv. Mater. 12, 640 (2000) 3.146 C. Petit, A. Taleb, M.-P. Pileni: Self-organization of magnetic nanosized cobalt particles, Adv. Mater. 10, 259–261 (1998) 3.147 G. Schmid, R. Pfeil, R. Boese, F. Bandermann, S. Meyer, S. G. Calis, J. W. A. Van Der Velden: Au55[P(C6H5)]12Cl6 ein Goldcluster ungewöhnlicher Größe, Chem. Ber. 114, 3634–3642 (1981) 3.148 V. Oleshko, V. Volkov, R. Gijbels, W. Jacob, M. Vargaftik, I. Moiseev, G. Vantendeloo: High-resolution electron-microscopy and electronenergy-loss spectroscopy of giant palladium clusters, Z. Phys. D34, 283–291 (1995) 3.149 C. B. Murray, D. B. Norris, M. G. Bawendi: Synthesis and characterization of nearly monodisperse CdE (E=S, Se, Te) semiconductor nanocrystallites, J. Am. Chem. Soc. 115, 8706–8715 (1993) 3.150 C. B. Murray, C. R. Kagan, M. G. Bawendi: Selforganization of CdSe nanocrystallites into 3dimensional quantum-dot superlattices, Science 270, 1335–1338 (1995) 3.151 M. A. Olshavsky, A. N. Goldstein, A. P. Alivisatos: Organometallic synthesis of GaAs crystallites exhibiting quantum confinement, J. Am. Chem. Soc. 112, 9438–9439 (1990) 3.152 C. Binns: Nanoclusters deposited on surfaces, Surf. Sci. Rep. 44, 1–49 (2001) 3.153 W. A. De Heer: The physics of simple metal clusters: Experimental aspects and simple models, Rev. Mod. Phys. 65, 611 (1993)

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3.134 E. Ganz, K. Sattler, J. Clarke: Scanning tunneling microscopy of the local atomic structure of twodimensional gold and silver islands on graphite, Phys. Rev. Lett. 60, 1856–1859 (1988) 3.135 G. W. Clark, L. L. Kesmodel: Ultrahigh vacuum scanning tunneling microscopy studies of platinum on graphite, J. Vac. Sci. Technol. B 11, 131–136 (1993) 3.136 H. Xu, K. Y. S. Ng: Scanning tunneling microscopy investigation of Co cluster growth and induced surface morphology changes on highly oriented pyrolitic graphite, J. Vac. Sci. Technol. B 13, 2160–2165 (1995) 3.137 H. Xu, K. Y. S. Ng: Surface process and interaction of Mo clusters on highly oriented pyrolytic graphite observed by scanning tunneling microscopy, J. Vac. Sci. Technol. B 15, 186–191 (1997) 3.138 A. Piednoir, E. Perrot, S. Granjeaud, A. Humbert, C. Chapon, C. R. Henry: Atomic resolution on small three-dimensional metal clusters by STM, Surf. Sci. 391, 19–26 (1997) 3.139 G. Springholz, V. Holy, M. Pinczolits, G. Bauer: Selforganized growth of three-dimensional quantumdot crystals with fcc-like stacking and a tunable lattice constant, Science 282, 734–737 (1998) 3.140 M. D. Levenson, N. S. Viswanathan, R. A. Simpson: Improving resolution in photolithography with a phase-shifting mask, IEEE Trans. Electron Devices ED-29, 1812–1836 (1982) 3.141 M. Brust, M. Walker, D. Bethell, D. J. Schiffrin, R. Whyman: Synthesis of thiol-derivatized gold nanoparticles in a 2-phase liquid–liquid system, J. Chem. Soc., Chem. Commun. 1994, 801–802 (1994) 3.142 R. P. Andres, J. D. Bielefeld, J. I. Henderson, D. B. Janes, V. R. Kolagunta, C. P. Kubiak, W. J. Mahoney, R. G. Osifchin: Self-assembly of a twodimensional superlattice of molecularly linked metal clusters, Science 273, 1690–1693 (1996)

References

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2.1 The Elements by Werner Martienssen

We thank Dr. G. Leichtfried, Plansee AG, A-6600 Reutte/Tirol for recently determined new data on the refractory metals Nb, Ta, and Mo, W.

Acknowl.

Acknowledgements

ductors: Data Handbook, which is about 700 pages long. I am much indebted to my colleague O. Madelung for kindly presenting me the manuscript of that Handbook prior to publication. [1] O. Madelung (Ed.): Semiconductors: Data Handbook, 3rd Edn. (Springer, Berlin, Heidelberg 2004)

4.1 Semiconductors by Werner Martienssen

In selecting the “most important information” from the huge data collection in Landolt–Börnstein, the author found great help in the new Semiconductors: Data Handbook [1]. Again, the data in this Springer Handbook of Condensed Matter and Materials Data represent only a small fraction of the information given in Semicon-

4.5 Ferroelectrics and Antiferroelectrics by Toshio Mitsui

The author of this subchapter thanks the coauthors of LB III/36 for their helpful discussions and suggestions. Especially, he is much indebted to Prof. K. Deguchi for his kind support throughout the preparation of the manuscript.

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About the Authors

Chapter 1.3

Johann Wolfgang Goethe-University Physics Department Frankfurt am Main, Germany [email protected] http://www.rz.uni-frankfurt.de/piweb/ kmlab/Leiter.html

Dr. Wolf Assmus (Kucera Professor) is Professor of Physics at the University of Frankfurt and Dean of the Physics-Faculty. He is a solid state physicist, especially interested in materials research and crystal growth. His main research fields are: materials with high electronic correlation, quasicrystals, materials with extremely high melting temperatures, magnetism, and superconductivity.

Stefan Brühne

Chapter 1.3

Johann Wolfgang Goethe-University Physics Department Frankfurt am Main, Germany [email protected]

Dr. Stefan Brühne, née Mahne, a chemist by education in Germany and England, received his PhD in 1994 from Dortmund University, Germany, on giant cell crystal structures in the Al–Ta system. Following a post doc position at the Materials Department (Crystallography) at ETH Zurich he spent seven years in the ceramics industry. His main activity was R&D of glasses, frits and pigments for high-temperature applications, thereby establishing design of experiment (DoE) techniques. Since 2002, at the Institute of Physics at Frankfurt University he has been investigated X-ray structure determination of quasicrystalline, highly complex and disordered intermetallic materials.

Fabrice Charra

Chapter 5.3

Commissariat à l’Énergie Atomique, Saclay Département de Recherche sur l’État Condensé, les Atomes et les Molécules Gif-sur-Yvette, France [email protected] http://www-drecam.cea.fr/spcsi/

Fabrice Charra conducts researche in the emerging field of nanophotonics, in the surface physics laboratory of CEA/Saclay. The emphasis of his work is on light emission and absorption form single nanoscale molecular systems. His area of expertise also extends to nonlinear optics, a domain to which he contributed several advances in the applications of organic materials.

Gianfranco Chiarotti

Chapter 5.2

University of Rome “Tor Vergata“ Department of Physics Roma, Italy [email protected]

Gianfranco Chiarotti is Professor Emeritus, formerly Professor of General Physics, Fellow of the American Physical Society, fellow of the Italian National Academy (Accademia Nazionale dei Lincei). He was Chairman of the Physics Committee of the National Research Council (1988–1994), Chair Franqui at the University of Liège (1975), Assistant Professor at the University of Illinois (1955–1957), Editor of the journal Physics of Solid Surfaces, and Landolt–Börnstein Editor of Springer-Verlag from 1993 through 1996. He has worked in several fields of solid state physics, namely electronic properties of defects, modulation spectroscopy, optical properties of semiconductors, surface physics, and scanning tunnelling microscopy (STM) in organic materials.

Claus Fischer

Chapter 4.2

Formerly Institute of Solid State and Materials Research (IFW) Dresden, Germany [email protected]

Claus Fischer recieved his PhD from the Technical University Dresden (Since his retirement in 2000 he continues to work as a foreign scientist of IFW in the field of high-Tc superconductors.) His last position at IFW was head of the Department of Superconducting Materials. The main areas of research were growth of metallic single crystals in particular of magnetic materials, developments of hard magnetic materials, of materials for thick film components of microelectronics and of low-Tc and high-Tc superconducting wires and tapes. Many activities were performed in cooperation with industrial manufacturers.

Authors

Wolf Assmus

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About the Authors

Authors

Günter Fuchs

Chapter 4.2

Leibniz Institute for Solid State and Materials Research (IFW) Dresden Magnetism and Superconductivity in the Institute of Metallic Materials Dresden, Germany [email protected] http://www.ifw-dresden.de/imw/21/

Dr. Günter Fuchs studied physics at the Technical University of Dresden, Germany, and received his PhD in 1980 on the pinning mechanism in superconducting NbTi alloys. Since 1969 he has been at the Institute of Solid State and Materials Research (IFW) in Dresden. His activities are in superconductivity (HTSC, MgB2 , intermetallic borocarbides) and the applications of superconductors. He received the PASREG Award for outstanding scientific achievements in the field of bulk cuprate superconductors in high magnetic fields in 2003.

Frank Goodwin

Chapter 3.1

International Lead Zinc Research Organization, Inc. Research Triangle Parc, NC, USA [email protected] http://www.ilzro.org/Contactus.htm

Frank Goodwin received his Sc.D. from the Massachusetts Institute of Technology in 1979 and is responsible for all materials science research at International Lead Zinc Research Organization, Inc. where he has conceived and managed numerous projects on lead and zinc-containing products. These have included lead in acoustics, cable sheathing, nuclear waste management and specialty applications, together with zinc in coatings, castings and wrought forms.

Susana Gota-Goldmann

Chapter 5.3

Commissariat à l’Energie Atomique (CEA) Direction de la Recherche Technologique (DRT) Fontenay aux Roses, France [email protected]

Dr. Susana Gota-Goldmann received her PhD in Materials Science form the Université Pierre et Marie Curie (Paris V) in 1993. After her PhD, she was engaged as a researcher in the Materials Science Division of the CEA (Commissariat à l’Energie Atomique, France). She has focused her scientific activity on the growth and characterisation of nanometric oxide layers with applications in spin electronics and photovoltaics. In parallel she has developed the use of synchrotron radiation techniques (X-ray absorption magnetic dicroism, photoemission, resonant reflectivity) for the study of oxide thin layers. Recently she has moved from fundamental to technological research. Dr. Gota-Goldmann is now working as a project manager at the scientific affairs direction of the Technology Research Division (CEA/DRT).

Sivaraman Guruswamy

Chapter 3.1

University of Utah Metallurgical Engineering Salt Lake City, UT, USA [email protected] http://www.mines.utah.edu/metallurgy/ MML

Dr. Guruswamy is a Professor of Metallurgical Engineering at the University of Utah. He obtained his Ph.D. degree in Metallurgical Engineering from the Ohio State University in 1984. He has made significant contributions in several areas including magnetic materials development, deformation of compound semiconductors, and lead alloys. His current work focuses on magnetostrictive materials and hybrid thermionic/ thermoelectric thermal diodes.

Gagik G. Gurzadyan

Chapter 4.4

Technical University of Munich Institute for Physical and Theoretical Chemistry Garching, Germany [email protected] http://zentrum.phys.chemie. tu-muenchen.de/gagik

Gagik G. Gurzadyan, Ph.D., Dr. Sci., has extensive experience in nonlinear optics and crystals, laser photophysics and spectroscopy. He has authored several books including the Handbook of Nonlinear Optical Crystals published by Springer-Verlag. He worked in the Institute of Spectroscopy (USSR), CEA/Saclay (France), Max-Planck-Institute of Radiation Chemistry (Germany). At present he works at the Technical University of Munich with ultrafast lasers in the fields of nonlinear photochemistry of biomolecules and femtosecond spectroscopy.

About the Authors

Chapter 4.3

High Tech Association Ltd. Higashikaya, Fukaya,Saitama, Japan [email protected] http://homepage1.nifty.com/JABM

Dr. Hideki Harada is chief advisor of magnetic materials and their application and President of High Tech Association Ltd., Saitama, Japan. He is Chairman of the Japan Association of Bonded Magnet Industries (JABM) and received his Ph.D. in 1987 with a work on electrostatic ferrite materials. He worked in research and development of magnetic materials and cemented carbide tools at Hitachi Metals where he also was on the Board of Directors. He received the Japanese National Award for Industries Development Contribution.

Bernhard Holzapfel

Chapter 4.2

Leibniz Institute for Solid State and Materials Research Dresden – Institute of Metallic Materials Superconducting Materials Dresden, Germany [email protected] http://www.ifw-dresden.de/imw/26/

Dr. Bernhard Holzapfel is head of the superconducting materials group at the Leibniz Institute for Solid State and Materials Research (IFW) Dresden, Germany. His main area of research is pulsed laser deposition of functional thin films and superconductivity. Currently he works on the development of HTSC high Jc coated conductors using ion beam assisted deposition or highly textured metal substrates. His work is supported by a number of national and European founded research projects.

Karl U. Kainer

Chapter 3.1

GKSS Research Center Geesthacht Institute for Materials Research Geesthacht, Germany [email protected] http://www.gkss.de

Professor Kainer is director of Institute for Materials Research at GKSS-Research Center, Geesthacht and Professor of Materials Technology at the Technical University of Hamburg-Harburg. He obtained his Ph.D. in Materials Science at the Technical University of Clausthal in 1985 and his Habilitation in 1996. In 1988 he received the Japanese Government Research Award for Foreign Specialists. His current research activities are the development of new alloys and processes for magnesium materials.

Catrin Kammer

Chapter 3.1

METALL – Intl. Journal for Metallurgy Goslar, Germany [email protected] http://www.giesel-verlag.de

Catrin Kammer received her Ph.D. in materials sciences from the Technical University Bergakademie Freiberg, Germany, in 1989. She has been working in the field of light metals and is author of several handbooks about aluminium and magnesium. She is working as author for the journal ALUMINIUM and is teaching in material sciences. Since 2001 she is editor-in-chief of the journal METALL, which deals with all non-ferrous metals.

Wolfram Knabl

Chapter 3.1

Plansee AG Technology Center Reutte, Austria [email protected] http://www.plansee.com

Dr. Wolfram Knabl studied materials science at the Mining University of Leoben, Austria and received his Ph.D. at the Plansee AG focusing on the development of oxidation protective coatings for refractory metals. Between 1996 and 2002 he was responsible for the test laboratories at Plansee AG and since October 2002 he is working in the field of refractory metals, especially material and process development in the technology center of Plansee AG.

Authors

Hideki Harada

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About the Authors

Authors

Alfred Koethe

Chapter 3.1

Leibniz-Institut für Festkörper- und Werkstoffforschung Institut für Metallische Werkstoffe (retired) Dresden, Germany [email protected]

Dr. Alfred Koethe is physicist and professor of Materials Science. He retired in 2000 from his position as head of department in the Institute of Metallic Materials at the Leibniz Institute of Solid State and Materials Research in Dresden, Germany. His main research activities were in the fields of preparation and properties of ultrahigh-purity refractory metals and, especially, of steels (stainless steels, high strenght steels, thermomechanical treatment, microalloying, relations chemical composition/microstructure/properties).

Dieter Krause

Chapter 3.4

Schott AG Research and Technology-Development Mainz, Germany [email protected]

Dieter Krause studied physics at the universities of Erlangen and Munich, Germany, where he received his Ph.D. for work on magnetism and metal physics. He was professor in Tehran, Iran, lecturer in Munich and Mainz, Germany. As scientist and director of Schott’s corporate research and development centre he was involved in research on optical and mechanical properties of amorphous materials, thin films, and optical fibres. Now he is consultant, chief scientist, and the editor of the “Schott Series on Glass and Glass Ceramics – Science, Technology, and Applications” published by Springer.

Manfred D. Lechner

Chapter 3.3

Universität Osnabrück Institut für Chemie – Physikalische Chemie Osnabrück, Germany [email protected] http://www.chemie.uni-osnabrueck.de/ pc/index.html

Professor Lechner has a PhD in chemistry from the University of Mainz, Germany. Since 1975 he is Professor of Physical Chemistry at the Institute of Chemistry of the University of Osnabrück, Germany. His scientific work concentrates on the physics and chemistry of polymers. In this area he is mainly working on the influence of high pressure on polymer systems, polymers for optical storage and waveguides as well as synthesis and properties of superabsorbers from renewable resources.

Gerhard Leichtfried

Chapter 3.1

Plansee AG Technology Center Reutte, Austria [email protected] http://www.plansee.com

Dr. Gerhard Leichtfried received his Ph.D from the Montanuniversität Leoben and is qualified for lecturing in powder metallurgy. For 20 years he has been working in various senior positions for the Plansee Aktiengesellschaft, a company engaged in refractory metals, composite materials, cemented carbides and sintered iron and steels.

Werner Martienssen

Chapters 1.1, 1.2, 2.1, 4.1

Universität Frankfurt/Main Physikalisches Institut Frankfurt/Main, Germany [email protected]

Werner Martienssen studied physics and chemistry at the Universities of Würzburg and Göttingen, Germany. He obtained his Ph.D. in Physics with R.W. Pohl, Göttingen, and holds an honorary doctorate at the University of Dortmund. After a visiting-professorship at the Cornell University, Ithaca, USA in 1959 to 1960 he taught physics at the University of Stuttgart and since 1961 at the University of Frankfurt/ Main. His main research fields are condensed matter physics, quantum optics and chaotic dynamics. Two of his former students and coworkers became Nobel-laureates in Physics, Gerd K. Binnig for the design of the scanning tunneling microscope in 1986 and Horst L. Störmer for the discovery of a new form of quantum-fluid with fractionally charged excitations in 1998. Werner Martienssen is a member of the Deutsche Akademie der Naturforscher Leopoldina, Halle and of the Akademie der Wissenschaften zu Göttingen. Since 1994 he is Editor-in-Chief of the data collection Landolt–Börnstein published by Springer, Heidelberg.

About the Authors

Toshio Mitsui

Chapter 4.5

Osaka University Takarazuka, Japan [email protected]

Toshio Mitsui is an emeritus professor of Osaka University. He studied solid state physics and biophysics at Hokkaido University, Pennsylvania State University, Brookhaven National Laboratory, the Massachusetts Institute of Technology, Osaka University and Meiji University. He was the first to observe the ferroelectric domain structure in Rochelle salt with a polarization microscope. He proposed various theories on ferroelectric effects and biological molecular machines.

1079

Authors

Manfred Müller

Chapter 4.3

Dresden University of Technology Institute of Materials Science Dresden, Germany [email protected]

Dr.-Ing. habil. Manfred Müller is a Professor emeritus of Special Materials at the Institute of Materials Science of the Dresden University of Technology. Before his retirement he was for many years head of department for special materials at the Central Institute for Solid State Physics and Materials Research of the Academy of Sciences in Dresden, Germany. His main field was the research and development of metallic materials with emphasis on special physical properties, such as soft and hard magnetic, electrical and thermoelastic properties. His last field of research was amorphous and nanocrystalline soft magnetic alloys. He is a member of the German Society of Materials Science (DGM) and was a member of the Advisary Board of DGM.

Sergei Pestov

Chapter 5.1

Moscow State Academy of Fine Chemical Technology Department of Inorganic Chemistry Moscow, Russia [email protected]

Dr. Pestov is a docent of the Inorganic Chemistry Department and a head of group on liquid crystals (LC) at the Moscow State Academy of Fine Chemical Technology. He earned his Ph.D. in physical chemistry in 1992. His research is focused on thermal analysis and thermodynamics of systems containing LC and physical properties of LC. He is an author of a Landolt–Börnstein volume and two books devoted to liquid crystals.

Günther Schlamp

Chapter 3.1

Metallgesellschaft Ffm and Degussa Demetron (retired) Steinbach/Ts, Germany

Günther Schlamp received his Ph.D. from the Johann-Wolfgang-Goethe University of Frankfurt/Main, Germany, in Physical Chemistry. His industrial activities in research include the development and production of refractory material coatings, high purity materials and parts for electronics, and sputter targets for the reflection-enhancing coating of glas. He has contributed to several Handbooks with repoprts on properties and applications of noble metals and their alloys.

Barbara Schüpp-Niewa

Chapter 4.2

Leibniz-Institute for Solid State and Materials Research Dresden Institute for Metallic Materials Dresden, Germany [email protected] http://www.ifw-dresden.de

Barbara Schüpp-Niewa studied chemistry in Gießen and Dortmund where she received her Ph.D. in 1999. Since 2000 she has been a scientist at the Leibniz-Institute for Solid State and Materials Research Dresden with a focus on crystal structure investigations of oxometalates with superconducting or exciting magnetic ground states. Her current research activities include coated conductors.

1080

About the Authors

Chapter 3.1

University of Vienna Department of Chemistry Vienna, Austria [email protected]

Professor Stickler received his master and Dr. degree from the Technical University in Vienna. From 1958 to 1972 he was manager of physical metallurgy with the Westinghouse Research Laboratory in Pittsburgh, Pa. In 1972 he accepted a full professorship at the University of Vienna heading a materials science group in the Institute of Physical Chemistry, and from 1988 he was head of this institute until his retirement as professor emeritus in 1998. He was involved in research and engineering work on superalloys, semiconductor materials and high melting point materials, investigating the relationship between microstructure and mechanical behavior, in particular fatigue and fracture mechanics properties. He was leader of a successful project on brazing under microgravity conditions in the Spacelab-Mission. Further activities included the participation in European COST projects, in particular as chairman of actions on powder metallurgy and light metals. He has authored and coauthored more than 250 publications in scientific journals and proceedings.

Authors

Roland Stickler

Pancho Tzankov

Chapter 4.4

Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy Berlin, Germany [email protected] http://staff.mbi-berlin.de/tzankov/

Pancho Tzankov studied laser physics at Sofia University, Bulgaria, and received his Ph.D. in physical chemistry from the Technical University of Munich, Germany. He is now a postdoctoral fellow at the Max Born Institute in Berlin, Germany. His research activities involve development of new nonlinear optical parametric sources of ultrashort pulses and their application for time-resolved spectroscopy.

Volkmar Vill

Chapter 5.1

University of Hamburg Department of Chemistry, Institute of Organic Chemistry Hamburg, Germany [email protected] http://liqcryst.chemie.uni-hamburg.de/

Professor Volkmar Vill received his Diploma in Chemistry in 1986, his Diploma in Physics in 1988 and his Ph.D. in Chemistry in 1990 from the University of Münster, Germany. In 1997 he earned his Habilitation in Organic Chemistry from the University of Hamburg where he is Professor of Organic Chemistry since 2002. He is the author of the LiqCryst – Database of Liquid Crystals and the Editor of the Handbook of Liquid Crystals, of Landolt–Börnstein, Organic Index, and Vol. VIII/ 5a, Physical Properties of Liquid Crystals.

Hans Warlimont

Chapters 3.1, 3.2, 4.2, 4.3

DSL Dresden Material-Innovation GmbH Dresden, Germany [email protected]

Hans Warlimont is a physical metallurgist and has worked on numerous topics in several research institutions and industrial companies. Among them were the Max-Planck-Institute of Metals Research, Stuttgart, and Vacuumschmelze, Hanau. He was Scientific Director of the Leibniz-Institute of Solid State and Materials Research Dresden and Professor of Materials Science at Dresden University of Technology. Recently he has established DSL Dresden Material-Innovation GmbH to industrialise his invention of electroformed battery grids.

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List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

XV

Part 1 General Tables 3 3 4 4 5 7 9

2 The International System of Units (SI), Physical Quantities,

and Their Dimensions Werner Martienssen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The International System of Units (SI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The SI Base Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Unit of Length: the Meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Unit of Mass: the Kilogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Unit of Time: the Second . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Unit of Electric Current: the Ampere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Unit of (Thermodynamic) Temperature: the Kelvin . . . . . . . . . . . . . 2.3.6 Unit of Amount of Substance: the Mole . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.7 Unit of Luminous Intensity: the Candela . . . . . . . . . . . . . . . . . . . . . . . . 2.4 The SI Derived Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Decimal Multiples and Submultiples of SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Units Outside the SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Units Used with the SI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Other Non-SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Some Energy Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 11 12 13 13 14 14 14 14 14 15 16 19 20 20 20 24 25

3 Rudiments of Crystallography Wolf Assmus, Stefan Brühne . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Crystalline Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Periodic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Aperiodic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Disorder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27 28 28 33 38

2.1 2.2 2.3

Detailed Cont.

1 The Fundamental Constants Werner Martienssen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 What are the Fundamental Constants and Who Takes Care of Them? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The CODATA Recommended Values of the Fundamental Constants . . . . . 1.2.1 The Most Frequently Used Fundamental Constants . . . . . . . . . . . . 1.2.2 Detailed Lists of the Fundamental Constants in Different Fields of Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Constants from Atomic Physics and Particle Physics . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.3 Amorphous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Methods for Investigating Crystallographic Structure . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39 39 41

Part 2 The Elements

Detailed Cont.

1 The Elements Werner Martienssen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 How to Use This Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Description of Properties Tabulated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Parts A of the Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Parts B of the Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Parts C of the Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Parts D of the Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Tables of the Elements in Different Orders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1 Elements of the First Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2 Elements of the Main Groups and Subgroup I to IV . . . . . . . . . . . . 1.5.3 Elements of the Main Groups and Subgroup V to VIII . . . . . . . . . . 1.5.4 Elements of the Lanthanides Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.5 Elements of the Actinides Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 45 45 46 46 46 48 49 49 49 54 54 59 98 142 151 158

Part 3 Classes of Materials 1 Metals Frank Goodwin, Sivaraman Guruswamy, Karl U. Kainer, Catrin Kammer, Wolfram Knabl, Alfred Koethe, Gerhard Leichtfried, Günther Schlamp, Roland Stickler, Hans Warlimont . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Magnesium and Magnesium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Magnesium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Melting and Casting Practices, Heat Treatment . . . . . . . . . . . . . . . . . 1.1.3 Joining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 Corrosion Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.5 Recent Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Aluminium and Aluminium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Production of Aluminium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Properties of Pure Al . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Aluminium Alloy Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.5 Classification of Aluminium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.6 Structure and Basic Mechanical Properties of Wrought Work-Hardenable Aluminium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . .

161 162 163 168 169 169 170 171 171 171 172 174 179 180

Detailed Contents

1.2.7

1.3

1.5

1.6

1.7

1.8

1.9

182 184 186 194 202 206 207 208 209 216 217 217 218 218 221 222 227 240 240 257 262 268 272 272 274 274 276 277 277 279 279 279 284 288 296 296 297 298 298 300 303 306 308 311 314

Detailed Cont.

1.4

Structure and Basic Mechanical Properties of Wrought Age-Hardenable Aluminium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.8 Structure and Basic Mechanical Properties of Aluminium Casting Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.9 Technical Properties of Aluminium Alloys . . . . . . . . . . . . . . . . . . . . . . . 1.2.10 Thermal and Mechanical Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.11 Corrosion Behavior of Aluminium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Titanium and Titanium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Commercially Pure Grades of Ti and Low-Alloy Ti Materials . . . 1.3.2 Ti-Based Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Intermetallic Ti–Al Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 TiNi Shape-Memory Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zirconium and Zirconium Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Technically-Pure and Low-Alloy Zirconium Materials . . . . . . . . . . 1.4.2 Zirconium Alloys in Nuclear Applications . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Zirconium-Based Bulk Glassy Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Iron and Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.1 Phase Relations and Phase Transformations . . . . . . . . . . . . . . . . . . . 1.5.2 Carbon and Low-Alloy Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.3 High-Strength Low-Alloy Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.4 Stainless Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.5 Heat-Resistant Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.6 Tool Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.7 Cast Irons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cobalt and Cobalt Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.1 Co-Based Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.2 Co-Based Hard-Facing Alloys and Related Materials . . . . . . . . . . 1.6.3 Co-Based Heat-Resistant Alloys, Superalloys . . . . . . . . . . . . . . . . . . . 1.6.4 Co-Based Corrosion-Resistant Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.5 Co-Based Surgical Implant Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.6 Cemented Carbides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nickel and Nickel Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.1 Commercially Pure and Low-Alloy Nickels . . . . . . . . . . . . . . . . . . . . . . 1.7.2 Highly Alloyed Ni-Based Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.3 Ni-Based Superalloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.4 Ni Plating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Copper and Copper Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8.1 Unalloyed Coppers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8.2 High Copper Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8.3 Brasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8.4 Bronzes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.8.5 Copper–Nickel and Copper–Nickel–Zinc Alloys . . . . . . . . . . . . . . . . . Refractory Metals and Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9.1 Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9.2 Chemical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9.3 Recrystallization Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.9.4 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Detailed Cont.

1.10 Noble Metals and Noble Metal Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10.1 Silver and Silver Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10.2 Gold and Gold Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10.3 Platinum Group Metals and Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.10.4 Rhodium, Iridium, Rhutenium, Osmium, and their Alloys . . . . 1.11 Lead and Lead Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.1 Pure Grades of Lead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.2 Pb–Sb Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.3 Pb–Sn Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.4 Pb–Ca Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.5 Pb–Bi Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.6 Pb–Ag Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.7 Pb–Cu, Pb–Te, and Pb–Cu–Te Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.8 Pb–As Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.9 Lead Cable Sheathing Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.11.10 Other Lead Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

329 330 347 363 386 407 407 411 414 416 419 420 421 421 421 421 422

2 Ceramics Hans Warlimont . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Traditional Ceramics and Cements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Traditional Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Cements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Silicate Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Refractory Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Oxide Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Magnesium Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Al–O–N Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4 Beryllium Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.5 Zirconium Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.6 Titanium Dioxide, Titanates, etc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Non-Oxide Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Non-Oxide High-Temperature Ceramics . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Borides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Carbides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.4 Nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.5 Silicides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

431 432 432 432 433 437 437 444 445 447 447 447 450 451 451 451 458 467 473 476

3 Polymers Manfred D. Lechner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Structural Units of Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Tables and Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Polyolefines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Vinyl Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

477 480 482 483 483 489

Detailed Contents

492 497 501 503 506 508 509 511 512 515 522

4 Glasses Dieter Krause . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Properties of Glasses – General Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Composition and Properties of Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Flat Glass and Hollowware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Flat Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Container Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Technical Specialty Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Chemical Stability of Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Mechanical and Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Electrical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Optical Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Chemical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.4 Thermal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Vitreous Silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Properties of Synthetic Silica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Gas Solubility and Molecular Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Glass-Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Glasses for Miscellaneous Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Sealing Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.2 Solder and Passivation Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.3 Colored Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.4 Infrared-Transmitting Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

523 526 527 528 528 529 530 530 533 537 539 543 543 549 550 556 556 556 557 558 559 559 562 565 568 572

Part 4 Functional Materials 1 Semiconductors Werner Martienssen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Group IV Semiconductors and IV–IV Compounds . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 III–V Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

575 578 604

Detailed Cont.

3.3.3 Fluoropolymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Polyacrylics and Polyacetals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.5 Polyamides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.6 Polyesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.7 Polysulfones and Polysulfides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.8 Polyimides and Polyether Ketones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.9 Cellulose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.10 Polyurethanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.11 Thermosets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.12 Polymer Blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1085

1086

Detailed Contents

Detailed Cont.

1.2.1 Boron Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Aluminium Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 Gallium Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 Indium Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 II–VI Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Beryllium Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Magnesium Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Oxides of Ca, Sr, and Ba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Zinc Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.5 Cadmium Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.6 Mercury Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

604 610 621 638 652 652 655 660 665 676 686 691

2 Superconductors Claus Fischer, Günter Fuchs, Bernhard Holzapfel, Barbara Schüpp-Niewa, Hans Warlimont . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Metallic Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Practical Metallic Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Non-Metallic Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Oxide Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Superconductors Based on the Y–Ba–Cu–O System . . . . . . . . . . . . 2.2.3 Superconductors Based on the Bi–Sr–Ca–Cu–O System . . . . . . . 2.2.4 Carbides, Borides, Nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

695 696 696 704 711 711 720 736 744 749

3 Magnetic Materials Hideki Harada, Manfred Müller, Hans Warlimont . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Basic Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Atomic Moment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Magnetocrystalline Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Magnetostriction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Soft Magnetic Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Low Carbon Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Fe-based Sintered and Composite Soft Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Iron–Silicon Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Nickel–Iron-Based Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Iron–Cobalt Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.6 Amorphous Metallic Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.7 Nanocrystalline Soft Magnetic Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.8 Invar and Elinvar Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Hard Magnetic Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Fe–Co–Cr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Fe–Co–V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Fe–Ni–Al–Co, Alnico . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Fe–Nd–B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

755 755 755 756 757 758 758 759 763 769 772 772 776 780 794 795 797 798 800

Detailed Contents

803 810 811 811 813 814

4 Dielectrics and Electrooptics Gagik G. Gurzadyan, Pancho Tzankov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Dielectric Materials: Low-Frequency Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 General Dielectric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Static Dielectric Constant (Low-Frequency) . . . . . . . . . . . . . . . . . . . . . 4.1.3 Dissipation Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.5 Piezoelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Optical Materials: High-Frequency Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Crystal Optics: General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Photoelastic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Electrooptic Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Nonlinear Optical Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Guidelines for Use of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Tables of Numerical Data for Dielectrics and Electrooptics . . . . . . . . . . . . . . Isotropic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic, Point Group m3m (Oh ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic, Point Group 43m (Td ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cubic, Point Group 23 (T ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hexagonal, Point Group 6m2 (D3h ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hexagonal, Point Group 6mm (C6v ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hexagonal, Point Group 6 (C6 ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonal, Point Group 3m (D3d ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonal, Point Group 32 (D3 ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trigonal, Point Group 3m (C3v ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tetragonal, Point Group 4mmm (D4h ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . Tetragonal, Point Group 4/m (C4h ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tetragonal, Point Group 422 (D4 ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tetragonal, Point Group 42m (D2d ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tetragonal, Point Group 4mm (C4v ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthorhombic, Point Group mmm (D2h ) Materials . . . . . . . . . . . . . . . . . . . . . . . Orthorhombic, Point Group 222 (D2 ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthorhombic, Point Group mm2 (C2v ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . Monoclinic, Point Group 2 (C2 ) Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

817 822 822 823 823 823 824 824 824 824 825 825 826 828 828 828 834 838 838 840 842 844 844 848 852 854 854 856 864 866 866 872 884 890

5 Ferroelectrics and Antiferroelectrics Toshio Mitsui . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Definition of Ferroelectrics and Antiferroelectrics . . . . . . . . . . . . . . . . . . . . . . . 5.2 Survey of Research on Ferroelectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

903 903 904

Detailed Cont.

3.3.5 Co–Sm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.6 Mn–Al–C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Magnetic Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Soft Magnetic Ferrites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Hard Magnetic Ferrites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5.3

Classification of Ferroelectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 The 72 Families of Ferroelectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Physical Properties of 43 Representative Ferroelectrics . . . . . . . . . . . . . . . . . . 5.4.1 Inorganic Crystals Oxides [3.1, 2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Inorganic Crystals Other Than Oxides [3.3] . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Organic Crystals, Liquid Crystals, and Polymers [3.4] . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

906 909 912 912 922 930 936

Part 5 Special Structures Detailed Cont.

1 Liquid Crystals Sergei Pestov, Volkmar Vill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Liquid Crystalline State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Chemical Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Physical Properties of Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Applications of Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.4 List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.5 Conversion Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Physical Properties of the Most Common Liquid Crystalline Substances 1.3 Physical Properties of Some Liquid Crystalline Mixtures . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

941 941 943 943 944 944 945 946 975 977

2 The Physics of Solid Surfaces Gianfranco Chiarotti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Structure of Ideal Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Diagrams of Surfaces [3.2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Crystallographic Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Surface Reconstruction and Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Definitions and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Electronic Structure of Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Magnetic Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Surface Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Semiconductors and Insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Atom–Surface Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 The Space Charge Layer at the Surface of a Semiconductor . . . . . . . . . . . . . 2.5.1 Definitions and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Useful Formulas and Numerical Values . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Surface Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Most Frequently Used Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

979 979 979 986 986 986 987 987 996 997 1003 1007 1012 1012 1017 1019 1020 1020 1022 1023 1026 1029

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1031 1031 1031 1032 1034 1034 1035 1035 1036 1036 1040 1042 1044 1044 1048 1048 1049 1060 1063 1063 1064 1064 1064 1065 1066

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . About the Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detailed Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1073 1075 1081 1091

Detailed Cont.

3 Mesoscopic and Nanostructured Materials Fabrice Charra, Susana Gota-Goldmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction and Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Historical Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Specific Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4 Organization of this Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Electronic Structure and Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Electronic Quantum Size Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Breakdown of the Momentum Conservation Rule . . . . . . . . . . . . . . 3.2.3 Excitons in Quantum-Confined Systems . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Vibrational Modes and Electron–Phonon Coupling . . . . . . . . . . . . 3.2.5 Electron Transport Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Electromagnetic Confinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Nanoparticle-Doped Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Periodic Electromagnetic Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Magnetic Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Spin Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Ultrahigh-Density Storage Media in Hard Disk Drives . . . . . . . . . . 3.5 Preparation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Molecular-Beam Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Metal-Organic Chemical Vapor Deposition (MOCVD) . . . . . . . . . . . . 3.5.3 Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 Nanocrystals in Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.5 Ex Situ Synthesis of Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1091

Subject Index

π-bonded chain geometry 993 π-bonded chain model – diamond(111)2 × 1 1005 α = 0 glass-ceramics 558 (CH3 NHCH2 COOH)3 · CaCl2 family 932 5CB – liquid crystals 948 8CB – liquid crystals 948 8OCB – liquid crystals 949

A

aluminium alloy – abrasion resistance 190 – aging 198 – behavior in magnetic fields 194 – binary Al-based systems 174 – classification of aluminium alloys 179 – coefficient of thermal expansion 192 – creep behavior 187 – elastic properties 194 – electrical conductivity 194 – hardness 186 – homogenization 198 – machinability 192 – mechanical properties 180, 182 – nuclear properties 194 – optical properties 194 – physical properties 192, 193 – sheet formability 190 – soft annealing 197 – specific heat 194 – stabilization 197 – stress-relieving 198 – structure 182 – technical property 186 – technological properties 190 – tensile strength 186 – thermal softening 195 – work-hardenable 180 aluminium antimonide – crystal structure, mechanical and thermal properties 610 – electromagnetic and optical properties 619 – electronic properties 616 – transport properties 618 aluminium arsenide – crystal structure, mechanical and thermal properties 610 – electromagnetic and optical properties 619 – electronic properties 616 – transport properties 618 aluminium casting alloys – mechanical properties 184 – structure 184 aluminium compounds – crystal structure, mechanical and thermal properties 610

Subject Index

Abbe value – glasses 543, 548 Abrikosov vortices 717 absorption and fluorescence spectra of CdSe 1039 absorption coefficient – two-photon 826 absorption spectra of spherical particles 1046 Ac actinium 84 acceptor surface level 1023 acceptor surface state 1022 accumulation layer 1020 accuracy 4 acids – liquid crystals 946 acoustic band 1012 acoustic surface wave 906 acronyms – solid surface 1026 actinium Ac – elements 84 adatom 995 adopted numerical values for selected quantities 23 Ag silver 65 Ag-based materials 344 age hardening 198 AISI (American Iron and Steel Institute) 221 Al aluminium 78 Al bronzes 298 alkali aluminium silicates – electrical properties 434 – mechanical properties 434 – thermal properties 434

alkali halides – surface phonon energy 1017 alkali–alkaline-earth silicate glasses 530 alkali–lead silicate glasses 530 alkaline-earth aluminium silicates – electrical properties 436 – glasses 530 – mechanical properties 435 – thermal properties 436 allotropic and high-pressure modifications – elements 46 alloy – cast irons 270 – cobalt 272 – elinvar 780 – invar 780 – lead, battery grid 413 – lead–antimony 412 – lead–tin 415 – magnesium 163 – Ti3 Al-based 210 – TiAl-based 213 – titanium 206 – wear resistant 274 alloy systems 296 Allred 46 Alnico 798 Al–O–N ceramics – dielectric properties 447 – optical properties 447 alum family 911 – ferroelectrics 911 alumina – electrical properties 446 – mechanical properties 445 – properties 445 – thermal properties 446 aluminium Al – aluminium alloys 171 – aluminium production 171 – chemical properties 172 – cold working 195 – corrosion behavior 204 – elements 78 – hot working 195 – mechanical properties 172 – mechanical treatment 195 – surface layers 204 – work hardening 195

1092

Subject Index

Subject Index

– electromagnetic and optical properties 619 – electronic properties 614 – mechanical properties 610 – phonon dispersion curves 612 – thermal conductivity 618 – thermal properties 610 – transport properties 617 aluminium nitride – crystal structure, mechanical and thermal properties 610 – electromagnetic and optical properties 619 – electronic properties 616 – transport properties 618 aluminium phase diagram – aluminium alloy phase diagram 174 aluminium phosphide – crystal structure, mechanical and thermal properties 610 – electromagnetic and optical properties 619 – electronic properties 616 – transport properties 618 aluminothermy 174 Al−Ni phase diagram 285 Am americium 151 americium Am – elements 151 amorphous alloys – cobalt–based 774 – iron–based 773 – nickel–based 774 amorphous materials 27, 39 amorphous metallic alloys 772 amount of substance – definition 14 ampere – SI base unit 14 amphiphilic compound 941 amphiphilic liquid crystal 942 anisotropic magnetoresistance 1058 annealing coefficient – glasses 548 annealing of steel 223 antiferroelectric crystal 903 antiferroelectric hysteresis loop 904 antiferroelectric liquid crystal 911 antiferroelectrics – definition 903 – dielectric properties 903 – elastic properties 903 – pyroelectric properties 903 antimony Sb

– elements 98 aperiodic crystals 27 aperiodic materials 33 apparent tilt angle 935 Ar argon 128 area of surface primitive cell – crystallographic formulas 986 argon Ar – elements 128 arsenic As – elements 98 ARUPS 997 As arsenic 98 astatine At – elements 118 ASTM 241, 242 ASTM (American Society for Testing and Materials) 330 ASW 906 At astatine 118 atomic moment 755 atomic number Z – elements 45 atomic radius – elements 46 atomic scattering 1019 atomic, ionic, and molecular properties – elements 46 atomically clean crystalline surface 979 atom–surface potential – surface phonons 1019–1020 Au gold 65 austenitizing 224

B B boron 78 Ba barium 68 back-bond state 1006 bainite 223 BaMnF4 family 922 band bending – solid surfaces 1023 band gap see energy gap 592 band pass filters – glasses 566 band structure – aluminium compounds 614 – beryllium compounds 653 – boron compounds 606 – cadmium compounds 679 – group IV semiconductors and IV–IV compounds 589–592 – indium compounds 643

– magnesium compounds 657 – mercury compounds 688 – oxides of Ca, Sr, and Ba 662 – zinc compounds 668 barium Ba – elements 68 barium oxide – crystal structure, mechanical and thermal properties 660 – electromagnetic and optical properties 664 – electronic properties 661 – transport properties 663 barium titanate 915 base quantities 12 – ISO 13 base unit – SI 13 basis – crystal structure 28 BaTiO3 915 bcc positions – surface diagrams 982 Be beryllium 68 becquerel – SI unit of activity 19 benzene 946 berkelium Bk – elements 151 beryllium Be – elements 68 beryllium compounds 652 – crystal structure, mechanical and thermal properties 652 – electromagnetic and optical properties 655 – electronic properties 653 – mechanical and thermal properties 652 – optical properties 655 – thermal properties 652 – transport properties 655 beryllium oxide 447 – crystal structure, mechanical and thermal properties 652 – electrical properties 448 – electronic properties 653 – mechanical properties 447 – thermal properties 448 beryllium selenide – crystal structure, mechanical and thermal properties 652 – electronic properties 653 beryllium sulfide – crystal structure, mechanical and thermal properties 652

Subject Index

– transport properties 608 boron B – elements 78 boron compounds – crystal structure, mechanical and thermal properties 604 – electromagnetic and properties 610 – electronic properties 606 – mechanical properties 604 – thermal properties 604 – transport properties 608 boron nitride – crystal structure, mechanical, and thermal properties 604 – electromagnetic and optical properties 610 – electronic properties 606 – transport properties 608 boron phosphide – crystal structure, mechanical, and thermal properties 604 – electromagnetic and optical properties 610 – electronic properties 606 – transport properties 608 borosilicate glasses 529, 530 Br bromine 118 Bragg equation 40 brasses 298 Bravais cell 979 – 2D lattice 980 Bravais lattice 32 – elements 47 breathing-mode acoustic oscillations 1040 Brillouin scattering 906 Brillouin zone 913 – aluminium compounds 614 – beryllium compounds 653 – boron compounds 606 – cadmium compounds 678 – gallium compounds 626 – group IV semiconductors and IV–IV compounds 589 – indium compounds 643 – magnesium compounds 657 – mercury compounds 688 – oxides of Ca, Sr, and Ba 661 – zinc compounds 668 Brillouin zone corner 921 bromine Br – elements 118 bronzes 298 BSCCO – films 738

– single crystal 739 – tapes 739 – wires 739 buckled dimer 991 bulk electron density 998 bulk glassy alloys 217, 218 bulk mobility 1026 bulk modulus – elements 47

C C carbon 88 Ca calcium 68 cadmium Cd – elements 73 cadmium compounds – crystal structure, mechanical and thermal properties 676 – electromagnetic and optical properties 683 – electronic properties 678 – mechanical and thermal properties 676 – optical properties 683 – thermal properties 676 – transport properties 682 cadmium oxide – crystal structure, mechanical and thermal properties 676 – electromagnetic and optical properties 683 – electronic properties 678 – transport properties 682 cadmium selenide – crystal structure, mechanical and thermal properties 676 – electromagnetic and optical properties 683 – electronic properties 678 – transport properties 682 cadmium sulfide – crystal structure, mechanical and thermal properties 676 – electromagnetic and optical properties 683 – electronic properties 678 – transport properties 682 cadmium telluride – crystal structure, mechanical and thermal properties 676 – electromagnetic and optical properties 683 – electronic properties 678 – transport properties 682 calamitic liquid crystal 941, 942

Subject Index

– electronic properties 653 beryllium telluride – crystal structure, mechanical and thermal properties 652 – electronic properties 653 Bethe–Slater–Pauling relation 755, 756 Bh Bohrium 124 Bi bismuth 98 biaxial crystals 826 binding energy 998 – metal 999 Bioverit – glasses 559 BIPM (Bureau International des Poids et Mesures) 3, 11, 12 bismuth Bi – elements 98 Bi − Sr − Ca − Cu − O (BSCCO) 736 Bi−Sr−Ca−Cu−O – coherence lengths 736 – London penetration depths 736 – maximum Tc 736 – structural data 736 – superconducting properties 741 – upper critical fields 736 BK 7 – glasses 537 Bk berkelium 151 blue phase 942 BNN – ferroelectric material 920 Bohrium Bh – elements 124 boiling temperature – elements 47 Bondi 46 boracite-type family 911, 921 borides – physical properties 452 Borofloat – glasses 528, 529 boron antimonide – crystal structure, mechanical, and thermal properties 604 – electromagnetic and optical properties 610 – electronic properties 607 – transport properties 608 boron arsenide – crystal structure, mechanical, and thermal properties 604 – electromagnetic and optical properties 610 – electronic properties 606

1093

1094

Subject Index

Subject Index

calcium Ca – elements 68 calcium oxide – crystal structure, mechanical and thermal properties 660 – electromagnetic and optical properties 664 – electronic properties 661 – transport properties 663 californium Cf – elements 151 candela – SI base unit 15 capacitor 903 capillary viscometer 943 carat 23 carbide – cemented 277 – electrical properties 466 – mechanical properties 466 – physical properties 458 – thermal properties 466 carbon C – elements 88 carbon equivalent (CE) 268 carbon fibers – physical properties 477 carbon steels 230 carrier concentration n i – gallium compounds 631 – indium compounds 647 cast – classification 268 cast iron 268 – grades 268 – mechanical properties 270 casting technology 170 catalysis 1020 Cd cadmium 73 Ce cerium 142 cell surface 943 cellulose 481, 509 – cellulose acetate (CA) 509, 510 – cellulose acetobutyrate (CAB) 509, 510 – cellulose propionate (CP) 509, 510 – ethylcellulose (EC) 509, 510 – polymers 509 – vulcanized fiber (VF) 509, 510 cement 432 cemented carbides 277 centering types – crystal structure 28 centrosymmetric media 1007 Cerabone

– glasses 559 ceramic capacitor 906 ceramic thin film 914 – ferroelectrics 903 ceramics 345, 431 – Al–O–N 447 – applications 432 – non-oxide 451 – oxide 437 – properties 432 – refractory 437 – silicon 433 – technical 437 – traditional 432 Ceran® – glasses 559 – linear thermal expansion 558 Ceravital – glasses 559 cerium Ce – elements 142 cesium Cs – elements 59 Cf californium 151 CGPM (Conférence Générale des Poids et Mesures) 11, 12 CGS – electromagnetic system 21 – electrostatic system 21 – Gaussian system 21 cgs definitions of magnetic susceptibility 48 chalcogenide glasses 568, 571 channel conductivity 1020 characterization of optical glasses 547 Charpy impact strength 478 – polymers 478 chemical disorder 38 chemical stability – glasses 530, 531 – optical glasses 550 chemical symbols – element 45 chemisorption 1020 chiral smectic C – liquid crystals 944 chlorine Cl – elements 118 cholesteric phase 942 cholesteryl (cholest-5-ene) substituted mesogens – liquid crystals 968 cholesteryl compound 944 chromium Cr – elements 114

CIP (current in the plane of layer) 1051 CIPM (Comité International des Poids et Mesures) 3, 11 Cl chlorine 118 clamped crystal 907, 921, 934 clamped dielectric constant 907 classifications of liquid crystals 942 climatic influences – glasses 550 cluster boundaries 907 cluster formation 907 CM – liquid crystals 970 Cm curium 151 CMOS (complementary metal-oxide-semiconductor) 1059 Co cobalt 135 Co17 RE2 805 Co5 RE 805 coating 943 cobalt – alloys 272 – applications 273 – hard-facing alloy 274 – mechanical properties 277 – superalloys 274 – surgical implant alloys 277 cobalt Co – elements 135 cobalt corrosion-resistant alloys 276 cobalt-based corrosion-resistant alloys 276 CODATA (Committee on Data for Science and Technology) 4 coefficient of expansion 478 – polymers 478 coefficient of thermal expansion – glasses 526 coercive field 904 coherence length 920 coherent phonon and Raman spectra 1041 colloidal synthesis – nanostructured materials 1065 colored glasses – colorants 567 – glasses 565 columnar phase 941 commensurate reconstruction 986 commercially pure titanium (cp-Ti) 206 communication technology 912

Subject Index

copper alloys 296, 297 copper Cu – elements 65 copper–nickel 300 copper–nickel–zinc 300 Co–RE – phase equilibria 805 corrosion 1020 – resistance 218 Coulomb blockade – nanostructured materials 1031, 1044 coupled plasmon modes 1048 Co−Sm 803 CPP (current flows perpendicular to the plane of the layer) 1051, 1054 Cr chromium 114 creep modulus 478 – polymers 478 critical field 904 critical slowing-down 907, 908 critical temperature – elements 47, 48 – Pb alloys 699 CrNi steels 252 Cronstedt, swedish mineralogist 1032 crystal axes 980 crystal morphology 30 crystal optics 824 crystal structure – beryllium compounds 652 – cadmium compounds 676 – group IV semiconductors 578 – III–V compounds 610 – indium compounds 638 – IV–IV compound semiconductors 578 – magnesium compounds 655 – mercury compounds 686 – oxides of Ca, Sr, and Ba 660 – zinc compounds 665 crystal structure, mechanical and thermal properties – III–V compounds 621, 638 – III–V semiconductors 604 – II–VI compounds 652, 655, 660, 665, 676, 686 crystal symmetry – elements 47 – ferroelectrics 915 crystalline ferroelectric 911 crystalline materials – definition 27 crystalline surface – atomically clean 979

crystallization – glasses 524 crystallographic formulas 986 crystallographic properties – elements 46, 47 crystallographic space group 946–952, 955–961, 964, 966, 968–971 crystallographic structure – methods to investigate 39 crystallography – concepts and terms 27 – rudiments of 27 crystals – biaxial 826 – cubic 826 – isotropic 826 – uniaxial 826 Cryston – glasses 559 Cs cesium 59 CS2004 – liquid crystals 975 Cu copper 65 cubic – dielectrics 828, 838 cubic BaTiO3 916 cubic boron nitride 451 cubic crystal 47 cubic system 986 Curie point 906 Curie temperature 906 – surface 1009 Curie–Weiss constant 931, 932 curium Cm – elements 151 current/voltage characteristics of films 1044 Cu−Ni – electrical conductivity 302 – thermal conductivity 303 Cu−Zn – electrical conductivity 302 – thermal conductivity 303 Cu−Zn phase diagram 299 cyclohexane 946 cycloolefine copolymer (COC) 486, 487 cyclosilicate 433

D D deuterium 54 damping constant – optical mode frequency 916 dangling bonds (DBs) 991

Subject Index

compacted (vermicular) graphite (CG) 268 complex perovskite-type oxide 909 complex refractive index – zinc compounds 674 composite medium 1045 – dielectric constant 1045 composite solder glasses – glasses 563 composite structures – crystallography 34 compound semiconductor 1003 compressibility 478 – polymers 478 compression modulus – elements 47 condensed matter 27 – classification 28 conductivity – frequency-dependent 823 conductivity tensor – elements 47 conductor – nanoparticle-based 1043 confined electronic systems – nanostructured materials 1035 confinement effect – nanostructured materials 1031 constants – fundamental 3 container glasses 529 continuous distribution of states 1022 continuous-cooling-transformation (CCT) diagram 238 controlled rolling 240 Convention du Mètre 12 conventional system – ISO 13 conversion factor 945 – density 945 – diamagnetic anisotropy 945 – dipole moment 945 – dynamic viscosity 945 – kinematic viscosity 945 – molar mass 945 – temperatures of phase transitions 945 – thermal conductivity 945 cooperative interactions 903 coordination number – elements 46, 47 copolymers – physical properties 477, 483 copper – unalloyed 297

1095

1096

Subject Index

Subject Index

DAS 991 data storage media – nanostructured materials 1031 Db dubnium 105 de Broglie wavelength 1035 Debye length – solid surfaces 1020 Debye temperature ΘD – boron compounds 605 – cadmium compounds 678 – gallium compounds 623 – group IV semiconductors 584 – indium compounds 640 – IV–IV compound semiconductors 584 – mercury compounds 687 – metal surfaces 1013 – oxides of Ca, Sr, and Ba 661 – solid surfaces 1014 – surface phonons 1012 – zinc compounds 667 decimal multiples of SI units 19 degree Celsius – unit of temperature 14 density 478, 945–954, 956–971 – aluminium compounds 611 – beryllium compounds 653 – boron compounds 604 – cadmium compounds 676 – elements 47 – gallium compounds 621 – group IV semiconductors and IV–IV compounds 579 – indium compounds 638 – magnesium compounds 656 – mercury compounds 686 – oxides of Ca, Sr, and Ba 660 – polymers 478 – temperature dependence 943 – zinc compounds 665 density of electronic states – magnesium compounds 658 density of electronic states see also density of states 658 density of phonon states see also density of states 658 density of states (DOS) – nanostructure 1034 dentistry 330 depletion layer 1020 – solid surfaces 1024 derived quantities 12 – ISO 13 derived units – SI 16 – special names and symbols 16

deuteration 925 deuterium D – elements 54 devices – optical 903 – piezoelectric 903 – pyroelectric 903 devil’s staircase 932 devitrifying solder glasses 562 DFB (distributed feedback) 1038 DFG (difference frequency generation) 825 diamagnetic anisotropy 943, 945 diamond – crystal structure, mechanical and thermal properties 578–588 – electromagnetic and optical properties 601 – electronic properties 589–594 – transport properties 595 diamond positions – surface diagrams 983 diamond-like structure 979 Dicor – glasses 559 dielectric – constant (low-frequency) 823 – dissipation factor 823 – elasticity 823 – general properties 822 – lossy 823 – low-frequency materials 822 – stiffness constant 823 dielectric anisotropy 943, 946, 947 dielectric anomaly 922, 934 dielectric constant ε 907, 947–958, 960–966, 968–971, 973, 1045 – aluminium compounds 619 – beryllium compounds 655 – boron compounds 610 – cadmium compounds 683 – elements 46 – gallium compounds 635, 637 – group IV semiconductors and IV–IV compounds 601–603 – indium compounds 650 – magnesium compounds 660 – mercury compounds 691 – oxides of Ca, Sr, and Ba 664 – zinc compounds 672 dielectric dispersion 907 dielectric dissipation factor – glasses 538 dielectric function 1001 – surface layer 1007 dielectric loss tan δ

– gallium compounds 635 dielectric material – properties 826 dielectric polarization 825 dielectric properties – glasses 538 dielectric strength – glasses 539 dielectric tensor 827 dielectrics – α-iodic acid, α-HIO3 868 – α-mercuric sulfide, α-HgS 846 – α-silicon carbide, SiC 840 – α-silicon dioxide, α-SiO2 846 – α-zinc sulfide, α-ZnS 842 – β-barium borate, β-BaB2 O4 848 – 2-cyclooctylamino-5-nitropyridine, C13 H19 N3 O2 874 – 3-methyl 4-nitropyridine 1-oxide, C6 N2 O3 H6 868 – 3-nitrobenzenamine, C6 H4 (NO2 )NH2 878 – 4-(N1N-dimethylamino)-3acetamidonitrobenzene 884 – ADA 856 – ADP 856 – aluminium oxide, α-Al2 O3 844 – aluminium phosphate AlPO4 844 – ammonium dideuterium phosphate, ND4 D2 PO4 856 – ammonium dihydrogen arsenate, NH4 H2 AsO4 856 – ammonium dihydrogen phosphate, NH4 H2 PO4 856 – ammonium Rochelle salt 870 – ammonium sulfate, (NH4 )2 SO4 872 – “banana” 872 – barium fluoride, BaF2 828 – barium formate, Ba(COOH)2 866 – barium magnesium fluoride, BaMgF4 872 – barium nitrite monohydrate, Ba(NO2 )2 · H2 O 842 – barium sodium niobate, Ba2 NaNb5 O15 872 – Barium titanate, BaTiO3 864 – BBO 848 – berlinite 844 – beryllium oxide, BeO 840 – BGO 838 – BIBO 884 – bismuth germanium oxide, Bi12 GeO20 838

Subject Index

– DRDP 860 – fluorite 828 – fluorspar 828 – forsterite 866 – gadolinium molybdate, Gd2 (MoO4 )3 876 – gallium antimonide, GaSb 834 – gallium arsenide, GaAs 834 – gallium nitride, GaN 840 – gallium phosphide, GaP 834 – gallium selenide, GaSe 838 – gallium sulfide, GaS 838 – germanium, Ge 830 – GMO 876 – greenockite 840 – halite 832 – hexagonal, 6 (C6 ) 842 – hexagonal, 6mm (C6v ) 840 – hexagonal, 6m2 (D3h ) 838 – high-frequency (optical) properties 817 – Iceland spar 844 – indium antimonide, InSb 836 – indium arsenide, InAs 836 – indium phosphide, InP 836 – Irtran-3 828 – Irtran-6 834 – isotropic 828 – KB5 880 – KBBF 846 – KDA 860 – KDP 860 – KLINBO 864 – KTA 880 – KTP 880 – LBO 878 – l-CTT 874 – lead molybdate, PbMoO4 854 – lead titanate, PbTiO3 864 – LFM 876 – list of described substances 818 – lithium fluoride, LiF 830 – lithium formate monohydrate, LiCOOH · H2 O 876 – lithium gallium oxide, LiGaO2 876 – lithium iodate, α-LiIO3 842 – lithium metagallate 876 – lithium niobate (5% MgO-doped), MgO:LiNbO3 848 – lithium niobate, LiNbO3 848 – lithium sulfate monohydrate, Li2 SO4 · H2 O 886 – lithium tantalate, LiTaO3 848 – lithium tetraborate, Li2 B4 O7 864 – lithium triborate, LiB3 O5 878

– low-frequency properties 817 – magnesium fluoride, MgF2 852 – magnesium oxide, MgO 830 – magnesium silicate, Mg2 SiO4 866 – Maxwell’s equations 824 – m-chloronitrobenzene, ClC6 H4 NO2 874, 875 – mNA 878 – m-nitroaniline 878 – MNMA 874 – monoclinic, 2 (C2 ) 884 – N,2-dimethyl-4-nitrobenzenamine, C8 H10 N2 O2 874 – N-[2-(dimethylamino)-5nitrophenyl]-acetamide 884 – nantokite 834 – numerical data 818, 828 – orthorhombic, 222 (D2 ) 866 – orthorhombic, mm2 (C2v ) 872 – orthorhombic, mmm (D2h ) 866 – paratellurite 854 – physical properties 817 – PMMA (Plexiglas) 828 – POM 868 – potassium acid phthalate, KH(C8 H4 O4 ) 878 – potassium bromide, KBr 830 – potassium chloride, KCl 830 – potassium dideuterium arsenate, KD2 AsO4 858 – potassium dideuterium phosphate, KD2 PO4 858 – potassium dihydrogen arsenate, KH2 AsO4 860 – potassium dihydrogen phosphate, KH2 PO4 860 – potassium fluoroboratoberyllate, KBe2 BO3 F2 846 – potassium iodide, KI 830 – potassium lithium niobate, K3 Li2 Nb5 O15 864 – potassium niobate, KNbO3 880 – potassium pentaborate tetrahydrate, KB5 O8 · 4H2 O 880 – potassium sodium tartrate tetrahydrate, KNa(C4 H4 O6 ) · 4H2 O 870 – potassium titanate (titanyl) phosphate, KTiOPO4 880 – potassium titanyl arsenate, KTiOAsO4 880 – proustite 850 – pyragyrite 850 – quartz 846

Subject Index

– bismuth silicon oxide, Bi12 SiO20 838 – bismuth triborate, BiB3 O6 884 – BK7 Schott glass 828 – BMF 872 – BSO 838 – cadmium germanium arsenide, CdGeAs2 856 – cadmium germanium phosphide, CdGeP2 856 – cadmium selenide, CdSe 840 – cadmium sulfide, CdS 840 – cadmium telluride, CdTe 834 – calcite, CaCO3 844 – calcium fluoride, CaF2 828 – calcium tartrate tetrahydrate, Ca(C4 H4 O6 ) · 4H2 O 874 – CBO 868 – CDA 858 – cesium dideuterium arsenate, CsD2 AsO4 856 – cesium dihydrogen arsenate, CsH2 AsO4 858 – cesium lithium borate, CsLiB6 O10 858 – cesium triborate, CsB3 O5 868 – cinnabar 846 – CLBO 858 – CNB 874, 875 – COANP 874 – copper bromide, CuBr 834 – copper chloride, CuCl 834 – copper gallium selenide, CuGaSe2 858 – copper gallium sulfide, CuGaS2 858 – copper iodide, CuI 834 – cubic m3m (Oh ) 828 – cubic 43m (Td ) 834 – cubic, 23 (T ) 838 – D(+)-saccharose, C12 H22 O11 888 – DADP 856 – DAN 884 – DCDA 856 – deuterated L-arginine phosphate, (NDx H2−x )+ 2 (CND)(CH2 )3 CH (ND y H3−y )+ COO− ·D2 PO− 4 · D2 O 884 – diamond, C 830 – dipotassium tartrate hemihydrate, K2 C4 H4 O6 · 0.5H2 O 886 – DKDA 858 – DKDP 858 – DKT 886 – DLAP 884, 886 – DRDA 860

1097

1098

Subject Index

Subject Index

– trigonal, 3m (C3v ) 848 – RDA 860 – RDP 862 – trigonal, 3m (D3d ) 844 – Rochelle salt 870 – urea, (NH2 )2 CO 862 – rock salt 832 – wurtzite 842 – RTP 882 – YAG 832 – rubidium dideuterium arsenate, – YAP 866 RbD2 AsO4 860 – YLF 854 – rubidium dideuterium phosphate, – yttrium aluminate, YAlO3 866 – yttrium aluminium garnet, RbD2 PO4 860 – rubidium dihydrogen arsenate, Y3 Al5 O12 832 RbH2 AsO4 860 – yttrium lithium fluoride, YLiF4 – rubidium dihydrogen phosphate, 854 RbH2 PO4 862 – yttrium vanadate, YVO4 852 – rubidium titanate (titanyl) – YVO 852 phosphate, RbTiOPO4 882 – zinc blende 842 – rutile 852 – zinc germanium diphosphide, – sapphire 844 ZnGeP2 862 – Silicon dioxide, SiO2 828 – zinc oxide, ZnO 840 – silicon, Si 830 – zinc selenide, ZnSe 836 – zinc telluride, ZnTe 836 – silver antimony sulfide, Ag3 SbS3 850 – zincite 840 – silver arsenic sulfide, Ag3 AsS3 difference frequency generation 850 (DFG) 825 – silver gallium selenide, AgGaSe2 differential conductance as function 862 of voltage 1043 – silver thiogallate, AgGaS2 862 diffraction method 39 – sodium ammonium tartrate diffusion coefficient 946–949, tetrahydrate, Na(NH4 )C4 H4 O6 956–960, 970 · 4H2 O 870 diffusion-controlled growth – nanostructured materials 1064 – sodium chlorate, NaClO3 838 dimensionality – sodium chloride, NaCl 832 – nanostructured materials 1033 – sodium fluoride, NaF 832 – sodium nitrite, NaNO2 882 dimensions – physical quantities 4, 13 – strontium fluoride, SrF2 832 dimer bond length 995 – strontium titanate, SrTiO3 832 – sucrose 888 dioxide – zirconium 448 – sylvine 830 dipole glass 906 – sylvite 830 dipole moment 945, 947–953, – TAS 850 955–963, 968–971 – tellurium dioxide, TeO2 854 direct gap – tellurium, Te 846 – group IV semiconductors and – tetragonal, 4/m (C4h ) 854 IV–IV compounds 592 – tetragonal, 4/mmm (D4h ) 852 direct piezoelectric effect 824 – tetragonal, 422 (D4 ) 854 director 943 – tetragonal, 4mm (C4v ) 864 discotic liquid crystal 941, 942, 972 – tetragonal, 42m (D2d ) 856 – physical properties 972 – TGS 888 – thallium arsenic selenide, Tl3 AsSe3 disk-like molecule 942 disordered materials 38 850 dispersion – titanium dioxide, TiO2 852 – glasses 543 – tourmaline, (Na,Ca)(Mg,Fe)3 B3 Al6 Si6 (O,OH,F)31 dispersion curves 850 – electronic structure of surfaces – triglycine sulfate, 999 (CH2 NH2 COOH)3 · H2 SO4 888 dispersion hardening 329 – trigonal, 32 (D3 ) 844 displacement of atoms

– surface phonons 1012 displacive disorder 38 displacive ferroelectrics 907 display lifetime 944 dissipation factor 826, 828 dissipative dispersion 907 dissociation energy of molecule – elements 46 DOBAMBC (liquid crystal) 934 domain pattern – perpendicular magnetization 1062 domain wall – ferroelectric 907 – ferromagnetic 907 donor surface state 1022 doping – chemical 576 DOS (density of states) 330, 1049 – nanostructured materials 1034 drain 1024 Drude-model metal 1045 drug delivery 944 DSP family 931 DTA (differential thermal analysis) 39 dubnium Db – elements 105 ductile iron 269 Duran – glasses 527, 531, 537 Dy dysprosium 142 dye dopant 944 dynamic viscosity 945–948, 955–959, 961, 962, 967, 969–971, 973 dysprosium Dy – elements 142

E E7 – liquid crystals 975 ECS 1011 EDX (energy-dispersive analysis of X-rays) 39 EELS 1013 effect of solute elements conductivity of Cu 297 effective masses – aluminium compounds 617 – boron compounds 607 – cadmium compounds 681 – group IV semiconductors and IV–IV compounds 593 – indium compounds 646 – mercury compounds 689

Subject Index

– III–V compounds 610, 619, 635, 650 – II–VI compounds 655, 660, 664, 672, 683, 691 electromagnetic concentration effect 1046 electromagnetic confinement – nanostructured materials 1044 electromechanical coupling constant 912, 918 electron affinity – elements 46 electron and hole mobilities – aluminium compounds 618 electron density of states 1034 – cadmium compounds 680 electron diffraction 41 electron effective mass m n 593, see effective mass 661 electron g-factor gc – gallium compounds 629 – indium compounds 646 electron microscope image – magnetic tunneling junction 1057 electron microscopy 1049 electron mobility µn 663, see mobility µ 682 – elements 48 – gallium compounds 631 – indium compounds 648 – mercury compounds 690 – oxides of Ca, Sr, and Ba 663 electron transport phenomena – nanostructured materials 1042 electron tunneling – phonon-assisted 1043 electronegativity – elements 46 electronic band gap – elements 48 electronic conductivity σ – zinc compounds 671 electronic configuration – elements 46 electronic dispersion curves 1000 electronic ground state – elements 46 electronic properties – group IV semiconductors and IV–IV compounds 589–594 – III–V compounds 606, 614, 626, 643 – II–VI compounds 653, 657, 661, 668, 678, 688

electronic structure – solid surfaces 996 electronic transport, general description – aluminium compounds 617 – beryllium compounds 655 – boron compounds 608 – cadmium compounds 682 – gallium compounds 629 – group IV semiconductors and IV–IV compounds 595 – indium compounds 647 – magnesium compounds 659 – mercury compounds 689 – oxides of Ca, Sr, and Ba 663 – zinc compounds 670 electronic work function – elements 48 electronic, electromagnetic, and optical properties – elements 46 electron–phonon coupling 1040, 1041 electrooptic coefficients 826 electrooptic modulators – nanostructured materials 1040 electrooptic tensor 827 electro-optical constants – zinc compounds 675 electro-optical effect 944 electrostrictive constant 930 elemental semiconductor 1003 elements 45 – allotropic modifications 48 – atomic properties 46 – electromagnetic properties 48 – electronic properties 48 – high-pressure modifications 48 – ionic properties 46 – macroscopic properties 46 – materials data 46 – molecular properties 46 – optical properties 48 – ordered according to the Periodic table 52 – ordered by their atomic number 51 – ordered by their chemical symbol 50 – ordered by their name 49 elinvar alloys 786 – antiferromagnetic 789 elinvar-type alloys – nonmagnetic 792 energy bands see band structure 590

Subject Index

– oxides of Ca, Sr, and Ba 661 – zinc compounds 670 effective masses m n and m p – gallium compounds 629 einsteinium Es – elements 151 elastic compliance 828 elastic compliance tensor 934 – elements 47 elastic constant cik 823 – aluminium compounds 611 – beryllium compounds 652 – cadmium compounds 676 – gallium compounds 621 – group IV semiconductors and IV–IV compounds 580 – indium compounds 638 – magnesium compounds 656 – mercury compounds 687 – oxides of Ca, Sr, and Ba 660 – zinc compounds 665 elastic modulus 478, see elastic constant 580 – elements 46, 47 – polymers 478 elastic stiffness 828 – elements 47 elastic tensor 827 elastooptic coefficient 825 elastooptic constant 828 elastooptic tensor 827 electric strength 478 – polymers 478 electrical conductivity – aluminium compounds 618 – boron compounds 608 – elements 46 – group IV semiconductors and IV–IV compounds 595 electrical conductivity see also electrical resistivity 659 electrical conductivity σ – indium compounds 647 – magnesium compounds 659 – mercury compounds 690 – oxides of Ca, Sr, and Ba 663 electrical resistivity – boron compounds 609 – elements 48 – gallium compounds 630 electrical steel 766 electroforming 288 electromagnetic and optical properties – group IV semiconductors and IV–IV compounds 601

1099

1100

Subject Index

Subject Index

energy diagram for a MIM tunnel junction 1053 energy dispersion curve 1000 energy equivalents 24 energy equivalents in different units 24 energy exchange time τe–ph 1041 energy gap – aluminium compounds 616 – beryllium compounds 654 – cadmium compounds 681 – gallium compounds 628 – group IV semiconductors 592, 593 – indium compounds 644 – IV–IV compound semiconductors 592, 593 – magnesium compounds 659 – mercury compounds 688 – oxides of Ca, Sr, and Ba 661 – zinc compounds 669 energy gaps – boron compounds 607 energy shifts in the luminescence peaks 1037 energy-storage cell 1043 engineering critical current density 741 enthalpies of phase transitions 946–973 enthalpy change – elements 47 enthalpy of combustion 477 – polymers 477 enthalpy of fusion 477 – polymers 477 entropy of fusion 477 – polymers 477 Er erbium 142 erbium Er – elements 142 Es einsteinium 151 Eu europium 142 europium Eu – elements 142 EXAFS (extended X-ray atomic fine-structure analysis) 39 excess carrier density 1023 excitation energy – nanostructured materials 1038 exciton binding energy – gallium compounds 628 – zinc compounds 669 exciton Bohr radii – semiconductors 1037

exciton energy – group IV semiconductors and IV–IV compounds 593 exciton peak energy – indium compounds 645 exciton Rydberg series 1038 excitons – nanostructured materials 1036 external forces 46 external-field dependence 46 extinction coefficient k – gallium compounds 635 – zinc compounds 674

F F fluorine 118 F2 – optical glasses 551 F5 – glasses 537 facets – crystallography 27 Fahrenheit 48 families of ferroelectrics 909 fast displays 903 fcc positions – surface diagrams 981 Fe iron 131 Fe14 Nd2 B – commercial magnets 804 – magnetic materials 803 Fe–C(-X) – carbide phases 224 Fe–Cr alloy 226 Fe–Mn alloys 226 Fe–Ni alloys 225 Fermi energy 998 Fermi function 1022 Fermi level pinning 1025 Fermi surface – nanostructured materials 1055 Fermi surface shift in an electric field 1050 Fermi surfaces – nanostructured materials 1049 Fermi wavelength – nanostructured materials 1035 fermium Fm – elements 151 ferrielectric triple hysteresis loop 936 ferrielectricity 927 ferrite – applications 812

– hard magnetic 813 – MnZn 812 – NiZn 813 – soft magnetic 811 ferroelectric ceramics 906 ferroelectric hysteresis loop 904 ferroelectric liquid crystal 906, 911, 945, 967 – physical properties 967 ferroelectric mixtures – liquid crystals 975 – physical properties 975 ferroelectric phase transition 906, 933 ferroelectric polymers 906 ferroelectric transducer 906 ferroelectrics – classification 906 – definition 903 – dielectric properties 903 – displacive type 906 – elastic properties 903 – families 909, 911 – general properties 906 – indirect type 906 – inorganic crystals 903 – inorganic crystals other than oxides 922 – inorganic crystals oxides 912 – liquid crystals 903, 930 – order–disorder type 906 – organic crystals 903, 930 – phase transitions 903 – piezoelectric properties 903 – polymers 903, 930 – pyroelectric properties 903 – symbols and units 912 ferromagnetic surface 1008 Fe−Co−Cr 795 Fe−Co−V 797 Fe−Nd−B 800 – phase relations 800 Fe−Ni−Al−Co 798 Fe−Si alloys – rapidly solidified 768 Fibonacci sequence 35 field-effect mobility 1024 – solid surfaces 1024 first Brillouin zone see Brillouin zone 657 flat glasses 528 flat-band condition 1020 fluorinated three-ring LC 944 fluorine F – elements 118

Subject Index

fused silica – glasses 534, 537

G Ga gallium 78 GaAs positions – surface diagrams 983 gadolinium Gd – elements 142 gallium antimonide – crystal structure, mechanical and thermal properties 621 – electromagnetic and optical properties 635 – electronic properties 626 – transport properties 631 gallium arsenide – crystal structure, mechanical and thermal properties 621 – electromagnetic and optical properties 635 – electronic properties 626 – transport properties 631 gallium compounds – crystal structure, mechanical and thermal properties 621 – electromagnetic and optical properties 635 – electronic properties 626 – mechanical and thermal properties 621 – thermal conductivity 634 – thermal properties 621 – transport properties 629 gallium Ga – elements 78 gallium nitride – crystal structure, mechanical and thermal properties 621 – electromagnetic and optical properties 635 – electronic properties 626 – transport properties 631 gallium phosphide – crystal structure, mechanical and thermal properties 621 – electromagnetic and optical properties 635 – electronic properties 626 – transport properties 631 gamma titanium aluminides 213 gas permeation 478 – polymers 478 Gd gadolinium 142 Ge germanium 88

germanium – band structure 590 – crystal structure, mechanical and thermal properties 578–588 – electromagnetic and optical properties 601 – electronic properties 589–594 – transport properties 598 germanium Ge – elements 88 g-factor – cadmium compounds 681 g-factor, conduction electrons – group IV semiconductors and IV–IV compounds 594 glass designation 544 glass formers 527 glass matrix 1040 glass number 8nnn 534, 537 glass number nnnn – sealing glasses 563 glass structure – sodium silicate glasses 524 glass temperature – glasses 524 glass transition temperature 477 – polymers 477 glass-ceramics 525, 526, 558 – density 558 – elastic properties 558 – manufacturing process 558 glasses 523 – Abbe value 547 – abbreviating glass code 543 – acid attack 532 – acid classes 533 – alkali attack 532 – alkali classes 533 – alkali–alkaline-earth silicate 530 – alkali–lead silicate 530 – alkaline-earth aluminosilicate 530 – amorphous metals 523 – armor plate glasses 529 – automotive applications 529 – band pass filters 566 – Borofloat 528, 529 – borosilicate 529, 530 – borosilicate glasses 529 – brittleness 536 – chemical constants 553 – chemical properties 549 – chemical resistance 549 – chemical stability 530, 531 – chemical vapor deposition 523 – color code 554 – composition 527

Subject Index

fluoropolymers 480, 496 – poly(ethylene-cochlorotrifluoroethylene) (ECTFE) 496, 497 – poly(ethylene-cotetrafluoroethylene) (ETFE) 496, 497 – poly(tetrafluoroethylene-cohexafluoropropylene) (FEP) 496, 497 – polychlorotrifluoroethylene (PCTFE) 496, 497 – polytetrafluoroethylene (PTFE) 496, 497 flux flow (FF) 718 Fm fermium 151 formation curve – glasses 524 formulas – crystallographic 986 Fotoceram – glasses 559 Fotoform – glasses 559 Foturan – glasses 559 Fourier map 926 four-ring system 964 Fr francium 59 francium Fr – elements 59 Frantz–Keldysh effect 1040 free dielectric constant 907 frequency conversion 825 Fresnel reflectivity – glasses 549 Friedel–Creagh–Kmetz rule 943 fundamental constants 3 – 2002 adjustment 4 – alpha particle 9 – atomic physics and particle physics 7 – CODATA recommended values 4 – electromagnetic constants 6 – electron 7 – meaning 4 – most frequently used 4 – neutron 8 – proton 8 – recommended values 3, 4 – thermodynamic constants 6 – units of measurement 3 – universal constants 5 – what are the fundamental constants? 3

1101

1102

Subject Index

Subject Index

– compound glasses 529 – container glasses 528, 529 – crack effects 536 – density 528 – dielectric properties 538 – Duran® 531 – elasticity 536 – electrical properties 537 – engineering material 523 – fire protecting glasses 529 – flat 528 – fracture toughness 537 – frozen-in melt 533 – halide glasses 568 – hydrolytic classes 533 – infrared transmitting glasses 568 – infrared-transmitting 571 – inhomogeneous 525 – internal transmission 554 – linear thermal expansion 536, 556 – long pass filters 566 – major groups 526 – manufacturers, preferred optical glasses 545 – melting range 533 – mixtures of oxide compounds 524 – neutral density filters 566 – optical 551 – optical characterization 547 – optical glasses 543 – optical properties 539, 543 – oxide glasses 568 – passivation glasses 562 – physical constants 553 – plate glasses 528 – properties 526 – quasi-solid melt 533 – refractive index 539 – Schott filter glasses 569 – sealing glasses 559 – short pass filters 566 – silicate based 526 – soda–lime type 528 – solder glasses 562 – strength 534 – stress behavior 535 – stress rate 535 – stress-induced birefringence 539 – supercooled melt 533 – surface (cleaning and etching) 533 – surface modification 532 – surface resistivity 538 – technical 530 – tensile strength 536

– thermal conductivity 556 – thermal strength 537 – transmittance 539 – viscosity 534 – vitreous silica 556 – volume resistivity 537 – wear-induced surface defects 535 glasses, colored – nomenclature 566 – optical filter 566 glasses, sealing – ceramic 562 – principal applications 561 – recommended material combinations 560 – special properties 561 glasses, solder and passivation – composite 563 – properties 564 glassy state – crystallography 39 GMO family – ferroelectrics 920 GMR (giant magnetoresistance) 1049, 1050 – mechanism 1051 – thickness dependence 1051 GMR ratio 1050 gold – alloys 347 – applications 347 – chemical properties 361 – electrical properties 356 – electrical resistivity 356 – intermetallic compounds 350 – magnetic properties 358 – mechanical properties 352 – optical properties 359 – phase diagrams 347 – production 347 – special alloys 361 – thermal properties 359 – thermochemical data 347 – thermoelectric properties 358 gold Au – elements 65 golden mean 35 granular materials 1043 gray – SI unit of absorbed dose 19 gray iron 269 gray tin – band structure 590 – crystal structure, mechanical and thermal properties 578–588

– electromagnetic and optical properties 601 – electronic properties 589–594 – transport properties 599 Griffith flaw – glasses 534 Group IV semiconductors 576, 578–603 – electron mobility 597 – hole mobility 597 Group IV semiconductors and IV–IV compounds – crystal structure 578 – electromagnetic and optical properties 601 – electronic properties 589–594 – mechanical properties 578 – thermal properties 578 – transport properties 595–601 groups of elements (Periodic table) 45

H H hydrogen 54 hafnium Hf – elements 94 Haigh Push-Pull test 408 Hall coefficient – elements 48 – group IV semiconductors and IV–IV compounds 595 Hall mobility – group IV semiconductors and IV–IV compounds 596, 597 Hall mobility see also mobility µ 596 halogen-substituted benzene 946 hard disk drive 1060 – limits 1060 – technology 1060 hard ferrites – magnetic properties 814 hard magnetic alloys 794 hardenability 237 hardmetals 277 hassium Hs – elements 131 Hatfield steel 226 HATOF 1013 HCl family 924 He helium 54 heat capacities c p , cV – boron compounds 605 – group IV semiconductors 584

Subject Index

– glasses 524 Hoya code – glasses 544 HPDC (high-pressure die casting) 168 HRTEM (high-resolution transition electron microscopy) 39 Hs hassium 131 Hume-Rothery phase 333, 350 Hume-Rothery phases 296 hydrogen H – elements 54 hydrostatic pressure 926 hyper-Raman scattering 915

I I iodine 118 IBA 991, 1024 ICSU (International Council of the Scientific Unions) 4 ideal surface 979 III–V compound semiconductors 604 II–VI semiconductor compounds 652 image potential 996 image state 996, 997, 999 – effective mass 999 impact strength 478 – polymers 478 impurity elements 206 impurity scattering – group IV semiconductors and IV–IV compounds 599 In indium 78 incommensurate phase 930 incommensurate phases 906 incommensurate reconstruction 986 index of refraction – complex 674 indirect gap – group IV semiconductors and IV–IV compounds 589 indium antimonide – crystal structure, mechanical and thermal properties 638 – electromagnetic and optical properties 650 – electronic properties 643 – transport properties 647 indium arsenide – crystal structure, mechanical and thermal properties 638 – electromagnetic and optical properties 650

– electronic properties 643 – transport properties 647 indium compounds – crystal structure, mechanical and thermal properties 638 – electromagnetic and optical properties 650 – electronic properties 643 – mechanical and thermal properties 638 – optical properties 650 – thermal properties 638 – transport properties 647 indium In – elements 78 indium nitride – crystal structure, mechanical and thermal properties 638 – electromagnetic and optical properties 650 – electronic properties 643 – transport properties 647 indium phosphide – crystal structure, mechanical and thermal properties 638 – electromagnetic and optical properties 650 – electronic properties 643 – transport properties 647 induced phase transition 904 inelastic neutron scattering 906 infrared-transmitting glasses 568, 571 inorganic ferroelectrics 903 inorganic ferroelectrics other than oxides 922 inosilicates 433 insulator – surface phonon 1017 intercritical annealing 240 interface state density – solid surface 1026 interlayer distance – crystallographic formulas 986 International Annealed Copper Standard (IACS) 296 international system of units 11 international tables for crystallography 31 International Union of Pure and Applied Chemistry (IUPAC) 15 International Union of Pure and Applied Physics (IUPAP) 14 internuclear distance – elements 46 intrinsic carrier concentration

Subject Index

– IV–IV compound semiconductors 584 heat capacity 477, 956–960, 970 – cadmium compounds 678 – gallium compounds 623 – indium compounds 640 – mercury compounds 687 – oxides of Ca, Sr, and Ba 661 – polymers 477 – zinc compounds 667 heat-resistant steels 258 HEIS (high-energy ion scattering) 989, 1013 helical structure 942 helium He – elements 54 Hermann–Mauguin symbols 30 hertz – SI unit of frequency 19 heterocycles 946 hexagonal BaTiO3 917 Hf hafnium 94 Hg mercury 73 high copper alloy 297 high-Tc superconductors – lower critical 716 – upper critical 716 high-frequency dielectric constant ε see also dielectric constant ε 601 high-Ni alloys 281 high-pressure die casting (HPDC) 168 high-pressure modifications 48 high-strength low-alloy 240 hip implants 277 HMF (half-metallic ferromagnet) 1055 Ho holmium 142 hole effective mass m p 594, see effective mass 661 hole mobility µp see mobility µ 682 – elements 48 – gallium compounds 631 – indium compounds 648 hollow-ware – glasses 528 holmium Ho – elements 142 holohedry – crystallography 30 homeotropic alignment 943 Hooke’s law 47, 823 hopping mechanism – nanostructured materials 1043 host–guest effect 944 hot forming

1103

1104

Subject Index

Subject Index

– group IV semiconductors and IV–IV compounds 595, 596 intrinsic charge carrier concentration – elements 48 intrinsic Debye length 1021 intrinsic Fermi level 1020 invar alloys – Fe−Ni-based 782 – Fe−Pd base 785 – Fe−Pt-based 784 Invar effect 385 inversion center 30 inversion layer 1020 – solid surfaces 1024 inversion layer channel 1024 iodine I – elements 118 ionic radius – elements 46, 49 ionization energy – elements 46 Ir iridium 135 iridium 393 – alloys 393 – applications 393 – chemical properties 398 – diffusion 398 – electrical properties 397 – lattice parameter 394 – magnetic properties 397 – mechanical properties 395 – optical properties 398 – phase diagram 393 – production 393 – thermal properties 398 – thermoelectrical properties 397 iridium Ir – elements 135 iron and steels 221 iron Fe – elements 131 iron miscibility gap 226 iron phase diagram 226 iron-carbon alloys 222 iron-cobalt alloys 772 iron–silicon alloys 763 Ising model 906 ISO (International Organization for Standardization) 12 isothermal transformation (IT) diagram 238 isotropic – dielectrics 828 isotropic liquid 943 IV–IV compound semiconductors 576, 578–603

– electron mobility 597 – hole mobility 597

J JDOS 1006 jellium 997 jellium model 998 – work functions 999 jewellery 330 joint density of states 1005 jominy apparatus 238 Josephson vortices 717 joule – SI unit of energy 19

K K 50 – glasses 537 K potassium 59 K10 – optical glasses 551 K7 – optical glasses 551 katal – SI unit of catalytic activity 19 KDP family 925 kelvin 48 – SI base unit 14 Kerr effect 825 – optical 826 Kerr ellipticity 1011 KH2 PO4 family 925 kilogram – SI base unit 14 kinematic viscosity 945, 947, 950, 951, 955, 962, 964–967, 969, 975 Kleinman symmetry conditions 825 KNbO3 913 knee joint replacements 277 KNO3 family 925 Knoop hardness – optical glasses 550 Kr krypton 128 KRIPES 997 Kroll process 206 krypton Kr – elements 128 KTaO3 913

L LA – phonon spectra 915 La lanthanum 84

Lamb theory of elastic vibrations 1040 lamellar (flake) graphite (FG) 268 langbeinite-type family 911, 930 lanthanum La – elements 84 LASF35 – optical glasses 551 LAT family 932 lattice concept – crystallography 28 lattice constants see lattice parameters 656 lattice dynamics 1012 lattice parameter 980 – aluminium compounds 610 – beryllium compounds 652 – boron compounds 604 – cadmium compounds 676 – gallium compounds 621 – group IV semiconductors and IV–IV compounds 579 – indium compounds 638 – magnesium compounds 656 – mercury compounds 686 – oxides of Ca, Sr, and Ba 660 – zinc compounds 665 lattice scattering – group IV semiconductors and IV–IV compounds 598 lattice vibration 906 lattices – planes and directions 28 Laue images 41 lawrencium Lr – elements 151 layer-structure family 909 LB (Langmuir–Blodgett) film 944 LC display 944 LC materials (LCMs) 944 LC–surface interaction 944 lead 407 – antimony 412 – arsenic alloys 421 – battery grid alloys 413 – bearing alloys 415 – bismuth 419 – cable sheathing alloys 421 – calcium–tin 417 – calcium–tin, battery grid 418 – coper alloys 421 – corrosion 408 – corrosion classification 411 – fusible alloys 420 – gamma-ray mass-absorption 412 – grades 407

Subject Index

– physical properties 973 liquid crystal two-ring systems with bridges – physical properties 955 liquid crystal two-ring systems without bridges – physical properties 947 liquid crystalline acids – physical properties 946 liquid crystalline compound 943 – mesogenic group 943 – side group 943 – terminal group 943 liquid crystalline mixtures – physical properties 975 liquid crystals – ferroelectric properties 905 liquid crystals (LCs) 941 list of described physical properties 822 lithium Li – elements 59 lithium niobate 919 lithography – nanostructured materials 1064 LithosilTM 551 LLF1 – optical glasses 551 local-field effect 1045 long pass filters – glasses 566 longitudinal acoustic branch 915 long-range order 39, 927 – glasses 524 long-range order of molecules 943 losses – dynamic eddy current 763 – hysteresis 763 low dielectric loss glasses 527 low-dimensional system – nanostructured materials 1034 low-frequency dielectric constant 917 low-temperature annealing 298 Lr lawrencium 151 LSMO (La0.7 Sr0.3 MnO3 ) 1056 Lu lutetium 142 lumen – non-SI unit in photometry 15 luminescence – nanostructured materials 1036 luminous flux – photometry 15 luminous intensity Iv – photometry 15 lutetium Lu

– elements 142 lyotropic liquid crystals 942

M M. Faraday 1032 Macor – glasses 559 magnesium alloys 163 – corrosion behavior 169 – heat treatments 169 – joining 169 – mechanical properties 168 – nominal composition 165 – solubility data 163 – tensile properties 167 – tensile property 166 magnesium compounds – crystal structure, mechanical and thermal properties 655 – electromagnetic and optical properties 660 – electronic properties 657 – mechanical and thermal properties 655 – optical properties 660 – thermal properties 655 – transport properties 659 magnesium Mg – casting practices 168 – elements 68 – magnesium alloys 162 – melting practices 168 magnesium oxide 444 – applications 444 – crystal structure, mechanical and thermal properties 655 – electrical properties 444 – electromagnetic and optical properties 660 – electronic properties 657 – mechanical properties 444 – thermal properties 444 – transport properties 659 magnesium selenide – crystal structure, mechanical and thermal properties 655 – electromagnetic and optical properties 660 – electronic properties 657 – transport properties 659 magnesium silicate – electrical properties 435, 436 – mechanical properties 435, 436 – thermal properties 435, 436 magnesium sulfide

Subject Index

– internal friction 408 – low-melting alloys 419 – mechanical properties 408 – quaternary eutectic alloy 420 – recrystallization 409 – silver alloys 420 – solder alloys 415 – solders 416 – tellurium alloys 421 – ternary alloys 413 – tin alloy 415 lead glasses 527 lead Pb – elements 88 lead–antimony – phase diagram 413 LEED (low-energy electron diffraction) 987, 1013 LEIS (low-energy ion scattering) 989, 1013 LF5 – optical glasses 551 Li lithium 59 Li2 Ge7 O15 family 920 LiBaO3 919 light transmittance – glasses 539 light-emitting diode 1043 LiNbO3 family 909, 919 linear thermal expansion – optical glasses 556 linear thermal expansion coefficient α – aluminium compounds 611 – beryllium compounds 653 – boron compounds 605 – cadmium compounds 677 – gallium compounds 623 – group IV semiconductors 582, 583 – indium compounds 639 – IV–IV compound semiconductors 582, 583 – magnesium compounds 656 – mercury compounds 687 – oxides of Ca, Sr, and Ba 660 – zinc compounds 666 LiNH4 C4 H4 O8 family 911 liquid crystal – anisotropy 943 – refractive index 943 – rod-like 943 liquid crystal family 911, 934 liquid crystal ferroelectrics 903 liquid crystal material (LCM) – degradation 944 liquid crystal salts 973

1105

1106

Subject Index

Subject Index

– crystal structure, mechanical and thermal properties 655 – electromagnetic and optical properties 660 – electronic properties 657 – transport properties 659 magnesium telluride – crystal structure, mechanical and thermal properties 655 – electromagnetic and optical properties 660 – electronic properties 657 – transport properties 659 magnet – Mn−Al−C 811 magnetic domain 1058 magnetic dots – nanostructured materials 1049 magnetic dots, arrays of 1061 magnetic field constant – fundamental constant 14 magnetic layers 1048, 1050 – spin valve 1052 magnetic materials 755 – Co5 Sm based 806 – hard 794 – permanent 794 magnetic nanostructures 1031, 1048, 1050 – information storage 1048 – read heads 1048 – sensors 1048 magnetic oxides 811 magnetic periodic structures 33 magnetic reading head 1053, 1058 magnetic recording – perpendicular discontinuous media 1060 magnetic sensors 1048, 1058 magnetic surface 1008 magnetic susceptibility 948–950, 956, 957 – elements 46, 48 magnetic tunnel junction 1054 – manganite-based 1057 magnetic tunneling junctions (MTJ) 1056 magnetization – elements 48 magnetocrystalline anisotropy 756 magnetoelectronic devices 1058 magnetoresistance effect 1050 magnetoresistance of Fe/Cr multilayers 1051 magnetostriction 757

magnets – 17/2 type 807 – 5/1 type 806 – TM17 Sm2 808 majority carriers 1023 malleable irons 270 manganese Mn – elements 124 manipulating the dot magnetization 1062 manufacturing – Fe−Nd−B magnets 801 manufacturing process – glasses 525 martensite 223 martensitic transformation 225, 226 mass magnetic susceptibility – elements 48 mass susceptibility – elements 48 mass-production glasses 526 materials – semiconductors 576 materials data – elements 46 material-specific parameters 46 matrix composites 170 Maxwell–Garnett model 1045 Maya blue color 1032 MBBA – liquid crystals 955 MBE (molecular-beam epitaxy) 991, 1032, 1049, 1063 – 0-D structures 1064 – 1-D structures 1064 – 2-D structures 1063 Md mendelevium 151 mechanical and thermal properties – III–V compounds 621, 638 – II–VI compounds 652, 655, 660, 665, 676, 686 mechanical properties – elements 46, 47 – group IV semiconductors 578–588 – III–V compounds 610 – III–V semiconductors 604 – IV–IV compound semiconductors 578–588 – optical glasses 550 – technical glasses 533 MEIS (medium-energy ion scattering) 989, 1013 meitnerium Mt – elements 135 melt viscosity 478

– polymers 478 melting point Tm – aluminium compounds 611 – beryllium compounds 653 – boron compounds 605 – cadmium compounds 677 – gallium compounds 622 – group IV semiconductors and IV–IV compounds 580 – indium compounds 639 – magnesium compounds 656 – mercury compounds 686 – oxides of Ca, Sr, and Ba 660 – zinc compounds 666 melting temperature 477 – elements 47, 48 – polymers 477 memory devices 903 mendelevium Md – elements 151 mercury compounds – crystal structure, mechanical and thermal properties 686 – electromagnetic and optical properties 691 – electronic properties 688 – mechanical and thermal properties 686 – thermal properties 686 – transport properties 689 mercury Hg – elements 73 mercury oxide – crystal structure, mechanical and thermal properties 686 – electromagnetic and optical properties 691 – electronic properties 688 – transport properties 689 mercury selenide – crystal structure, mechanical and thermal properties 686 – electromagnetic and optical properties 691 – electronic properties 688 – transport properties 689 mercury sulfide – crystal structure, mechanical and thermal properties 686 – electromagnetic and optical properties 691 – electronic properties 688 – transport properties 689 mercury telluride – crystal structure, mechanical and thermal properties 686

Subject Index

– aluminium compounds 618 – cadmium compounds 682 – group IV semiconductors and IV–IV compounds 597–599 – indium compounds 648 MOCVD (metal-organic chemical vapor deposition) 1064 modulated crystal structure 924 modulated structures – crystallography 34 moduli see elastic constant 580 Mohs hardness 822, 826 – elements 47 molar enthalpy of sublimation – elements 47 molar entropy – elements 47 molar heat capacity – elements 47 molar magnetic susceptibility – elements 48 molar mass 945–972 – glasses 527 molar susceptibility – elements 48 molar volume – elements 47 mole – definition 14 – SI base unit 14 mole fraction – glasses 527 molecular architecture 477 molybdenum Mo – elements 114 momentum-conservation rule 1036 monocrystalline material 47 monolithic alloys 170 monophilic liquid crystal 942 MOS devices 979 MOS field-effect transistor 1020 MOSFET – electron and hole mobility 1025 – equilibrium condition 1024 – schematic drawing 1025 Mott–Wannier exciton 1037 MQW (multiple quantum well) 1038 MRAM (magnetic random access memories) 1058 MRAM cell – schematic diagram 1059 Mt meitnerium 135 MTJ (magnetic tunnel junction) 1053, 1054 MTJ sensor

– operation principle 1059 multi-component alloys 219 multiphase (MP) alloys 276 multiple hysteresis loops 932 multiple quantum wells 1042 MVA-TFT (multidomain vertical-alignment thin-film transistor) 944

N N nitrogen 98 N16B – glasses 537 – sealing glasses 563 N-4 – liquid crystals 959 Na sodium 59 NaNO2 family 924 nanocrystal 1038 nanoimprint lithography 1061 nanoimprinted single domain dots – images 1061 nanoimprinting 1061 nanolithography 1031 nanomaterial 1032 nanometric multilayers 1049 nanoparticle 1031 – doped material 1045 – local-field 1045 nanopatterning 1061 nanophase materials 1032 nanoporous materials 1032, 1043 nanoscience 1032 nanostructured material 1031, 1032 – classification scheme 1034 – conductance 1043 – definition 1032 – electrical conductivity 1043 – manufacturing 1063 – preparation 1031, 1035 – zeolites 1065 nanostructures – magnetic 1048 nanotechnology 1032 Nb niobium 105 N-BAF10 – optical glasses 551 N-BAF52 – optical glasses 551 N-BAK4 – optical glasses 551 N-BALF4 – optical glasses 551 N-BASF64 – optical glasses 551

Subject Index

– electromagnetic and optical properties 691 – electronic properties 688 – transport properties 689 mesogen 943 mesogenic group 943 mesophase 941 mesoscopic material – conductivity 1044 – nanoparticle doped 1044 – waveguide applications 1045 mesoscopic materials 1031, 1033 – manufacturing 1033 mesoscopic system – quantum size effect 1035 – thermodynamic stability 1035 metal – nanoparticle 1040 – resonance state 999 – surface 987 – surface core level shifts (SCLS) 998 – surface Debye temperature 1013 – surface phonon 1012 – surface state 999 – work function 997 metal surface 987 – jellium model 998 metals 997 – vertical relaxation 989 meter – SI base unit 13 metrologica, international journal 12 MFM image of a written line on an array of dots 1063 MFM image of arrays of dots 1063 MFM image of domain pattern 1062 – sidewalls 1062 Mg magnesium 68 MHPOBC (liquid crystal) 935, 967 microphase separation 941 Mie theory 1045 Miller delta 825 Miller indices 28 M–I–M (metal–insulator–metal) heterostructure 1053 minority carriers 1023 missing-row reconstruction 987 Mn manganese 124 Mn−Al−C 810 – phase relations 810 Mo molybdenum 114 Mo-based alloys 317 mobility µ

1107

1108

Subject Index

Subject Index

Nb-based alloys 318 N-BK7 – glasses 548 – optical glasses 551 Nd neodynium 142 Nd−Fe−B – physical properties 802 Ne neon 128 near field microscopy 1049 nematic mixtures – liquid crystals 975 – physical properties 975 nematic phase – liquid crystals 941 nematic–isotropic transition 945 nematic-phase director 943 Neoceram – glasses 559 neodynium Nd – elements 142 neon Ne – elements 128 Neoparies – glasses 559 neptunium Np – elements 151 nesosilicate 433 neutral density filters – glasses 566 neutron diffraction 41, 926 neutron scattering 915 neutron spectrometer scan 916 new rheocast process (NRC) 170 newton meter – SI unit of moment of force 19 N-FK51 – glasses 548 – optical glasses 551 N-FK56 – optical glasses 551 (NH4 )2 SO4 family 927 (NH4 )3 H(SO4 )2 family 928 (NH4 )HSO4 family 928 (NH4 )LiSO4 family 928 Ni nickel 139 Ni superalloys 294 nickel – alloys 279 – application 279 – carbides 285 – low-alloy 279 – mechanical properties 280 – plating 288 nickel Ni – elements 139 nickel-based superalloys 284

nickel–iron alloys 769 nickel-silvers 300 NIMs (National Institutes for Metrology 4 niobium Nb – elements 105 nitride – electrical properties 467 – mechanical properties 467 – thermal properties 467 nitrides – physical properties 468 nitrogen N – elements 98 N-KF9 – optical glasses 551 N-KZFS2 – optical glasses 551 N-LAF2 – optical glasses 551 N-LAK33 – optical glasses 551 N-LASF31 – optical glasses 551 No nobelium 151 nobelium No – elements 151 noble metals 329 – Ag 329 – alloys 329 – applications 330 – Au 329 – catalysts 330 – corrosion resistance 329 – hardness 329 – Ir 329 – optical reflectivity 330 – Os 329 – Pd 329 – Pt 329 – Rh 329 – Ru 329 – vapour pressure 330 NOL (nano-oxide layer) 1053 noncrystallographic diffraction symmetries 36 nondestructive testing 941 nonlinear field-dependent properties 46 nonlinear optical coefficients – nanostructured materials 1039 nonlinear optical device 903, 925 nonlinear optical susceptibility 920 nonlinear susceptibility tensors 827 non-oxide ferroelectrics 905 non-SI units 11, 20

normalizing 224 Np neptunium 151 N-PK51 – optical glasses 551 N-PSK57 – optical glasses 551 N-SF1 – optical glasses 551 N-SF56 – optical glasses 551 N-SF6 – glasses 548 – optical glasses 551 N-SK16 – optical glasses 551 N-SSK2 – optical glasses 551 nuclear incoherent scattering 916 nuclear reactor 218

O O oxygen 108 occupied electron shells – elements 46 Ohara code – glasses 544 one-dimensional liquid 943 one-electron potential 999 opal – nanostructured materials 1032 opals 1048 OPO (optical parametric oscillation) 825 optical constants – gallium compounds 635 – group IV semiconductors and IV–IV compounds 601–603 – indium compounds 651 optical constants n and k – cadmium compounds 684 optical glasses 526, 543 – thermal properties 556 optical materials – high-frequency properties 824 optical mode frequency 916 optical parametric oscillation (OPO) 825 optical parametric oscillator 920 optical phonon scattering – group IV semiconductors and IV–IV compounds 598 optical phonon scattering see also phonon scattering 598 optical phonon softening 913 optical properties

Subject Index

– thermal properties 660 – transport properties 663 oxygen O – elements 108

P P phosphorus 98 Pa protactinium 151 PAA – liquid crystals 958 pair distribution function – crystallography 40 palladium Pd – alloys 364 – applications 364 – electrical properties 370 – elements 139 – lattice parameters 366 – magnetic properties 372 – mechanical properties 368 – phase diagrams 364 – production 364 – thermoelectric properties 370 parabolic band 1000 Parkes process 330 partially stabilized zirconia (PSZ) – electrical properties 449 – mechanical properties 449 – thermal properties 449 particle in a box model 1035 particle intensity Ip – radiometry 15 passivation glasses 562, 564 – glasses 565 – properties 564 pattern transfer by imprinting 1061 Pauling 46 Pb lead 88 PbHPO4 family 927 PbTiO3 916 PbZrO3 918 Pb−Ca−Sn – battery grid alloys 418 PCH-7 – liquid crystals 950 Pd palladium 139 pearlite 222 Pearson symbol – elements 47 percolation density – nanostructured materials 1033 periodes of elements (Periodic table) 45 Periodic table – elements 45

Periodic table of the elements 53 permanent magnets – Co−Sm 806 perovskite-type family 909, 911, 912 perovskite-type oxide 909 phase diagram – Fe–C 222 – Fe–Cr 226 – Fe–Mn 225 – Fe–Ni 225 – Fe–Si 227 – Ti–Al 210 – Zr–Nb 218 – Zr–O 218 phase separation – glasses 525 phase transition temperature 943 phase-matching angle 826 phase-matching condition 825 phonon confinement – nanostructured materials 1042 phonon density of states – gallium compounds 623, 625 – indium compounds 642 phonon dispersion – surface phonons 1012 phonon dispersion curve – aluminium compounds 612 – gallium compounds 623–625 – indium compounds 641 – surface phonons 1015–1026 phonon dispersion relation – group IV semiconductors 585–587 – IV–IV compound semiconductors 585, 588 phonon energies – nanostructured materials 1040 – solid surfaces 1013 phonon frequencies ν – cadmium compounds 678 – gallium compounds 624 – group IV semiconductors 585 – indium compounds 640 – IV–IV compound semiconductors 585 – magnesium compounds 657 – mercury compounds 687 – oxides of Ca, Sr, and Ba 661 – zinc compounds 667 phonon frequencies ν see also phonon wavenumbers ν˜ 605 phonon instability 921 phonon mode frequency 908 phonon scattering

Subject Index

– group IV semiconductors and IV–IV compounds 601 – III–V compounds 610, 619, 635, 650 – II–VI compounds 655, 660, 664, 672, 683, 691 optical second-harmonic generator 903 optical transparency range 826 optical visualization 941 optoelectronic devices – nanostructured materials 1038 order parameter 946–952, 956–960, 962, 963 order parameter, S 943 order principle for mesogenic groups 946 organic ferroelectrics 903 orientational order 941 Os osmium 131 osmium Os – alloys 402 – applications 402 – cathodes 404 – chemical properties 406 – electrical properties 404 – elements 131 – lattice parameter 402 – magnetic properties 405 – mechanical properties 404 – phase diagrams 402 – production 402 – thermal properties 405 – thermoelectric properties 404 outer-shell orbital radius – elements 46 over-aging 201 oxidation states – elements 46 oxide 437 – beryllium 447 – magnesium 444 – physical properties 438 oxide ceramics – production of 444 oxide ferroelectrics 903, 905 oxide superconductors – low-Tc oxide 711 oxides of Ca, Sr, and Ba – crystal structure, mechanical and thermal properties 660 – electromagnetic and optical properties 664 – electronic properties 661 – mechanical and thermal properties 660

1109

1110

Subject Index

Subject Index

– group IV semiconductors and IV–IV compounds 598 phonon wavenumbers ν˜ see also phonon frequencies ν 605 – aluminium compounds 612 – cadmium compounds 678 – gallium compounds 624 – indium compounds 640 – magnesium compounds 657 – mercury compounds 687 – zinc compounds 667 phonon wavenumbers ν˜ /frequencies ν – boron compounds 605 phonon–phonon coupling 907 phosphorus P – elements 98 photochromic glasses – nanostructured materials 1032 photoconductive crystal 922 photoelastic effect 824 photoemission spectra for Ag quantum wells 1036 photoluminescence spectra of CdSe 1039 photometry – intensity measurements 15 photonic band-gap materials 1048 phyllosilicate 433 physical properties – liquid crystals 943 physical quantities 12 – base 11, 12 – data 13 – definition 12 – derived 11, 12 – general tables 4 piezoelectric – element 918 – material 917 – strain constant 918 – strain tensor 824 – tensor 827 piezoelectricity 824, 906 piezooptic coefficient 825 planar alignment 943 planar electromechanical coupling factor 918 Planck radiator 15 plasmon excitations – nanostructured materials 1031 plasmon oscillation – nanostructured materials 1032 plasmon peak – metals 1045 plasmon resonance 1045

plastic crystal 941 platinum group metals (PGM) 363 – alloys 363 platinum Pt – alloys 376 – applications 376 – catalysis 385 – chemical properties 385 – electrical properties 381 – elements 139 – magnetical properties 384 – mechanical properties 378 – optical properties 385 – phase diagrams 376 – production 376 – thermal properties 385 – thermoelectric properties 382 plutonium Pu – elements 151 PLZT – ceramic material 918 Pm promethium 142 Po polonium 108 Pockels effect 825 point groups – crystallography 30 Poisson equation 1022 Poisson number – elements 47 Poisson’s ratio 478 – optical glasses 550 – polymers 478 polarization microscopy 943 polonium Po – elements 108 poly(4-methylpentene-1) (PMP) 488, 489 poly(ethylene-co-acrylic acid) (EAA) 486, 487 poly-(ethylene-co-norbornene) 486, 487 poly(ethylene-co-vinyl acetate) (EVA) 486, 487 poly(vinyl chloride) 492, 495 – plastisized (60/40) (PVC-P2) 492, 495 – plastisized (75/25) (PVC-P1) 492, 495 – unplastisized (PVC-U) 492, 494–496 polyacetals 480, 497 – poly(oxymethylene) (POM-H) 497–500 – poly(oxymethylene-co-ethylene) (POM-R) 497, 498, 500 polyacrylics 480, 497

– Poly(methyl methacrylate) (PMMA) 497–499 polyamides 480, 501 – polyamide 11 (PA11) 501 – polyamide 12 (PA12) 501 – polyamide 6 (PA6) 501, 502 – polyamide 610 (PA610) 501, 502 – polyamide 66 (PA66) 501, 502 polybutene-1 (PB) 488, 489 polyesters 481, 503 – poly(butylene terephthalate) (PBT) 503–505 – poly(ethylene terephthalate) (PET) 503–505 – poly(phenylene ether) (PPE) 504–506 – polycarbonate (PC) 503, 504 polyether ketones 481, 508 – poly(ether ether ketone) (PEEK) 508, 509 polyethylene 483–486 – high density (HDPE) 483–486 – linear low density (LLDPE) 484–486 – low density (LDPE) 484–486 – medium density (MDPE) 484–486 – ultra high molecular weight (UHMWPE) 484–486 polyethylene ionomer (EIM) 486, 487 polyimides 481, 508 – poly(amide imide) (PAI) 508 – poly(ether imide) (PEI) 508, 509 – polyimide (PI) 508 polyisobutylene (PIB) 488, 489 polymer – physical properties 483 polymer blend 515 – physical properties 477, 483 – poly(acrylonitrile-co-butadiene-coacrylester) + polycarbonate (ASA + PC) 515–517 – poly(acrylonitrile-co-butadiene-costyrene) + polyamide (ABS + PA) 515–517 – poly(acrylonitrile-co-butadiene-costyrene) + polycarbonate (ABS + PC) 515–517 – poly(butylene terephthalate) + poly(acrylonitrile-co-butadiene-coacrylester) (PBT + ASA) 517, 521 – poly(butylene terephthalate) + polystyrene (PBT + PS) 515, 519, 520

Subject Index

– melt viscosity 478 – melting temperature 477 – physical properties 477 – physicochemical properties 477 – Poisson’s ratio 478 – refractive index 478 – relative permittivity 478 – shear modulus 478 – shear rate 478 – Shore hardness 478 – sound velocity 478 – steam permeation 478 – stress 478 – stress at 50% strain (elongation) 478 – stress at fracture 478 – stress at yield 478 – structural units 479–481 – surface resistivity 478 – thermal conductivity 478 – Vicat softening temperature 477 – viscosity 478 – volume resistivity 478 polyolefines 480, 483–486 polypropylene (PP) 488, 489 polysulfides 481, 506 – poly(phenylene sulfide) (PPS) 506, 507 polysulfones 481, 506 – poly(ether sulfone) (PES) 506, 507 – polysulfone (PSU) 506, 507 polyurethanes 481, 511 – polyurethane (PUR) 511, 512 – thermoplastic polyurethane elastomer (TPU) 511, 512 polyvinylidene fluoride – ferroelectrics 911 porous aluminium silicates – electrical properties 436 – mechanical properties 436 – thermal properties 436 Portland cement – ASTM types 433 – chemical composition 432 positional order 941 potassium K – elements 59 potential barrier 1022 powder-composite materials 277 Powder-in-Tube (PIT) 739 power-law dependence of conductivity on film thickness 1042 Pr praseodynium 142 practical superconductors

– characteristic properties 705 praseodynium Pr – elements 142 prefixes – decimal multiples of units 19 primitive cell – crystal structure 28 projected band structure 996 projected bond length 995 promethium Pm – elements 142 property tensor 46 – independent components 827 protactinium Pa – elements 151 proton distribution 926 pseudopotential calculation 1006 Pt platinum 139 p-type diamond – Debye length 1021 Pu plutonium 151 pulsed infrared lasers 1040 pyrochlore-type family 909 pyroelectric coefficient 917 pyroelectric measurement 931 PZT – piezoelectric material 917

Q quantum confinement 1036 – nanostructured materials 1042 quantum dots – nanostructured materials 1031, 1035 quantum size effect – nanostructured materials 1031, 1035 quantum transport – nanostructured materials 1053 quantum well – coupled 1043 – nanostructured materials 1031, 1035 quantum wires – nanostructured materials 1035 quantum-well superlattices 1033 quasicrystals 34 QWIP (quantum well infrared photodetector) 1042

R Ra radium 68 radiant intensity Ie – radiometry 15

Subject Index

– poly(ethylene terephthalate) + polystyrene (PET + PS) 515, 519, 520 – poly(phenylene ether) + polyamide 66 (PPE + PA66) 517, 521 – poly(phenylene ether) + polystyrene (PPE + PS) 520, 521 – poly(styrene-co-butadiene) (PPE + SB) 517, 520, 521 – poly(vinyl chloride) + chlorinated polyethylene (PVC + PE-C) 515, 518 – poly(vinyl chloride) + poly(acrylonitrile-co-butadiene-coacrylester) (PVC + ASA) 515, 518 – poly(vinyl chloride) + poly(vinyl chloride-co-acrylate) (PVC + VC/A) 515, 518 – polycarbonate + liquid crystal polymer (PC + LCP) 515, 519, 520 – polycarbonate + poly(butylene terephthalate) (PC + PBT) 515, 519, 520 – polycarbonate + poly(ethylene terephthalate) (PC + PET) 515, 519, 520 – polypropylene + ethylene/propylene/diene rubber (PP + EPDM) 515, 516 – polysulfone + poly(acrylonitrile-cobutadiene-co-styrene) (PSU + ABS) 517, 521 polymer family 911, 936 polymer ferroelectrics 903 polymer matrix 1040 polymers 477 – abbreviations 482 – Charpy impact strength 478 – coefficient of expansion 478 – compressibility 478 – creep modulus 478 – crystallinity 477 – density 478 – elastic modulus 478 – electric strength 478 – enthalpy of combustion 477 – enthalpy of fusion 477 – entropy of fusion 477 – ferroelectric properties 905 – gas permeation 478 – glass transition temperature 477 – heat capacity 477 – impact strength 478

1111

1112

Subject Index

Subject Index

radiation sources and exposure techniques in lithography 1065 radiometric and photometric quantities 16 radiometry – intensity measurements 15 radium Ra – elements 68 radon Rn – elements 128 Raman scattering 906 Raman scattering spectroscopy 1040 Raman spectrum 908 RAS 997 Rayleigh mode 1012 Rb rubidium – elements 59 Re rhenium – elements 124 real and imaginary parts ε1 and ε2 of the dielectric constant see dielectric constant ε 602 – gallium compounds 637 reconstruction model 987 – solid surfaces 991 reconstruction of semiconductors 991 reconstruction of surface 986 – metals 987 recording media – arrays of magnetic dots 1061 reduced surface state energy 1022 reduced wave vector 1012 reduced-dimensional material geometries 1033 references – solid surfaces 1029 reflectance anisotropy spectroscopy (RAS) 1007 refractive index 478, 829, 946–972 – elements 48 – glasses 539, 543 – polymers 478 – Sellmeier dispersion formula 547 – temperature dependence 548 refractive index n 619 – boron compounds 610 – cadmium compounds 684 – gallium compounds 635 – group IV semiconductors and IV–IV compounds 601–603 – indium compounds 650 – mercury compounds 691 – zinc compounds 672 refractories

– boride-based 452 – carbide-based 458 – nitride-based 468 – oxide-based 438 – silicide-based 472 refractory ceramics 437 refractory metals 303 – alloys 303 compositions 305 dispersion-strengthened 304 – annealing 311 – chemical properties 308 – crack growth behavior 325 – creep elongation 316 – creep properties 327 – dynamic properties 318 – evaporation rate 307 – fatigue data 321 – flow stress 316 – fracture mechanics 322 – grain boundaries 314 – high-cycle fatigue properties 319 – linear thermal expansion 306 – low-cycle fatigue properties 320 – mechanical properties 314 – metal loss 308 – microplasticity 318 – oxidation behavior 308 – physical properties 306 – production routes 304 – recrystallization 311 – resistance against gaseous media 309 – resistance against metal melts 309 – specific electrical resistivity 307 – specific heat 307 – static mechanical properties 315 – stress–strain curves 320 – thermal conductivity 306 – thermomechanical treatment 314 – vapor pressure 307 – Young’s modulus 307 refractory metals alloys – application 306 – products 306 refractory production – raw materials 444 relative permittivity 478 – polymers 478 relaxation of semiconductors 991 relaxation of surface 986 – metals 987 relaxor 906, 909, 918 remanent magnetization 922 remanent polarization 918

residual resistance ratio (RRR) 397 residual resistivity ratio (RRR) 338 resistivity – gallium compounds 630 response of material 46 Rf rutherfordium 94 Rh rhodium – elements 135 RHEED (reflection high-energy electron diffraction) 990 rhenium Re – elements 124 rhodium – alloys 386 – applications 386 – chemical properties 392 – electrical properties 390 – magnetical properties 391 – mechanical properties 387 – optical properties 392 – phase diagrams 386 – production 386 – thermal properties 392 – thermoelectrical properties 391 rhodium Rh – elements 135 ribbon silicates 433 RIE (reactive ion etching) 1061 Rn radon 128 Rochelle salt 904 Rochelle salt family 932 rod-like molecule 942 RT (room temperature) 49 RTP (room temperaure and standard pressure) 49 Ru ruthenium 131 rubidium Rb – elements 59 ruthenium Ru – alloys 399 – applications 399 – chemical properties 402 – electrical properties 401 – elements 131 – lattice parameter 400 – magnetic properties 401 – mechanical properties 400 – optical properties 402 – phase diagrams 399 – production 399 – thermal properties 402 – thermoelectric properties 401 rutherfordium Rf – elements 94 RW (weighted sound reduction) 409

Subject Index

S

shape memory 298 – nickel 279 shape-memory alloys – TiNi 216 shear modulus 478 – elements 47 – polymers 478 shear rate 478 – polymers 478 SHG (second-harmonic generation) 825, 906 Shore hardness 478 – polymers 478 short pass filters – glasses 566 short-range order 39 – glasses 524 Shubnikov groups – crystallography 33 SI (Système International d’Unités) 3, 11 SI (the International System of Units) 12 SI base unit 13 SI definitions of magnetic susceptibility 48 SI derived units 16, 17 – with special names 17, 18 SI prefixes 19 Si silicon 88 SI units – base quantities 13 – base units 13 Si3 N4 ceramics 451 Si3 N4 powders 472 SiC ceramics 451 side group 943 sievert – SI unit of dose equivalent 19 silica – glasses 524 silicate 433 silicate based glasses 526 silicide 473 – physical properties 472 silicon – electromagnetic and optical properties 601 – electronic properties 589–594 – transport properties 598 silicon carbide – band structure 590 – crystal structure, mechanical and thermal properties 578–588 – electromagnetic and optical properties 601

Subject Index

S sulfur 108 SAE (Society of Automotive Engineers) 221 SAM (self-assembled monolayer) 944 samarium Sm – elements 142 SAW (surface acoustic wave ) 912 Sb antimony 98 SbSI family 922 Sc scandium 84 SC(NH2 )2 family 930 scandium Sc – elements 84 scattering – nanoscale objects 1048 scattering losses of a waveguide 1045 Schoenflies symbol 30 – elements 47 Schott AG 523 Schott code – glasses 544 Schott filter glasses – glasses 569 Schott glasses 8nnn 540, 541 SDR 997 Se selenium 108 seaborgium Sg – elements 114 sealing glasses 527 – glasses 559 second – SI base unit 14 secondary hardening 263 second-harmonic generation (SHG) 825, 906 second-order elastic constants see elastic constant 580 second-order phase transition 907 selenium Se – elements 108 Sellmeier dispersion formula – glasses 547 Sellmeier equations 826 SEM (scanning electron microscopy) 39 semiconductor 1003 – covalent 992 – field-effect mobility 1024 – III–V compounds 1004 – intrinsic Debye length 1021

– nanocrystal 1040 – polar 992 – quantum confinement 1036 – reconstruction 1004 – reconstruction model 991 – surface 990 – surface core level shift 1003 – surface Debye temperature 1017 – surface phonon 1017 – surface shift 1004 semiconductor band bending 1020 semiconductor nanostructures 1035 semiconductor surface – Fermi level pinning 1025 – ionization energy 1003 semiconductors – aluminium compounds 610 – boron compounds 604 – cadmium compounds 676 – chemical doping 576 – gallium compounds 621 – group IV semiconductors and IV–IV compounds 578–603 – III–V compounds 576, 604 – II–VI compounds 576, 652 – indium compounds 638 – introduction 575 – IV–IV compounds 576 – magnesium compounds 655 – mercury compounds 686 – oxides of Ca, Sr, and Ba 660 – physical properties 577 – table of contents 575 – zinc compounds 665 semi-solid metal processing (SSMP) 170 sensor – chemiresistor-type 1043 SF1 – optical glasses 551 SF11 – optical glasses 551 SF2 – optical glasses 551 SF6 – glasses 537, 548 – optical glasses 551 SF66 – optical glasses 551 SFG (sum frequency generation) 825 SFM (superfluorinated material) 975 Sg seaborgium 114

1113

1114

Subject Index

Subject Index

– electronic properties 589–594 – transport properties 595 silicon nitride 467 silicon Si – crystal structure, mechanical and thermal properties 578–588 – elements 88 silicon steels – grain-oriented 765 – non-oriented 763 silicon technology 1036 silicon-based lasers 1036 silicon–germanium alloys – band structure 590 – transport properties 601 silicon-germanium alloys – crystal structure, mechanical and thermal properties 578–588 – electromagnetic and optical properties 601 silicon–silicon oxide interface 1025 silver 330 – alloys 330 – application 330 – chemical properties 344 – crystal structures 333 – diffusion 342 – electrical properties 338 – intermetallic phases 333 – magnetic properties 339 – mechanical properties 335 – optical properties 341 – phase diagrams 331 – production 330 – ternary alloys 345 – thermal properties 340 – thermodynamic data 331 – thermoelectric properties 339 silver Ag – elements 65 simple perovskite-type oxide 909 single hysteresis loop 904 SiO2 – glasses 524 SK51 – optical glasses 551 Sm samarium – elements 142 smectic C∗ phase 934 smectic phase 942 Sn tin 88 SNR (signal-to-noise ratio) 1060 soda lime glasses 528, 529, 534 sodium Na

– elements 59 soft annealing 224 soft magnetic alloys 758 – nanocrystalline 776 soft magnetic materials – composite 759 – sintered 759 soft-mode spectroscopy 906 solar cell 1043 solder alloy 345 solder glasses 562 sol–gel synthesis – nanostructured materials 1065 solid material – structure 27 solid material, structure 27 solid surface energy 944 solid-state polymorphism 943 sorosilicate 433 sound velocity 478, 947–949, 956–962, 968–971 – elements 47 – polymers 478 source 1024 sp3 -bonded crystal 991 space charge function – solid surfaces 1022 space charge layer – semiconductor surface 1020 – solid surfaces 1020 space groups – crystallography 31 SPARPES 1011 speed of light – fundamental constant 13 spheroidal (nodular) graphite (SG) 268 spheroidite 223 spin accumulation 1049 spin diffusion length 1050 spin electronics – applications 1057 – nanostructured materials 1031, 1049 spin polarization 1055 – nanostructured materials 1049 spin valve multilayers 1052 spin valve read head – schematic diagram 1058 spin valve sensor 1053 spin-asymmetric material 1049 spinel structure – crystallography 33 spin-electronic switch 1055 spin–orbit splitting energy ∆so – aluminium compounds 617

– cadmium compounds 681 – gallium compounds 628 – group IV semiconductors and IV–IV compounds 593 – indium compounds 644 – mercury compounds 689 – zinc compounds 670 spintronics – nanostructured materials 1031, 1049 SPLEED 1011 spontaneous electric polarization 903 spontaneous polarization 917, 945 Sr strontium 68 Sr2 Nb2 O7 family 920 SRI (sound reduction index) 409 SrNb2 O7 family 909 SrTeO3 family 919 SrTiO3 913 stabilized zirconia (PSZ) 448 stacking faults – crystallography 41 stain resistance – optical glasses 550 stainless steels 240 – austenitic 252 – duplex 257 – ferritic 246 – martensitic 250 – martensitic-ferritic 250 standard electrode potential – elements 46 standard entropy – elements 47 standard temperature and pressure (STP) 46 Stark effect – nanostructured materials 1040 static dielectric constant 826 – elements 48 static dielectric constant 828–889 STC (sound transmission classification) 409 steam permeation 478 – polymers 478 steel – austenitic 259 – carbon 227 – ferritic 258 – ferritic austenitic 259 – hardening 237 – heat-resistant 258, 261 – high-strength low-alloy (HSLA) 240

Subject Index

– diamond-like 979 structure type – crystallography 33 Strukturbericht type 47 sublattice 903 sublattice polarization 904 submicrometer magnetic dots 1060 substituted mesogens (liquid crystals) – physical properties 968 sulfur S – elements 108 sum frequency generation (SFG) 825 superalloys – Ni-based cast 288 – nickel 294 superconducting high-Tc – crystal structure 712 superconducting oxides – high-Tc chemical composition 712 superconductivity – elements 48 superconductor 695 – borides 745 – borocarbides 746, 747 – carbides 745 – commercial Nb3 Sn 709 – critical temperature 699 – crystal structure 712 – Debye temperature 696 – device applications 719 – high-Tc cuprates 712, 713, 720 – industrial wire performance 719 – metallic 696 – Nb alloys 702 – non-metallic 712 – Pb alloys 696 – pinning 717 – practical metallic 704 – production Nb3 Sn 708 – Sommerfeld constant 696 – SQUIDs 720 – structural data 720 – thermodynamic properties 696 – Type I 695 – Type II 695 – V alloys 700 – vortex lines 717 – Y−Ba−Cu−O 723 supercooled liquid – glasses 524 supercooled mesophase 945 superstructures

– crystallography 41 supertwisted nematic (STN) effect 944 Supremax – glasses 527 surface – Curie temperature 1009 – diagram 979 – ionization energy 1003 – magnetic 1008 – semiconductor 990 – structure of an ideal 979 surface band structure 996 surface Brillouin zone (SBZ) 996 surface conductivity – solid surfaces 1024 surface core level shifts (SCLS) 998 – solid surfaces 1003, 1004 surface differential reflectivity (SDR) 1008 surface excess conductivity 1024 surface magnetization 1011 surface mobility 1024 surface of diamond 1004 surface phonon 1012 – dispersion 1019 – metal 1013 – mode 1012 surface plasmon – absorption of nanoparticles 1046 – dispersion curve 1001 surface resistivity 478 – polymers 478 surface resonance 996 – phonons 1012 surface response – dielectric theory 1007 surface state – acceptor 1022 – band 1005 – donor 1022 – transitions 1005 surface state bands – solid surfaces 1004 surface states 996 surface tension 948–950, 955–962, 968–971, 975 – elements 47 surface tension (γ LV ) 943 surfaces 979 surgical implant alloys – cobalt-based 277 susceptibility

Subject Index

– low-alloy carbon steel 227 – mechanical properties 237 – stainless 240 – tool 262 stibiotantalite family 909 stiffness constant see elastic constant 580 STM (scanning tunneling microscopy) 988, 992, 997 STM spectroscopy 1005 STN (supertwisted nematic) effect 944 STO (SrTiO3 ) 1056 storage capacity of hard disks 1048 storage density evolution of hard disk drives 1048 storage media 1060 – arrays of nanometer-scale dots 1060 – limits 1060 – technology 1060 storing information on the sidewalls of the dots 1062 strain – polymers 478 strength – glasses 534 stress 478 – polymers 478 stress at 50% strain (elongation) 478 – polymers 478 stress at fracture 478 stress at yield 478 – polymers 478 stress birefringence – glasses 539, 549 stress intensity factor – glasses 534 strong-confinement regime – nanostructured materials 1037, 1038 strontium oxide – crystal structure, mechanical and thermal properties 660 – electromagnetic and optical properties 664 – electronic properties 661 – transport properties 663 strontium Sr – elements 68 strontium titanate 913 structural parameters 990 structural phase transitions 906 structure

1115

1116

Subject Index

– magnetic 48 – mass 48 – molar 48 – nonlinear dielectric 825, 829 – second-order nonlinear dielectric 826 – third-order nonlinear dielectric 826 SV (spin valve) 1052 symmetry elements of point groups 30 synthesis of clusters – gas-phase production 1066 – nanostructured materials 1065 synthetic silica – glasses 557

T

Subject Index

T tritium 54 TA – phonon spectra 915 Ta tantalum 105 Ta-based alloys 318 tailoring of the electronic wave function 1032 tantalum Ta – elements 105 Tb terbium 142 TC 12 (Technical Committee 12 of ISO) 12 Tc technetium 124 Te tellurium 108 technetium Tc – elements 124 technical ceramics 437 technical coppers 297 technical glasses 527, 530 technical specialty glasses 526 tellurium Te – elements 108 TEM (transmission electron microscopy) 39 TEM image of a superlattice of Au clusters 1066 TEM views of single dots 1062 temper graphite (TG) 268 temperature dependence of carrier concentration – group IV semiconductors and IV–IV compounds 596 temperature dependence of electrical conductivity – indium compounds 647 temperature dependence of electronic mobilities

– indium compounds 649 temperature dependence of energy gap – indium compounds 645 temperature dependence of linear thermal expansion coefficient – cadmium compounds 677 – magnesium compounds 656 temperature dependence of the lattice parameters – group IV semiconductors and IV–IV compounds 580–582 temperature dependence of thermal conductivity – group IV semiconductors and IV–IV compounds 599, 600 – indium compounds 650 temperatures of phase transitions 946–976 tempering of steel 223 template synthesis 944 tensile strength – elements 47 tensor – elastooptic 826 – piezoelectric strain 826 terbium Tb – elements 142 terminal group 943 ternary alloys 298 terne steel coatings 415 TFT (thin-film transistor) 944 TGS family 932 Th thorium 151 thallium Tl – elements 78 thermal and thermodynamic properties – elements 46 thermal conductivity κ 478, 945, 947–949, 956, 958 – aluminium compounds 618 – cadmium compounds 682 – elements 46, 47 – gallium compounds 634 – group IV semiconductors and IV–IV compounds 599 – indium compounds 650 – magnesium compounds 659 – mercury compounds 690 – oxides of Ca, Sr, and Ba 663 – polymers 478 – zinc compounds 670 thermal expansion – glasses 526 thermal expansion coefficient, linear

– elements 47 thermal gap – indium compounds 645 thermal properties – group IV semiconductors 578–588 – III–V compounds 610, 621, 638 – III–V semiconductors 604 – II–VI compounds 652, 655, 660, 665, 676, 686 – IV–IV compound semiconductors 578–588 – technical glasses 533, 536 thermal vibrations – surface phonons 1012 thermal work function – elements 48 thermally activated flux flow (TAFF) 718 thermochromic material 944 thermodynamic properties – elements 47 thermoelectric coefficient – elements 48 thermoelectric power – oxides of Ca, Sr, and Ba 664 thermography 941, 944 thermomechanical treatment (TMT) 314 thermosets 481, 512 – diallyl phthalate (DAP) 512, 514 – epoxy resin (EP) 514, 515 – melamine formaldehyde (MF) 512, 513 – phenol formaldehyde (PF) 512, 513 – polymers 512 – silicone resin (SI) 514, 515 – unsaturated polyester (UP) 512–514 – urea formaldehyde (UF) 512, 513 thermotropic liquid crystal 942 thin film 906 thin-film transistor (TFT) 944 thixomolding 170 thorium Th – elements 151 three and four-ring systems – liquid crystals 964 three-dimensional long-range order 941 three-ring system 964 three-wave interactions – in crystals 825 thulium Tm – elements 142

Subject Index

– colored glasses 566, 567 transmission window – glasses 524 transmittance – glasses 548 transmittance of glasses – color code 549 transport properties – group IV semiconductors and IV–IV compounds 595–601 – III–V compounds 608, 617, 629, 647 – II–VI compounds 655, 659, 663, 670, 682, 689 transverse acoustic branch 915 transverse optical branch 915 transverse optical mode 906 triple point of water 48 tritium T – elements 54 truncated crystal 986 tungsten bronze-type family 909, 920 tungsten W – elements 114 tunnel junction – magnetic 1053 tunnel magnetoresistance – function of field and temperature 1057 tunnel magnetoresistance as a function of magnetic field 1055 tunneling – nanostructured materials 1053 tunneling mechanism – nanostructured materials 1043 twisted nematic (TN) effect 944 two-dimensional liquid 942 two-photon absorption coefficient 829 two-ring systems with bridges – liquid crystals 955 two-ring systems without bridges – liquid crystals 947 Type II superconductors – anisotropy coefficients 716 – coherence lengths 716 – high-Tc cuprate compounds 716 type metals 414

U U uranium 151 ultrahigh density storage media 1049, 1060

unalloyed coppers 296 uniaxial crystals 826 Unified Numbering System for Metals and Alloys (UNS) 296 unit cell of Si(111) 7 × 7 995 units – amount of substance 14 – atomic 21 – atomic units (a.u.) 22 – candela 15 – CGS units 21 – coherent set of 20 – crystallography 21 – electric current 14 – general tables 4 – length 13 – luminous intensity 15 – mass 14 – natural 21 – natural units (n.u.) 21 – non-SI 22 – non-SI units 20, 21 – other non-SI units 23 – temperature 14 – the international system of 11 – time 14 – used with the SI 20 – X-ray-related units 22 units of physical quantities – fundamental constants 3 units outside the SI 20 UNS (Unified Numbering System) 221 UPS 998 uranium U – elements 151 UTS – ultimate tensile strength 219

V V vanadium 105 van der Waals attraction 1019 vanadium V – elements 105 vertical nanomagnets 1062 vertical relaxation of metals 989 VFT (Vogel, Fulcher, Tammann) equation – glasses 533 Vicat softening temperature 477 – polymers 477 Vickers hardness – elements 47

Subject Index

Ti titanium 94 time-temperature-transformation (TTT) diagram 238 tin Sn – elements 88 titanates 450 titanium 206 – commercially pure grades 207 – creep behavior 208 – creep strength 210 – hardness 207 – high-temperature phase 206 – intermetallic materials 210 – phase transformation 206 – sponge 207 – superalloys 210 – titanium alloys 206 titanium alloys 209 – applications 209 – chemical composition 209 – chemical properties 213 – mechancal properties 213 – mechanical properties 209 – physical properties 213 – polycrystalline 213 – single crystalline 213 – thermal expansion coefficient 214 titanium dioxide – mechanical properties 450 – thermal properties 450 titanium oxide – phase diagram 206 titanium Ti – elements 94 Tl thallium 78 Tm thulium 142 TMR (tunnel magnetoresistance) 1054, 1055 TN (twisted nematic) – liquid crystals 944 TO 915 tool steels 262 torsional modulus – optical glasses 550 total losses 763 transformation temperature – glasses 524 transition range – glasses 524 transition temperature – glasses 525 transitions – surface states 1005 transmission spectra

1117

1118

Subject Index

Subject Index

vinylpolymers 480, 489–492 – poly(acrylonitrile-co-butadiene-costyrene) (ABS) 492–494 – poly(acrylonitrile-co-styrene-coacrylester) (ASA) 492–494 – poly(styrene-co-acrylnitrile) (SAN) 489, 490, 492 – poly(styrene-co-butadiene) (SB) 489–491 – poly(vinyl carbazole) (PVK) 492, 493 – polystyrene (PS) 489–491 VIP (viewing-independent panel) 975 viscosity 478, 948, 950–954, 963–965, 967, 968, 975 – dynamic 943 – elements 47 – glasses 524 – kinematic 943 – optical glasses 556 – polymers 478 – technical glasses 533 – temperature dependence 525 viscosity of glasses – temperature dependence 534 vitreous silica – electrical properties 557 – gas solubility 557 – glasses 526, 556 – molecular diffusion 557 – optical constants 557 vitreous solder glasses 562 Vitronit – glasses 559 volume compressibility – elements 47 volume magnetization – elements 48 volume of primitive cell – crystallographic formulas 986 volume resistivity 478 – polymers 478 volume–temperature dependence – glasses 524 VycorTM – glasses 527

W W tungsten 114 wavelength dependence of refractive index n – indium compounds 651

WDX (wavelength-dispersive analysis of X-rays) 39 weak-confinement regime – nanostructured materials 1037, 1038 wear-induced surface defects – glasses 535 Weibull distribution – glasses 535 weight fraction – glasses 527 Wood’s metal 420 work function Φ – metal 997 – solid surfaces 997 work hardening wrought copper alloys 300 wrought alloys 298 wrought magnesium alloys 164 wrought superalloys 284 wtppm (weight part per million) 407 Wyckoff position – crystallography 32

X Xe xenon 128 xenon Xe – elements 128 X-ray diffraction 39 X-ray interferences – crystallography 27

Y Y yttrium 84 Yb ytterbium 142 Young’s modulus 823 – elements 47 – optical glasses 550 YS – yield stress 219 ytterbium Yb – elements 142 yttrium Y – elements 84 Y−Ba−Cu−O – critical current density 733 – crystal defects 728 – crystal structure 723 – electric resistivity 730 – grain boundaries 730 – hole concentration 733 – lattice parameters 726 – lower critical field 734 – oxygen content 724

– pinning 735 – substitutions 725 – superconducting properties 731 – thermal conductivity 730 – transition temperature 733 – upper critical field 734

Z zeolites – nanostructured materials 1031, 1065 Zerodur® – glasses 558 – linear thermal expansion 558 zinc compounds – crystal structure, mechanical and thermal properties 665 – effective hole mass 670 – electromagnetic and optical properties 672 – electronic properties 668 – mechanical and thermal properties 665 – optical properties 672 – thermal properties 665 – transport properties 670 zinc oxide – crystal structure, mechanical and thermal properties 665 – electromagnetic and optical properties 672 – electronic properties 667 – transport properties 670 zinc selenide – crystal structure, mechanical and thermal properties 665 – electromagnetic and optical properties 672 – electronic properties 667 – transport properties 670 zinc sulfide – crystal structure, mechanical and thermal properties 665 – electromagnetic and optical properties 672 – electronic properties 667 – transport properties 670 zinc telluride – crystal structure, mechanical and thermal properties 665 – electromagnetic and optical properties 672 – electronic properties 667 – transport properties 670

Subject Index

zinc Zn – elements 73 zircaloy 219 – irradiation effect 219 zirconium – alloys 217

– bulk glassy alloys 218 – bulk glassy behavior 220 – low alloy materials 217 – nuclear applications 218 – technically-pure materials 217 zirconium dioxide 448

1119

zirconium Zr – elements 94 ZLI-1132 – liquid crystals 975 Zn zinc 73 Zr zirconium 94

Subject Index

1120

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Springer Handbook of Condensed Matter and Materials Data Organization of the Handbook

Part 1 covers the fundamentals of the physics of condensed matter. Fundamental physical constants are qualitatively described and recently recommended numerical values are presented. A short review of The International System of Units (SI) is given and the concepts of base physical quantities and derived physical quantities on which the SI is founded is explained. A number of non-SI units which are still in use are also discussed. Periodic solids are used to introduce basics of modern crystallography.

Part 1 General Tables 1 The Fundamental Constants 2 The International System of Units (SI), Physical Quantities, and Their Dimensions 3 Rudiments of Crystallography

Part 2 The Elements provides tables of the physical and physicochemical properties of the elements. Emphasis is placed on properties of the elements in the condensed state. Most of the tables deal with the properties of elements of one particular group of the Periodic Table. Only the elements of the first period, the lanthanides, and the actinides are arranged according to the periods. This synoptic representation is intended to provide a transparent overview of the trends in the data.

Part 2 The Elements 1 The Elements

Part 3 Classes of Materials starts with the selective treatment of metals that are applied as base and alloying elements of metallic materials. The next class of materials discussed are ceramics. Detailed groupings and definitions of technical ceramics are given and traditional ceramics and cements, silicate ceramics, refractory ceramics, oxide ceramics, and nonoxide ceramics are treated. The physical and physicochemical properties of those polymers, copolymers, and polymer blends which are widely used for scientific applications and in industry are described in the next chapter. The last chapter serves as a source of data and commercial product information on glasses as engineering materials of practical importance.

Part 3 Classes of Materials 1 Metals 2 Ceramics 3 Polymers 4 Glasses

Part 4 covering functional materials is organized in a two-step approach. The first step corresponds to searching for the substance of interest, that is, the relevant group of substances. The second step corresponds to the physical property of interest. Materials covered are semiconductors, superconductors, magnetic materials, dielectrics and electrooptics, and ferro- and antiferroelectrics.

Part 4 Functional Materials 1 Semiconductors 2 Superconductors 3 Magnetic Materials 4 Dielectrics and Electrooptics 5 Ferroelectrics and Antiferroelectrics

Part 5 covers special structures such as liquid crystals, solid surfaces and mesoscopic and nanostructured materials. The chapter on liquid crystals covers physical properties of the most common liquid crystalline substances as well as some liquid crystalline mixtures. Data compiled in the chapter on solid surfaces refer to atomically clean and well characterized surfaces. The values reported are mainly averages from different authors where reference to the original papers is made. In the chapter on nanostructured materials emphasis is placed on size and confinement effects. The properties associated with electronic confinement are addressed and particular attention is drawn to semiconductor-doped matrices. The two main applications of nanostructured magnetic materials, spintronics and ultrahigh-density data storage media, are also treated.

Part 5 Special Structures 1 Liquid Crystals 2 The Physics of Solid Surfaces 3 Mesoscopic and Nanostructured Materials

Periodic Table of the Elements IUPAC Notation CAS Notation Atomic Number Element Symbol

18 VIIIA

2

He

Unstable Nuclei

Main Groups 1 IA

1

2 IIA

13 IIIA

14 IVA

15 VA

16 VIA

17 VIIA

2

H

3

4

Li

11

19

37

55

87

12

Na

38

Rb

56

Cs

88

Fr

13

Mg

20

K

5

Be

31

Ca

49

Sr

14

Al

32

Ga

50

In

81

Ba

6

B

82

Tl

7

C

15

Si

51

Sn

83

Pb

84

Bi

35

Se

52

Sb

17

S

34

As

9

O

16

P

33

Ge

8

N

53

Te

85

Po

10

F

18 VIIIA

Shells

He

K

Ne

K–L

Ar

K–L–M

Kr

–L–M–N

Xe

–M–N–O

Rn

–N–O–P

18

Cl

36

Br

54

I

86

At

–O–P–Q

Ra

Subgroups 3 IIIB

21

39

57

89

4 IVB

22

Sc

40

Y

72

La

5 VB

23

Ti

41

Zr

73

Hf

104

Ac

V Nb Ta

105

Rf

Db

6 VIB

24

Cr

42

Mo

74

W

106

Sg

7 VIIB

8 VIII (1)

25

26

Mn

43

75

44

Tc

76

Re

107

27

Fe

45

Ru

Co Rh

77

Os

108

Bh

9 VIII (2)

Ir

109

Hs

Mt

10 VIII (3)

28

46

Ni Pd

78

Pt

110

Ds

11 IB

29

47

79

30

Cu

48

Ag

80

Au

111

12 IIB

Shells

Zn

–L–M–N

Cd

–M–N–O

Hg

–N–O–P

112

Rg

–O–P–Q

Lanthanides (Shells –N–O–P) 58

59

90

91

Ce

Pr

60

Nd

61

Pm

62

Sm

63

Eu

64

65

66

67

68

69

70

71

96

97

98

99

100

101

102

103

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Actinides (Shells –O–P–Q)

Th

Pa

92

U

93

Np

94

Pu

95

Am

Cm

Bk

Cf

Es

Fm

Md

No

Lr

Most Frequently Used Fundamental Constants CODATA Recommended Values of Fundamental Constants Quantity

Symbol and relation

Numerical value

Unit

Relative standard uncertainty

Speed of light in vacuum

c

299 792 458

m/s

Fixed by definition

Magnetic constant

µ0 = 4π × 10−7

12.566370614 . . . × 10−7

N/A2

Fixed by definition

Electric constant

ε0 = 1/(µ0 c2 )

8.854187817 . . . × 10−12

F/m

Fixed by definition

Newtonian constant of gravitation

G

6.6742(10) × 10−11

m3 /(kg s2 )

1.5 × 10−4

Planck constant

h

4.13566743(35) × 10−15

eV s

8.5 × 10−8

Reduced Planck constant

~ = h/2π

6.58211915(56) × 10−16

eV s

8.5 × 10−8

Elementary charge

e

1.60217653(14) × 10−19

C

8.5 × 10−8

Fine-structure constant

α = (1/4πε0 )(e2 /~c)

7.297352568(24) × 10−3

Magnetic flux quantum

Φ0 = h/2e

2.06783372(18) × 10−15

Wb

8.5 × 10−8

Conductance quantum

G 0 = 2e2 /h

7.748091733(26) × 10−5

S

3.3 × 10−9

Rydberg constant

R∞ = α2 m e c/2h

10 973 731.568525(73)

1/m

6.6 × 10−12

Electron mass

me

9.1093826(16) × 10−31

kg

1.7 × 10−7

Proton mass

mp

1.67262171(29) × 10−27

kg

1.7 × 10−7

Proton–electron mass ratio

m p /m e

1836.15267261(85)

4.6 × 10−10

Avogadro number

NA , L

6.0221415(10) × 1023

1.7 × 10−7

Faraday constant

F = NA e

96 485.3383(83)

C

8.6 × 10−8

Molar gas constant

R

8.314472(15)

J/K

1.7 × 10−6

Boltzmann constant

k = R/NA

1.3806505(24) × 10−23 8.617343(15) × 10−5

J/K eV/K

1.8 × 10−6 1.8 × 10−6

Josephson constant

K J = 2e/h

483 597.879(41) × 109

Hz/V

8.5 × 10−8

von Klitzing constant

RK = h/e2 = µ0 c/2α

25 812.807449(86)

Ω

3.3 × 10−9

Bohr magneton

µB = e~/2m e

927.400949(80) × 10−26 5.788381804(39) × 10−5

J/T eV/T

8.6 × 10−8 6.7 × 10−9

Atomic mass constant

u = (1/12)m(12 C) = (1/NA ) × 10−3 kg

1.66053886(28) × 10−27

kg

1.7 × 10−7

Bohr radius

a0 = α/4πR∞ = 4πε0 ~2 /m e e2

0.5291772108(18) × 10−10

m

3.3 × 10−9

Quantum of circulation

h/2m e

3.636947550(24) × 10−4

m2 /s

6.7 × 10−9

3.3 × 10−9

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System requirements: · Windows 95/98/ME 32 MB RAM, Windows NT 4/2000/XP 64 MB RAM · MAC OS 9 or higher, 64 MB RAM, 333 MHz recommended · LINUX Pentium I /166 MHz, 64 MB RAM