Intermetallics Research Progress

INTERMETALLICS RESEARCH PROGRESS INTERMETALLICS RESEARCH PROGRESS YAKOV N. BERDOVSKY EDITOR Nova Science Publishers...

Author: Yakov N. Berdovsky

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INTERMETALLICS RESEARCH PROGRESS

INTERMETALLICS RESEARCH PROGRESS

YAKOV N. BERDOVSKY EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2008 by Nova Science Publishers, Inc.

All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com

NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS.

Library of Congress Cataloging-in-Publication Data Intermetallics research progress / Yakov N. Berdovsky, editor. p. cm. ISBN-13: 978-1-60692--4 1. Intermetallic compounds. 2. Alloys. I. Berdovsky, Yakov N. TA483.I68 2007 620.1'6--dc22 2007034989

Published by Nova Science Published by Nova Science Publishers, Publishers, Inc. ;Inc. New YorkNew York

CONTENTS Preface

vii

Chapter 1

High Temperature Corrosion of Intermetallics Zhengwei Li and Wei Gao

Chapter 2

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds Igor S. Golovin

Chapter 3

Nonstoichiometric Compounds V. P. Zlomanov and A. Ju. Zavrazhnov

Chapter 4

Semiconducting Intermetallic Compounds ---with Special Interest in Silicides and Related Compounds Yoji Imai

1

65 135

175

Chapter 5

Ductile, Stoichiometric B2 Intermetallics Alan M. Russell

213

Chapter 6

Ultra Slow Dynamics in Intermetallic Thin Films Marcus Rennhofer

237

Chapter 7

Crystallization Behavior and Magnetic Properties of Fe-Based Bulk Metallic Glasses Mihai Stoica, Stefan Roth, Jürgen Eckert and Gavin Vaughan

Index

261

279

PREFACE Intermetallics is concerned with all aspects of ordered chemical compounds between two or more metals and notably with their applications. This book covers new and important research on the crystal chemistry and bonding theory of intermetallics; determination and analysis of phase diagrams; the nature of superlattices, antiphase domains and order-disorder transitions; the geometry and dynamics of dislocations and related defects in intermetallics; theory and experiments relating to flow stress, work-hardening, fatigue and creep; reponse of deformed intermetallics to annealing; magnetic and electrical properties of intermetallics; structure and properties of grain and interphase boundaries; the effect of deviations from stoichiometry on physical and mechanical properties; crystallization of intermetallics from the melt or amorphous precursors. Chapter 1 - Intermetallic compounds can be simply defined as ordered alloy phases formed between two or more metallic elements. These materials have different crystal structures from those of the constituent metallic components and exhibit as long-range ordered superlattices. Their relatively low density, high melting point, high specific strength and due ductility make them the promising high temperature structural materials for aviation and aerospace applications. Among the big family of intermetallics, Fe-Al, Ni-Al and Ti-Al systems are attracting most of the attention. The objective of studies is to develop and utilize these intermetallic compounds as a type of important structural material whose overall properties is between nickel-based superalloys and advanced ceramics. However, a balance cannot always be achieved between mechanical and environmental properties. For example, iron aluminides have excellent resistance against oxidation and hot corrosion, however, their strength is relatively low. The higher specific strength and modulus than conventional Ni-based superalloys make Ti-Al intermetallic compounds of interest for aero-engine components, but the oxidation resistance of Ti-containing intermetallics is much lower than desirable; thus a key factor in increasing the maximum temperature in service is enhancing their oxidation and hot corrosion resistance while maintaining the excellent mechanical properties. This chapter is then intended to give an overview on the major efforts made over the last 20 years on high temperature oxidation and protection of intermetallic compounds including Fe-Al, Ni-Al and Ti-Al. In particular, the focus will be given to Ti-Al systems. After a general introduction on the structural and mechanical properties, the studies on the oxidation behaviors of these intermetallic compounds will be summarized based on the experimental observation reported in open literature. The emphasis will be put on the effects of alloying

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element, microstructure and coating/surface treatment. It should also be noted that only high temperature oxidation properties in air or oxygen will be addressed; no discussion on hot corrosion, carburization, nitridation and sulfidation. In the concluding remarks, the prospects of development and application for intermetallic compounds will be briefly discussed. Chapter 2 - A short introduction into anelastic behaviour of metallic materials is given, and a method of mechanical spectroscopy is introduced for better understanding of relaxation and hysteretic phenomena discussed in this chapter. Several examples of anelasticity due to different structural defects in disordered Fe-based alloys (Fe-Al, Fe-Ge, Fe-Si) are considered with special emphasis on the analyses of the carbon Snoek-type relaxation with respect to ‘carbon - substitute atom’ interaction in iron. The effect of ordering of substitute atoms on anelasticity in Fe-based alloys is analysed in terms of substitute atom content and type of order. Anelastic behaviour of iron-based D03 (e.g. Fe3Al) and D019 (e.g. Fe3Ge) intermetallic compounds is reported for a wide range of temperatures and vibrating frequencies to identify damping mechanism. Contribution from interstitial and substitute atoms, dislocations and vacancies in ternary iron-aluminium based alloys Fe-Al-Me (Me = metal: Co, Cr, Ge, Mn, Nb, Si, Ta, Ti, Zr) are analysed. Study of elastic and anelastic behaviour is supported by structural characterisation (XRD, TEM, DSC, magnetometry) of studied alloys, also considering sources for high damping capacity of some compositions. The following anelastic phenomena are found in studied alloys and discussed in this chapter: the Snoek-type (caused by interstitial atom jumps in Fe-Me ferrite) and the Zener (caused by reorientation of pairs of substitute atoms in iron) relaxation, the vacancy and dislocation related relaxations, amplitude dependent magneto-mechanical damping. A family of low-temperature internal friction peaks recorded due to self interstitial atoms in ultra fine grained intermetallics is used to characterise thermal stability of severely deformed (Fe,Me)3Al compounds. These effects are discussed using data available from literature and the author’s experimental data in the Hz and kHz ranges of vibrating frequencies for Fe-Al, Fe-Ge, Fe-Si binary and several ternary systems in disordered and ordered ranges of the phase diagrams including intermetallic compounds of Fe3Me type. Chapter 3 - A key issue in materials research is the preparation of semiconducting solid, intermetallic and other nonstoichiometric compounds with predetermined composition, structure, and, hence, properties. In connection with this, this paper scrutinizes the concepts of stoichiometry, nonstoichiometry, and deviation from stoichiometry and the use of phase diagrams in selecting conditions for the synthesis of nonstoichiometric compounds. Since nonstoichiometry and properties of compounds are associated with defects, attention is also paid to defect classification and formation. The behavior of defects in solid oxides, chalcogenides, carbides, and other compounds of transition metals ranges from the point defect regime, controlled by entropy, to the enthalpy-controlled regime. To develop an appropriate theory of nonstoichiometric compounds, it is then necessary to address crystalchemical and thermodynamic issues. This paper is also concerned with the defect structure of highly imperfect nonstoichiometric compounds with a broad homogeneity range: the concepts of defect and structural transition due to defect interactions and temperature effect. The thermodynamic aspect of the problem includes criteria for evaluating the stability of imperfect nonstoichiometric solids. It is considered the specifics of the concepts of existing, stable, and metastable phases, spinodal decomposition conditions, and issues associated with phase equilibria in homologous series of compounds with narrow homogeneity ranges. The

Preface

ix

paper also deals with synthesis methods and criteria for evaluating the homogeneity of nonstoichiometric solids. Chapter 4 - A growing number of B2 intermetallic compounds has been reported to exhibit high room temperature tensile ductility in the polycrystalline form when tested in normal room air at ambient temperature. These are noteworthy findings, since poor room temperature ductility and low fracture toughness are major impediments to wider engineering use of intermetallic compounds [1]. Most intermetallic compounds can achieve high tensile ductility at room temperature only by means of one or more “contrivances”, such as testing single crystals, testing in an ultra-dry atmosphere, testing specimens with a metastable disordered crystal structure, or testing compositions that are off-stoichiometry or to which third elements have been added. The first of these inherently ductile compounds, AgMg, was reported in the early 1960’s to have good room temperature tensile ductility without the need for any of these contrivances. A few years later, even greater room temperature ductility was reported for another B2 compound, AuZn. Within the past few years, similar reports have been made for B2 CoZr and a large family of rare earth B2 intermetallics (DyCu, YAg, YCu, and several others). Most of these compounds share several common characteristics: substantial differences in the atomic radii and electronegativities of the two constituent elements; existence in the binary equilibrium phase diagram as a Daltonide, line-compound with no perceptible deviation allowed from precise equimolar stoichiometry; the absence of stressinduced twinning or shape-memory-type phase transformations; and a positive temperature dependence of yield strength above room temperature. This chapter describes the experimental findings reported for these materials; the factors thought to contribute to their high ductility; the commonly observed yield strength maxima at elevated temperatures; the strain aging effects seen in some of these materials; the potential applications these materials may have; and the possibilities that “lessons learned” from their study may suggest ductilizing strategies that could be applied to other intermetallic compounds. Chapter 6 - Diffusion studies on the mesoscopic and macroscopic scale were done up to now via radiotracer technique for a wide range of diffusivities. Nevertheless, the resolution of diffusion depths is limited by the detector efficiencies and sputtering resolving power. On the other hand scattering methods with atomic resolution like quasielastic Mössbauer spectroscopy, nuclear resonant scaterring and quasielastic neutron scattering have very limited range of accessible diffusion coefficients, especially for slow diffusion at low temperatures. The authors advantageously applied grazing incidence nuclear resonant scattering (GINRS) of synchrotron radiation for the study of iron self-diffusion in technically most promising intermetallic thin films (L10-FePt, L10-FePd and B2-FeSi). The investigations are non-destructive and non-contaminating. It is possible to measure very low . The diffusion coefficients accessible rates of diffusion of about for investigation can be tuned in a certain range. The application of GINRS gives no direct access to jump frequencies and jump vectors of the diffusing atoms. Nevertheless, combining the method with results from "order-order" dynamics or Monte Carlo simulations allows the determination of the diffusion model. Chapter 7 - The expression “glass” in its original sense refers to an amorphous or noncrystalline solid formed by continuous cooling of a liquid, while a solid is defined somewhat arbitrarily as any body having a viscosity greater than 1014 Pa·s. A glass lacks three-

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dimensional atomic periodicity beyond a few atomic distances. It is characterized by a limited number of diffuse maxima in X-ray, electron and neutron diffraction and no sharp diffraction contrast in high-resolution electron microscopy. The glass-forming tendency varies widely. Some oxide mixtures form a glass at normal slow cooling rates of ~1 K/min, while monoatomic metals with possible incorporation of impurities require rates as high as ~1010 K/s. During the solidification no essential change in spatial atomic configuration occurs. A glass may be considered as a solid with frozen-in liquid structure. It is in general not in an internal equilibrium state and thus relaxes structurally to a more stable equilibrium state whenever atoms attain an appreciable mobility. Furthermore, a glass is metastable with respect to crystalline phase(s) and transforms to the latter upon heating through nucleation and growth. As a result of the requirement for rapid cooling, amorphous alloys have usually been prepared in form of thin sheets with a thickness below 0.1 mm. In the last 10-15 years it was found that a number of transition metal-based alloy systems may form bulk metallic glasses (BMGs). These alloys require much lower cooling rates for amorphization or bypassing crystallization upon cooling. Fe-, Co- or Ni- based metallic glasses are good candidates for application as soft magnetic materials because of the lack of crystal anisotropy. Fe-based alloys able to form magnetic BMGs are of the type transition metal – metalloid and often contain 5 or more elements. Usually, the metalloid content is around 20 at.%. In some cases, the magnetic properties of such BMGs can be enhanced by partial devitrification upon heating at a constant rate or by isothermal annealing. The change in magnetic properties is due to structural changes induced upon heating/annealing. Usually, the Fe-based BMGs form intermetallic metastable phases at elevated temperatures, which finally transform into crystalline stable phases if the heating goes further. Despite several studies published in the literature about Fe-based BMGs and their magnetic properties, just few of them deal with crystallization behavior and crystallization kinetics. The aim of this work is to present the crystallization behavior of some Fe-based BMGs and to link the structural changes with modification of the magnetic properties.

In: Intermetallics Research Progress Editor: Yakov N. Berdovsky, pp. 1-64

ISBN: 978-1-60021-982-5 © 2008 Nova Science Publishers, Inc.

Chapter 1

HIGH TEMPERATURE CORROSION OF INTERMETALLICS Zhengwei Li and Wei Gao Department of Chemical and Materials Engineering, The University of Auckland, Private Bag 92019, Auckland, New Zealand

ABSTRACT Intermetallic compounds can be simply defined as ordered alloy phases formed between two or more metallic elements. These materials have different crystal structures from those of the constituent metallic components and exhibit as long-range ordered superlattices. Their relatively low density, high melting point, high specific strength and due ductility make them the promising high temperature structural materials for aviation and aerospace applications. Among the big family of intermetallics, Fe-Al, Ni-Al and Ti-Al systems are attracting most of the attention. The objective of studies is to develop and utilize these intermetallic compounds as a type of important structural material whose overall properties is between nickel-based superalloys and advanced ceramics. However, a balance cannot always be achieved between mechanical and environmental properties. For example, iron aluminides have excellent resistance against oxidation and hot corrosion, however, their strength is relatively low. The higher specific strength and modulus than conventional Ni-based superalloys make Ti-Al intermetallic compounds of interest for aero-engine components, but the oxidation resistance of Ti-containing intermetallics is much lower than desirable; thus a key factor in increasing the maximum temperature in service is enhancing their oxidation and hot corrosion resistance while maintaining the excellent mechanical properties. This chapter is then intended to give an overview on the major efforts made over the last 20 years on high temperature oxidation and protection of intermetallic compounds including Fe-Al, Ni-Al and Ti-Al. In particular, the focus will be given to Ti-Al systems. After a general introduction on the structural and mechanical properties, the studies on the oxidation behaviors of these intermetallic compounds will be summarized based on the experimental observation reported in open literature. The emphasis will be put on the effects of alloying element, microstructure and coating/surface treatment. It should also

2

Zhengwei Li and Wei Gao be noted that only high temperature oxidation properties in air or oxygen will be addressed; no discussion on hot corrosion, carburization, nitridation and sulfidation. In the concluding remarks, the prospects of development and application for intermetallic compounds will be briefly discussed.

1. INTRODUCTION Intermetallic compounds can be simply defined as ordered alloy phases formed between two or more metallic elements. These materials have different crystal structures from those of the constituent metallic components and exhibit as long-range ordered superlattices. In comparison with conventional metallic materials, intermetallic compounds have the advantages of low density, high melting point, high specific strength and due ductility, which make them the promising high temperature structural materials for automobile, aviation, and aerospace applications. The ordered nature of intermetallic compounds also exhibits attractive high temperature properties due to the presence of long-range-ordered superlattices, which reduce dislocation mobility and diffusion processes at elevated temperatures [1]. Aluminide based intermetallics are distinctly different from conventional solid-solution alloys. For example, Ni3Al exhibits an increase in yield strength with increasing temperature, whereas conventional alloys exhibit a general decrease in strength with temperature [2-3]. Nickel and iron aluminides also possess sufficiently high concentration of aluminium, thus the formation of a continuous and adherent alumina scale on the external surface of the material could always be achieved. In contrast, most of the alloys and superalloys capable of operating above 700oC in oxygen-containing environments contain less than 2wt.% aluminium, and invariably contain high concentration of chromium for oxidation protection with chromia. Nickel and iron aluminides therefore could provide excellent oxidation resistance at temperatures ranging from 1100 to 1400oC owing to their high aluminium contents and high melting points [4]. Among the big family of intermetallic compounds, Fe-Al, Ni-Al and Ti-Al systems are attracting most of the attention; and the objective of studies is to develop and utilize these intermetallic compounds as a type of important structural materials whose overall properties will be between nickel-based superalloys and advanced ceramics. However, a balance cannot always be achieved between their mechanical and environmental properties. For example, iron aluminides have excellent resistance against oxidation and hot corrosion, however, their strength is relative low. The higher specific strength and modulus than conventional Ni-based superalloys make Ti-Al intermetallic compounds of interest for aero-engine components, but the oxidation resistance of Ti-containing intermetallics is much lower than desirable at elevated temperatures. Thus a key factor for Ti-Al based intermetallics in increasing the maximum temperature in service is to enhance their oxidation and hot corrosion resistance while maintaining the excellent mechanical properties.

High Temperature Corrosion of Intermetallics

3

2. IRON ALUMINIDES 2.1. Introduction Due to their excellent oxidation resistance first noted in 1930s [5-6], iron alumindes have been subjected to extensive studies with respect to structural and functiuonal applications [7]. Iron aluminide with an Al content around 25at.% corresponds to Fe3Al, which exists in DO3 structure and is stable in the compositions ranging from 22 to 36at.% Al and from room temperature to about 550oC [8]. Above 550oC, the DO3 structure transforms to an imperfectly ordered B2 structure, which ultimately changes to a disordered solid solution. In addition to their superior environmental resistance (oxidation and sulfidation), iron aluminides also offer the advantages of low material cost, conservation of strategic elements, and a lower density in comparison with stainless steels. Therefore they have long been considered for applications in the petrochemical industries, conventional power plants, coal conversion plants, automobile and other industrial valve components, catalytic converter substrates and components for molten salt applications [9-10]. However, limited ductility at room temperatures, a sharp drop in strength above 600oC, and inadequate high temperature creep resistance render their acceptance for structural applications [11-12]. Elements such as Nb, Cu, Ta, Zr, B and C were considered for precipitation strengthening; while Cr, Ti, Mn, Si, Mo, V and Ni were added into iron aluminides for solid solution strengthening. In general, the addition of elements either for precipitation strengthening or solid solution strengthening to improve high temperature tensile strength and creep resistance resulted in low room temperature tensile elongations [13-25]. Chromium was found to be an effective addition to enhance the ductility of iron aluminides at higher aluminium contents, and a combination of alloying elements might lead to the optimization of overall mechanical properties. Iron aluminide with an Al content ranging from 36 to 50 at.% corresponds to FeAl with a B2 structure at room temperature. FeAl intermetallic alloys are lower in density by as much as 30 to 40%, compared with steels and other commercial Fe-based alloys. Due to their much higher Al contents, they all exhibit much better corrosion and high temperature oxidation resistance than Fe3Al and other conventional Fe-based alloys. However, associated with their intrinsic grain-boundary weakness and high environmental embrittlement sensitivity, they suffer from low room temperature ductility. Their mechanical properties, such as yield strength, fracture strength, creep strength, ductility and toughness could be improved by alloying (B, Zr, Hf etc), by heat terement and/or thermomechanical processing through microstructural control, and/or by composite development using fine oxide dispersions [2644]. High temperature oxidation resistance of metallic materials relies essentially on the formation of a slow-growing and mechanically-stable external Al2O3, Cr2O3 or SiO2 scale on their surface. Studies on the phase stabilities in the Fe-Al-O system demonstrate that Al2O3 will form on iron aluminides even at extremely low oxygen partial pressures. In practice, it has been found that approximately 15at.% Al is needed to suppress internal oxidation and overgrowth of the alumina scale by iron oxides at 800oC [45]. Obviously, the Al content in Fe3Al, FeAl and derived alloys are well in excess of this critical concentration; and as expected, alumina can form readily at temperatures above approximately 500oC upon exposure to oxidizing environments [46-48]. This alumina scale can provide superior

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Zhengwei Li and Wei Gao

corrosion resistance to iron aluminides not only in air or oxygen, but also under a variety of mixed gas and salt conditions. However, under real corrosion conditions, the protecvitity of this alumina scale will be dependent on its rate of formation and growth, its uniformity, and more importantly its adherence to the underlying alloys when undergoing thermal cycling. It is well known that alumina has many thermal stable and metastable phase structures. The predominant oxide formed on iron aluminides below 900oC is found to be γ- or θ-Al2O3, while α-Al2O3, the most thermaldynamically stable phase, forms after oxidation at temperatures higher than this level [46, 49-50]. The addition of Cr to Fe-Al based alloys can decrease the critical Al concentration for the formation of pure Al2O3 and reduce the oxidation rate of alloys containing less than 19.5at.% Al [51]. However, for iron aluminides (Fe3Al and FeAl) with quite high Al contents, air oxidation behaviour might not be dramatically affected by the addition of Cr [52].

2.2. Oxidation of Fe3Al and Its Alloys Alloying Fe3Al with additional elements can modify its mechnical properties as well as its oxidation behaviours. For example, it was found that an addition of Cr might decrease the oxidation and sulfidation resistance of Fe3Al based alloys [48, 53-54]. Similarly, the addition of Ti, V and/or Mo degrades their oxidation resistance in air. However, it has been found that additions of small amount of reactive elements, such as Zr and Y, could generally result in improved high temperature oxidation resistance of Fe3Al based alloys [52]. In the following sections, the influences of various alloying elements on the oxidation behaviours of Fe3Al and its alloys will be briefly summarized.

2.2.1. Effect of Cr The mechanical properties of Fe3Al can be improved most efficiently by adding 2-6at.% Cr, together with thermomechanical treatment [55-57]. Babu et al. studied the influences of Cr on the high temperature oxidation resistance of Fe3Al in oxygen [58]. They found that Cr addition increased the mass gain during the initial oxidation stage, which was supposed to be the result of the formation of chromia in this stage or the faster θ → α transformation favored by hexagonal chromia. Tortorelli and DeVan also observed that addition of Cr, even at concentrations as high as 10at.%, was detrimental to the oxidation resistance of Fe3Al between 800 and 900oC [48]. This was due to a faster oxygen uptake during initial stages, leading to overall higher parabolic constants. Velon et al. evaluated the role of Cr during the early stages of oxidation of Fe3Al containing 2 and 4 at.% Cr in dry air at 500oC [59], they concluded that the addition of 2 and 4% Cr increases the oxide growth rate of Fe3Al. At 500oC and low Cr content, the oxides, Cr2O3 and Al2O3, having the same corundum structure form a complete solid solution. It is therefore suggested that Cr2O3 forms a mixed oxide with Al2O3 by substitution of Al3+ by Cr3+. The oxidation resistance of Fe3Al at 500oC is then lost by the breakdown of the protecting properties of the continuous alumina layer because of the presence of Cr, leading to a faster diffusional transport of Fe ions through the mixed oxide (Al,Cr)2O3 layer compared to pure Al2O3 and growth of Fe oxides at the surface. Lee et al. also studied the oxidation Fe3Al containing 0, 2, 4 or 6at.% Cr at 1000oC in air [60]. The oxidation rate increased in the order of Fe28Al, Fe28Al6Cr, Fe28Al2Cr and Fe28Al4Cr. Cr


5

therefore was not beneficial to oxidation resistance. The oxide scales that formed on Fe3Al-Cr alloys consisted primarily of α-Al2O3 containing a small percentage of Fe and less than 1% of Cr. The higher Fe concentration and the alloying with Cr are expected to give more foreign ion contamination in the alumina scale, leading to a higher growth rate. These scales were also non-adherent and fragile.

2.2.2. Effect of Ti An addition of Ti to Fe3Al could significantly affect the DO3-B2 transition temperature and change the phase fields as well as the thermal anti-phase boundary microstructure [6165]. Studies also indicated that Ti addition has prounced effects on the mechanical, trobological and aqueous corrosion properties of Fe3Al based alloys [66-72]. High temperature oxidation study showed that the parabolic rate constant of the Ti-bearing Fe3Al alloy was higher than that of unalloyed Fe3Al [58]. The presence of Ti influenced the initial oxidation stage and acted as a getter for oxygen since the free energy for the formation of Ti oxide is more negative than that of Fe. The oxide scale was adherent and composed of equiaxed grains and some nodules. The surface oxide predominantly contains Al with a small amount of Ti and traces of Fe, while the nodules contain a large amount of Ti, certain amount of Al and trace of Fe. The enhanced scale adherence by Ti alloying however was not clear. 2.2.3. Effect of carbon Iron aluminides produced recently by an electroslag-remelting process (ESR) were found to have improved strength when carbon was added as an alloying element [73-74]. This has been attributed to solid solution strengthening by the interstitial carbon atoms at low concentrations and precipitation hardening at high concentrations of carbon atoms. These alloys were further shown to exhibit a reduced susceptibility to environmental embrittlement. The authors have attributed the reduced susceptibility to the presence of carbides in the aluminides, although no study has been undertaken to examine the role of carbides. The effect of carbon on the oxidation behavior of Fe3Al alloys in the temperature range 700-1000oC in air has also been investigated by these authors [75-77]. In general, carbon is very detrimental to oxidation resistance of Fe-Al alloys, especially when the Al content is low. Fe3AlC0.69 carbide in Fe-Al-C alloys contains less Al than the Fe3Al matrix. About 30at.% Al of the carbide is replaced by C, probably making the carbide prone to oxidation attack [78-79], though no detailed studies had been found to correlate the Al content of carbide to its oxidation resistance. The difference in thermal stabilities of Fe3AlC and Fe3Al at the oxidizing temperatures might affect the overall oxidation behavior of the materials. However at higher temperatures, the carbide might decompose to Fe3Al, leading to a reduction in its volume fraction and offsetting the temperature effect in enhancing the oxidation tendency of the alloy. 2.2.4. Effect of RE Elements Yu et al. investigated the effects of cerium (Ce) addition on the oxidation resistance of Fe3Al-based alloys. The RE addition is aiming at the improvement of their oxidation resistance at the temperature above 1000oC [80]. In comparison with the Ce-free alloys, the most important features caused by a small amount of Ce addition are: (1) the oxidation rate decreases notably; (2) the alumina scale adherence is improved significantly; and (3) the

6


ability of the oxide scale resisting to varied stress impact is improved. The authors believed that Ce addition has an effect on preventing outward diffusion of cations through the shortcircuit paths during oxidation and then the scale on the alloy may develop primarily by inward anion transport. This accounts for the elimination of cavities in the near oxide scale/alloy substrate interfacial area and the dramatic improvement in scale adhesion. Ce addition to the Fe3Al based alloys also results in significant refinement of oxide grains and reduction of Fe or Cr oxides in the alumina scale, which improves the strength of an alumina scale, due to the absence of cracks on the scales and a significant decrease of the oxidation rate. The effect of Y addition on the oxidation behavior of Fe3Al alloys was investigated in terms of oxidation rate and oxide adhesion in the temperature range of 800 to 1100oC by Kim et al [81-82]. The oxidation rates of these unalloyed and alloyed Fe3Al intermetallics are basically the same, however, the stabilities of the thermally grown oxide scales are quite different. Oxide layers formed on the Y-free Fe3Al alloys were severely convoluted and the alloy substrates were partially exposed due to scale spallation. The interface is wavy and the surface of the substrate is deformed due to the stresses generated during oxidation and cooling. Meanwhile, the oxide scales formed on the Y-containing Fe3Al alloys were flat, dense and adherent to the underlying alloy substrates. And the oxide scale/substrate interface seems to be straight with little deformation. Pegs at the oxide scale/substrate interface were also observed in Y-containing alloys. The pegs are enriched with O, Al and Y, and deficient in Fe, and are developed at the grain boundaries of the substrate near the oxide scale/substrate interface due to internal oxidation. The authors believed that the growth of oxide scales on Yfree alloys was governed by the countercurrent diffusion of Al and O. This growth mechanism indicated that new oxides would be formed in the oxide scales, and large stresses could be generated in the scales during oxidation, which may eventually lead to spallation of alumina scale. Y addition changed the growth process to predominant oxygen diffusion, leading to the formation of pegs and lower oxide growth stresses which then enhanced the adhesion of alumina scale to the alloy substrate. The influences of addition of mischmetal (a mixture of rare earth elements, 43wt.% Ce, 23 La, 18 Nd, 5 Pr, 3 Sm and 8 Fe) to Cr-alloyed iron aluminide (Fe-28Al-2Cr) on its high temperature oxidation behavior in oxygen were also studied [83]. The addition of mischmetal (Mm) to Cr-alloyed iron aluminides decreased the isothermal oxidation rate of the intermetallic compound in pure oxygen at 1057oC to the same level as that of the base intermetallic. The improvement in oxidation resistance due to Mm addition has been attributed to the lower rate of oxidation in the initial stages of oxidation.

2.2.5. Effect of RE Oxides Extensive studies with oxide dispersion strengthened Ni-based and FeCrAl-based high temperature alloys suggest that the creep resistance of materials could be dramatically improved by dispersion of fine stable oxide particles, such as Al2O3, Y2O3 and/or Y2O3-Al2O3 [84-88]. The use of reactive element oxide dispersions has also significantly improved the oxidation resistance of various Al2O3-forming alloys such as FeCrAl [89-91] and NiCrAl [9293]. Small additions of reactive elements such as Zr, Y or Ce to Fe3Al have been found to promote the oxide scale spallation resistance. The high temperature oxidation behavior of oxide dispersion-strengthened Fe3Al alloys has been characterized by Pint et al [94-96]. The results indicated that Al2O3 dispersion did not produce any typical RE effects though Al2O3


7

dispersion flattened the thermally grown α-Al2O3 scale. The oxide scale formed at the same rate and had the same morphology and grain structure as a scale formed on an undoped Fe3Al alloy. The Al2O3-dispersed alloy also exhibited a shorter lifetime than that of the cast and undoped alloy. The lifetime was reduced as the Al2O3 content increased. This may be a result of particle coarsening. Large Al2O3 particles in the substrate may allow rapid transport of oxygen into the substrate when these particles come into contact with the scale. The addition of Y2O3 improved the alumina scale adhesion relative to a Zr alloy addition at 1200 and 1300°C. However, the Y2O3 dispersion was not as effective in improving scale adhesion in Fe3Al as it is in FeCrAl. This inferior performance is attributed to a larger amount of interfacial void formation on ODS Fe3Al. However, it appears that the large coefficient of thermal expansion (CTE) of ODS-Fe3Al alloy is the major reason for the great tendency for scale spallation. The stress generated by the CTE mismatch was apparently sufficient to lead to buckling and limited loss of scale at temperatures up to 1100oC, with an increasing amount of substrate deformation at 1200oC and above. This deformation led to increased scale spallation by producing an out-of-plane stress distribution, resulting in cracking or shearing of the oxide.

2.3. Oxidation of FeAl and Its Alloys 2.3.1. Effect of Ti Alloying with Ti could significantly improve the mechanical properties of FeAl alloys, for example, the high temperature creep resistance could be enhanced and superplasticity was observed by optimizing chemical composition and heat treatment processes [97-101]. The influence of Ti addition on the high temperature oxidation behavior of FeAl intermetallic alloys in air at 1000oC and 1100oC has also been investigated [102]. The parabolic rate constants show that the oxide scale formed on the surface of Fe-36.5Al-2Ti (at.%) alloy has a better protective effect than that of Fe-36.5Al alloy. There is only α-Al2O3 on Fe-36.5Al alloy while there are α-Al2O3 and TiO on Fe-36.5Al-2Ti alloy. In Fe-36.5Al alloy the Al2O3 grains are much finer than those in the Fe-36.5Al-2Ti alloy, which leads to the fast growth of Al2O3 scale. The authors therefore believed that Ti addition has a beneficial effect on improving the oxidation resistance of FeAl alloy and the positive influences of Ti can be summarized as the followings: (1) Ti addition can significantly improve the compactness of thermally grown oxide scales on the surface; (2) TiO has a better adherence to the substrate of FeAl alloy, leading to a better spallation resistance; (3) the coefficient of thermal expansion of TiO (10×10-6/K) is between α-Al2O3 (6×10-6/K) and FeAl (21×10-6/K). Therefore TiO in the oxide scale can reduce the thermal expansion difference between the oxide scale and the base alloy, resulting in reduced thermal stresses; and (4) Ti addition may improve the toughness of the oxide scales, therefore reducing the possibility of oxide scale fracture. 2.3.2. Effect of REs The effects of rare earth alloying elements, such as Hf, Y or Zr on the oxidation behavior of FeAl alloy have been studied by some researchers [103-105]. Smialek et al. studied the oxidation behaviors of Fe-40at.%A1 alloys doped with 1Hf, 1Hf + 0.4B and/or 0.1Zr + 0.4B at 900, 1000 and 1100oC. During isothermal oxidation, the Zr-doped alloy spalled extensively

8


at all three temperatures, while the Hf- and B-doped alloy spalled only at 1100oC. During cyclic oxidation tests, formation of HfO2 particles within the scales associated with the oxidation of Hf-rich precipitates, A16Fe6Hf, in the alloy accelerated the scale spalling problem. Zr and/or B containing alloys were also lack of good cyclic oxidation performance and the large thermal-expansion mismatch between Al2O3 and FeA1 was the main concern for scale stability subjected to fast thermal cycling. In the tests with smaller amount of cylces, Xu’s results while indicated that addition of Y and/or Zr increased the scale spallation resistance of Fe-37at.%Al at temperatures ranging from 1000 to 1200oC significantly [104105]. FeAl alloys containing Zr did not show any spallation in this temperature range though the oxidation mass gain was slightly increased. The preferential oxidation of Y or Zr at the FeAl grain boundaries formed the teethlike oxides and played a role of ‘pinning’ centres and enhanced the adhesion of the oxide scales to the alloy substrate. Incorporation of Y or Zr in the scale/substrate interfacial area may change the nature and microstructure of the interface and prevent vacancy condensation. It was also supposed that doping of Y or Zr could improve the toughness of Al2O3 scales and reduce the tendency of scale fracture. Fine oxide dispersions (less then 50 nm) have been widely used to improve the creep strength of FeAl alloys at high temperatures [106-109]. Fe-40Al alloys with and without Y2O3 dispersion (0.5wt.%) were prepared by mechanical alloying and their isothermal and cyclic oxidation behaviors were characterized in the temperature range of 756 to 1118oC [110]. The ODS FeAl, in general, had a slightly higher oxidation rate than the FeAl alloy in the isothermal oxidation tests. Formation of cavities and voids was observed on the surfaces of both materials after oxidation and the addition of Y2O3 did not change the morphology and transport mechanism of the oxide scale. A higher content of Y2O3 dispersion in FeAl (1.0wt.%) however, may lead to enhanced oxidation properties at 1100oC as shown in Montealegre’s work [111]. In this study, the scale growth rate of the ODS FeAl is considerably lower than that of PM 2000, and this is the result of the development of a chemically purer alumina scale or one with a lower density of defects. The formation of dense scales on this ODS FeAl alloy is not accompanied by the void formation at the oxide scale/alloy interface, commonly observed in FeAl alloys after oxidation [112-114], so that a good adherence of the oxide scale to the alloy substrate can be inferred. However, the large differences in the thermal expansion coefficients of the oxide scale and the substrate still generate significantly large stresses during cooling and eventually lead to a strong tendency for spallation. This ODS FeAl alloy had been studied further between 750 and 1000oC in artificial atmospheres (20% oxygen + 80% nitrogen) [115]. The results confirmed that 1wt.% Y2O3 addition could decrease the isothermal oxidation rate of FeAl and increase the scale spallation resistance. Morphological observations suggested that the cation mobility might not be completely suppressed and could still have a contribution to the oxide scale formation. This result is further supported by Pedraza’s study [116]. The effects of Y2O3 content might be summarized as: (1) at lower temperatures, the increase of the Y2O3 content promotes the fast formation of α-Al2O3, leading to a more protective and thinner scale with a significant decrease of the oxidation rate; and (2) at higher temperatures, the increase of the Y2O3 content decreases the average grain size of the scale, hence yielding a relatively thicker scale due to enhanced reactant diffusion [117]. The most striking feature is the absence of scale spallation either during oxidation or during cooling of thin Fe-40Al foils [118-119], which contrasts with the spallation observed during the oxidation of massive specimens of similar aluminides at temperatures above


9

900oC. The absence of scale spallation on the FeA1 foil was related to the fact that the alloy contains sufficient Zr [119] or to the changes in the dimensions of the specimens during oxidation [118], likely by a relaxation process of the residual thermal stresses by the creep of the substrate. However, partial scale spallation after relatively short exposures was still observed on Fe-40Al-1wt.%Y2O3 foil [120]. This has been attributed to the elevated residual compressive stresses induced by the difference in the thermal expansion coefficients of the alumina scale and the substrate. It was also believed that an ‘overdopping’ effect in the investigated alloy could not be discarded.

3. NICKEL ALUMINIDES 3.1. Oxidation of Ni3Al and Its Alloys 3.1.1. Introduction Ni3Al, which has an ordered fcc structure (L12), is one of the most attractive ordered intermetallics as high temperature structural materials due to its superior high temperature properties. The most attractive property of Ni3A1 is that its yield strength increases with increasing temperature from near ambient temperature, to approximately 600oC [121-123]. Single crystalline Ni3Al is highly ductile, whereas polycrystalline Ni3Al is brittle at ambient temperature and undergoes intergranular fracture. An extrinsic factor, i.e., environmental embrittlement, has been shown to be the major cause of low ductility and brittle intergranular fracture in binary Ni3Al. Alloying with B or Cr and/or grain refinement have been found to be the most effective way to improve the tensile ductility of Ni3Al when tested in air at room temperature [124-127]. Ni3Al can dissolve a substantial amount of alloying elements, and its mechanical and metallurgical properties can then be improved by controlling the solute concentration and second-phase formation [128-146]. The beneficial contribution of some typical alloying elements in Ni3Al alloys is described below [4]: (1) B: Reduces moisture-induced hydrogen embattlement and enhances the grain boundary cohesive strength; (2) Cr: Reduces oxygen embrittlement at elevated temperatures; (3) Hf: Provides high tmeprature strength through solid solution and prevents surface reaction of Zr with the ceramic shell material during investment casting by forming a protective oxide film; (4) Zr: Provides high temperature strength through solid solution, reduces solidification shrinkage and macroporosity through the formation of low melting point eutectic, and improves oxide spallation resistance during thermal cycling; and (5) Mo: Improves strength al low and high temperatures. In general, Ni3A1 has very high oxidation and corrosion resistance due to its high ability for the formation of α-Al2O3 scales which can ensure the isolatation of the alloy substrate from the aggressive enviroments. The phase composition of the alumina scales formed on Ni3Al however is relatively complex and is highly dependent on the oxidation conditions, in

10


particular, temperature and time. At temperatures lower than 1000oC, the scales formed may consist mainly of an outer layer of NiO, an intermediate layer of NiAl2O4, and an inner layer of α-A12O3. Only α-Al2O3 will be formed on Ni3A1 at temperatures higher than 1200oC [147150]. During the initial stage of oxidation at low temperatures, NiO, NiAl2O4 and/or metastable transient (γ or θ) Al2O3 will form as commonly observed on Al2O3-forming FeCrAl alloys [151-159]. As the exposure time or the temperature increased, a phase transformation from these transient Al2O3 to the thermodynamically stable α-Al2O3 occurred. Thus the steady-state oxidation mechanism is governed by mass transportation through αAl2O3 grain boundaries, although the results may vary according to the real oxidizing conditions [160].

3.1.2. Effect of Alloy Production The production route of the alloys will exert some influences on the scaling behavior, therefore the uncertainties and discrepancies should be considered when collectively analyzing the oxide formation mechanism. Perez et al. studied the oxidation behavior of Ni3Al alloys prepared by power metallurgy [161-164]. Rapidly-solidified powders were produced by argon gas atomization. The powder was sieved and classified into different particle size. Particles were then canned and consolidated by hot isostatic pressing (HIPing) under 150 MPa pressure for 2 hrs at 1100oC. At low oxidation temperatures (10%), Nb, Ta, Al and Si all significantly enhance oxidation resistance to temperatures as high as 815oC. Optimization of these beneficial elements in Ti alloy has led to the development of various advanced titanium-base alloy systems with excellent strength and lightweight properties and environmental resistance, e.g., Beta-21S alloy (Ti-15Mo-3Al-3Nb-0.3Si, wt.%), IMI-834 (-829), Ti-1100, Ti-V-Cr(+C, Al or Si), etc [298-303]. The Beta-21S alloy is ~100 times more resistant than Ti-15V-3Al-3Sn-3Cr at 815oC. However, Beta-21S is still not as resistant as α2 or γ titanium aluminide materials and certainly not as good as the nickel-base alloys, such as René41 or IN718 [298]. The IMI series alloys can only tolerate prolonged exposure in air up to 500oC. Therefore, small addition of various elements for the protection of Ti or its alloy is not highly reliable for material protection, especially for those materials will be possibly used at elevated temperatures, although this type of titanium-base alloys will still be used for some components in aeroegine and automotive. Several coating systems are being examined for improving the oxidation resistance in the temperature range of 600-750oC [304-313]. In order to further improve the temperature limit, new alloy systems should be developed, and this has led to the development of titanium aluminides, titanium powder metallurgy alloys, and titanium matrix composites with more balanced properties [314-322].

4.3. Oxidation of Titanium Aluminides 4.3.1. Introduction At the beginning of 1970s, Ti-Al intermetallic compounds were developed as the first intensive and successful structural materials with fundamental deformation studies [323]. Actually, titanium aluminide based intermetallic compounds have been becoming attractive structural materials for application to aviation industry because of their low density, high melting point, high specific strength, and due ductility. The aim for development of titanium aluminides is to develop a sort of materials whose properties are between those of nickel-base superalloys and high temperature ceramics. According to the Ti-Al binary phase diagram [324], there are four intermetallic phases of interest for high temperature applications: Ti3Al (α2), TiAl (γ), TiAl2 and TiAl3. The development of Ti3Al and its alloys has been driven by the need to bridge the gap in temperature capability between conventional near-α Ti alloys and Ni-base superalloys such as INCO 718 or INCO 713. Ti3Al has a specific modulus and stress rupture resistance comparable to that of the superalloys however, the complete absence of room temperature


21

plasticity posed the primary challenge in using as a structural material. Additions of alloying elements and sutiable heat treatments can significantly improve its room temperature mechanical properties, and these become to be the key-points for the current development of Ti3Al-base alloys. γ-TiAl and its alloys are pursued mainly because of the desire to raise the thrust-to-weight ratio of high performance aircraft engines. γ-TiAl remains ordered to melting point at about 1440oC, this helps to retain strength and resist creep to high temperatures, and also results in high stiffness over a wide temperature range. Although the difficulty in plastic deformation also hinders its development, γ-TiAl and its alloys are still the most attractive candidate materials for components in aeroengines. TiAl3, having a tetragonal structure and the highest oxidation resistance, is of interest in the development of a new class of structural materials as well. As to their possible applications in elevated temperatures, it should always be remembered that long-term exposure at elevated temperatures needs a long-term protection provided by the oxide scale formed on the alloy surface. This protection is generally associated with a stable and adherent alumina, in which the diffusion of reactants is slow. However, of the titanium aluminide intermetallic phases, only TiAl2 and TiAl3 are capable of protective alumina scale formation over a wide range of temperatures. The critical concentration of Al required for the formation of exclusively external alumina scale is much higher than that in binary Ni-Al binary alloys. This kind of oxidation behaviour of titanium aluminide intermetallic compounds could generally be ascribed to the followings [325]: (1) The thermodynamic stabilities of the oxides of Ti and Al are quite similar, which can potentially make it difficult to establish an Al2O3 scale due to the competition from TiO or TiO2; (2) The activity of Al deviates from the ideal or regular solution obviously, and is much smaller than unity in Ti3Al and TiAl [326-327]. Combining the activities with standard free energy data for the oxides of TiO, TiO2 and Al2O3, it appears that TiO/TiO2 is more stable than Al2O3 for the alloys containing Al less than 50at.%; and (3) Ti and Ti-Al alloys are highly permeable to oxygen, and Al has a low diffusivity in lower-aluminium-containing alloys.

4.3.2. Oxidation of Ti3Al and Its Alloys 4.3.2.1. Introduction The structure of Ti3Al is DO19, and is the ordered structure of α-Ti, also names as α2phase. The compositional stability of α2-Ti3Al ranges from 22 to 39at.% Al. This compound is congruently disordered at 1180oC and an Al content of 32at.%. The stoichiometric composition, Ti-25at.%Al, is stable up to ~1090oC. The density of Ti3Al with stoichiometrical composition is 4.2 g/cm3, while its alloys have the density about 4.1-4.7 g/cm3. The Young’s modulus is in the range of 100-145 GPa, the shear elasticity is about 58 GPa, and the Poisson ration is 0.29 [328-330]. The mechanical properties (strength, ductility and creep) of Ti3Al alloys can be improved by alloying with Nb and/or processing control [331-341]. Ti3Al-base alloys under developed are basically based on Ti-(23-25at.%)Al-(1030at.%)Nb with additional alloying elements for further strengthening. It was believed that substitution of Ti by Nb could promote more slip systems in operation, then affecting the

22


ductility. While, higher Nb concentration, results in the formation of further phases, i.e., β-Ti in the disordered state with an α2 structure or in the ordered state with a B2 structure and/or orthorhombic O-phase, which limit the slip length and have a significant and beneficial effect on the ductility. The O-phase exhibits better strength and toughness than Ti3Al. Single phase alloys of ordered orthorhombic have excellent creep resistance particularly after beta heat treatment. The creep resistance of the alloys could be improved with increasing volume fraction of the O-phase and decreasing volume fraction of the α2 phase. Based on the Nb concentration and phase structure, Ti3Al-base alloys can be divided into three groups: α2 or super-α2 alloys with 10-12at.%Nb, α2 + β (B2) alloys with 14-17at.%Nb, and O-phase alloys with 23-27at.%Nb. The mechanical properties of these alloys are highly dependent on the size, shape, distribution, composition, crystal structure and neighbourhood relationships of the various grains. The phase distribution can be varied appreciably by proper selection of the alloy composition and by heat treatment, e.g., thermomechanical treatments (TMT). The best combination of strength and ductility can be obtained through adjusting the size and amount of primary α2 phase, the proportion of α2 and β phases, and their distribution. In general, the development of Ti3Al-base alloys is focused on the O-phase alloys. Other alloying elements for improving the strength are Cr, Ta and Mo [342-347]. The latter is also advantageous for the creep resistance. Minor alloying additions of Fe, C and Si affect the creep behaviour significantly, with Fe having the most deleterious effect. V and Sn were also used for improving the properties [348]. Alloying with Zr increases both the strength and ductility, and microalloying with Y and B has been used to control the grain size and improve the ductility and workability. Very fine and stable grain sizes can be produced by rapid solidification of alloys with fine dispersions of rare earth oxides. In such alloys the small grain size improves the ductility, whereas the dispersoids enhance the strength at the expense of ductility. Similar effects can be produced by the precipitation of strengthening phases, such as the alloying of Ti3Al with Si to produce Ti5Si3 as a strengthening second phase.

4.3.2.2. Oxidation Behaviour and Resistance The protective oxidation behaviour, i.e., the formation of a continuous Al2O3 external scale, could not be expected due to the considerably low Al activity in Ti3Al and its alloys. Its oxidation kinetics between 600 and 950oC are generally reported to follow a parabolic rate law and the rate constants are slightly smaller than those of typical TiO2 formers. The oxide scales, normally layered and stratified, consist of an inner TiO2-rich region, an intermediate Al2O3-rich region, and an outer TiO2 region [349-350]. The oxidation of Ti3Al is generally more rapid in oxygen than in air [351]. It was believed that this is the result of a layer of TiN, which formed at the oxide scale/alloy interface during air exposures, and acted as a diffusion barrier for reactants. The detailed microstructure of the subsurface zone underneath the external oxide scale formed on Ti3Al alloys was studied by Dettenwanger and Schutze [352]. They found that the subsurface region has a complex microstructure and shows three distinct layers: an internal-oxidation zone with α-Ti(Al,O) and α-Al2O3; a ternary phase with composition Ti-21Al-15O; and α2-Ti3Al with dissolved oxygen. The oxidation resistance of Ti3Al can be improved through the addition of alloying elements, such as Nb, Si, Mo, Mn, V, W, Re and Ta. Nb, as a β-stabilizing element, can


23

improve the poor room temperature ductility of Ti3Al, and also was proved to be a beneficial alloying element to the oxidation resistance. According to Reddy et al. [353], the oxidation kinetics of Ti3Al-Nb alloy was substantially reduced at temperatures ranging from 7501100oC in oxygen atmosphere in comparison with that of Ti3Al. Okafor and Reddy [325] found that the oxidation kinetics of Ti-30Al-2.7Nb follows a parabolic rate law in the temperature range of 750-1100oC. It was also shown that a denser oxide scale was formed on the Nb-containing alloy [354]. The oxidation products consisted mainly of rutile and alumina; no Nb oxides were identified. Wu et al. studied the individual/synergetic effects of Nb (0-20at.%) and Si (0-15at.%) on the oxidation behaviour of Ti3Al at 800 and 900oC in air [355-356]. For alloys with Nb addition, the alloy with about 10at.% Nb is found to yield the best oxidation resistance at both temperatures, consistent with other studies [357-361]. At 800oC, after 100 hrs exposure, no spallation of oxide scales on Nb-containing alloys can be found and the kinetics approximately obeys the parabolic rate law. While at 900oC, tiny spallation can be found. Based on the XRD and SEM results, the authors concluded that, the beneficial effects of Nb addition on the improvement of the oxidation resistance of the Ti3Al-base alloys are twofold. One is the doping effect both in the matrix and in the scale. First, the dissolved Nb in the matrix restrains the oxygen dissolution into the matrix ahead of scale formation. Second, the Nb doped oxide forms a compact scale with less porosity. Another positive effect of Nb addition is to promote the earlier formation of TiN at the scale/matrix interface of the Nbcontaining Ti3Al alloys [362-363]. The presence of TiN is a barrier to the inward diffusion of oxygen. The dissolved Si in the matrix can either reduce the oxygen dissolution at the beginning of oxidation or improve the scale morphology by doping. However, the effect of Si addition on the oxidation behaviour of Ti3Al-base alloys is essentially dependent on their microstructures and phase constitutions of the matrix. Their results also showed that when Si addition exceeded the solubility limit of Si in α2 phase, Ti5Si3 was introduced. At low temperature (< 800oC), the reported oxidation resistance of Ti5Si3 was really good. However, the Ti5Si3 formed was always in discontinuous distribution, so a continuous SiO2 layer seems to be impossible for Si-containing alloys, and actually was not revealed by experimental observations [364]. The combined addition of Nb and Si is more effective for improving the high temperature oxidation resistance of Ti3Al-base alloys than alloying alone. Oxidation behaviour of Ti-Al-Nb alloys with high Nb contents had also been studied. In the work of Mungole et al. [365], the parabolic rate constants of Ti-24Al-20/27Nb oxidized in oxygen in the temperature range of 850-1050oC were higher than that of alloys with lower Nb contents, such as Ti-24Al-11Nb and Ti-24Al-15Nb [363, 366]. They believed that the formation of Nb2O5 (the major constituent of the oxides formed was TiO2 while Al2O3 and Nb2O5 were the minor constituents) as a separate phase is possibly related to the lower oxidation resistance. The long-term oxidation behaviour of Ti-22Al-25Nb in air between 650 and 800oC for 500-4000 hrs was studied by Leyens and Gedanitz [359]. The alloy exhibited reasonable oxidation resistance (< 1 mg/cm2) in air at 650oC up to 4000 hrs and at 700oC up to 500 hrs, whereas at 800oC breakaway oxidation occurred after about 100 hrs. The isothermal oxidation behavior of Ti-25Al-18Ta had been investigated in pure oxygen at temperatures ranging from 850 to 1100°C by Reddy et al [367]. The oxidation kinetics followed a parabolic rate. The oxidation products were a mixture of TiO2, Al2O3 and small amounts of tantalum oxide. The addition of Ta to Ti3Al alloy decreased the oxidation rate of

24


the alloy. However, the oxidation scale was not compact and exhibited significant spallation especially at high temperatures. At 1000oC, Ta was enriched at the interface between the oxide scale and the base alloy, resulting in the improved oxidation resistance. However, the addition of Ta appears to be less profitable than Nb addition. Ta addition to orthorhombic Ti2AlNb alloy (Ti-23Al-13Nb-5Ta-3Mo) also exhibits positive effect on the oxidation behaviour though this effect is not fully understood yet [368].

4.3.2.3. Oxidation Protection of Ti3Al and Its Alloys The most popular way for protection of Ti3Al based alloys is pack cementation [369374]. TiAl3 coatings could be produced on Ti3Al alloys through the simple pack aluminizing process. These coatings offered substantial improvement over the uncoated alloys in oxidation tests at elevated temperatures. The oxidation resistance of siliconized coatings is also superior [375]. However, cracks might be formed in the thick coatings (aluminide or silicide) due to their brittle nature, then have an adverse effect on the long-term oxidation process. Al film was sputtering deposited onto Ti3Al alloy and then subjected to interdiffusion treatment at 600oC for 24 hrs in high vacuum to form a TiAl3 layer on the surface [376]. This TiAl3 layer exhibits good adhesion with the substrate and plays a positive role in oxidation protection. Cyclic and isothermal oxidation tests at 800oC in air demonstrated that the Ti3Al alloy with an Al film of 3-5 μm thick could dramatically reduce its oxidation rate. The TiAl3 layer not only results in the formation of a continuous α-Al2O3 scale on the outer surface, but also inter-reacts with Ti3Al substrate to form a γ-TiAl layer during oxidation. The layered structure of α-Al2O3/γ-TiAl/α2-Ti3Al can maintain the integrity of the α-Al2O3 layer without microcracks and spallation. Li et al. used an electro-spark deposition technique to increase the Al content in the near surface region of a Ti3Al-Nb alloy. The results showed that a TiAl3 layer with a metallurgical bonding to the underlying alloy substrate was formed through this fast melting and solidification process. Significantly improved oxidation and scale spallation resistance could be observed at temperatures of 800 and 900oC up to 200 hrs exposure in air [377]. However, a potential problem associated with these Al-rich coatings is the interdiffusion between coating and substrate. These processes will result in the loss of Al from the coating and therefore long-term stability of alumina scale cannot be maintained. Sputtering deposited Ni-20Cr coating also provided certain protection to the Ti3Al-Nb alloy at high temperatures which is dependent on the formation of Cr and Ni protective oxides [378]. Plasma-sprayed MCrAlY and MCr type coatings deposited over a thin diffusion barrier of chromium or tungsten have been found effective in protecting alloys of Ti-24Al-12.5Nb1.5Mo and Ti-24Al-8Nb-2Mo-2Ta during 1000 hrs exposure in air at 815oC against oxidation and embrittlement [379]. A single sputtered-NiCrAlY coating and a complex coating with an inner ion-plated TiN layer and an outer sputtered-NiCrAlY layer have been established on a Ti3Al-Nb alloy with an attempt to improve the high temperature oxidation resistance [380]. Exposures at 850 to 950°C indicated that these coatings could, to some extent, improve the oxidation resistance. The main aspects of the oxidation of Ti3Al-Nb with and without coatings are as follows: oxide scales on uncoated Ti3Al-Nb at 850 to 950°C consisted of an external thin Al2O3-rich scale incorporating some TiO2 and an inner TiO2-rich scale doped with Nb. The NiCrAlY- and NiCrAlY-TiN-coated alloys were able to form an Al2O3 scale. Meanwhile, Ti oxides formed throughout the scales from the coating surface to the coating-alloy interface. The TiN layer had a beneficial effect on the corrosion resistance of the NiCrAlY coatings by


25

inhibiting the diffusion of Ti, Ni, etc. The deterioration of the NiCrAlY-TiN coating is much slower. Nevertheless, coating-substrate interdiffusion and formation of Ti oxides in some regions still occur and partially destroy the protective ability of the coating system, which may be due to the defects existing in the coating. Al2O3, CeO2 and Y2O3 thin films were applied onto Ti3Al-Nb alloys by using sol-gel or electrochemical deposition techniques [381-382]. The results showed that oxidation and scale spallation resistance of the alloys could be improved by CeO2 and Y2O3 films. However, the effects of Al2O3 films on the oxidation resistance of Ti3Al alloys reported in these studies are controversial. Detrimental effects on oxidation and scale spallation ressitance were observed in Li’s study, while a benefical influence was reported in Zhu’s experiments. It is suggested that the different preparation methods and then different structural properties of the Al2O3 films might be responsible for these different observations. Anodic films were also prepared in solutions containing phosphoric acid and Na2SiO3 on Ti3Al alloys. The testing results indicate that the anodized Ti3Al can remarkably reduce the oxidation rate at 800oC and the improvement increases with the increasing anodizing voltage up to 350 V [383]. Enamel coating with a nominal composition of SiO2 (58.2wt.%), Al2O3 (6.3), ZrO2 (5.3), ZnO (9.0), CaO (4.1), and others (17.0) was applied onto Ti3Al alloys with different Nb contents [384]. Oxidation was conducted discontinuously at 750oC in air for 100 hrs. It was found that enamel coating could protect Ti3AlNb alloys from oxidation attack by acting as a diffusion barrier to oxygen and metallic components. However, the coating might degrade due to the rapid formation of Nb enriched sublayer and depletion layer at the interface of enamel/Ti3Al alloys with high Nb contents (23 and 27at.%). At the interface of enamel/Ti3Al17Nb, a dense mixture oxides layer formed at the side of enamel due to the outward diffusion and oxidation of Al and Ti. This thin interfacial interdiffusion layer probably improves the adhesion of the coating to the substrate. Nevertheless, a Nb enriched sublayer formed at the interface of enamel/Ti3Al-(23,27)Nb during oxidation. And a porous depletion layer was observed beneath this Nb enriched layer due to the outward diffusion of metallic components. As a result, oxygen could diffuse inwardly through the imperfect barrier layer and depletion layer to initialize internal oxidation.

4.3.3. Oxidation of TiAl and Its Alloys 4.3.3.1. Introduction Titanium aluminide, TiAl, normally named as γ-phase, has a L10 ordered face-centered tetragonal structure [385-387]. γ-TiAl can exist in a wide Al content ranging from 49 to 66at.%. This phase apparently remains ordered up to its melting point, approximately 1450oC. It has been found that single γ-phase TiAl alloy is brittle with practically no defromability at temperatures up to 700oC, and only above that temperature was plastic deformation observed. Correspondingly, it has a fracture strength of nearly 500 MPa up to about 700oC. Above that temperature, thermally activated softening occurs making plastic deformation possible, and the resultant yielding leads to yield strengths below the fracture strengths. Formation of Ti3Al as a second phase by reducing Al content can improve its ductility. It has been confirmed experimentally that the strength and ductility of two-phase α2 + γ TiAl alloy is higher than that of single γ-TiAl alloy. The mechanical properties of two-phase TiAl alloys can be optimized through suitable control of grain size and microstructure, i.e., appropriate heat

26


treatments and thermomechanical processing microstructures for the two-phase TiAl alloys:

[388-409].

There

are

four

typical

(1) “Near-γ” microstructure (NG): consisting of equiaxed γ grains and some very fine α2 grains or precipitates; (2) Duplex microstructure (DP): consisting of γ grains and lamellae colonies, and a few small α2 precipitates in γ grains; (3) “Near-lamellar” microstructure (NL): consisting of γ/α2 lamellae and small amount of equiaxed γ grains in the form of full lamellar structure; and (4) “Fully-lamellar” microstructure (FL): consisting of fully γ/α2 lamellae. Different structures may result in significantly different mechanical properties. For example, TiAl alloys with FL microstructures have high temperature strength, fracture toughness and creep resistance, but low ductility at low temperatures. Alloys with a duplex structure may have good tensile ductility, but their fracture toughness, high temperature strength and creep resistance might be poor. In the following section, we will also see that TiAl alloys with different microstructures might exhibit different responses to oxidation attack. TiAl alloys with the best balance of mechanical properties will have a bright future for applications to turbine blades of aero-engines, nozzle components such as flaps, nacelle structures, acoustic honeycombs, car turbochargers and exhaust valves [410-417]. Besides carefully controlled heat treatments and thermomechanical processing (TMP), small additions of alloying elements are often used for optimization of the mechanical properties of the two-phase α2 + γ TiAl alloys [418-439]. V, Hf, Cr and Mn increase the ductility significantly and produce solid solution strengthening, with Cr being most effective and Mn being least effective. Nb, Ta and W also produce solid solution strengthening, but they decrease the ductility. Interstitial elements such as C and N affect the ductility, depending on the Al concentration and pre-treatments, and in particular they improve the creep resistance. However, it should be pointed out that the mechanisms on the influence of alloying elements on the mechanical behaviour of TiAl alloy are not fully understood yet, further studies are still needed. Huang summarised the effects of various alloying elements on the properties of TiAl alloys [440].

4.3.3.2. Oxidation Behaviour and Resistance The oxidation resistance of TiAl (and its alloys) is some higher than that of Ti3Al because of its higher Al concentration, but it is still orders of magnitude lower than that of typical alumina-forming alloys, e.g., NiAl. Oxidation of TiAl alloys with sufficient high Al concentration, i.e., single-phase alloys with at least 50at.% Al, leads to the formation of Al2O3 scales with correspondingly low oxidation rates only at temperatures below about 1000oC, whereas at higher temperatures complex scales develop with an outer rutile layer over a mixed layer of rutile and alumina, with markedly increased oxidation rates. According to Becker et al., the scale morphology formed in air can be divided into three types with the following layer system [441-442]: (1) metal⎪⎢fine grained TiO2 + Al2O3⎪⎢coarse grained TiO2 + Al2O3⎪⎢air; (2) metal⎪⎢fine grained TiO2 + Al2O3⎪⎢Al2O3⎪⎢TiO2⎪⎢air; and


27

(3) metal⎪⎢Al2O3⎪⎢TiO2 + Al2O3⎪⎢air. The fine-grained inner (TiO2 + Al2O3) layer grows by inward diffusion of oxygen, while the coarse grained outer (TiO2 + Al2O3) layer as well as the outer TiO2 layer grow by outward cation transport. Along with heating or with increasing oxidation temperature, the composition, phase structure and microstructure of the oxide scale formed on TiAl alloy samples exposed to the oxidizing atmosphere are changing. Correspondingly, the oxidation kinetic curve could be divided into three stages [441, 443]. Stage I is the period for heating the sample to the oxidation temperature or during the initial/incubation period of oxidation at relatively low temperatures. In this stage, the scale is enriched with Al2O3 and the oxidation rate is low. The oxide scale formed has the structure of: TiAl ⎢⎢Al-depleted zone ⎢⎢Al2O3 ⎢⎢gas. During Stage II, the oxidation rate is high, the scale becomes to be a mixture of TiO2 and Al2O3, and the structure is: TiAl ⎢⎢Al-depleted zone ⎢⎢fine dispersive TiO2 + Al2O3 ⎢⎢Al2O3 ⎢⎢coarse dispersive TiO2 ⎢⎢gas. After a long enough exposure at a high temperature the breakaway oxidation might occur. This is explained in term of the formation of relatively large cracks in the scale. At very high temperatures, small cracks can be self healed by sintering of the outer TiO2 layer, resulting in repeated acceleration for short periods in the oxidation kinetics. The dissolution of Al2O3 grains adjacent to the outer TiO2 layer into it and their subsequent reprecipitation near the outer scale surface might also contribute to this breakaway. The scale structure in this stage is: TiAl ⎢⎢Al-depleted zone ⎢⎢fine dispersive TiO2 + Al2O3 ⎢⎢ coarse dispersive TiO2 + Al2O3 ⎢⎢gas. The phase composition and structure in the interfacial and subsurface regions were also subjected to detailed characterization. With Auger Electron Spectroscopy (AES) analysis, Beye and Gronsky found that when enough Al is withdrawn from the alloy matrix to maintain the formation and growth of the surface oxides, the interfacial region transforms into either Ti10Al6O or Ti10Al6O2, depending on the local oxygen concentration. Behind this transformation front, Ti10Al6O grains are transformed into Ti10Al6O2 with the introduction of oxygen from the outside [444]. Their further results with TEM and microanalysis revealed that the subscale consisted of two phases: one is hexagonal with a composition close to Ti6Al3O4, and the other is cubic with a composition of Ti3Al2O3. The hexagonal phase is actually a solid solution of O in Ti3Al and the cubic phase is new [445]. The phase structure of the subsurface depletion layer was also studied by other researchers with an attempt to clarify the crystal structure of the potential phases presented [446-455]. Zheng and Quadakkers believed that one phase is α2-Ti3Al with a high concentration of oxygen, and the other is a cubic phase with a composition close to Ti5Al3O2 (named as Z-phase, which is basically same as X-phase reported in other studies). The formation and maintenance of this phase during oxidation has significant influences on the formation and development of protective oxide scales on the TiAl surface. Protective alumina formation on TiAl alloys could be achieved if the composition of the sub-surface layer consists of Z-phase (Ti5Al3O2) rather than α2-Ti3Al. However the Z-phase was found to be metastable and eventually decomposed to α2(O) + Al2O3, on which the exclusive Al2O3 scale growth cannot be sustained. The “nitrogen effect” is also demonstrated on TiAl alloys. Contrary to that on Ti3Al alloys, the effect of nitrogen on the oxidation of TiAl appears to be detrimental due to the

28


formation of intermixed TiN (or Ti2AlN) and Al2O3 at the metal/scale interface, even in the initial oxidation stage, retarding the formation of continuous Al2O3 scale with high protectiveness [453, 456-460]. Several mechanisms have been postulated [461]: (1) Nitrogen doping of an initial TiO2 scale results in more rapid oxygen transportation to the interface between oxide scale and Al-depleted zone; (2) The grain boundary diffusion of nitrogen through the oxide leads to the formation of AlN or possibly AlON at the interface between oxide scale and Al-depleted zone; and (3) Nitrogen grain boundary diffusion through the oxide scale to the interface between oxide scale and Al-depleted zone, consequently, stabilizes the Al-depleted zone with relatively low Al activity, thus, promotes the growth of TiO2 scale with a high growth rate and poor protectiveness. However, beneficial effects of nitrogen on the oxidation resistance of TiAl alloys could also be expected: (1) nitrogen might reduce the amount of oxygen dissolved in the alloy, so the oxygen embrittlement could be reduced [462]; and (2) nitrogen is beneficial as long as a near-continuous nitride layer, which is probably in equilibrium with the Z-phase, is stable beneath the oxide layer. In this way the formation of a wide α2-containing subsurface depletion layer, accompanied by internal oxidation, destruction of the outer alumina barrier layer and high oxide growth rates is prevented [463]. It is well known that many metals or alloys oxidize faster in water vapor containing atmospheres than in dry oxygen. For Fr-Cr, Fe-Si and/or Fe-Al alloys, the protective scale (Cr2O3, SiO2 or Al2O3), which develops in dry oxygen, fails to develop or cannot maintain after certain period of exposure in water vapour containing atmospheres [464-477]. It is normally observed that after an incubation period breakaway oxidation will take place and accompany by the fast formation and growth of nonprotective solvent metal oxides. However, the mechanisms involeved in these accelerataed diffusion and growth processes are not fully understood. Water in oxidizing atmospheres also has great influences on the scaling behaviour and the protectiveness of the oxide layer formed on TiAl alloys since H2O affects significantly TiO2 and leads to the anisotropic and enhanced growth of TiO2 due to enhanced diffusion. Kremer and Auer studied the effects of water vapour on the oxidation of Ti-50 at.%Al alloy at 900oC in O2 or O2-H2O-gas mixtures (p(H2O) = 3.8, 12.5, 15.4, 19.3 mbar; p(O2) = 0.2 bar) [478]. In the initial oxidation stage, the mass gain is less in water vapour containing oxygen atmospheres compared to dry conditions. After that rapid breakaway oxidation follows in wet oxygen. The oxidation is faster in wet oxygen than in dry oxygen and the oxidation rate increases with increasing p(H2O) and decreasing p(O2). The presence of water vapour in the oxidizing atmosphere also alteres the oxide scale microstructure. In dry oxygen the oxide scale establishes an intermediate, compact Al2O3 barrier layer, while in wet oxygen no such a compact barrier layer is formed, instead separate Al2O3 particles are formed and embedded in the outer TiO2 layer. Taniguchi et al. also found that the thin Al2O3-rich layer, which is usually formed during oxidation in dry oxygen or air, cannot be developed during exposure in wet oxygen or in wet argon atmospheres at 827 and 927oC [479]. The study by Zeller et al. focused on the oxidation behaviour of Ti47Al1CrSi in dry air and air containing 10 vol.% H2O at temperatures of 700 and 750oC [480]. Similarly, they found the presence of water accelerated the oxidation kinetics. However, after switching back to the dry


29

air, the oxidation rate was immediately reduced. An oxygen-rich layer was observed on the samples exposed to water-containing air. This layer consisted of α-Ti and α-Al2O3 which were formed due to either internal oxidation or decomposition of the cubic Al-depletion phase. These authors also found that the presence of water would affect the high temperature fatigue lifetime due to the increased brittle subsurface zone [481]. The effects of alloying elements on the oxidation behaviour of TiAl have been studied extensively. The objectives of alloying are to decrease the growth rate of the intermixed TiO2/Al2O3 scale, to favour the formation of Al2O3, and to stabilize the Al2O3 scale. According to Taniguchi et al., the selection of alloying elements can be guided by the following proposed mechanisms [482-483]: (1) Valence-control rule: If the formation of TiO2 were suppressed or minimized, then the situation will become more favourable for the formation of an Al2O3-rich or an exclusive Al2O3 scale. For this purpose, the valence-control rule (VCR), or WagnerHauffe rule, is applicable. Diffusion of oxygen via oxygen vacancies will contribute to the growth of TiO2. Therefore, alloying elements that can decrease the oxygen vacancies in TiO2 will be very effective to decrease the overall oxide scale growth rate by inhibiting the fast growth of TiO2; (2) Wagner’s scaling model: The suppression of internal oxidation of Al to form discrete Al2O3 particles/platelets in the alloy substrate is also effective to produce a continuous Al2O3 scale on the specimen surface. The critical concentration of alloying element for its transition from internal to external oxidation was derived by Wagner and is shown as [484-485]:

N Al

⎛ πg ∗ S DOValloy ⎞ ⎟ NO ; ⎜⎜ D AlVoxide ⎟⎠ ⎝ 3

1

2

(3) It can be clearly seen that the transition can be enhanced through increasing the diffusion of Al, DAl, or decreasing the inward diffusion of oxygen, DO, or its surface S

concentration, N O ; Formation of a barrier layer: If the alloying elements can form discrete or near continuous aggregates with enough high stability in the oxide scale near the scale/substrate interface, the enrichment of Al2O3 might be resulted in near this interface, then the oxidation rate can be decreased. Also, if the enrichment of alloying element in the alloy substrate could take place, the oxygen solubility in alloy can be decreased, this will contribute to the decreased oxidation rate; and (4) Modification of the initially formed scale: If the nucleation, growth, nature or stability of Al2O3 formed in the initial oxidation stage can be modified or enhanced, the scale formed might be very rich in Al2O3. Experimentally, the effects of various ternary additions on the oxidation behaviour of TiAl alloy had been thoroughly studied. In the works of Shida and Anada, a variety of ternary elements were added into Ti-34.5wt.%Al [486-488]. The oxidation tests were conducted in

30


air at 800 to 1000oC for 100 hrs. Based to the oxidation kinetics measured, these ternary elements were then classified into three groups according to their effects: (1) detrimental: V (0.5-5.0wt.%), Cr (0.5-5.0), Mn (1.5-5.0), Pd (2.0), Pt (2.0), and Cu (2.0); (2) neutral: Y (1.0wt.%), Zr (2.0), Hf (2.0), Ta (2.0), Fe (2.0), Co (2.0), Ni (1.5), Ag (2.0), Au (2.0), Sn (2.0), O; and (3) beneficial: Nb (2.0wt.%), Mo (1.5-6.0), W (2.0-6.0), Si (1.0), Al (37.5/63), C and B McKee and Huang studied the oxidation behaviour of a number of ternary and quaternary TiAl alloys in air under rapid thermal cycling conditions for periods of hundreds of hours in temperature range 850-1000oC [489]. It was found that, 4at.% additions of W or Nb increased oxidation resistance, whereas the presence of a similar concentration of Ta, Cr or V had an adverse effect. However, higher Cr (>8at.%) and Cr + Ta, Cr + Nb, Mn + Ta, Mn + Nb and Mn + W alloying combinations added to TiAl gave very oxidation resistant alloys [489-490]. It is commonly observed that the individual alloying with Nb is beneficial to the oxidation properties of TiAl as it did in Ti3Al alloys [491-500]. In general, enhancement of an external Al2O3 scale formation due to Nb addition could be possibly explained by the following mechanisms: (1) For β alloys, addition of Nb can stabilise the β phase in Ti-Al alloy. The diffusivity of Al in β phase is high, so according to Wagner’s criterion for the transition from internal to external oxidation, the critical concentration of Al for this transition can be formed with lower Al concentrations [501-502]. However, this approach appears to be impossible for TiAl alloy because of lower Al diffusivity in γ-phase than in βphase; (2) In TiAl alloys, the activities of Al and Ti deviate from the regular solution largely, the ratio between Al activity and Ti activity is so small that thermodynamically TiO or TiO2 is much more stable than Al2O3. The addition of Nb might increase the activity of Al at the interface of scale/alloy substrate, resulting in a decrease in Ti activity and increasing tendency to form protective Al2O3 [327, 499]. However, some researchers believed that the activity ratio (aTi/aAl) was not changed significantly by the addition of Nb either in α2-phase or in γ-phase [441, 503]. Further discussion on this point is difficult due to the lack of necessary data; (3) The major defect in rutile formed during oxidation in air at high temperatures is supposed to be the doubly charged oxygen vacancy. Some results indicated that Nb5+ substitutes for Ti4+ in rutile, i.e., the substitution of two foreign Nb cations with a valence of 5 will reduce one oxygen vacancy in the rutile lattice, then reduce the mobility of oxygen anion, and finally suppress the fast rutile growth [494, 504-507]. It is also possible that Nb5+ doping could decrease the solubility of Al in TiO2 therefore stimulate the formation an inner alumina barrier at the metal/subsurface region [508]; (4) Nb may stabilize the γ-phase. The consequence with regard to TiAl-Nb oxidation could be that the initially formed scale is in contact with the γ-phase over a longer period before Al depletion leads to α2 formation in the subsurface zone. According to


31

the Al-Ti-O phase diagram, contact with the γ-phase should promote protective Al2O3 formation. This tendency is additionally supported by Nb enrichment in the subsurface zone during transient oxidation [441]; (5) Nb-rich oxides have been observed at the scale/alloy substrate interface, and can act as a barrier to diffusion under certain conditions [509]. It was also reported that the addition of Nb could accelerate the formation of Al2O3 and change the structure of the diffusion barrier against oxidation [492]. Additionally, it was suggested that the dissolution of oxygen into the matrix might be suppressed by Nb addition by which the weight gain could be decreased [494]; and (6) It is commonly observed that exposure of γ-TiAl alloys containing Nb at elevated temperatures in air will lead to the formation of such an interfacial structure: enrichment of Al beneath a Ti nitride layer [510-511]. This structure can, to a certain extent, provide resistance to oxidation, though above it an intermixed layer of TiO2 and Al2O3 was formed which is not as resistant as protective and thin α-Al2O3 layer. Effect of Cr addition on the oxidation behaviour of TiAl is also complex. Addition of up to 4at.% Cr to Ti and TiAl resulted in an increase in oxidation rate [282, 489-490, 493, 496, 512-513], however the presence of doped Cr might improve the adhesion of oxide scale with substrate alloy and benefit the thermal cyclic resistance [514]. The reason can be explained as the VCR, i.e., the incorporation of Cr3+ ions into the rutile can cause: (1) an increase in the number of anionic vacancies, and (2) migration of Ti4+ ions to interstitial positions. However, at higher concentrations (> 8at.%), Cr promotes the formation of continuous external layer of Al2O3. The possible mechanisms are summarized as the followings: (1) According to Luthra, the formation of Al2O3 protective scale on TiAl alloy is dominated by thermodynamic factors [327]. Substitution of Cr for Ti, therefore, can decrease Ti activity, while, Al activity is comparable or higher, i.e., the Al/Ti activity ratio increases, and results in the shift of thermodynamic stabilities of Al2O3 and TiO or TiO2. If Cr content is sufficient high, Al2O3 may become to be more stable than TiO or TiO2. However, some experimental phase studies of Ti-Al-O showed that there is no Ti-Al-O thermodynamic barrier to protective Al2O3 formation in the composition range of the Cr effect [515-517]; (2) The substitution of Cr for Ti, in sufficient quantities, leads to the formation of Ti(Cr,Al)2 Laves phase, which exhibits a low oxygen permeability and is capable of protective Al2O3 formation [518-523]. Therefore, alloys containing a significant volume fraction of Laves phase can form Al2O3 protective scale at lower Al concentrations. Furthermore, it is presumed that the “nitrogen effect” apparently does not operate in the presence of sufficient amount of Cr addition in the TiAl alloys. These two possible effects act together, promoting the formation and stabilization of alumina scale; and (3) Cr can act as ‘traps’ for oxygen then effectively reduce both the solubility and diffusivity of oxygen in titanium, therefore decrease the critical Al content for the external scale formation according to the criterion for the transition from internal to external oxidation proposed by Wagner [501].

32


A surprising finding is the chlorine effect [524-533]. Kumagai et al. found that reactivesintered TiAl-Mn containing 200-1600 ppm chlorine exhibited excellent oxidation resistance in comparison with the cast TiAl [524]. As shown in the AES and XPS results, chlorine existed as Cl- ions in titanium oxide near the oxide/alloy interface. Also, according to the VCR, oxygen ion vacancies will decrease due to the replacement of oxygen ions with Clions, resulting in the smaller diffusion of oxygen in TiO2 lattice. Then the growth of TiO2 was inhibited. On the other hand, the formation of dense oxide scales containing chlorine in the initial oxidation stage, to a certain degree, can decrease the solubility and diffusion of oxygen into the alloy substrate, and then enhance the transition from internal to external oxidation of Al at lower concentration. Studies by Schutze et al. also indicated that other halogen elements, such as fluorine, iodine and bromine, have the same positive effect on oxidation resistance of TiAl alloys when they were doped into the alloys through ion implantation or wetting treatment [534-541]. The vaporization of Ti chloride was proposed as an effective mechanism according to Taniguchi, because this process might enrich Al in the surface layer [483]. Schutze et al. developed a metal chloride transportation model based on thermodynamic calculations of the stability diagram for the system of Ti-Al-O-Cl [525, 527, 530]. Basically, it is believed that this beneficial halogen effect is based on the selective transport of volatile Al halides and their subsequent oxidation on the surfaces of pores and microcracks within the inner region of the initially-formed scales. Taking chlorine as the example, it was assumed that there is a window in the chlorine concentration. In this window, the vapour pressure of volatile Al chlorides will be significantly higher than that of the Ti chlorides, resulting in considerable evaporation of Al phase. Consequently, Al could be preferentially transferred into the gas phase as AlCl and, oxidized to Al2O3. If the pressure of chlorine is so low that either the pressure of AlCl or the pressure of TiCl3 can reach the critical value, the transportation of metal can be negligible, no chlorine effect can be observed. Similarly, if the chlorine pressure is very high, both the transportation of Al and Ti are significant, negative chlorine effect will be observed. This mechanism is applicable to other halogen elements, since the vapour pressure of Al monobromide or monoiodide is orders of magnitude higher than those of the most volatile Ti halogenides. Other alloying elements, which can be possibly used to improve the oxidation resistance of TiAl alloy, are: (1) Mo, which may reduce oxygen solubility in the alloy or promote the formation and thickening of a protective continuous nitride layer [542-543]; (2) W, which may reduce oxygen solubility in the alloy or enhance the diffusivity of Al [512, 544]. Doping of W could also suppress the growth of TiO2 and then decrease the oxidation mass gain. The continuous nitride layer formed in W containing alloys seems to have an important role in stabilizing the protective Al2O3 scale [545]; (3) Si can form SiO2 which is acting as a barrier against oxidation together with the Al2O3 layer in the oxide scale [492-493]; (4) Ta, which might suppress the formation of α2 phase during exposure therefore increase the oxidation resistance [546]; (5) Sb, which possibly retards the dissolution of Al2O3 and stabilize the diffusion barrier [547];


33

(6) Ag: Addition of approximately 2% Ag was found to improve the oxidation resistance of TiAl based alloys during oxidation at 800oC in air by promoting the formation of a continuous, external alumina based scale. Z-phase in the Al-depletion region could be stabilized by Ag addition and thus the formation of harmful α2-Ti3Al is suppressed [455, 548-553], hence the stability of the Al2O3 scale could be maintained. The mechanism concerning the Z-phase stablization by Ag is unclear and the effect is decreased as the oxidation temperature increases; (7) Ru: Precious metal alloying with 2at.% Ru leads to a 20% increase of the oxidation resistance of Ti-55Al under isothermal oxidation at 900oC in air. This influence is attributed to the formation of a protective layer of the ternary compound (G-phase) around the grains of the γ-phase. Initially, cyclic oxidation, Ru-alloyed TiAl alloy exhibited significant exfoliation of the oxide scale, however, this undesirable process stopped after oxidation for 220 hrs and was not observed during further thermal cycling exposure up to 450 hrs [554]; and (8) Rear earth elements and/or their oxides (Zr, La, Hf or Y): addition of RE (900oC) and mechanical mismatch (CTEs and thermal stresses) between the coating and the substrate must be carefully considered.

4.3.3.3.3. Ceramic Coatings Alumina coating produced by chemical vapour depsotion (CVD), micro-arc oxidation (MAO) or reactive sputtering process can provide limited protection for TiAl alloys [634637]. While it was also reported that enamel coating can provide very good protectiveness for TiAl under isothermal and cyclic oxidation [637-638]. SiO2 coating was also applied onto TiAl alloys by magnetron sputtering [639]. Oxidation tests at 850oC in air showed that the cyclic oxidation properties of TiAl alloys could be improved since this coating could serve as a barrier layer to the inward diffusion of oxygen and outward diffusion of metallic ions. An anodic alumina layer has also been applied onto TiAl alloy substrate by sputter-depositing aluminum and subsequent anodizing of the Al layer [640]. This thin alumina layer, less than 500 nm thick, can suppress effectively the interdiffusion between the oxidation-resistant alloy coating (Al-21at.%Nb-10at.%Cr alloy) and the TiAl substrate, particularly when a thin Al layer is remained beneath the anodic alumina. Silicon nitride (Si3N4) films of different thicknesses (0.5, 1 and 2 μm) had been deposited onto TiAl by ion-beam-enhanced deposition (IBAD) [641-643]. Cyclic oxidation tests carried out at 1027oC for at least 30 cycles (600 hrs) showed that the nitride film of 0.5 μm thickness has an excellent oxidation resistance. However, this effect decreases as the thickness of the coating increases. The excellent oxidation resistance comes from the formation of a thin layer rich in Al2O3 beneath the outer TiO2 layer. The less effectiveness for oxidation resistance of the thicker film is related to the local fracture of the coating and the spalling off of the oxide scale. Thermal barrier coatings (TBCs) have also been applied onto TiAl alloys to to reduce the service temperatures on the component surfaces and then to prolong the service life of these alloys [644-646]. Before the application of the TBCs (zirconia or partially yttria stabilized zirconia coatings), the surfaces of the TiAl alloys were subjected to suitable treatments, such as preoxidation or deposited with TiAl3 or TiAl2 diffusion coatings, or Ti-Al-Cr, TiAlCrYN coatings. Oxidation tests showed that the oxidation resistance of the material system is highly dependent on the surface treatment of the TiAl alloy. TiAl3 aluminide coating provided an excellent oxidation protection associated with the formation of a continuous alumina scale. The TBCs did influence the oxidation behaviour: (1) interdiffusion and/or reaction processes between TBCs and thermally grown oxides were observed; and (2) fast growth and cracking of titania scales on sample surface without enough oxidation protection finally led to the failure of the thermal barrier coating systems. 4.3.3.3.4. Ion Implantation Ion implantation can add an element into the surface layer of an alloy in a well-controlled and reproducible manner (depth and dose) [647]. This processing can dramatically change the composition and microstructure of the surface or near surface region, while the properties of the bulk material will be remained. It can thus serve as a powerful tool to study the influence


37

of various elements on the oxidation behavior of TiAl. Similar with alloying approach, it has been found that ion implantation of Nb [648-659], Si [660-661], Cr [662], Zn [663], Ta [664], Mo [665-666], W [667-668], C [669], Al [670] and/or combined ion implantation [671-672] showed a large beneficial effect on the oxidation behaviour. The improved oxidation resistance is mainly attributable to the formation of Al2O3 layers or Al2O3 rich layers in the oxide scale during the initial stages of oxidation or to the decreased anion and cation transport in the scale (due to decreased defect concentration or formation of other diffusion barriers). C implantation leads to the formation of a C rich layer which acts as a barrier to the inward diffusion of O in the early stage of the oxidation, but this effect will disappear soon due to the fast consumption of C. Combined implantation of C and Nb could get a better effect on oxidation resistance enhancement. On the other hand, implantation with smaller doses might be ineffective for improving oxidation resistance, neutral or even detrimental effects on the oxidation resistance of TiAl alloys therefore had also been found. The main problems associated with ion implantation are: (1) difficult to perform implantation over parts with complex shapes or on large areas with high uniformity; (2) expensive for operation; and (3) holding the beneficial effects for longer exposures.

4.3.3.3.5. Preoxidation at Low Oxygen Partial Pressures The preoxidation treatment of TiAl alloys in SiO2, TiO2 or Cr2O3 powder packs resulted in very thin scales, virtually Al2O3 scales after further oxidation at higher oxygen atmospheres (pure oxygen or air) [556, 673-675]. It was also found that the scale thickness decreased as the dissociation pressure of the powder decreased. The superior oxidation resistance was attributable to the formation of a scale very rich in alumina by the preoxidation. Similar results had been observed on TiAl-Mn alloy preoxidized in CO-CO2 gas mixture with a very low equilibrium partial pressure of oxygen then oxidized at 1000oC up to 600 hrs [676]. Gray et al. observed that the heat treatment of TiAl alloy in a silica capsule under low oxygen partial pressures at 1010oC for 50 hrs produces a thin (1-2μm) Ti5Si3 external film on the sample surface [677]. The Ti5Si3 layer is formed by dissociation of the silica capsule to form SiO, which reacts with Ti in TiAl at very low oxygen partial pressures. The Ti5Si3 layer confers significant improvements in oxidation resistance for at least 500 hrs in air at 900oC. TiAl alloys were oxidized in argon atmospheres with low oxygen partial pressures (Po2 ≈ -17 10 and 10-20 atm) at 800oC to investigate the potenetial of Al selective oxidation [678]. The low Po2 atmospheres were created by using a solid-state oxygen pump system [679-680]. GAXRD and FE-SEM characterizations did not support the preferential formation of aluminium oxides in the initial oxidation stage, instead, titanium oxides, such as Ti2O or TiO were detected. Similarly, Legzdina et al. found that annealing of single phase Ti-52.1Al-2Ta (at.%) in the temperature range 550-900oC in low partial pressures of oxygen (10-5 or 10-9 atm) resulted in the formation of a multi-layered surface oxide structure with the outer layer being Al2O3 followed by a layer of TiO2 [681]. These results are quite different from those observed in oxide packs. It is suggested that this might be related to the relatively high oxygen patial pressures in comparion with the equilibrium dissociation pressures of Al and Ti oxides at these temperatures, or related to the presence of trace amount of water, nitrogen or other impurities in the annealing atmospheres [682]. The oxidation resistance can also be improved through preoxidation in air followed by polishing [683]. This characteristic is attributed to the compressive stress relief associated

38


with the removal of the outer TiO2 layer, the stress relief will alleviate cracking or rupture of the scale simultaneously reduce the stress-assisted diffusion in the scale. Also, removal of TiO2 can reduce the catalytic effect, which favours the dissociation of molecular oxygen into oxygen atoms.

4.3.3.3.6. Presulfidation in S-Containing Atmospheres In S-containing atmospheres, Ti can react with S preferentially to form titanium sulfides. As the sulfides grow by the outward diffusion of Ti, Al will be enriched on the substrate surface, resulting in the formation of Al-rich titanium aluminide layers, such as TiAl3 and/or TiAl2, which has a better oxidation resistance than TiAl substrate [684-687]. In comparison with conventional pack cementation, lower stresses present in the coatings. Addition of Cr to the TiAl can also improve the oxidation resistance of TiAl alloys after sulfidation treatment. It was found that sulfidation processed TiAl-10Cr alloy showed very good oxidation resistance at 900oC up to 750 hrs, due to the formation of a continuous Ti(CrAl)2 Laves layer, which was formed by a reaction between TiAl2 and the (Cr,Ti)Al2 formed by sulfidation. A protective Al-rich oxide scale was developed on the continuous Ti(CrAl)2 Laves layer. Other elements, including Ag, Co, Cu, Fe, Ge, La, Mn, Mo, Nb, Ni, Si, Ta, V, W, V, Zr and Y (2at.%), have been added into the alloy substrate to investigate their potential infleunces on the oxidation behaviour of sulfidation processed TiAl alloys. TiAl alloys containing Cr, Fe, Ge, La, Mo, Nb, Ni, Ta, W and Y oxidized slower than unalloyed TiAl, while, alloys containing Ag, Co, Cu, Mn, Si, V and Zr may oxidize slightly faster than the binary TiAl. The enhanced oxidation property is mainly due to the formation of a continuous layer of Laves phase Ti(Al,X)2, formed from X-Al and TiAl3 layers. 4.3.3.3.7. Nitridation Treatment The effects of nitridation on the oxidation behaviour of TiAl were investigated by Perez and Adeva [688]. The Ti-48Al-2Cr alloy samples were subjected to nitridation treatment at 800oC for 10 hrs and then oxidized at 800oC in air. It was found that nitridation resulted in the formation of a thin and continuous nitride layer consisting of a mixture of TiN, AlN and Ti2AlN which can act beneficially as a diffusion barrier during the initial transient stage, preventing oxygen dissolution in the α2-Ti3Al phase of the alloy and decreasing the total oxidation mass gain. The oxidation mechanism of the alloys was not changed due to the nitridation, however, the formation over the mixed alumina-rutile layer of an alumina-rich layer could reduce the oxidation rate. 4.3.3.3.8. Phosphoric Acid Surface Treatment Ti-48Al-2Cr-2Nb alloy, treated by surface painting with phosphoric acid (85% in water) and calcination, oxidized at 800oC in air up to 500 hrs with a significantly lower rate than untreated materials [689]. It was found that the reduced oxidation rate was associated with a continuous or near continuous inner alumina layer, as compared to an intermixed alumina/titania scale on the untreated specimen. However, the mechanisms invoved in the enhanced formation of alumina layer was not clear. Polished Ti-50Al alloys were also treated by anodization in the electrolytic solution of 4 wt% phosphoric acid at 18oC for 45 min. The anodic films, which are amorphous and contain substantial amount of phosphorus, can slow down the formation of rutile and α-Al2O3 during


39

cyclic oxidation in air at 800oC. The doping effect of phosphorus ions in Ti oxide can account for the improvement of high temperature oxidation of Ti-50Al alloy [690]. Brou et al. dipped Ti-54Al alloy specimens into a low concentration orthophosphoric acid solution (0.3M) at room temperature for 1 min, and then dried in air for 24 hrs [691]. They found that this chemical treatment can significantly decrease the oxidation mass gain of the TiAl alloy during an exposure at 800oC in air up to 500 hrs. They believed that this treatment gives rise to a homogeneous deposit containing orthophosphates groups and the subsequent oxidation mainly induces the formation of pyrophosphate, TiP2O7, instead of the usual TiO2/Al2O3 mixed phase. The pyrophosphate layer is responsible for the drastically reduced oxidation kinetic.

4.3.3.3.9. Fluidized Bed Treatment A surface treatment using a fluidized bed with WO3 powders had been developed to improve the high temperature oxidation resistance of TiAl alloys [692]. The reagent used was a mixture of 40wt%WO3 powder with 60%Al2O3 powder. The bed was fluidized by an argon gas flow. Specimens were treated in the bed at 1000oC for 2 hrs. The oxidation tests were carried out at 900 and 950oC for 200 hrs in air and in a typical exhaust gas atmosphere. The cyclic oxidation resistance of TiAl-base alloys was significantly improved. The excellent oxidation resistance obtained is attributable to a continuous and sound Al2O3 surface layer formed during the treatment. This protective layer acts as a barrier against the formation of a complex oxide scale consisting of a TiO2 layer and a porous inner layer of TiO2 and Al2O3. 4.3.3.3.10. Micro- and Nano-Crystallization Micro- and/or nano-crystallization are very effective in promoting the formation of protective alumina scale on the alumina forming alloys [693-699]. Sputtering is then used to build up a fine-grained TiAl coating on the alloy substrtae with similar compositions. The cast TiA1 alloy normally forms a TiO2-Al2O3 mixed scale, and this scale type cannot be changed by microcrystallization as revealed in Wang’s experiements [700]. The authors believed that microcrystallization may also increase the solubility and diffusivity of oxygen or enhance the diffusion of Ti, therefore, preferential oxidation of Al could not be promoted. However, the scale adhesion was significantly improved by microcrystallization since (1) the bonding between the oxide scale and the metallic substrate is enhanced by many pegs formed along the columnar structure, which anchor the scale to the metal; and (2) stress relaxation in the oxide scale could be enhanced due to plastic deformation of the fine grained metallic substrate. Wendler et al. found that nano-crystalline coatings alloyed with ternary or quaternary elements (Ag, Cr, Mo, Nb, Si, Ta or W) could improve the oxidation resistance of Ti40at.%Al alloy [544, 701]. The oxidation parabolic rate constants of some coatings are five orders of magnitude less than that of the bare TiAl substrate. The higher oxidation resistance of the coatings is a result of the thin α-Al2O3 layer formation on the surface of the substrate during oxidation, and this dense, adherent and uniform α-Al2O3 layer composed of fine oxide grains is due to a fine-crystalline structure of the magnetron deposited coating as well as the effect of the alloying element.

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4.3.4. Oxidation of TiAl2 and Its Alloys 4.3.4.1. Introduction TiAl2 is one of the four intermetallic phases in the Ti-Al binary system, which has been largely overlooked, probably due to the fact that this phase did not appear in early compilations of Ti-Al phase diagrams. TiAl2 was first determined to have the HfGa2-type, tetragonal, space group I41/amd [702]. Mabuchi et al. used the pack cementation technique to produce TiAl3 coatings on TiAl, and found that the intermediate layers crystallize in the HfGa2 structure type [574]. TiAl2 is a re-entrant phase: at low and high temperature TiAl2 has the ZrGa2 type of structure, orthorhombic, space group Cmmm, labeled as h-TiAl2, and in the intermediate temperature the crystal structure is of HfGa2 type [703-705]. With its higher aluminium content, TiAl2 would be expected to have a lower density and better oxidation resistance than Ti3Al and TiAl, potentially making it an attractive elevated temperature alloy. However, the studies now available are mainly focused on its phase stability and crystal structure. The very limited works on its mechanical and oxidation properties were finished by Benci et al. [706-707]. Actually, their research group has been characterizing the structural and mechanical properties of TiAl2 as a function of the processing method. TiAl2, which has been rapidly solidified by melt spinning, has the L10 crystal structure. As-cast, cast and annealed, cast and HIPed, and melt-spun and annealed TiAl2 all have the HfGa2 crystal structure. Furthermore, they evaluated the possibility of using TiAl2 as high temperature structure materials. The TiAl2 specimens were prepared in three conditions: as-cast, cast and hot isostatically pressed, and hot isostatically pressed powders. The mechanical properties were determined with measurement of the compressive yield strength at various temperatures. The compressive yield strength of as-cast and cast and HIPed TiAl2, which is about 700 MPa at room temperature and decreases with increasing temperature to about 400MPa at 800oC, is about four times greater than the yield strength of cast TiAl3. The compressive yield strength of powder-processing TiAl2 is approximately 1350 MPa at room temperature, much higher than that of as-cast, cast and HIPed, cast TiAl3, and powder-processing TiAl. However, the yield strength decreases rapidly with increasing temperature. At 850oC, it is about 350 MPa. But at 700oC, the yield strength of powderprocessing TiAl2 is still about 50% greater than that of PP TiAl. The plastic engineering strain-to-failure for as-cast TiAl2 is low at room temperature, about 0.3%, and increases gradually with increasing temperature, to about 4% at 850oC. This extent of plastic deformation is still larger than that of TiAl3. The plastic strain-to-failure for powderprocessing TiAl2 is the highest among these three materials. At room temperature the plastic strain-to-failure was measured to be 5%, increasing to 17% at 500oC and over 60% at temperature above 775oC. 4.3.4.2. Oxidation Behaviour and Resistance The oxidation tests were carried out at 815 and 982oC in air for a time period of 100 hrs [706]. The comparisons with other kind of Ti-Al materials clearly indicate that the oxidation resistance of TiAl2, especially powder-processing TiAl2, is much better than that of other TiAl intermetallics with lower Al contents and is comparable with that of TiAl3 under this oxidation condition. The morphology observed on PP-TiAl2 showed a multi-layer structure,


41

some parts are rich in the oxide of Al, however on other parts, oxide of Ti is formed. Oxidation data showed that Al2O3 might be formed at temperatures higher than 800oC. However, no long-term study of TiAl2 oxidation is available in open literature. So, the oxidative lifetime of TiAl2 is still complicated due to the potential formation of a subscale layer of the TiAl phase resulted from the limited solubility range of Al in TiAl2 and consumption of Al from TiAl2 to form Al2O3. It was believed that the formation of underlying subscale layer of the TiAl phase could degrade the ability to maintain Al2O3 formation in air. TiAl2 coating about about 20 μm thick was also applied onto TiAl alloy using magnetron sputtering deposition [708]. It was found that an external Al2O3 layers with a θ-phase structure was formed on the TiAl2 coatings at 800 and 900oC, and the θ-Al2O3 scales showed a high protective ability with low mass-gains and good scale adherence. Fine-grained coating microstructure of the TiAl2 coating was believed to have played a role in promoting the formation of Al2O3. After oxidation, an inter-diffusion region of about 5 μm was observed between the TiAl2 coating and the γ-TiAl substrate, which could act as a metallurgical bonding between the coating and the substrate.

4.3.5. Oxidation of TiAl3 and Its Alloys 4.3.5.1. Introduction TiAl3 is one of the intermetallic compounds named as trialuminide [709]. It crystallizes with the tetragonal D022 structure. The Young’s modulus of polycrystalline TiAl3 at room temperature reaches the level of 216 GPa, and is of the order of that of the Ni-base superalloys. The strength of TiAl3 at room temperature is low compared with other titanium aluminides. At the same time, TiAl3 is extremely brittle at temperatures below 600oC because of its low symmetry D022 structure with few slip systems. It is believed that the microstructure can be changed from D022 to L12 through alloying process. The cubic L12 structure is more symmetric than the tetragonal D022 structure and has a sufficient number of slip systems; thus it should be more deformable. Ternary L12 phases have been obtained by alloying TiAl3 with Cr, Mn, Fe, Co, Ni, Rh, Pt, Pd, Cu, Ag, Au and Zn. It has been reported that these modified TiAl3-base alloys showed compressive ductility to some extent at room temperature and a small tensile ductility [710-720]. Elastic moduli have been measured and the Young’s moduli have been found to be 200 GPa for Ti-67Al-8Ni and 192 GPa for Ti67Al-8Fe. The compressive yield strength of Ti-66Al-9M with M = Fe, Cr, Mn or mixtures of these transition metals is of the order of 300 MPa between room temperature and about 800oC, i.e., there is a strength plateau or a slight positive temperature dependence. Much better mechanical properties can be obtained by variations in the composition and the microstructure, and in particular by the development of multiphase composites [721-722]. 4.3.5.2. Oxidation Behaviour and Resistance Because of its extremely high Al content, TiAl3 and its alloys should be able to form a protective external Al2O3 scale on the surface and maintain the stability. Therefore TiAl3 is an attractive material for high temperature applications. The comparison between the oxidation resistance of TiAl and TiAl3 had been conducted by Umakoshi et al [723]. Their result showed that the oxidation kinetics of TiAl3 in pure oxygen at temperatures between 800 and 1000oC followed the parabolic rate law, and its oxidation resistance is much better than that

42


of TiAl under the same oxidation conditions, and the tendency became more remarkable with increasing oxidation temperatures. Oxidation kinetics of cast TiAl3 had also been studied by Smialek et al [724]. It was shown that the isothermal exposure of drop cast TiAl3 above 1000oC exhibited parabolic oxidation behaviour controlled by protective α-Al2O3 scale formation. Below 1000oC, high anomalous rates at short times can be observed, this phenomenon was explained as the inhomogeneous microstructure of the TiAl3 casting, and the internal oxidation resulted from the existence of second phase. Actually, it was noted that the processing of TiAl3-X alloys is crucial since the cast alloys usually contain residual pores and second phase particles. The elimination of these defects by post-solidification treatments, i.e., heat treatment, hot working, hot extrusion, or forging, is difficult. From this result, it can also be found that the microstructure must be taken into account when oxidation resistance was compared in wide temperature range or between different researchers. Oxidation behaviours of TiAl3 alloyed with Ag, Cr, Cu, Fe, Mn and Ni had also been studied [372, 725-729]. The results obtained showed that both Ti-67Al-8Ni and Ti-66Al-9Fe exhibited excellent oxidation resistance in air at temperatures up to 1100oC following approximately parabolic rate law. Microstructural analysis of these two TiAl3-base alloys showed continuously protective Al2O3 oxide scale on the oxidized specimens in the entire testing temperature range. Neither internal oxidation nor the oxides containing Ni or Fe was found. The scales adhere well to the substrate material so that no spalling occurred. In contrast with Ni and Fe modified alloys, mass gains of TiAl3-Mn over 1000oC increased quickly, pits consisting of Al2O3 mixed with TiO2 particles started to develop locally through the Al2O3 scale and the growth of tiny TiO2 crystals at these places on outer surface. At 1200oC, Ti-67Al-8Cr alloy exhibited excellent cyclic oxidation resistance; the oxide formed was primarily α-Al2O3. At lower oxidation temperature, such as 800 and 1000oC, thin and continuous Al2O3 scale formed on Ti-67Al-8Cr and Ti-66Al-9Mn, and showed low oxidation rate. Addition of 10at.% Cu into TiAl3 did not improve the oxidation property since the oxide scale was composed of TiO2 and CuO in addition to Al2O3. Dense and protective α-Al2O3 scale was developed on Ag alloyed TiAl3 oxidized at 1000oC in air for a long exposure of 30 days. These results make some researchers believe that modified TiAl3 alloys with L12 structure might become to be the potential high temperature structural materials because of their good oxidation resistance and applicable ductility. Actually, TiAl3 and its alloys have widely used as protective coatings for Ti, Ti3Al, TiAl and also steel substrates used in high temperature corrosion and erosion environments [730-737].

5. CONCLUDING REMARKS Resistance to environmental degradation is one of the key requirements for the practical application of a special material due to the consideration of economy and safety. Oxidation at elevated temperatures in oxygen-containing atmospheres is one of the most common degradation forms induced by the interactions between a material and the environment. Aluminides based intermetallic compounds, such as Fe-Al, Ni-Al and Ti-Al, rely on the formation of a highly protective alumina scale on their external surface to effectively isolate the underlying alloy substrate from the aggressive atmosphere. These aluminides have much higher aluminium contents in their bulks in comparison with conventional iron- or nickel-


43

based alumina forming alloys (FeCrAl or NiCrAl). However, the formation, growth and maintenance of the alumina scale may vary considerably amongst these intermetallic compounds. The study on the high temperature scaling behaviour of these intermetallic compounds and their derived alloys therefore has been a topic for the materials research community; and the majority of the works focuses on the potential influences of alloy composition and microstructure on the formation ability and characteristics of the protective alumina scale. The extensive lab tests do provide new knowledge for a better understanding of the mechanisms involved in the growth and failure processes of the alumina scale, and for the successful design and development of new materials. However, fundamental studies on thermodynamic equilibrium phase diagrams, defects, diffusion processes, phase transformations, crystal structures and electronic structures are lack. Compuational modelling together with sound experimental supports will be a powerful tool to develop strategy for material design, and should be strengthened in future studies. Practical applications, i.e., the commercial utilization of parts fabricated with these materials, however, will require more information concerning the properties of these materials since the enviroments in which the parts will be exposed are much more complex than the conditions set in lab tests. Corrspondingly, the response of the materials might be some different to that observed in lab. At present, the tests of these intermetallic compounds and their derived alloys in simulated or real environments are very limited. Furthermore, lab tests are normally carried out for a limited exposure time although at temperatures slightly higher than the practical ones. Long-term tests are necessary to evaluate the lifetime of the working pieces, and should be emphasized. Coating is an effective way to protect the underlying alloy substrate from attack. However, a satisfactory coating system requires at least the following characteristics: (1) excellent adhesion to the underlying alloy substrate; (2) superior oxidation resistance by forming highly protective and mechanically strong oxide scales within long exposures; and (3) limited interdiffusion between the coating and the substrate that does not result in the formation of depletion zones and/or brittle phases. Unfortunately, for some intermetallic compounds, the coating systems under investigation could not meet these requirements. The solutions therefore may largely rely on the development of materials with more rational alloying and strengthening strategy and on the realization of innovative coating design.

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Chapter 2

ANELASTICITY OF IRON-BASED ORDERED ALLOYS AND INTERMETALLIC COMPOUNDS Igor S. Golovin* Physics of Metals and Materials Science Department Tula State University, Lenin ave. 92, Tula 300600 Russia

ABSTRACT A short introduction into anelastic behaviour of metallic materials is given, and a method of mechanical spectroscopy is introduced for better understanding of relaxation and hysteretic phenomena discussed in this chapter. Several examples of anelasticity due to different structural defects in disordered Fe-based alloys (Fe-Al, Fe-Ge, Fe-Si) are considered with special emphasis on the analyses of the carbon Snoek-type relaxation with respect to ‘carbon substitute atom’ interaction in iron. The effect of ordering of substitute atoms on anelasticity in Fe-based alloys is analysed in terms of substitute atom content and type of order. Anelastic behaviour of iron-based D03 (e.g. Fe3Al) and D019 (e.g. Fe3Ge) intermetallic compounds is reported for a wide range of temperatures and vibrating frequencies to identify damping mechanism. Contribution from interstitial and substitute atoms, dislocations and vacancies in ternary iron-aluminium based alloys Fe-Al-Me (Me = metal: Co, Cr, Ge, Mn, Nb, Si, Ta, Ti, Zr) are analysed. Study of elastic and anelastic behaviour is supported by structural characterisation (XRD, TEM, DSC, magnetometry) of studied alloys, also considering sources for high damping capacity of some compositions. The following anelastic phenomena are found in studied alloys and discussed in this chapter: the Snoek-type (caused by interstitial atom jumps in Fe-Me ferrite) and the Zener (caused by reorientation of pairs of substitute atoms in iron) relaxation, the vacancy and dislocation related relaxations, amplitude dependent magneto-mechanical damping. A family of low-temperature internal friction peaks recorded due to self interstitial atoms in ultra fine grained intermetallics is used to characterise thermal stability of severely deformed (Fe,Me)3Al compounds. These effects are discussed using data available from literature and the author’s experimental data in the Hz and kHz ranges of vibrating frequencies for Fe-Al, *

Now with the Department of Physical Material Science, The Faculty of Physics and Chemistry, State Technological University, Moscow Institute of Steel and Alloys, 4 Leninsky prospekt, 119049 Moscow, Russia, [email protected]

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Igor S. Golovin Fe-Ge, Fe-Si binary and several ternary systems in disordered and ordered ranges of the phase diagrams including intermetallic compounds of Fe3Me type.

Key words: anelastic relaxation, mechanical spectroscopy, internal friction, Fe-based alloys and intermetallic compounds, ordering.

INTRODUCTION a) Internal Friction Mechanical spectroscopy (MS), referred to as the internal friction (IF) method in earlier literature, offers special opportunities to study elastic and anelastic phenomena in metals and alloys at the atomic level, providing response, e.g., from interstitial atoms, vacancies, substitutional atoms, dislocations, grain and magnetic domains boundaries, phase transformations, etc. Fundamentals of this method are given in several textbooks and monographs: Zener 1948 [1], Mason 1958 [2], Krishtal et al. 1964 [3], Nowick and Berry 1972 [4], De Batist 1972 [5], Postnikov [6], Lakes (1999) [7], Schaller et al. 2001 [8], Blanter et al. (2007) [9], and for this reason are considered in this chapter very shortly with respect to studied alloys only. A mechanical loss peak (Q-1) in case of a relaxation effect with a single relaxation time no matter which relaxation mechanism is involved - is well-known as described by a Debye equation with respect to IF:

Q −1 (ω ) = Δ ⋅

ωτ 1 + (ωτ ) 2

(1a)

and elastic modulus:

E (ω) = ER (1 + Δ

ω2τ 2 Δ ) = EU (1 − ), 1 + ω2τ 2 1 + ω2τ 2

where τ is the relaxation time, Δ is the relaxation strength,

(1b)

ω = 2π f with f being the

frequency of the mechanical vibrations, ER and EU are relaxed and unrelaxed modulus. Two values: τ and f can be varied in eq. (1) in experiments. Consequently two types of amplitude independent tests can be carried out: (i) In frequency dependent IF tests (FDIF) at a fixed temperature (τ is a constant in eq. (1a) for a given temperature), the frequency f is varied over a few orders of magnitude. This method allows direct measurements of Q-1 and E spectra vs. ω⋅τ as introduced by eq. (1) or vs. f, and leads to the result shown in Figure 1.a.

Anelasticity of Iron-Based Ordered Alloys and Intermetallic Compounds

67

(ii) Most of the existing mechanical spectroscopy set-ups (e.g., vibrating reeds, torsion pendula) allows measurements of Q-1 as a function of temperature (T) but not frequency, i.e. to measure temperature-dependent internal friction (TDIF) (Figure 1.b). The temperature dependence (e.g., for jumps of atoms) is typically described by the Arrhenius equation:

τ = τ 0 exp( H / kT ) ,

(2)

where H is the activation energy (or enthalphy) of the physical phenomenon which controls the relaxation process. For a fixed frequency and a single relaxation time, the temperature dependence of Q-1 is described by the equation:

⎧ H ⎛ 1 1 ⎞⎫ Q −1 (T ) = Qm−1 cosh −1 ⎨ ⎜⎜ − ⎟⎟⎬ . ⎩ R ⎝ T Tm ⎠⎭

(3)

Thus, relaxation phenomena can be described in terms of either frequency or temperature. Analytical solutions for more complex cases, e.g. for distribution of relaxation times, can be found in literature (e.g.[8]). Collection of such data for different metallic materials can be found in [9-11].

(a)

E(ω)

EU ER

(b) E (T)

ER(T)

Δ/2

EU(T)

-1

Q (ω)

-1

Q (T)

1.144

-2

-1

0

log ωτ

1

2

Tm

T

Figure 1. Dynamic modulus E and internal friction Q−1 of the standard anelastic solid [9]: (a) as a function of frequency on a log ωτ scale; (b) as a function of temperature at constant frequency. In the latter case, the relaxation-induced step in E(T) is superimposed on the intrinsic temperature dependence of EU(T) and ER(T) [9].

Amplitude dependent IF (ADIF) tests allow us to study damping capacity of metals and alloys, to distinguish and analyse magnetic and non-magnetic, most often dislocation, damping as a function of amplitude of vibrations. A specific damping index (SDI) is the quantitative specific damping capacity Ψ (Ψ = ΔW/W, where ΔW is the energy absorption during one cycle, and W is the maximum elastic stored energy during the cycle; Q − 1 = ΔW/2 π W = Ψ /2 π ) measured by means of a torsion pendulum, when the maximum surface shear stress amplitude is one-tenth of the 0.2 tensile yield strength. This measure is denoted as

68

Igor S. Golovin

Ψ0.1σ YS

or more shortly as Ψ0.1, and compared for various materials [12]: Those with Ψ0.1 < 1% are called low damping materials, those with 1 < Ψ0.1 < 10% medium damping, and those with Ψ0.1 > 10% high damping materials. Five structural mechanisms responsible for high damping are recently distinguished [13].

b) Materials Discussed in this Chapter Several groups of iron-based materials are discussed in this paper. Some of them are “true” intermetallic compounds (I) while the rest of them are either alloys on the basis of these compounds (II) or alloys with the compositions in which amount of alloying elements is not sufficient for forming an intermetallic compound (III) in iron but is helpful for better understanding of physical origin of acting anelastic mechanisms: I)

Fe3Al, Fe3Si, Fe3Ge;

II) Fe3(Al,Me) or (Fe,Me)3Al alloys, where Me stays for Cr, Si, Ge, Mn, Co etc.; III) Fe-Al, Fe-Si, Fe-Ge, Fe-Ga, Fe-Al-Si, Fe-Al-Cr ordered and disordered alloys. The second (II) group is built by using the following ternary Fe-Al alloys: 1) strongly carbide forming elements like Ti, Nb, Zr, Ta were added to trap carbon, some of these elements enhance the yield strength by Laves phases; 2) elements providing increased ductility and strength like Cr, which is also a carbide forming element; 3) elements which enhance the tendency to ordering (Si), and are not strongly form carbides; 4) elements (Mn, Ge, Co) which do not strongly affect the interstitial carbon concentration and may affect ordering in different ways. In the Fe-rich corner of the Fe−Al phase diagram there are three phases, namely disordered A2, ordered D03 and differently ordered B2 phases. In the D03 ordered (Fe3Al) structure there are three types of sublattices with sites denoted as 4a, 4b, and 8c in Wyckoff’s notation. In the binary D03 structure the 4a positions are occupied by Al atoms, while 4b and 8c positions are occupied by Fe atoms; in B2 Al atoms are randomly distributed on 4a and 4b sites. In ternary alloys each or all of these sublattices can be occupied by Me atoms. In case of the D03 structure the 4b sublattice, i.e. Fe antisite positions, are preferably occupied by Me atoms; this structure type is called L21. At higher temperatures or higher Al concentration the D03-to-B2 transformation takes place. The Curie temperature TC for a given alloy is different in the A2, B2, and D03 phases. Alloying Fe-Al by a “third” element (Me) changes the parameters of order and the temperatures of phase transformation: Si improves the D03 order and thus increases the transition temperature TO from D03 to B2; Nb and Zr have the same effect on TO, and in addition they produce Laves phases; Co stabilises the B2 phase; Cr and Mn change TO only


69

slightly up to certain concentrations; Ge being added in significant amount produces L21 order and at lower concentrations increases TO. Interstitial atoms, which in the case of Fe−Al-based alloys are mainly carbon atoms, occupy octahedral interstice positions in bcc iron and also in derivatives from the bcc lattice, i.e. in D03, B2 or L21 lattices. The interaction between Me1Me2 and C-Me atoms and its influence on the parameters of anelasticity (e.g., the Snoek-type and Zener relaxation) is one of the main subjects of this paper. The third (III) group of studied alloys with amount of alloying elements from 3 to 13 at.% was used to clarify these effects in disordered alloys. Different types of order take place in Fe-Ge alloys with Ge < 40 at.%: namely there are the B2 (α1), D03 (α2), and L12 (ε′) cubic phases, and the D019 (ε) and B81 (β) hexagonal phases. Several Fe-Ga alloys are also studied. The B2 and D03 order takes place in Fe-Si binary alloys. Tendency to ordering increases in these systems from left to right: Fe-Al, FeGe, Fe-Si [14]. Most of the Fe-(3÷50)Al, Fe-Al-(Si, Ge, Cr, Co, Mn), Fe-Si, Fe-Ge alloys (∗) were produced at the Institute for Physics of Condensed Matter at the Technical University of Braunschweig by induction melting of 99.98% Fe, 99.999% Al and additions of the third elements under argon atmosphere in a vacuum induction furnace (Mrs. U. Brust). A small amount of carbon (typically from 0.005 to 0.04 %) was added in order to attain a sufficiently developed Snoek peak to study carbon related effects. That is why it would be more correct to speak about multi-component Fe−Al−(Me)−C alloys, however, for simplicity the indication of carbon is omitted everywhere below. Several Fe-(10-12)%Al alloys were produced at the Moscow Central Research Institute of Iron and Steel Industry (Dr. I.B. Chudakov). The FeAl-Me (Me = Ti, Nb, Zr, Ta) and several Fe-Al-Si alloys were produced at the Max-PlanckInstitut für Eisenforschung GmbH, Düsseldorf (Dr. F. Stein): details of the compositions, structures and production procedure are given in the cited papers. The nominal compositions of all alloys used in this research and the compositions were determined by inductively coupled plasma optical emission spectroscopy (ICPOES analysis) and for carbon by combustion to CO2. The amount of nitrogen in our alloys was at least two orders of magnitude lower than that of carbon, and therefore neglected in further consideration.

c) Mechanical Spectroscopy Equipment Damping Q-1 and modulus change (shear modulus G or Young’s modulus E, both are ∼ f , where f is the resonance frequency of torsional or flexural vibrations, respectively) were measured in several set-ups: 2

1) in two inverted torsion pendula using free decay vibrations in the frequency range from 0.5 to 3 Hz at Tula State University (Russia) Figure 2 carried out in saturated magnetic field 2400 A/m in the temperature range below 930K and at the Rosario National University (Argentina) in the temperature range from RT to 1300K; 2) in vibrating-reed set-ups (from 0.2 to 3 kHz) at the Technical University of Braunschweig (Germany), two of them with optical detection of the vibrations Figure ∗

All compositions in this paper are given in atomic per cents if not specified differently

70

Igor S. Golovin 3, the third one with electrostatic registration: all in the temperature range from 80 to 900 K;

Figure 2. Inverted torsion pendulum PKM-TPI (Tula State University): 1 - lower cover, 2,8 –let and outlet, 3 – window from quartz glass, 4, 14 – damper, 5 – mirror, 6, 16 upper cover “bell”, 7 – insulator, 9 – bottom of bell, 10 – thermocouple, 11 – internal pipe, 12 – torsion mandrel, 13 – stand, 15 – magnetos, 17 – to vacuum system, 18 - specimen, 19 – jaw. 1

Vacuum chamber (a): 1 2 3 4 5 6 7 8 9 10

2 3 4 5 6

Entry for liquid nitrogen Entry for furnace (upper part) Entry for furnace (lower part) Entry for three thermocouples Current feedthrough for electrode Flange for sample holder Helmholtz-coils Furnace with specimen holder and specimen Laser with adjusting holder Double thermo isolation

Stereomicroscope (b): 11 Outlet for photodiode 12 Power supply for photodiods 13 Motor microscope adjusting

7 8

9 11 12 13 10 7

Vacuum chamber (a)

Stereomicroscope (b)

Figure 3. Vibrating reed (Technical University of Braunschweig)


71

3) in two inverted torsion pendula using forced vibrations in the frequency range from 10-4 to 10 Hz (FDIF) in the temperature range from RT to 900 K at the ENSMA Futurscope (France), and TDIF (f from 0.1 to 1 Hz) at Ecole polytechnique fédérale de Lausanne (Switzerland). This complex of different mechanical spectroscopy techniques allowed us to study main features of most of the phenomena listed in the introduction with respect to temperature, frequency and amplitude of vibrations. The measurements were mainly carried out at vibrating reeds of TU-Braunschweig (in cooperation with Profs. H.-R. Sinning and H. Neuhäuser) [15, 16] and at torsion pendula Tula State University [17]. Several IF tests were carried out in cooperation with colleagues in different places: isothermal studies of the Zener relaxation using frequency dependencies of IF (FDIF) at ENSMA Futurscope (Prof. A. Rivière), high-temperature low-frequency tests at Rosario National University (Prof. O. Lambri), and low-temperature low-frequency tests at Ecole polytechnique fédérale de Lausanne (Prof. R. Schaller). For specimen characterisation TEM (transmission electron microscopy), SEM (scanning electron microscopy), LOM (light optical microscopy), XRD (X-ray diffraction), DSC (differential scanning calorimetry), positron annihilation and vibrating sample magnetometry methods were applied. There structural results are only shortly mentioned in this paper due to the problem of length of the chapter, and similar studies in other chapters in this book. Nevertheless these studies were taken into account in the interpretation of IF effects and reported in the cited papers.

ANELASTIC RELAXATION MECHANISMS I. Dilute Iron Based Alloys: The Snoek and the Snoek-Type Relaxation I.1. Definition and General Theory The effect of anelastic relaxation in a steel tuning fork with a bcc lattice, which later became classical, was for the first time experimentally described more than a century ago [18]. Its nature was related to the presence of interstitial atoms (carbon and nitrogen) in iron in 1939 [19]. Its full physical interpretation as an effect of directional diffusion of interstitial atoms under stress was given by Dr. Jacobus Louis Snoek in 1941 [20]. Later, a similar effect was revealed in a whole number of bcc metals of group VB (V, Nb, Ta) and VIB (Cr, Mo, W) of the periodic table and was called the Snoek effect [4]. Most recently this phenomenon has been reviewed with respect to pure metals by Weller in [21]. The activation energy of the Snoek relaxation process is equal to the activation energy H of the interstitial atoms diffusion: both processes have the same origin. The Snoek peak temperature Tm is determined by the diffusion characteristics of dissolved atoms as: Tm=H/{Rln[π a02 f/(18D0)]},

(4)

where f is the imposed frequency of mechanical vibrations, a0 is the lattice parameter, D0 is the pre-exponential factor in diffusion equation: τ0 = a02/(36D0), see eq. (2).

72

Igor S. Golovin

The peak maximum Qm-1 depends on 1) the atomic fraction of interstitial atoms in the solution (C0), 2) the value of “elastic dipole strength” (| λ2 - λ1 |) produced by interstitial atoms (IA) located in octahedral interstices of the bcc lattice of metals, and on the direction of the stress applied to the crystal lattice (Г): for polycrystalline samples, averaging for all grain orientations which gives Г ≈ 0.2: Qm-1 ~ C0⋅(λ1 - λ2)2⋅F(Г)/(RTm) .

(5)

In α-Fe carbon content up to 1 ppm can be detected in commercial steels [22]. Substitution atoms (SA) in a host lattice must influence the parameters of the original Snoek relaxation by SA-IA interaction, i.e. by a change in the activation energy of the relaxation, and by a change of the value (λ1−λ2), i.e. the relaxation strength. Already at the early 1950s, first attempts were done to investigate the parameters of the Snoek peak by temperature dependence of internal friction not only in pure metals but also in bcc alloys, first of all in iron-based alloys (Wert [23-25], Dijkstra and Sladek [26]). Finally, the Snoek relaxation can also be observed in many bcc dilute alloys [9]. The theory of the influence of SA–IA interaction on the Snoek relaxation was given by Koiwa [27,28] and has been proved in many experimental papers mainly for iron-based alloys. The important question is if the Snoek-type relaxation can also be observed in bcc alloys with significant concentration of substitutional atoms. The substitute atoms create energetically non-equivalent positions for interstitial atoms in the host bcc lattice: the interaction between interstitial (i) and substitutional (s) atoms must influence the relaxation parameters. For this reason the Snoek-type relaxation in alloys is sometimes denoted in literature as the “i-s” peak. Nevertheless, this “i-s” relaxation in alloys can be explained in terms of the Snoek theory supplied with additional parameter of the SA–IA interatomic interaction in the crystal lattice (which leads to a change in the activation energy of diffusion of dissolved IA near the relatively immobile SA), one can define this anelastic phenomena as the Snoek-type relaxation, i.e. the relaxation with the same mechanism originally proposed by Snoek.

I.2. Review of Experimental Results Those trends which are known from the behaviour of heavy interstitial atoms (C, N)1 in low alloyed iron are inherited by Fe-based alloys and intermetallic compounds born from bcc structure (e.g. the B2, D03 and L21 structures), and thus these trends are interesting for our consideration. Substitutional atoms in a host lattice must influence the parameters of the original Snoek relaxation via IA-SA (or “i-s”) interaction, i.e., by a change in the activation energy of the relaxation, and by a change of the value (λ1 − λ2), i.e., the relaxation strength. In spite of more than 50 years of study since the pioneering works of Wert on alloyed iron, the experimental situation about the influence of SA on the Snoek relaxation has remained not well systemised. Some SA may not affect the position and height of the Snoek peak, others may reduce the

1

Oxygen (O) does not contribute to the Snoek relaxation in iron.


73

peak height, lead to the appearance of additional peaks at higher temperature besides the height reduction, or suppress the Snoek peak and produce new peaks at higher temperatures. In the case of carbon Snoek relaxation in iron a clear effect of substitute atoms in Fe-Al and Fe-Si systems has been noticed in literature [25, 29-36] in contrast with no-effect or very little influence in Fe-Ni, Fe-Ge. One can also find contradicting results in the literature for example with respect to Co and Cr in α-Fe. In some cases existing controversies can be explained by the fact that the authors studied alloys with different amounts of alloying elements. The nitrogen Snoek peak in iron is influenced by the presence of Cr [37], Mn [38,39], Mo and V. All these elements do not produce ordering in corresponding binary ironbased phase diagrams. The nitrogen Snoek peak plays a much less important role in Fe-Albased alloys and intermetallics due to trapping of N into AlN, and is not considered in corresponding subchapters as well as the hydrogen Snoek peak. A review on these peaks can be found in [9,40]. We do not consider in this paper the effect of interstitial atom complexes on the Snoek relaxation which results most generally in the peak broadening. Examples of the carbon Snoek peak in Fe-Al, Fe-Co, Fe-Ge, Fe-Si with ~3% of substitute atoms are given in Figure 4. Similar examples for Fe-Al-Si alloys are given in §III. Fitted Debay peaks are added in insets to Figs. 4. The following fitting method was applied in this paper: Computer analysis of TDIF and FDIF spectra. The program employed (∗) for the analysis of relaxation spectra is based on the eq.(1a) that describes the relaxation “Debye” maximum of IF as a function of temperature at a constant imposed vibration frequency (ω = 2πf) assuming an Arrhenius law for the frequency (1/τ) of atomic jumps (eq.(2)). In the case of a normal (Gaussian) distribution of the relaxation times τ, the shape of the IF curve is determined by the broadening parameter β (distribution of relaxation times): −1 Q −1 (T ) = Qmax

−1 max

Q

⋅ ω ⋅τ 0

∞

exp(− z 2 ) ⋅ ω ⋅ τ ⋅ exp( β z )dz ∫ 1 + [ω ⋅τ ⋅ exp(βz )]2 = −∞

∞

exp(− z ) 2 dz ∫ exp(−( H / RT + βz)) + (exp(H / RT + βz)) −∞ ,

(6)

where z = lnτ, H is the effective enthalpy of activation of the relaxation process, and R is the universal gas constant. The program permits one to use two fitting parameters: the number of peaks that are introduced and the parameters of broadening of each peak. The enthalpy of the relaxation process can be taken from an independent source rather than be used as an adjustable parameter in the analysis of experimental data. The fitting technique used for the analysis of frequency dependent IF spectra is similar: The program based on the eq.(1a) that describes the relaxation “Debye” maximum of IF as a function of frequency at a constant temperature. The relaxation time τ0, the activation energy H, and the distribution of relaxation times β can be fitted in the program. In case none of these parameters is known from the Arrhenius plot, they can be estimated from this fit for a given temperature of measurements, in case some of them are known from the Arrhenius plot they can be fixed in the program: ∗

Semin, V.A.; Golovin, S.A.; Golovin, I.S. Program for analyses of temperature (i) and frequency (ii) dependent internal friction data (Russian registration number № 2005611581 (i) and № 2006610674 (ii)).

74

Igor S. Golovin

f ( x, β ) =

( )

2 1 ∞ ωτ ⋅ exp ( βξ ) exp −ξ ⋅ d ξ = ∫ 2 π −∞ 1 + ( ωτ ) exp ( 2βξ )

Q −1 −1 2Qmax

,

(7)

where z = ln(τ/τ0) and x = ln(ωτ0). (a) -1

Q

Fe-3Ge

(b) -1

Q

490

T1=388 K

experim. Fe-C-Fe

0.008

0.009

-1

T1=389 K

experim. Fe-C-Fe

Q

Fe-3Co

H1=0.86 eV

H1=0.9 eV

0.006

β1=0.71

Q

0.006

β1=0,5

485

-1 0.004

0.009 0.004

0.002 -1

0.002

0.0020

0.006

0.0024

0.0028

1/T [K ]

0.006

-1

1/T [K ]

f [Hz]

0.0020

480

0.0024

0.0028

0.0032

480

0.0032

f [Hz]

475 0.003

0.003 470

470

300

350

400

450

500

300

T [K]

350

(c) Fe-3Al

Q

0.006 -1

450

500

T [K]

(d) experim. Fe-C-Fe Fe-C-Me sum.

-1

0.004

Q

400

-1

T1=388, Q =0.0048 H1=0.84, β1=0.68

Q

-1

T2=429, Q =0.0033

3%

-1

Fe-3Si Fe-2Si

H2=1.1, β2=1.35

530

0.002

470

460

0.006

-1

1/T [K ]

0.004

0.0020

0.0024

0.0028

0.0032

450

520

0.004

f [Hz]

2%

f [Hz]

0.002

400

0.002

510 390

300

350

400

450

500

550

T [K]

300

350

400

450

500

T [K]

Figure 4. Influence of Ge, Co, Si and Al (all elements ~3 at.%) on the carbon Snoek peak. Insets: fit of experimental data by Debye peaks.

Results of the Snoek-type mechanism studies can be summarised with respect to alloying elements in bcc iron in the following way: Every substitute (Al, B, Co, Cr, Cu, P, Si) reduces Snoek peak height even if the amount of solute C is the same, and this causes an increase in the proportionality constant between the Snoek peak height and carbon content. In the range where substitutes content is dilute, Co, Mn, Cr, Si, P and Al lead to decreases in Snoek peak height in this ascending order. Cu leads to additional damping component which is explained by C-Cu interaction. The solute carbon presence in the region where the lattice distortion around the substitute atoms is greater than the threshold value (the order of 10-3) cannot contribute to the Snoek peak and the volume of influence region increases as the difference in atomic size increases. The strain field generated by a substitutional atom due to the difference in atomic size is the reason for the reduction in Snoek peak height [35]. The Snoek peak in Fe-C-Ge and Fe-C-Co alloys is unimodal (Figure 4 a,b) at least up to a certain concentration of SA; its parameters are relatively close to those of the carbon Snoek peak in iron. Cobalt (≤4% [36]) increases the activation energy of the peak slightly, at higher


75

concentration of Co in Fe the Fe-C-Co component of the Snoek peak can be observed [32]. The Snoek peak in Fe-C-Al alloys is formed by two components (Figure 4c): a peak in which parameters correspond to those of the Snoek peak in pure iron (Fe-C-Fe) and a second peak whose parameters are determined by an additional interaction between C and Al atoms (Fe-CAl). The Snoek peak in Fe–C–Si (Figure 4d) is at least broadened (as shown for Fe-3Si by dotted line); in some tests the Fe-C-Si relaxation component is clearly observed (Figure 4d) [30, 36, 41]. The shape of the Snoek-type peak in Fe-Si alloys is sensitive not only to the heat treatment regime but also to inhomogeneous distribution of Si in Fe and can be slightly different from sample to sample: for that reason it is difficult to conclude if the peak at ~450K (Figure 4.d) is a part of the Snoek peak or has another reason (see also §III.3). The activation energy of the Fe-C-Al peak is higher than the basic peak by ~0.2 eV due to an additional (elastic) C-Al interaction in the solid solution. The Fe-C-Al peak is twofold as wide as the basic (Fe-C-Fe) peak, which reflects the existence of a set of different (in their energy state) positions for C atoms depending on their distance from an atom or atoms of Al. Based on the magnitude of the critical concentration at which the basic (Fe-C-Fe) peak vanishes and only the Fe-C-Al remains (~12%Al), i.e., at which the C atom always feels the Al atoms, the range of the C-Al interaction was estimated as equal to at least three coordination shells [36]. At a comparable concentration of Al and Si in the Fe-Al-Si alloys, Al exerts a greater effect on the profile of the temperature dependence of IF in the range of the Snoek relaxation, which is explained by its more efficient contribution to the long range elastic interaction with C atoms [36, 56]. In both binary (Fe-Al, Fe-Si) and ternary (Fe-Al-Si: see §III.3) alloys, an increase in the temperature of heating for quenching leads to an increase in the Fe-C-Fe component at the decrease in the Fe-C-Me component of the Snoek peak. Low temperature ( 10-12%. The pronounced effect of ordering (annealing below 675K) and disordering (quenching from 1075-1275K) was recorded for Fe-22Al alloy [58]. Disordering results in the peak broadening due to an increase in different types of positions for C atoms in bcc Fe(Al) solution, while the peak height decreases correspondingly. If ordering takes place, the number of positions for C atoms in Fe(Al) ordered solution decreases and the peak becomes more narrow but correspondingly higher. The effect of ordering depends on time and temperature of annealing [58]. The effect of ordering in as quenched and annealed alloys with a different Al content is shown in Figure 6 [59]. The peak width in as quenched from disordered A2 range specimens increases significantly with increase in Al% in iron from ~10 to ~ 22%Al (βmax > 3), then decreases to β = 1.5-2.0 in the D03 and B2 ordered ranges. Similar effect in quenched and aged specimens is smaller because of short and long range ordering even for alloys with less than 22%Al, and β ≤ 1.5 for alloys with Al > 22%.

-1

(Q (T)-Qb )/(Q (Tmax)-Qb )


Fe-C-Al

-1

-1 -1

-1

0.8

-1

0.6

Fe 0.68Al 1.51Al 2.30Al 5.86Al 8.79Al 11.1Al

8.79 0.68 2.3 5.86 1.51

0.4

11.1

0.2 ~1.2 Hz 0.0 300

350

(a)

400

450

T [K]

500

-1

Q -Qb /Qmax -Qb

-1

Fe-C-Fe

1.0

Fe 2.9Al 7.1Al 8.5Al 10.6Al

1.0

0.8

Fe-C-Fe

77

Fe-C-Al

0.6

8.5 0Al

2.9

7.1 10.6

0.4

0.2 ~ 500 Hz 0.0 300

350

400

450

T [K]

500

(b)

Figure 5. Influence of Al content (in the range between 0 and 12 at%) on “normalized” TDIF in bcc FeAl alloys: a) as measured at torsion at ~1.2 Hz by Tanaka [52], original data are presented in inset, and b) as measured at bending at ~500 Hz by Strahl et al. [56]. For better visualisation the peaks height is normalised to one: two components of the peak can be seen in both cases.

Influence of C content. The effect of carbon on the peak height was reported by several authors in 1970-1980 (e.g. in [50-53]) but questioned more recently in [63,64], and reviewed in [60]. The increase in the peak height with increase in C content in Fe-25/31Al alloys can be seen in Figure 7 [61]. The dependence of the area under the peak on carbon content is practically linear. The usage of single crystals of Fe-26Al confirms the typical for the Snoek relaxation orientation dependence of the Qm-1 on Г [62]. Influence of other Me atoms. The additions of carbide and non-carbide forming elements to Fe-(20-25)Al alloys acts differently on damping spectra. While non-carbide forming elements (Si, Ge, Co, Mn) produce like in α-Fe little influence on the Snoek-type peak height, shape and temperature in Fe-Al, strong carbide formers (Nb, Ta, Ti, Zr) completely eliminate the Snoek-type peak confirming the carbon Snoek-type origin of this effect. Cr, being a less strong carbide-forming element, decreases peak, modifies peak shape and shifts it to a higher temperature. See §III for further details. Contribution of vacancies. The diffusivity of thermal vacancies in Fe-39Al (B2 phase of Fe-Al phase diagram) studied by positron lifetime spectroscopy [63,64] are characterized by the effective enthalpies HF = 0.98 eV for vacancy formation and HM = 1.7 eV for vacancy migration. These values are close to the activation energy of the Snoek type and X relaxation (see §II.2). In case of quenching from high temperature these two types of relaxation (due to carbon and due to vacancies) can overlap in the same temperature range in Fe-Al alloys [59, 65]: increase in Al% and annealing temperature above 1275K before quenching increases contribution of vacancies. Nevertheless the peak drastically decreases in the presence of carbide forming elements proving the dominating role of carbon.

78

Igor S. Golovin

β for the Snoek peak

4

quenched from B2

quenched from A2

in quenched state quenched and aged

3

2

1 short-range order

long-range order

0 0 10

15

20

25

30

35

40

at. % Al in Fe Figure 6. Influence of Al concentration and regime of heat treatment (quenched = partly disordered state, aged = ordered state) on the width β of the Snoek-type peak. Arrows indicate influence of ordering [59].

(a) Fe-31%Al

100

31.0Al-0.006C ~270 Hz

-1

~ 500 Hz Fe-26% Al + 0.3% Nb + 2% Ti

80 60

with Ti or Nb

~2 Hz

-1

30

~ 2 Hz Fe-26% Al + 0.3% Nb + 2% Ti

without Ti and Nb

-4

30.7Al-0.003C ~400 Hz

S

120

31.2Al-0.009C ~520 Hz

Q , 10

-4

40

Q -Qb , 10

50

-1

60

(b)

20 10

heating

X

~500 Hz

40 20

cooling

0 400

0

500

600

T [K]

400

500

600

T [K]

700

Figure 7. a) Influence of carbon content in alloys of Fe-31%Al (quenching from 1220 K) on the Snoektype peak height at heating. No peaks occur during subsequent cooling. b) Influence of carbide forming elements (Nb and Ti) and measuring frequency (~2 and ~500 Hz) on the temperature dependent IF for Fe-26%Al alloy after water quenching from 1270 K [61].

Modelling. Results presented in Figure 5 were used in the simulations as a Snoek-type effect. They show that the Fe-C-Fe, i.e. “pure iron” component is not seen more in the Snoektype peak if the Al concentration in iron is more than 10-12%. It means that if there are 1012%Al in iron the Al atoms always affect C atom jumps in the Fe(Al) solid solution. From this the effective distance of the C-Al interatomic interaction can be estimated from

5 ⋅a /2

(a is lattice parameter) or as three coordination spheres as a minimum and 9 ⋅ a / 2 (six coordination spheres) as a maximum [56]. Monte Carlo simulations based on KhachaturianBlanter approach (see Appendix) using energies of the long-range strain-induced (‘elastic’) pair interatomic C-Al interaction supplemented by ‘chemical’ repulsion demonstrate [55] the


79

strong influence of ordering reaction on carbon redistribution around Al atoms and correspondingly on parameters of the Snoek-type peak (Figure 6): this effect is stronger in FeAl alloys with Al < 25% with the A2-to-D03 transition [55] than in alloys with Al > 25at.% with the B2-to-D03 transition [59]. The main factor which determines the effect of Al on the carbon Snoek-type peak is the long-range (up to five coordination shells [55]) ‘elastic’ interaction. The ‘elastic’ C-Al attraction significantly increases the peak temperature and the ‘chemical’ C-Al repulsion according to Lennard-Jones potential compensates this increase but not completely: the carbon Snoek peak temperature in Fe-Al is higher than in α-Fe. Concluding remarks to §II.1. The mechanism of the Snoek relaxation in metals may be extended to the Snoek-type mechanism in bcc alloys, in particular in Fe-Al alloys. The Snoek-type mechanism means that the origin of this phenomena in alloys is the same with the Snoek relaxation in metals: an interstitial (in our case carbon) atom jumps under the stress in alloyed iron with bcc stucture, and parameters of these jumps, i.e. parameters of the relaxation process are influenced by interstitial (C) – substitutional (Al) atoms interaction in solid solution. Foreign Me atoms and vacancies can modify parameters of the Snoek-type peak or contribute in the same range of temperatures independently.

II.2. The Vacancy and Vacancy-and-Carbon Complexes Related Phenomena (The X Peak). This relaxation effect with average activation energy about 1.7 eV has been repeatedly observed in Fe-Al alloys since 1996 by different authors [63-67]. The term “X peak” was introduced in our papers [59, 60] to call somehow this relaxation effect. The temperature location and the peak height at TDIF for the X relaxation curve (for f ~1 and 0.1 Hz) can be seen in Figure 8, and for f ~ 500 Hz in Figure 7. The X relaxation is practically not observed for alloys with Al < 25%, which is nevertheless possible is case of very quick quenching from high temperatures and using low frequency measurements even in Fe-12Al alloys. Proposed mechanisms. An elegant interpretation of the X peak (e.g. in Fe-37.5Al alloy the peak parameters are: activation enthalpy H = 1.7 eV, τ0 = 10-13 s and Qm-1 = 0.0012) was suggested in terms of vacancy reorientation: as reorientation related effect of “pure” vacancies [64] or iron-cite-vacancy VFe-and-Fe atom complexes [63]. A strong argument favouring this approach is that the activation energy for vacancy migration and the activation energy deduced from X-peak are rather similar. A similar explanation but in terms of movement of Al atom by means of thermal vacancies was given more recently for the IF peak in Fe-29Al alloy with parameters: H = 1.64 eV, τ0 = 1.2×10-15 s and Qm-1 ~ 0.001 in [68]. Contrary to the above vacancy-and-metal atom-related explanations it was noticed that a similar peak (H = 1.6 eV, τ0 = 1.7×10-14 s) in Fe-32Al depends on the carbon content and the peak was explained as the “second” Snoek-type peak (i.e. jumps of carbon atoms) in the presence of an additional phase, other than equilibrium D03 [66, 67,69]. At the same time the “ordinary” Snoek-type peak in the D03 structure was reported at lower temperatures. The hypothesis of C-vacancy complex formation in Fe-Al-C-vac system is discussed in [70].

Igor S. Golovin

-1

Q , 10

-4

80

< 25 % Al

50

α -F e

40

1 1 .7 % A l 2 2 .5 % A l

30

S

20 10 0 80

300

500

-4

60

T [K ]

700

X

> 25 % Al 3 1 .5 % A l 35% Al 40% Al

-1

Q , 10

Z

40 20 0

400

600

T [K ]

800

(a) 0.012

2.3

-1

2.2 0.008 2.1

G, arb

tanφ (Q )

Fe-25%Al, f=0.1 Hz

0.004 2.0 Snoek peak

X peak

0.000

1.9 300

400

500

600

T [K]

(b) Figure 8. Examples of the X peak: a) overview of the Snoek-type, X and Zener peaks in Fe-Al alloys (~1 Hz) and b) TDIF in Fe-25Al (0.1 Hz: forced vibrations), changes in relative shear modulus (right scale) are discussed in §II.6.)

Experimental results. Several tests have been carried out to study the mechanism of the X relaxation peak in Fe-Al alloys (the X peak was also recorded in Fe3Al intermetallic compound after quenching [58, 71]). The summary of these experiments shows that: a) The peak increases with increase in Al content at least between 25 and 40% (Figure 8a) [58,71]. In the range above 40%, the situation is more complicated; increase in


81

annealing temperature before quenching (i.e. increase in concentration of thermal vacancies) increases the peak height. The difference of activation energies between the Snoek-type peak and the X peak remains about 0.5 eV in almost all tests [74], b) The peak height is very sensitive to heating rate during TDIF measurements: the annealing of alloys decreases it drastically; moreover, the peak decreases at the same time with the measurements of the Q-1 as a function of temperature. For this reason a decrease in resonance frequency, i.e. temperature of the peak, helps always to have a higher peak (Fig 8b): e.g. increase in the frequency from 0.1 to 500 Hz decreases the peak by nearly one order of magnitude (see Figure 7b and 8b). This effect of heating rate on the peak height was recently studied by Han [65,75]. c) The peak dependence of the C content in as quenched Fe-25Al and Fe-31Al alloys was demonstrated mainly on a qualitative level [61] because of the peak instability with respect to heating during TDIF tests. In ternary Fe-Al-Me (Me = Cr, Ge, Mn, Nb, Si, Ta, Ti, Zr) alloys (see in §III) the peak was never recorded in the presence of strong carbide forming elements Ti, Nb and Zr, Ta; the same concerns also the Snoek-type peak. The peak parameters are modified if Cr added in Fe-Al: peak shifts to higher temperature, i.e. higher activation enthalpy and the peak height decreases. At cooling the X peak decreases more than the Snoek peak. The peak is only little changed if Si, Ge or Mn are added, some weak tendency to decrease in the peak temperature can be seen in the presence of Si and Ge in Fe-Al. d) The peak splits into two peaks if Al concentration in Fe-Al is above 30% (see e.g. Figure 8a, curve for Fe-35Al or in [59]), the height of each partial peak depends on quenching temperature and exhibits more complicated behaviour in alloys with more than 40%Al presenting probably both carbon-and-vacancy and triple vacancy complexes contribution. This later viewpoint was recently studied for alloys with >40%Al in [65,75]. Simulations. Computer simulations of the X relaxation in Fe3Al were carried out using a model of carbon atom diffusion under the applied cyclic stress in an Fe3Al-vacancy-C solid solution (see Appendix); the results of these simulations were compared with experimental data. The following factors were taken into account in the modeling: concentration of C atoms, vacancies and degree of Al atom ordering (Figure 9). The simulations show that carbon atom jumps near vacancies in the Fe3Al intermetallic compound can lead to an anelastic relaxation with activation energy higher than that of the carbon Snoek-type relaxation. In terms of internal friction this type of anelasticity leads to the appearance of the X peak. Thus, the X peak is a complex effect in which both interstitial atoms and vacancies are involved [72, 73, 75]. From these experimental results and calculations it can be concluded that the peak is strongly affected by the presence of both carbon and vacancies in Fe(Al) solid solution. It can be suggested that complexes carbon-and-vacancy and vacancy-and-vacancy are responsible for the X relaxation [74]. These two peak components are recently distinguished in [65, 75]: the 1st – smaller but more stable with respect to annealing - due to carbon-and-vacancy, the 2nd – due to vacancies complexes in Fe-Al-C-vac system. This second vacancy-related peak is very sensitive to heating, that is why it can be recorded only if a high heating rate (> 5 K/min) is used. At slower heating this peak decreases due to vacancy decrease during the measurements.

-1

0.6 0.5

QX /Qo

-1

QX /Qo

0.8

-1

Igor S. Golovin

-1

82

degree of order

0.4 0.3

0.6

carbon

0.2 0.1

0.7

0.8 η

0.9

1.0

0.4

vacancies 0.2

0.0 0.00

0.02

0.04

0.06

0.08

0.10

at. %

Figure 9. Dependence of the X peak height (arb. units) on carbon concentration (1) at vacancy concentration 0.094% and on vacancy concentration (2) at carbon concentration 0.047 %. Inset: Dependence of additional peak high on a long-range order parameter (C = 0.047 %, vac = 0.094 %).

II.3. The Zener Relaxation The existence of solute next neighbour atom pairs in crystalline lattice results in a relaxation maximum, well known as the Zener peak [76] in a temperature range where the solute atoms are mobile and enable reorientation of the solute atom pair in the lattice under the action of the applied stress. The Zener relaxation in Fe-Al was first reported in 1960 by Shyne and Sinnot [77] and then by several authors. The origin of this phenomenon is stressinduced ordering of Al atom pairs in iron by short-range diffusion jumps. The theory of the Zener relaxation proposes the relaxation magnitude (δJ) is [4]:

δJ = [ f ( χ o , C Al ) × (C Al2 (1 − C Al ) 2 ) / k BT ] × β a 2 ( dU p / da p ) 2

(8)

where T is temperature, kB is Boltzmann’s constant, the term CAl2(1-CAl2) exhibits the concentration dependence of δJ: CAl is the atomic concentration of Al in iron; the function f(χo,CAl) reflects the effect of order of Al atoms on δJ: χo is a parameter of short range order in the absence of external stress, f(χo,CAl)=1 for the disordered state and f(χo,CAl)=0 for the complete ordered state (the Zener relaxation is impossible in 100% ordered alloy); β is a dimensionless geometrical parameter, a is the interatomic spacing, ap – the same in the direction “p”, Up is the ordering energy in the direction “p”, p is a direction of applied stress. Activation energy of the Zener relaxation should be close to the activation energy of Al atoms diffusion in iron [78, 79]. Effect of Al atoms Concentration and Ordering a) Temperature dependent internal friction (TDIF). The Zener peak temperature in Fe-Al alloys as measured at frequency ~1 Hz is close to 790-805K, and moves to a higher temperature if the frequency of measurements is higher [49, 50, 80]. These temperatures


83

correspond to the A2 disordered range of the Fe-Al phase diagram for alloys with Al 20%. The temperature for the D03-to-B2 order transition in binary Fe-Al alloys with Al concentration close to 25% is about 820K, i.e. close to the Zener peak position if measured at ~10 Hz. The disadvantage of the TDIF tests in the temperature range close to the orderdisorder or order-order phase transformations is that the structural state of alloys changes during TDIF tests, which restricts applicability of the Arrhenius plot to determine activation diffusion of Al in iron.

100 -4 -1

75

T, K

Qm , 10

frequency in kHz: 850 1 [50] 0.3 [104] 0.2 [56] 0.05 [66]

frequency in Hz: 1.3 [80,122] 3 [63,64] 1.4 [49] 1.8 [58]

B2'

Lines of the Fe-Al diagram

50

800

B2L

750 25

D03

A2 0

0

10

20

30

B2 40

700

at. % Al in Fe Figure 10. Zener peak height (QZ-1) vs. Al %.

The TDIF tests demonstrate the Zener peak broadening in Fe-Al-Me (Me = Cr, Si) alloys mainly from high-temperature side. This effect comes from a contribution of Me atoms to the Zener effect [81, 82], i.e. to the short-range diffusion jumps. The Zener relaxation in Fe-Al-Si ternary alloys, as studied by TDIF, demonstrates a double-headed Zener peak caused by AlAl and Si-Si pairs reorientation under stress Fe-Al-Si alloys [82]. The broadening of the Zener peak from high temperature side in Fe-Al-Cr alloys was observed by TDIF [81] and FDIF [86] tests (see §II.4). b) Frequency dependent internal friction (FDIF). The isothermal FDIF spectroscopy allows one to measure a peak at a fixed temperature [83], i.e. practically at equilibrium conditions in different ranges of the phase diagram (Figure 11a, inset). Such tests demonstrate a difference in the Zener peak parameters in different phases, i.e. the difference in the relaxation strength (Figure 11a) and activation energy (Figure 11b) of the Zener relaxation in the D03 or B2 ordered and the A2 disordered states of the Fe-Al alloys [84, 85] and gives values of the activation energy in these phases very close to the diffusion experiments [78,79].

84

Igor S. Golovin

The activation energies of the Zener relaxation in A2, B2 and D03 phases are in the same sequence as the activation energies of diffusion in these phases, i.e. HA2 < HB2 < HD03 (Table 1). 40

T=738 K 1.165

Modulus arb. units

4

Q (10 )

100

-1

30

80

882 856 833

4

1.160

20

2

809

step-by-step: heating cooling

60

ln (freq./Hz)

10

4 -1

Q x10

Fe-25.8Al

1.155 0 -3

-2

-1

0

1

2

log10(freq./Hz)

738 692 723 40 668 708

783

768

753

0 -2 -4 -6

20

D03

-8

-3

-2

-1

0

1

B2

-10

2

1.6

1.5

1.4

1.3

log10 (freq./Hz)

1000/T (K)

(a)

(b)

1.2

1.1

Figure 11. Zener relaxation in the Fe-25.8Al alloy: (a) overview of Zener peaks measured at different temperatures between 668 and 882 K; inset in left-upper corner: isothermal tests at 738 K: IF and relative modulus supplied with exponential background, and IF peak after background subtraction; (b) Arrhenius plot [84].

Table 1. Parameters of the Zener relaxation in Fe-21.7Al, Fe-25.9Al and Fe-28Al-3Cr [84,85] alloys and diffusion data for Fe-25.5Al [78,79]. Alloy, at.%

Zener relaxation f [Hz]

Fe-21.7Al

Fe-25.9Al

T [K]

10-4-102

10-4-102

H [kJ/mol]

Activation energy of diffusion (Fe-25.5Al), kJ/mol

τ0

[sec]

Interdiffusion [79]

2

Fe-28Al-3Cr 10 -10

Al tracer Fe tracer diffusion diffusion [79] [78]

< 730

271±6

9.1×10-18

D03+A2

730-773

238±6

4.3×10-17

A2

< 820

286±8

4.8×10-19

> 820

235±2

8.0×10-17

269±17 231±5

-4

Structure

< 835

276±5

2.8×10-19

236±3

278±5

D03

232±2

B2

217±8

A2 D03 / B2


85

The increase in the activation energy of the self-diffusion with increase in order parameter (η) is in agreement with the Girifalco’s theory: H(η) = Hη=0×(1+ αη2), where α is a parameter. The activation energies of the Zener relaxation are lower than the activation energies of interdiffusion in B2 and are practically the same as the activation energy of the Al tracer diffusion in B2 [79], i.e. the Al self diffusion in Fe-26Al. Practically exact fit in the B2 range can be incidental: the Zener reorientation mechanism involves vacancy and host atom jumps but not only single Al atoms diffusion, and should be slightly below the activation energies for solvent and solute self diffusion. It is notable that the FDIF provides an opportunity to study diffusion at relatively low, untypical for diffusion experiments, temperatures, i.e. in low-temperature phases like the D03 phase in Fe-Al. The f(χo,CAl) function in eq. (8) can be analytically determined in case the degree of order can be quantified in the same temperature range with FDIF tests. As yet we have not succeeded in the corresponding X-ray experiments in situ due to oxidation of the specimen surface which might be interesting in the future. The mechanism of the Zener relaxation in ternary Fe-AlMe alloys should be studied carefully to find out contribution of Al-Al, Me-Me and Al-Me pairs.

II.4. High temperature relaxation: grain boundary / dislocations Grain boundary (GB) relaxation is one of the earliest examples of damping in polycrystals. Zener found for polycrystals (grain size d) with random GB (width δ) a relaxation time τσ [87]:

τσ =

ηd σd = , GU δ GU v(0)

(9)

where η is an appropriate viscosity for grain boundary sliding (correlated with atomic self diffusion: η = kT/Da, D = ½νja2 is the diffusion constant, νj is the jump frequency, a is the atomic distance), GU is unrelaxed shear modulus, σ is acting stress, v(0) = σb/η is initial shear velocity. Later studies have shown that the GB relaxation in alloys is more complex, and should be associated with dislocations rather than with grain boundary sliding [88]. The GB-related peak in Fe-Al is mentioned in several papers [50, 81, 83]. According to Hren [50] the GB peak in Fe-24.8Al (at ~970 K, 950 Hz) is recorded only at ~50K higher temperature than the Zener relaxation for the same alloy. Wert [89] reported the GB peak in Fe-28.3%Al at higher temperature 1023K (torsion frequency is not indicated in this paper but from the specimen size one can estimate it to be ~1 Hz). In both cases the increase in the grain size leads to a decrease in the IF peak height, and from this the GB origin of the peak was concluded. The IF peak at ~750 K (~4 Hz) with H ≈ 1.8 eV and τ0 = 10-14 s in Fe-50%Al nanocrystalline alloy was also attributed by the authors to the GB peak [90]. Pavlova et al. [82] explained a decrease in the IF of Fe-Al-Si alloys in the temperature range from 870 to 980K with increase in annealing temperature of the specimens and corresponding growth of grain size by the GB relaxation. Lambri et al. [91] has repeated the measurements of the same Fe-Al-Si alloys and

86

Igor S. Golovin

found that the IF peak at (~1000°C) depends very much on the temperature of the D03-to-B2 transition (Figure 12): contrary to a symmetrical peak in B2 phase, the high temperature peak is very much suppressed in the D03 phase which can be explained by lower dislocation mobility in the D03 structure (see §III.3).

120

3

Q [10 ]

100

-1

80

Fe-6Al-10Si Fe-8Al-7Si Fe-5Al-20Si Fe-12Al-12Si Fe-26Al

60 40 20 0 600

700

800

900

1000

1100

1200

1300

T [K] Figure 12. Q-1(T) curves in the range of elevated temperatures (f ~ 1 Hz) for Fe-5Al-10Si, Fe-8Al-7Si, Fe-25Al, Fe-12Al-13Si, and Fe-5Al-20Si specimens after background subtraction.

High temperature IF peaks in Fe-38Al alloy were studied by San Juan et al. [92] using a forced torsion pendulum (10−3 to 10 Hz). Two peaks have been observed at about 780 and 1100K (1 Hz), which are largely superposed in the intermediate temperature range. Both peaks were attributed to relaxation mechanisms. The low temperature peak was identified as the Zener relaxation of Al atoms. The activation energy of the high-temperature peak has been determined to be Hact = 2.87 (±0.05) eV, a pre-exponential factor τ0 =10−15 s, and a broadening of the peak of the Gaussian distribution with β ≈ 4. The opportunity for the GB relaxation in this alloy was according to authors completely blocked by the presence of the Y2O3 particles, and other very small particles (less than 50 nm) of Y and Al oxides. The peak was attributed to the kink pair formation (KPF) mechanism of the 〈100〉 dislocations on their {100} glide planes. The measured τ0 ( = 10−15 s), corresponds well to a dislocation motion controlled by the KPF mechanism: in bcc metals the value of τ0 for the so-called γ peak due to KPF on screw dislocations is between 10−13 and 5×10−17 s [93], and in particular it is in between 4×10−13 and 1.2×10−15 s for pure iron [94]: (the activation energy of the γ peak in iron is lower). Thus this peak is associated with the intrinsic motion of such 〈100〉 dislocations in the B2 ordered phase which is in agreement with Lambri’s conclusion about dislocation-related origin of this peak [91] (see also in III.3). Similar high temperature peaks were observed using FDIF technique in Fe-25Al-(3, 9, 15)Cr alloys by Rivière in [86] Figure 13: the high temperature background was lower in these experiments as compared with [92] which makes a question about the Y2O3 particles contribution due to a difference in the thermal expansion coefficient of the matrix and


87

particles. The activation parameters (τ0, H, and β) for the P1 (Zener) peak and the P2 (GB) peak at higher temperature for Fe-25Al-9Cr were estimated by fitting by the program discussed in §I.1 and are given in Figure 13. (see also in III.2).

200

T=838 K

P2

150

927 K

867

300 -4

838

898

Q , 10

100

-1

823

150

0

-4

-2

0

2

lo g 1 0 (fre q ./H z )

-1

estim ated background

Q , 10

200

experim ental curve

Fe-25Al-9Cr T=838 K

experiment

P1 P2 sum

-4

50

β2=1.9 -17

P2

P1 (Zener)

P1

-4

-3

-2

-1

0

1

log 10 (freq./H z)

(a)

2

3

-18

τ01=5x10

P2 H2=2.95

P2 50

difference

β1=0.95

100

100

0

P1 Zener H1=2.54

0 -4

-3

-2

-1

0

1

τ02=1x10

2

3

log10 (freq./Hz)

(b)

Figure 13. Q-1(f) curves at elevated temperatures for specimens of Fe-25Al-9Cr alloys: a) experimental data at 838K with and without background. Inset: peaks at different temperatures, b) results of the peak deconvolution (Golovin and Rivière).

II.5. Low temperature relaxation: effect of deformation A broad, sometimes plateau-like, IF peak has been recorded in several Fe-(20-30)Al alloys at low temperatures (Figure 14a) [61]. It was suggested to be caused by dislocations and point defects (vacancies, self interstitial atoms) and enhanced by deformation (D-peak), in the temperature range of 200 to 300 K (activation enthalpy is roughly about 0.43 to 0.65 eV). The D peak is observed in a temperature range where from plastic deformation studies it is known that the strain rate is controlled by single (partial) screw dislocations moving in the ordered lattice by nucleation and rapid sidewise motion of double kinks [95] with an activation enthalpy for double kink formation of 2Hk = 1.08 eV, i.e. roughly twice the D activation enthalpy. During vibration with low amplitude, on dislocations which are in general inclined to the Peierls valleys, single kinks (generated at the anchoring points of dislocations) move in the microyield region according to the picture in [96], interacting with point defects. The large width of the D “peak” may be due to different kinds and configurations of obstacles for this sidewise kink motion and may be supposed to be composed of γ peak [97] and Hasiguti peaks [98], consisting of reversible and irreversible components [99]. The inverse modulus (E(T)) effect accompanied the D peak in some tests [61] may also result from dragging of points defects according to [100], where “dragging” means in fact short-range diffusion in the dislocation core region.

88

Igor S. Golovin

30

F e -2 5 % A l: 1 0 0 0 °C , a ir c o o lin g

-1

Q , 10

-4

A larger peak is observed after quenching than after slow cooling [61], quenching produces a high vacancy concentration (vacancies can help in dislocation kink formation and migration), and additional dislocations may have been also produced due to thermal stresses. The D peak divides IF background into two parts: below peak temperature of the lowtemperature background is higher, and above the peak – background is lower. This amplitude dependent effect is bigger if higher amplitude of deformation is used (Figure 14a). The decrease of the D peak itself with increase in Al concentration (in quenched alloys with 22 to 31%Al) indicates a contribution of vacancies whose concentration is known to increase [101]. For high Al concentrations (> 30 at.% Al) the D peak seems to be suppressed. While the Snoek and X peak height clearly correlates with the C content, the D peak shows a complex behaviour, possibly because the dislocation kink mobility is affected by carbon, vacancies and self interstitial atoms. The D peak is also observed in several ternary, e.g. in Fe-Al-Cr, alloys [102].

D

5 20

4 3 2

10

1

1)

ε o ~ 0.7 1 0

2)

5 εo

200

-5

3)

10 εo

4)

20 εo

5)

23 εo

T [K ]

300

Fe-27Al

-1

Q , 10

-4

6 5 4

300

200

3

Q m ax

2

Q m in

-1

-1

100

S

1 0

1

ε, %

(bending)

2

Area under the D peak [arb. units]

specimen is broken

(a)

(b) Figure 14. The D peak in Fe-25Al alloys: a) Influence of amplitude of measurements (curves 1 to 5) on TDIF in Fe-25Al alloy after air cooling from 1270 K; b) Influence of cold-work deformation by bending on the D peak height (left scale) and area under the peak (right scale) for Fe-27Al. Before and between cold working the specimen was annealed at 775K, 1 h.


89

Fig 14b shows an example of the D peaks in Fe-26.6at%Al after annealing at 500 oC and step by step bending deformation. The increase of QDmax-1 up to a strain of ε ≈ 1 % reflects the increase of dislocation density in microyield, where long straight screw dislocations are produced by sidewise movement of the easily mobile edge components [96]. The observed dependence supports the idea that at least a part of the damping effect is due to kink nucleation and motion in dislocations.

Figure 15. Structure of Fe-25Al (dark field): a) antiphase D03 domains in annealed at 573 K state ([110](111)) prior to deformation, b) size of grains after HPT deformation, and c) HTP specimen after heating to 923 K: antiphase D03 domains. All images are taken in ~3 mm from the specimen center. Deconvolution of the D peak into several partial peaks for Fe-25Al (d) and Fe-25Al-9Cr (e): Insets dependence of partial peaks from annealing temperature for Fe-25Al and Fe-25Al-9Cr alloys [96, 98].

As low ductility of Fe3Al prevented a closer study of the influence of bending deformation, samples of the intermetallic compound Fe3Al were subjected to high pressure torsion (HPT) deformation. Typically, the average grain size ( d ) in as cast Fe3Al is ~0.1 mm. Well-annealed (72 h at 573 K) Fe3Al is characterised by D03 atomic order with clearly visible domains and antiphase boundaries (Figure 15a). After the HPT deformation (P = 3 GPa, γ = 160) [103], d is comparable to the average size of the D03 domains: ultra fine

90

Igor S. Golovin

grains with a mean size of ~100 nm (at 3 mm distance from the centre, Figure 15b) are dominating in the outer parts of the HPT specimen. Further heating to 920 K during the TDIF tests not only removes the IF peaks but also leads to recrystallisation, grain growth, and atomic ordering (Figure 15c). The D-peak in Fe-25Al is shaped by HPT into a family of five IF peaks: 1, 21, 22, 23, 3 (Figure 15d) which were separated by a numerical decomposition procedure (dashed lines). The D peaks family was also recorded in different Fe-Al-Me alloys (Me = Cr, Ge, Mn, Si etc.) [104]. Comparison between the D peaks in Fe-26Al and Fe-26Al-5Cr [102] shows a difference in the magnitude of the partial peaks from the D-family (Figure 15e). These single peaks are similar to the Hasiguti peaks [98] in cold worked / irradiated metals, i.e. they are caused by coupling of dislocations and different point defects [97]. A distinct group is formed by the “2n“ peaks, which are reduced by annealing more effectively than the other peaks (Figure 15 c,d). These 2n peaks are apparently caused by relatively unstable configurations or associations of point defects. After heating to 500 K with 1 K/min, neither a modulus defect nor the group of the 2n peaks are detected any more. Generally these peaks can be classified as Hasiguti peaks, which typically consist of a several Debye peaks caused by coupling of dislocations and point defects and their segregations. The interaction of the strain field of a dislocation with the strain field of point defects leads to relaxation effects if either the dislocation or the point defect move, or if the dislocation breaks away from the point defect with a characteristic thermally activated relaxation time. Better understanding of atomistic mechanism of the single peaks in Fe3Al should contribute to better understanding of both dislocation behaviour at low amplitudes of vibration in Fe-Al and instability at early stages of annealing of severely deformed alloys [102].

II.6. Elasticity Temperature dependence of elastic modulus of Fe-(24-28)Al alloys in the range from room temperature to 600 °C depends mainly on two factors: the order-disorder (mainly the D03-to-B2) transition, and ferro-paramagnetic (D03(f) to D03(p)) transition [105, 106]. We would only emphasise the contribution of the third factor: the contribution of anelastic relaxation phenomena such as the Snoek-type or X relaxation to the E(T) dependence. Modulus of elasticity, E, is proportional to the resonance frequency: E ~ f2. In this paper we did not calculate exact values of modulus, instead the results are given in terms of resonance frequency (f). Quenching leads to formation of the Snoek and X peaks: TDIF curves for the same alloy with 25.5%Al in well annealed (curve 1) and as quenched (curve 2) states is shown in Figure 16. The relaxation peaks are supplied with decrease in modulus (resonance frequency) and denoted as the ΔS and ΔX effects, correspondingly, in agreement with the scheme given in Figure 1. Relation between dissipated energy and modulus is known as Kronig-Kramers relation (eqs. (1a) and (1b)). Increase in quenching temperature increases ΔS and ΔX effects by increase in C and vacancy concentration in solid solution. In contrast with quenched-in state this effect does not take place in well annealed state (curve 1). Concentration dependence of Curie temperature (TC) is much stronger than temperature of the D03-to-B2 (TO) transition [114]. If phase and magnetic transitions in Fe-25Al alloy are


91

close to each other, an increase in Al concentration up to ~28% practically does not influence temperature of phase transition, while Curie point decreases significantly. Experimental curves for Fe-(23-26)Al can be found in [107, 108]. Alloying of Fe-25Al alloys by most of the studied elements (Cr, Ge, Mn, Si, Ta, Ti) decreases Curie point while influence of these elements on the temperature of the D03-to-B2 transition is different: Cr and Mn do not influence this temperature at least up to 5% solute element, Ge, Si and Ti increases this temperature and thus influence the temperature dependence of modulus [104].

Fe-25.5Al S

D03 D03(f)

460

B2

f [Hz]

D03(p)

100

220

450

Z -4

Q , 10

215

X

1 2

-1

440

ΔS

210

ΔX

2

10

430

205

1

400

500

600

700

800

900

T [K]

Figure 16. Temperature dependent internal friction and resonance frequency curves in Fe-25.5%Al alloy: (1) in well annealed (f ~ 200 Hz) and (2) in as quenched states (f ~ 400 Hz)

Pseudoelastic behaviour of D03 ordered Fe3Al single crystals (Al = 22–25%) with high recovery ratio both in tension and compression was reported [155, 156]. The recovery ratio in D03 ordered state shows a maximum near Al = 23%. In contrast, the recovery ratio of the crystals annealed in the α, B2, (α+B2) and (α+D03) phase regions was small. When large pseudoelasticity takes place, superpartials with b = 1/4[111] moved independently leaving the nearest-neighbour antiphase boundaries. During unloading, the nearest-neighbour antiphase boundaries pulled back the superpartials resulting in the pseudoelasticity. The pseudoelastic behaviour of the D03-ordered Fe3Al single crystals depends strongly on the ordered domain structure. The fine domain structure accelerated the individual motion of 1/4[111] superpartials and suppressed the activation of the secondary slips resulting in the superior pseudoelasticity near Al = 23%.

II.7. Histeretic Effects Dislocations and magnetic domain walls (DW) give contributions to amplitude dependent internal friction (ADIF). These contributions in Fe-Al can be separated using external saturated magnetic field in which magnetic contribution is completely suppressed: see Figure

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Igor S. Golovin

17a for ADIF for Fe-10.4Al alloy at torsion. Both dislocations and magnetic domain walls contributions to amplitude dependent internal friction are also temperature dependent and practically frequency independent in Hz and kHz ranges. High damping capacity due to magnetomechanical hysteresis is determined by irreversible movement of domain walls (90°type for Fe-Al alloys) – see TEM picture of magnetic domains inserted into the Figure 17a. The dissipated energy accompanying DW motion depends on the DW mobility. The mobility of DW is controlled by three factors: a. Structure and size of magnetic domains and DW, i.e. magnetic parameters of alloys; b. Structure of the crystalline lattice in which the DW moves; c. Interaction between the DW and imperfections of the crystalline lattice. There is only a limited number of papers considering all these three points together. Phenomenologically the energy loss ΔW due to magnetic domains for a vibration stress (σ) below some critical stress (σc) is given by the Rayleigh law:

ΔW = Dσ3 ( σ < σc ; D is constant).

(10.a)

For large stresses ΔW saturates and is given by:

ΔW = kλSσc ( σ > σc ),

(10.b)

and the specific damping capacity Ψ is defined as Ψ = ΔW/W. The magnetomechanical damping in ferromagnetic materials has its source in the stressdriven irreversible movement of the magnetic DW. The maximum damping at ADIF is proportional to λSE/σi (λS is the saturation magnetostriction, and σi is the average internal stress opposing domain boundary motion, k = 1 is a constant characteristic of the shape of the hysteresis loop) [109]. For a Maxwell distribution of internal stresses the value of hysteretic IF (Qh-1) was described by Smith and Birchak as: Qh-1 = 0.34kλSE / πσi (at σ ≈ σmax),

(11.a)

Qh-1 = 4 kλSE / 3πσi2 (at σ < σmax).

(11.b)

The dependence of Qh-1 on σi for constant amplitude of external stresses σ : Qh-1 ~ 1/σim, where m = 2 ( for σ « σi ) and m = 1 (for σ = σmax), which corresponds to the data in Figure 17a. The magneto-mechanical amplitude-dependent contribution to IF in Fe−Al alloys was studied in several research papers [60, 89, 110-112, 161, 162]: it was shown that this contribution occurs at room and elevated temperatures, and that it is high enough to consider Fe-(10−12)%Al alloys as high damping materials with Ψ up to 60% (Figure 17b). The temperature dependence of the magneto-mechanical contribution to damping for Fe-25Al (Figure 17c) is in reasonable agreement with the magnetisation curve (Figure 17d), its contribution to the elastic modulus below the Curie point can be seen directly in the f(T) curve in Figure 16. The magnetisation curve is affected by the D03-to-B2 transition. This results in


93

two “Curie points” as known since 1935 [113]. The data extrapolation from the D03 range gives the Curie temperature in the vicinity of 800 K (TC(D03)), while the Curie point at higher temperatures represents some contribution of the disordered phase, in agreement with the Fe−Al phase diagram [114, 115].

Figure 17. Amplitude dependent internal friction in Fe-Al alloys: a)

Typical ADIF curve (Fe-10%Al) with the peak due to magnetomechanical losses, torsion. Inset: magnetic domains – source of high damping. The Lorentz image of magnetic structures after saturating with an external field of 2T (tilted at +30).

b)

Influence of Al content and heat treatment (cooling in air, in furnace, stepwise regulated cooling) on maximal damping (δmax) [106,107],

c)

Influence of measuring temperature on ADIF in Fe-25%Al at torsion [60],

d)

Influence of measuring temperature on magnetization in Fe-26%Al alloy.

Concluding Remarks to §II. Several conclusions about mechanisms of different effects in binary Fe-Al based alloys were done in corresponding paragraphs. The following anelastic phenomena (relaxation peaks) are recognised in Fe-Al alloys and contribute to temperature dependent properties of Fe-Al alloys:

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Igor S. Golovin 1. the Snoek-type relaxation (carbon atom jumps in Fe-Al solid solution: H = 0.9-1.25 eV), 2. the Zener relaxation (substitution atom (Al) pairs reorientation: 2.3-2.9 eV), 3. the vacancy-and-carbon related relaxation (the “X” peak: 1.5-1.8 eV), 4. the vacancy complexes reorientation phenomena (1.6-1.8 eV), 5. the grain boundary peak, also interpreted as dislocation-related peak (~ 3 eV), 6. the deformation-related (“D”) relaxation at subzero temperatures (0.43-0.65 eV), 7. powerful amplitude dependent magnetomechanical damping in Fe-(10-12)Al alloys.

At present the anelastic effects related to the point defects (the Snoek-type and Zener peaks) diffusional reorientation are studied both on qualitative and quantitative levels. The “map” of activation energies for three peaks: the Snoek-type (S), Zener (Z), and the X peak (relaxation effects numbered above as n.3 and n.4 are considered in this “map” as one X peak) against Al% is given in Figure 18 as a function of Al content in iron. More complicated anelastic effects due to complexes of point defects (the Hasiguti and X peaks) are studied mainly on a qualitative level, and their better understanding is needed prior to their possible applications for structural studies. Nevertheless they can give some information about vacancy contribution to anelastic properties (the “X” peaks n.3 and n.4) or about the beginning of recovery processes of severely deformed alloys (the “D” peak family) at least on the qualitative level. Very little as yet known from mechanical spectroscopy about high temperature (grain boundary?) dislocation behaviour in differently ordered and disordered phases of iron aluminides which is probably the most actual direction for future study. There is a reasonable understanding of magnetic contribution to mechanical damping in Fe-Al alloys which allows one to use some of them for high damping applications. Pseudoelastic behaviour of Fe3Al-based alloys should be considered for different applications.

III. TERNARY FE-AL BASED ALLOYS Fe−Al based alloys have gained considerable interest owing to their attractive mechanical properties which can be improved by addition of appropriate third elements (e.g. see proceedings of Discussion Meetings on the Development of Innovative Iron Aluminium Alloys (Düsseldorf 2004; Toulouse 2005; Mettmann 2006; Interlaken 2007)). Fe−Al alloys with strengthening intermetallic phases are promising candidates for structural applications. In this chapter we provide further evidence and arguments in favour of the mechanisms proposed in Sect. II, by checking the changes of the peak parameters with additions of third elements, e.g. those which trap carbon interstitials into strongly bound carbides. They are grouped in the Sections III.1. Fe−Al−(Nb, Ta, Ti, Zr); III.2. Fe−Al−Cr; IV.3. Fe−Al−Si; III.4. Fe−Al−(Co, Ge, Mn), and the results are discussed with respect to their anelastic mechanisms identified in binary Fe−Al alloys.


95

III.1. Ternary Fe−Al−Me Alloys, Me = Nb, Ta, Ti, Zr These four systems have some similarities and can be discussed together: the Ti, Nb, Zr and Ta having different solubility in Fe−Al are strong carbide forming elements in iron-based alloys: they produce MeC carbides, e.g. TiC, TaC, and NbC in Fe-(15−26)Al alloys [116]. The Nb, Ti and Ta increase the temperatures of the D03-to-B2 and the B2-to-A2 transformations in Fe−Al [117], which agrees with our own DSC data (0.3 at.% Nb: TO = 823 K, 2 at.% Ti: TO = 945 K, 4 at.% Ti: TO = 1048 K), and Ti and Ta in alloys with higher concentration lead to the L21 order, in which not only Fe and Al atoms are D03-ordered but also Ti and Ta atoms occupy positions of the (4b) sublattice. Nb and Zr have low solubility in Fe-Al and in particular in the D03 phase.

Figure 19. Structure of Fe-23Al-15Zr (a) and Fe-25Al-6Ta (b) alloys.

In all these alloys neither the Snoek-type nor the X peaks were recorded (Figure 7): Ti, Nb, Zr, Ta trap free C interstitials into MeC carbides, thus suppressing the Snoek and X peaks. This effect takes place even in Fe−Al alloys containing 0.1 at.% Zr or 0.3 at.% Nb: already such small amounts of Zr or Nb erase the S and X peaks. Very little influence of carbide forming elements on the vacancy concentration in these alloys after different regimes of quenching was found [54]. The fact that both the Snoek and the X peaks are suppressed in all alloys containing a strong carbide former supports the conclusion about C in solid solution as the decisive ingredient for these relaxations, similar to those discussed for the binary alloys (§II.1 and §II.2).

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Igor S. Golovin

If a certain concentration of Ti, Ta or Zr in Fe−Al is exceeded, these elements produce different second phases (Figure 19), e.g. Laves phases: Zr2(Fe,Al) hexagonal C14 (λ1) and cubic C15 (λ2), ThZr12-type τ1 phase in Fe−Al−Zr alloys, and hexagonal C14 Laves phases (Fe,Al)2Ti, (Fe,Al)2Nb or (Fe,Al)2(Ti,Nb) in Fe-Al-Ti,Nb alloys, or (Fe,Al)2Ta precipitates [116-119]. In the examples of Figure 18 the phases could be distinguished by Vickers hardness measurements (HV) as follows: For Fe-23Al-5Zr (Figure 19a) the dark phase (HV = 712) represents a eutectic, the bright one (HV = 1085) the Laves phase; for Fe-25Al-6Ta (Figure 19b) the dark phase (HV = 1145) is the eutectic, and the bright phase (HV = 430) mainly Fe−Al solid solution. Two temperature ranges can be distinguished in such “peak-free” Q-1(T) curves for Fe20Al-0.1Zr in Figure 20 between 100 and 800 K, (I) below 400 K, and (II) above 450 K. Taking into account the related increase in f(T) and the start of decrease in the heat flow (DSC signal), this effect can be explained by the higher dislocation mobility in quasi-quenched disordered specimens in range “I”, while the decrease of mobility and consequently of the damping background between 400 and 450 K is supposed to be the result of ordering. Indeed the effect is smaller in the second heating run of the same specimen, which has been cooled down in the vibrating-reed furnace instead of quenching: in the second run the specimen is better ordered as compared to the quenched one. The increase in Zr content to 4% (in Fe40Al) and to 12.5% (in Fe-20Al) leads to a well pronounced decrease of this effect. This may be due to the Laves phase in the 12.5Zr containing alloy which restricts the dislocation motion in the Fe−Al phase. Similar effect in Zr-free Fe-25Al alloy was observed at lower temperature (Figure 14a).

4 -1

D03 + A2

(A2) as quenched

A2 (ferro)

50 Fe-20Al-0.1Zr (wq 1273 K) test-1 40 test-2 f 30 DSC 20 Fe-20Al-12.5Zr

560

TC 0.09

DSC, mW/mg

10

0.14

f [Hz]

Q [10 ]

60

540

0.04

(I)

(II)

520

0 200

400

600

800

T [K]

Figure 20. Fe-20Al-0.1Zr (quenched from 1273K): Damping Q-1 (T), frequency f(T), and DSC curves. Q-1(T) for Fe-20Al-12.5 Zr is added for comparison.

Ti (2 and 4 at.%) decreases the Zener peak in Fe-26Al while no clear effect of the low content of Nb (0.3 at.%) was recorded in Fe-26Al [61], neither 0.1 nor 12.5 % Zr in Fe-20Al change substantially the range of Zener relaxation (Figure 20) due to the low solubility in FeAl. The Zener peak decreases if the transformation temperature TO increases by alloying and


97

if the added metals have reasonable solubility (e.g., Ti); no effect on the Zener peak occurs in case of low solubility (e.g., Zr, Ta, Nb). Alloying by Zr – contrary to the effect of Ti, Ta or Nb – leads to a prominent effect between 370 and 470 K: the level of IF decreases with increasing temperature in this range, although the increase in temperature does significantly influence neither the volume fraction nor the composition of phases in Fe−Al−Zr alloys [118]: The Zr content of the Laves phase in the Fe-23Al-15Zr alloy is 24.0 (after quenching from Tq = 1070K), 23.6 (Tq = 1270K), and 23.3 at.% (Tq = 1420K). At the same time after these treatments the IF differs in the low-temperature range (see also Figure 14).

III.2. Ternary Fe−Al−Cr Alloys An important feature of this system is the high solubility of both Al and Cr in bcc iron. Fe-25Al alloys are often additionally alloyed by Cr, in order to increase not only their yield stress but also their ductility and workability. The Cr atoms occupy the 4b or 8c positions, with some preference of next nearest neighbour Al positions [120]. The lower dissociation energy W(Cr −Al) = 0.6960 eV for Cr-Al pairs than for Fe−Al pairs (W(Fe−Al) = 0.7457 eV) is responsible for the mentioned decrease of the APB energy. The ordering transition temperature is not changed significantly [121] by Cr addition of 20 at.%Al in binary alloys.

150

Δ

Ternary: Si+Al (Si/Al)

Binary: Si [126] Si [160] Al [126] Al [160]

100

4/9 6/8

12/13 and 20/5

10/5

5/6 50

2/6

150

Δ 100

50

5/20

Ternary: Si+Al (Si)

Binary: Si [126] Si [160] Al [126] Al [160]

5 2 20

10

5

6

2/18

4 12

2

0

0 5

10

15

20

at. %

(a)

25

30

5

10

15

20

at. %

25

30

(b)

Figure 30. The relaxation strength of the Zener peak (Δ in binary Fe–Si and Fe–Al and in ternary Fe– Si–Al alloys. Some data for binary alloys were added from [126] (open triangles: up – for Si, down – for Al). Data for ternary alloys [160] are shown by circles. In the left figure, Δ is given as a function of the total amount of Si+Al in at.% and the respective Si and Al contents are indicated at the experimental point as Si/Al. In the right figure, Δ is given as a function of the Al content and the amount of Si in at.% is indicated at the experimental points.

In ternary alloys, the occurrence of Si-Al pairs may reduce the contribution to the Zener relaxation compared to the binary alloys. Indeed the Zener relaxation in all ternary alloys is significantly lower than in binary alloys. This can be seen in the plot of the peak height as a function of the total amount of substitute atoms (Figure 30a). There are at least two reasons for that. Firstly, ordering, which leads to a decrease in the Zener peak height, starts at lower alloying element concentrations in Fe–Si–Al alloys than in Fe–Al alloys. The second reason is that Al and Si atoms in iron at least partly compensate for the elastic distortions produced by each species. This effect can be seen in Figure 30b: For a constant Al content, the addition of Si strongly reduces the Zener peak height (the alloy Fe–9.6Si–5.4Al seems to be an exception; the reason for that is not clear at the moment). Figure 31 shows the lattice parameter in dependence on the Si/Al ratio. As expected, Si decreases and Al increases the lattice parameter of α-Fe. In the ternary alloys it is lower than in α-Fe if Si/Al > 1 and vice versa. Al results in an additional increase of the hardness of the Fe–Si alloys (Figure 31b). However, the effect of Al on the hardness increase in Fe–Si–Al alloys is weaker than that of Si. The height of the high temperature peak (Figure 12) depends on the order degree of the Fe-Al-Si alloys as it can be judged by in situ neutron diffraction studies (wavelength was λ =


107

1.28 Å) performed at the D1B powder diffractometer in the Institut Laue Langevin, Grenoble, France (Figure 32) [91]. The diffraction pattern measured at room temperature for the Fe12Al-13Si specimen (empty circles), the Rietveld refinement (full line) [163] and the difference between measured and calculated profiles are shown in Figure 31,a. The sample exhibits a D03 order. The small differences between the fitted pattern (full lines) and the experimental points are due to preferential orientation (texture effects) of the grains. Figure 31,b shows the evolution of the relative integrated intensity of the (111)/(220) and (200)/(220) reflections as a function of temperature. During cooling the order degree is restored. The (200)/(220) intensity ratio shows an increase below ~800 K that can be attributed to an initial increase of the B2 nearest neighbours order. The as quenched sample recovers the B2 order degree since the B2 - A2 transition is well above the measured temperature range. On the other side, the D03 order evolves mainly near the equilibrium value of the D03 order parameter since the D03 - B2 transition is at a lower temperature. HV

2,90

1.8/17.7

a, A

0/25

5.5/6.8 300

2/4

2,88

Fe

1.8/17.7 0/25

1.9/6.9

7/8 250

12.9/12.4

6/3

2,86

4.7/5.9

9/6 200

2,84

1.9/6.9

25/0 14/0 0

[a]

5

10

15

20

Si+Al (at.%) in Fe

5

25

[b]

Si/Al, at.%

2/4

150

2,82

10

15

20

25

Si + Al (at.%) in Fe

Figure 31. Lattice parameter (a) and hardness (b) of studied alloys in dependence on Si+Al content in Fe (numbers near experimental points indicate Si/Al contents in at.%.

The dislocation structure and solute atoms interacting with grain boundaries control the damping spectrum (Figure 12). The absence of the peak at ~1000K during heating in Fe25(Al+Si) and some Fe-15(Al+Si) alloys is due to a reduced dislocation and grain boundary mobility in the D03 state: dislocations can move in the D03 state in pairs only which leads to a decrease in their mobility. The appearance of the damping peak during cooling in Fe15(Al+Si) can be associated with a higher mobility of the recovered grain boundaries [91]. In conclusion to section III.3: the substitution of Al by Si, forming no carbides and improving the D03 order (increasing the transition temperature to B2) preserves the Snoektype and X peaks, although they are smaller than in Fe−Al and shifted to lower temperatures, indicating the difference in C-Si and C-Al interaction in solid solution, however, keeping C interstitial jumps as essential reasons for these peaks. Si also tends to lower the concentration of vacancies, in agreement with the reduction of the X peak. The Zener peak is again a mixture of the corresponding Fe-Al and Fe-Si peaks, significant decrease in the Zener peak relaxation strength can be a result of formation A-Si pairs. The anelastic phenomenon at

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Igor S. Golovin

about 1000K (~1 Hz) can be most probably attributed to interaction of dislocations and grain boundaries in ordered and disordered phases.

Figure 32. a) Rietveld refinement of the Fe-12Al-12Si specimen at room temperature. The fitting is performed according to the D03 structure; b) Evolution of the relative integrated intensity of the (111)/(220) and (200)/(220) reflection as a function of temperature.

III.4. Ternary Fe-Al-(Co, Ge, Mn) Alloys In spite of many differences in these alloys (e.g., Ge improves the D03 order, Co improves the B2 order, and Mn ( 630K) than in the ferromagnetic state at lower temperatures.

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Igor S. Golovin

f [Hz]

1)

1273K, 24 h., air

620

600

n.I n.II 1

580

2

2) 560 300

plus 650K,100 h.,air 400

500

600

700

800

T [K] Figure 46. Temperature dependencies for resonance frequency (E ~ f2) for different specimen states: 1) homogenized at 1273K (24h) and slowly cooled down in air – heating and cooling curves, and 2) additionally aged at 650K (100 h) after homogenising at 1273 K, 24 h.

-1

Q , 10

-4

40

[1] 1273K, 24 h., air [1a] heating, [1b] cooling plus 650K, 100 h. [2]

20 [1а] [1b] [2]

0 400

500

600

700

800 T

[K]

Figure 47. Temperature dependencies of internal friction (resonance frequency see in Figure 46) for different specimen states: (1) homogenised at 1273 (24 h) and slowly cooled down in air – heating and cooling curves, and (2) additionally aged at 650K (100 h) after homogenising at 1273K (24 h).

A well defined IF peak can be seen around 670K as measured for bending vibrations (roughly at 500 Hz) – Figure 47. This peak is a relaxation peak and a change in the resonance


123

frequency shifts the peak temperature. For example the peak position is about 570K if it is measured at ~2 Hz. As can be seen from Figure 47, neither the peak height, nor the peak position appreciably change if measured during heating or cooling and for specimens after different heat treatments. Such a lacking variation of the peak position is normally attributed to a phase transformation which needs overheating or undercooling to initiate the reaction. A variation in the peak height might be reasonably expected if heating changes the concentration of defects responsible for the peak formation (e.g., the carbon Snoek-type peak in Fe-3Ge or 12Ge alloys). The carbon Snoek-type peak is not observed for the Fe-27Ge composition: contrary to Fe-3Ge and Fe-12Ge alloys with bcc structure, this peak is crystallographically forbidden [1] in the hexagonal phases dominating the structure of Fe-27Ge. The activation enthalpy and the pre-exponential frequency factor were estimated for the peak using an Arrhenius plot and result in H = 1.78 eV and τ0 = 2⋅10-17 s, respectively. The activation enthalpy obtained is lower than that determined for the ε′ phase formation (~2.6 eV according to [148]). The values of H and τ0, as well as the stability of the peak height and position with respect to heating - cooling experiments rather suggest that this peak can be classified as a Zener peak, i.e. the peak is caused by reorientation of pairs of substitutional atoms (Ge in Fe) under the applied stress. 0.0020

Fe-27Ge 1000°С, 24hrs, air

-1

Q

0.0020

Fe-27Ge 1000°С, 24hrs + 375°С, 100hrs experiment peak 1 peak 2 simulations

-1

Q experiment peak 1 peak 2 simulations

0.0015

0.0015

-1

T1=660, Q =0.0016

0.0010

-1

T1=654, Q =0.0017

0.0010

H1=1.78, β1=1.20

H1=1.78, β1=1.20

-1

-1

T2=599, Q =0.0007 H2=1.26, β 2=0.92

0.0005

0.0000

T2=591, Q =0.0006 H2=1.02, β2=0.98

0.0005

0.0000

0.0014

0.0016

1/T, K

0.0018 -1

0.0020

0.0014

0.0016

0.0018

0.0020

0.0022

-1

1/T, K

Figure 48. Simulations of temperature dependencies of internal friction data for two states: 1273 (24 h), and 1273 (24 h) plus additionally aged at 648 K (100 h): Temperatures, height, activation energies (eV) and relaxation time distribution for two simulated peaks are shown at each figure.

It should also be noticed that the relaxation strength of the IF peak (Δ = 2Qmax-1) in all cases was Δ ≈ 0.0036 except for the case of quenching from 1273K. The reason for an increase of the peak height after quenching is not finally clear and, taking into account the observed inverse dependence of f(T), cannot be completely assigned to a relaxation process. Two hypotheses can be considered: first, quenching increases the vacancy concentration and decreases the degree of order in the studied alloy, both factors should increase the Zener peak height. The order-disorder transition may lead to the “anomalous” increase in elastic modulus. Second, the relaxation (Zener) peak can overlap around 673K with a phase transition peak (from undercooled ε to ε′ phase), which is not studied in this paper. This latter idea is partly supported by low frequency tests [133], where in addition to the main peak at ~573K another peak at ~673K was recorded. In any case distinguishing between different contributions to the

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Igor S. Golovin

IF peak at around 673K is not possible if measured at 400 - 600 Hz, and further analysis of the IF peak at around 673K should be performed using states of the alloy closer to equilibrium. Computer analysis of TDIF spectra were carried out according to eq. (6). The information on the enthalpy of activation of the relaxation process is taken from an Arrhenius plot of the reciprocal peak temperature on the logarithm of the frequency of vibrations (Н = 1.78 eV, τ0 = 2⋅10-17 s). The approximation of experimental data (practically independent of heat treatment) by one Debye peak shows values β ≥ 2 and does not fit well to the experimental data due to an asymmetry of the peak. This peak asymmetry and values β ≥ 2 are not typical for a Zener relaxation. Taking into account the coexistence of at least two phases in the specimen structure (ε and β), two Debye peaks were introduced into the fit procedure: peak n.1 with the mean value of activation energy deduced from the Arrhenius plot, and peak n.2 with all parameters free. The results of computer simulations with two introduced peaks fit the experimental results more reasonably (Figure 48) with a least square deviation of < 10-5. It should be noticed that a very small difference in the deconvolution of experimental data into partial simulated peak is achieved in all cases except for water quenching from 1273K with strongly non-equilibrium structure. The mechanism of the second peak found by this procedure at lower temperature (1/T > 0.0017) is probably a Zener relaxation in the phase with lower volume fraction (β phase).

Summary to section IV. The structures and magnetic states of several Fe-Ge alloys studied by DSC, XRD, and magnetometry agree (with few exceptions) reasonably with those in published phase diagrams, better with the phase diagram given by Massalski. In the following, we summarize the new results on IF (mechanical spectroscopy) achieved in this investigation for alloys of Fe with 3…27 at.%Ge. A Snoek-type peak is recorded in Fe-3Ge and Fe-3Ga with parameters close to those for pure Fe. The peak has a slightly larger width (parameter β = 0.4….1.4). A similar Snoek-type peak overlapping with another relaxation process (P3) with slightly higher activation energy is found in Fe-12Ge and Fe-19Ge, corresponding most probably to carbon atom jumps in FeC-Fe, Fe-C-Ge, and Fe-C-Ga surroundings. This indicates some long-range (mainly elastic) interaction between C and solute atoms. The P3 relaxation is attributed to contribution of vacancies. A Zener peak was recorded in the Fe-12Ge and Fe-13Ga alloys. Zener peak in Fe19 and -21Ge alloys is weaker due to ordering effect. High damping capacity was recorded in Fe-12 and 17Ga specimens. While the previous alloys are all based on the bcc structure mainly (in as quenched state Fe-19 and -21Ge alloys have two phase (α + ε) structure), the Fe-27Ge alloy is basically hexagonal, and a high stability of the high temperature hexagonal ε (D019) phase at room temperature is confirmed, much below the range in the common phase diagrams. The second phase at room temperature is the hexagonal β (B81) phase, and a little amount of the cubic ε′ phase is also present in the alloy. The variations of the elastic modulus are consistent with the phase changes mentioned before. A broad asymmetric relaxation internal friction peak is found around 670 K. Its relaxation strength Δ ≈ 0.0036 being independent of the heat


125

treatment regime, a relaxation time distribution corresponding to a broadening parameter of β ≈ 2, a mean value of the activation enthalpy H of about 1.8 eV, and the pre-exponential relaxation time τ0 = 2⋅10-17 s suggest that this peak arises from Zener relaxations in the mixture of the ε and β phases in the Fe-27Ge alloy. An increase in the Ge content in Fe decreases the ferromagnetic properties of the alloys and consequently decreases their damping capacity.

ACKNOWLEDGEMENTS The author is grateful to H. Neuhäuser, H.-R. Sinning, F. Stein (Germany), A. Rivière (France), O. Lambri (Argentina), M.S. Blanter (Russia) and S.A.T. Redfern (UK) for longrunning cooperation, to U. Brust and D.W. Zachmann for the help in producing and chemical analyses of the alloys, to S.B. Golovina, Ch. Grusewski, S. Jäger, T. Abraham, C. Mennerich, C. Siemers, J. Čížek, M. Maikranz-Valentin for valuable help in experiments, to former and recent students A. Strahl, T. Pavlova, T. Sazonova, T. Ivleva, and O. Sokolova for their enthusiasm. Financial support by DFG, the Royal Society and RFFI is gratefully acknowledged.

APPENDIX Method of computer simulation. The internal friction Q−1 is calculated as a sum of Debye contributions of different interstitials, in this case carbon atoms [149, 150]: N

Q −1 = ∑ [δ ⋅ (ω ⋅τ p ) /(1 + (ω ⋅τ p ) 2 )]

(A1)

p =1

where: N is the number of C atoms in the model crystal; ω and f (=1Hz) are the angular frequency and the frequency of oscillation, respectively; δ is the relaxation strength per carbon atom; T is the temperature; τp is the relaxation time for the p-th interstitial atom: τp = τ0exp(Hp/kBT),

(A2)

where Hp is the diffusion barrier for the p-th atom, kB is the Boltzmann constant, τo is the preexponential factor of the relaxation time. HP = H - EP, where H - the diffusion barrier (activation energy of the Snoek relaxation) in Fe-C dilute solid solution, and Ep is the energy of p-th carbon atom interaction with other C atoms, Al atoms, and vacancies:

E p = ∑W j

( C −C )

(r p − r j )C (r j ) + ∑ W (C − Al ) (r p − rm )C (rm ) + ∑ W (C −vac) (r p − rk )C (rk ) m

k

(A3)

126

Igor S. Golovin

where the vectors rp and r j describe the positions of the octahedral interstices, rm and rk those

of

the

crystalline

lattice

points;

W ( C −C ) ( rp − rj ) , W ( C − Al ) ( rp − rm )

and

W ( C −vac ) ( rp − rk ) are the energies of C-C, C-Al, and C-vacancy pair interactions, respectively, and C( r ) are the corresponding occupation numbers on the octahedral interstices and lattice points. C( r )=1, if the interstitial or lattice point is occupied by a solute atom or a vacancy; C( r )=0, otherwise. Taking the solute interaction into account, the following assumptions were made: (i)

The long-range C-C and C-Al pair interactions as well as the short-range Cvacancy interaction affect the energy of C atoms in the octahedral interstices EP. This changes both the C distribution (short-range order of C atoms) and the diffusion barriers Hp of the individual C atoms.

(ii)

The pre-exponential factor τ0 of the relaxation time τ is independent of the solute interaction.

(iii)

Each C atom has the same relaxation strength δ, which is inverse proportional to temperature according.

Monte Carlo simulations were carried out to calculate the short-range order configuration, energy changes, energy distribution and individual diffusion barriers of the carbon atoms. The internal friction was calculated at each temperature by averaging Q-1 over the atomic configurations obtained from the Monte Carlo simulation. Easily-moved carbon ♣ atoms (0.0235-0.094 at. %) are distributed randomly at the octahedral interstices of a crystalline lattice in a model crystal of size 22×22×22 a3 (a is the lattice parameter of the bcc host lattice) with periodic boundary conditions. Immobile Al atoms (25 at. %) and vacancies (0.0235-0.094%) were distributed in the crystalline lattice by different methods. The Al atoms were placed in the D03 lattice with different degrees of order (η): η = (P - СAl) / (1-q) , where q = 0.25 is the fraction of Al sites in the D03 structure of the perfect Fe3Al intermetallic compound, CAl = 0.25 is the Al concentration in the alloy, and P is the part of the Al sublattice in the D03 structure that is actually occupied by Al atoms. The other Al atoms were randomly distributed on the Fe sublattice. We have varied the degree of order in our simulations between η = 1 (completely ordered alloy: Fe3Al) and η = 0.67. This allows to find out regularities of the influence of ordering on the parameters of the relaxation (or internal friction) spectrum. Vacancies were distributed either randomly through all possible positions or only through the Al sublattice in the D03 ordered structure. The Hamiltonian χ of the system is equal to the sum of all pair interaction energies [150]:

∑

∑

⎧ W ( C − C) (rp − r j )C(rp )C(r j ) + W ( C− Al) (rp − rm )C(rp )C(rm )⎫ ⎪⎪ p, m 1 ⎪⎪ p, j χ= ⎨ ⎬ 2 ⎪+ W ( C − vac) (rp − rk )C(rp )C(rk ) ⎪ ⎪⎩ p, k ⎪⎭

∑

♣

this carbon concentration corresponds to carbon content in the experiments

(A4)


127

These Hamiltonian was minimised by Monte Carlo method, the equilibrium state was chosen to correspond to it’s minimum.

Energies of interatomic interactions. The configuration term of the internal energy is usually considered in similar problems [151]. That is why the energies of the atomic pair interactions which do not contribute to the configuration term are not taken into account by eq. (A3). For this reason, Al-Al, Al-vacancy and vacancy-vacancy interactions are missing in eq. (A3): for the temperature range chosen in this simulations only carbon atoms are considered to be mobile. Also, the interactions with the host metal atoms (Fe) are not considered, because such interactions do not give rise to the configuration energy. The interaction of solute atoms with the host atoms was taken into account indirectly during the calculations of the C-C, C-Al and C-vacancy interaction energies. There are still no reliable first-principles calculations of C-C and C-substitutional atom interaction energies. This implies that we used the energies of the long-range strain-induced (elastic) C-C pair interactions in α-Fe from [149] and C-Al from [152] supplemented by Coulomb repulsion between interstitials and “chemical” interstitial-substitutional interaction in two nearest coordination shells. These values of the C-Al energies are displayed in Table 2 of Ref. [55]. The Coulomb C-C repulsion is taken into account according to [153]. The energy of “chemical” C-Al interaction was equal to +0.4 eV in the first coordination shell (negative values mean attraction, positive ones repulsion). The energy of C-vacancy interaction was taken into account in the first coordination shell only. This value was calculated by the first-principles calculation in [154] and is equal to – 0.24 eV. The following parameters of the carbon Snoek relaxation in pure α-Fe are used in our calculations: H = 0.87 eV and τ0 = 2 × 10-15 s.

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[134] Golovin, I. S.; Jäger, S.; Mennerich, Chr.; Siemers, C.; Neuhäuser, H. Structure and anelasticity of Fe3Ge alloy; Intermetallics, 2007, Vol 15/12, pp 1548-1557. [135] Jartych, E.; Oleszak, D.; Kubalova, L.; Vasilyeva, O. Ya.; Zurawicz, J. K.; Pikule, T.; Federov, S. A. J Alloys Comp 2007, 430, 12-17. [136] Chen, Q. Z.; Ngan, A. H. W.; Duggan, B. J. J Mater Sci 1998, 33, 5404-5414. [137] Yamamoto, H. J Phys Soc Japan 1965, 20, 2166-2169. [138] Drijver, J. W.; Sinnema, S. G.; van der Wonde, F. J Phys F: Metal Phys 1976, 6, 21652177. [139] Adelson, E.; Austin, A. E. J Phys Chem Solids 1965, 26, 1795-1804. [140] Cabrera, A. F.; Sánchez, F. H. Phys Rev B 2002, 65, 094202-1-9 [131] Elyatin, O. P.; Khachatryan, M. Kh. Metallovedeie Termicheskaya Obrabotka Met 1972, 11, 15-18. [142] Konygin, G. N.; Yelsukov, E. P.; Porsev, V. E. J Magn Magn Mat 2005, 288, 27-36. [143] Turbil, J. P.; Billiet, Y.; Michel, A. C R Seances Acad Sci C 1969, 269, 309. [144] Kanematsu, K.; Yasukochi, K.; Ohoyama, T. J Phys Soc Jpn 1963, 18, 1429-1436. [145] Oleszak, D.; Jartych, E.; Antolak, A.; Pekala, M.; Szymanska, M.; Budzynski, M. J All Comp 2005, 400, 23-28. [146] Yasukochi, K.; Kanematsu, K.; Ohoyama, T. J Phys Soc Jpn 1961, 16, 429-433. [147] Kanematsu, K. J Phys Soc Jpn 1965, 20, 36-43. [148] Predel, B.; Frebel, M. Z Metallkde 1972, 63, 393-397. [149] Blanter, M. S.; Khachaturyan, A. G. Metall Trans A 1978, 9, 753. [150] Blanter M. S. Phys Rev B 1994, 50, 3603. [151] Khachaturyan, A. G. Theory of Structural Transformations in Solids; Wiley: New York, 1983. [152] Blanter, M. S. Phys Met Metallography 1981, 51, 136 (in Russian). [153] Blanter, M. S.; Fradkov, M. Ya. Acta Metall Mater 1992, 40, 2201. [154] Slane, J. A.; Wolverton, C.; Gibala, R. Mat Sci Eng A 2004, 370, 67-72. [155]. Yasuda, H.Y; Nakajima, T.; Nakano, K.; Yamaoka, K.; Ueda M.; Umakoshi Y. Acta Materialia 53 (2005) 5343–5351 [156] Yasuda, H.Y; Nakajima, T.; Murakami, S.; Ueda M.; Umakoshi Y. Intermetallics. Intermetallics 14 (2006) 1221-1225 [157] Ishimoto, M.; Numakura, H.; Wuttig, M. Mat Sci Eng A 442 (2006) 195–198 [158] Ershov, N.V; Arzhnikov, A.K; Dobysheva, L.V; et al. Physics of Solid State, 2007, Vol. 49, No. 1, p. 67-74. [159] Zheng-Cun Zhou, Materials Science and Engineering A, in press [160] Golovin, I.S.; Serzhantova, G.V.; Sokolova, O.A.; Semin, V.A.; Jäger, S.; Sinning, H.R.; Stein, F.; Golovin, S.A. Abstract book IIAPS XI, Tula, Russia, 24-28.09.2007, p. 55: to be published in Solid State Phenomena [161] Mielczarek, A.; Riehemann, W.; Sokolova, O.A.; Golovin, I.S. Abstract book IIAPS XI, Tula, Russia, 24-28.09.2007, p. 97: to be published in Solid State Phenomena. [162] Chudakov, I.B.; Polyakova, N.A.; Mackushev, S.Yu.; Udovenko, V.A. Abstract book IIAPS XI, Tula, Russia, 24-28.09.2007, p. 93: to be published in Solid State Phenomena. [163] The Rietveld Method, Edited by R. A. Young, International Union of Crystallography, Oxford University Press, Great Britain,1993.


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Chapter 3

NONSTOICHIOMETRIC COMPOUNDS V. P. Zlomanov∗1 and A. Ju. Zavrazhnov2 1

Department of Chemistry, Moscow State University, Vorob’evy gory 1, Moscow, 119899 Russia 2 Department of Chemistry, Voronezh State University, Universitetskaya pl. 1, Voronezh, 394-006 Russia

ABSTRACT A key issue in materials research is the preparation of semiconducting solid, intermetallic and other nonstoichiometric compounds with predetermined composition, structure, and, hence, properties. In connection with this, this paper scrutinizes the concepts of stoichiometry, nonstoichiometry, and deviation from stoichiometry and the use of phase diagrams in selecting conditions for the synthesis of nonstoichiometric compounds. Since nonstoichiometry and properties of compounds are associated with defects, attention is also paid to defect classification and formation. The behavior of defects in solid oxides, chalcogenides, carbides, and other compounds of transition metals ranges from the point defect regime, controlled by entropy, to the enthalpy-controlled regime. To develop an appropriate theory of nonstoichiometric compounds, it is then necessary to address crystal-chemical and thermodynamic issues. This paper is also concerned with the defect structure of highly imperfect nonstoichiometric compounds with a broad homogeneity range: the concepts of defect and structural transition due to defect interactions and temperature effect. The thermodynamic aspect of the problem includes criteria for evaluating the stability of imperfect nonstoichiometric solids. It is considered the specifics of the concepts of existing, stable, and metastable phases, spinodal decomposition conditions, and issues associated with phase equilibria in homologous series of compounds with narrow homogeneity ranges. The paper also deals with synthesis methods and criteria for evaluating the homogeneity of nonstoichiometric solids.

∗

E-mail: [email protected]

136

V. P. Zlomanov and A. Ju. Zavrazhnov

1. STOICHIOMETRY, NONSTOICHIOMETRY AND DEVIATION FROM STOICHIOMETRY In chemistry and materials research, relationships between interacting substances are governed by the laws of stoichiometry (by stoichiometry). These characterize the composition of chemical substances and have been derived by systematizing experimental data. Among the most important laws of stoichiometry are the law of constant composition and the law of multiple proportions. The law of constant composition states that the chemical composition of a substance is independent of the method by which the substance was prepared. It turns out, however, that preparation conditions may have a significant effect on the composition of substances. According to the law of multiple proportions, the weight fractions of the elements forming a chemical compound are in the ratio of small whole numbers. Both laws stem from the atomistic theory and indicate that, when molecules are formed from atoms, the resulting chemical bonds must be saturated. Indeed, any change in the number of atoms, their nature, or their mutual arrangement corresponds to the formation of a new molecule with new properties. Are the laws of constant composition and multiple proportions always obeyed? It was long thought that only those chemical compounds exist whose composition meets the law of multiple proportions. Such compounds are stoichiometric and were named daltonides in honor of Dalton. However, with advances in analytical techniques, the properties of most inorganic solids—vapor pressure, electrical conductivity, diffusion,and others—were found to depend on their composition.The structure of such compounds, i.e., the spatial arrangement of their components, remains unchanged, while their concentrations vary continuously in a certain range, which is called the homogeneity range. Such compounds are called nonstoichiometric or compounds of variable composition.Earlier, they were called berthollides, in honor of Claude Louis Berthollet, a compatriot of Prouste. Nonstoichiometric compounds can be thought of as solid solutions of their components, e.g., of cadmium and tellurium in CdTe. The width of the homogeneity range is characterized by deviations from stoichiometry. The stoichiometric composition of a solid chemical compound, e.g. AnBm, where n and m and prime integers, is the composition which meets the law of multiple proportions. A deviation from stoichiometry, Δ, or nonstoichiometry, is the difference in the ratio of the number of nonmetallic atoms B per formula unit to that of metallic atoms A between nonstoichiometric, AnBm+δ (δ ≠ 0) and stoichiometric AnBm (δ = 0) solid

Δ=

m +δ m δ − = n n n

(1)

In an A–B–C ternary, it is convenient to express the composition of a solid phase, (A1– through the mole fraction x of the binary compound and nonstoichiometry? Nonstoichiometry can then be quantified by the difference in the ratio of equivalent numbers of nonmetallic and metallic atoms between nonstoichiometric and stoichiometric solids. For example, for (Pb1–xGex)1–yTey structure) we have

xBx)1–yCy,

Nonstoichiometric Compounds

137

Δ = y /(1 − y ) − 1 / 1 = (2 y − 1) /(1 − y )

(2)

The mole fraction of a binary compound (molarity) determines fundamental properties of nonstoichiometric crystals, such as their band gap and heat capacity. Nonstoichiometry influences the carrier (electron or hole) concentration and, therefore, the galvanomagnetic and optical properties of nonstoichiometric crystals.

2. NONSTOICHIOMETRY AND DEFECTS Solid chemical compounds (SAB) can be grown from vapor, melts (solutions), or other solid phases, which are called nutrient (N). The synthesis process can be thought of as transfer of atoms of components A and B from the nutrient to normal lattice sites and in the structure of compound AB, (3)

x + V x + ΔG А N =АА B 1 K1 =

(3.1)

[A Ax ][VBx ] = exp(−ΔG1 /( kT )) aA

(4)

x + V x + ΔG B N = BB A 2 K2 =

[ BBx ][VAx ] = exp(− ΔG2 /(kT )) aB

(4.1)

х

х

where aA and aB are the activities of the components. The formation of VB and VА

vacancies in reactions (3) and (4) is necessary for maintaining the ratio of A and B sites unchanged. Since the A and B atoms differ in size, and the Gibbs energy ΔG1 differs from ΔG2, reactions (3) and (4) differ in equilibrium constant, K1 ≠ K2, and, hence, the crystal contains х

different amounts of A and B atoms, [ А Ах ] ≠ [ В В ]. This means a deviation from stoichiometry, i.e., the B: A atomic ratio in the crystal differs from that in a stoichiometric crystal. х

Note that the properties of crystals are influenced not by nonstoichiometric А Ах and В В atoms, which occupy normal lattice sites, but by the resulting defects (structural х

х

х

х

imperfections). Such defects include VА and VB vacancies А i and B i interstitials:

A n = A ix + ΔG3

(5)

138


B n = B ix + ΔG 4

(6) х

х

This is associated with the fact that the А А and В В species are incorporated into the х

х

crystal without altering its energy structure. At the same time, near defects ( VАх , VB , А i х

and B i ) the energy field and, hence, the electrical, chemical, mechanical, and other properties of the crystal are altered (Figure 1). Thus, defects play an important role in determining the structure and properties of crystals.

Figure 1. Schematics of the energy spectra of (a) an ideal crystal and (b) imperfect crystal containing VA vacancies.

3. CLASSIFICATION AND FORMATION OF DEFECTS In an ideal (perfect) crystal, all of the structural elements (atoms, ions, molecules, and others) reside in normal lattice sites, characteristic of its structure. Heating, irradiation with


139

high-energy particles, or mechanical influences break down the ordering of atoms on normal lattice sites, causing some of them to leave their positions. Imperfections in the arrangement of atoms on lattice sites are called defects. According to defect geometry and size, one distinguishes extended and point defects (Figure 2) [1]. The size of point (0D) defects is comparable to interatomicdistances. 0D defects include electronic defects (holes, electrons, and excitons), energy defects (phonons and polarons), and atomic point defects (APDs). The APDs in crystals of a nonstoichiometric х

х

compound AB are VАх and VB vacancies (vacant lattice sites); А iх , B i and Fiх interstitials; and impurity atoms F (symbol x signifies that the defect is neutral relative to its environment). Since the formation of APDs is an endothermic process, with a small energy consumption, Ef = 0.5–3 eV, APDs are in equilibrium, and their density depends on synthesis conditions: temperature and partial vapor pressures of the components. The size of APDs is not very large, 0.1− 0.5 nm, but they give rise to polarization of their local environment, resulting in small displacements of the neighboring ions, and have a significant effect on the physical and chemical properties (diffusion,electrical, solubility, and others) of nonstoichiometric solids. Vacancies, interstitials, and antisite ( А Вх , В Ах , FAх , FBх ) defects are native defects of crystals. The density of such defects is in thermodynamic equilibrium at any temperature T > 0 and is given by Cj = exp(–Wj /(kT), where Wj is the formation energy, 0 < Wj < 3 eV. With increasing temperature, the APD density increases. During cooling of a crystal to room temperature, some of the APDs may annihilate by different mechanisms.

Figure 2. Classification of defects.

140


Nevertheless, even after extremely slow cooling the crystal contains a large amount of APDs. Excess APDs may originate not only from heating or stoichiometry changes due to reactions (3, 4, 5−6) but also from fast-electron (>1 MeV) irradiation at very low temperatures. Vacancies and interstitials result then from Rutherford collisions of electrons with atoms of the crystal and are frozen in the lattice, where they can be investigated. To determine the symmetry and structure of defects, special methods are needed, capable of probing the defect structure on an atomic scale. Such methods include electron paramagnetic resonance (EPR), electron–nuclear double resonance (ENDOR), optically detected EPR and ENDOR, local vibrational mode spectroscopy [2,], scanning tunneling microscopy (STM), atomic probe field ion microscopy, and electron energy loss spectroscopy [3]. Oppositely charged APDs may attract one another, forming new APDs − electrically

(

neutral defect complexes, e.g. ( VA− ⋅ VB+

)

x

(

and VA− FB+

)

x

. Dipole − dipole interaction leads

to the formation of ATD accumulations or clusters, which may serve as nuclei for phases with other compositions in nonstoichiometric crystals (see Section 4.2). Extended defects include linear (1D), 2D, and 3D defects [4−7] (Figure 2). Consider some of their characteristic features. Linear defects, or dislocations, are similar to point defects in two dimensions, where their size is comparable to the lattice parameter. In the third dimension, dislocations have a significant, or even infinite, length. The simplest type of dislocation is an edge dislocation − an edge of an extra half-plane inserted in a solid crystal. The atoms along an edge dislocation are not fully coordinated, and the two parts of the crystal along them are displaced relative to one another by one interatomic distance. In the case of an edge dislocation, the force responsible for the displacement of the two parts of the solid is normal to the dislocation line. Another important type of linear defect is a screw dislocation. In this case, the displacement vector is parallel to the dislocation line. Screw dislocations convert subsequent atomic planes to spiral surfaces. One possible mechanism of dislocation generation is through the formation of planar vacancy clusters. The atoms along a dislocation have unsaturated (“dangling”) chemical bonds. The excess energy of such atoms reduces kinetic barriers and influences the rates of mass transfer, crystal growth, and chemical reactions. The ease of dislocation nucleation and propagation leads to plasticity and a strong reduction in the mechanical strength of many materials, primarily, metals. At the same time, dislocations may raise strength and hardness. The reason for the hardening is that impurity atoms and grain boundaries impede dislocation movement. Dislocations are electrically active defects: they may act as donors, acceptors, recombination centers (reducing the lifetime of minority carriers), and scattering centers. Dislocations originate from mechanical influences on the solid. Their propagation is closely related to APDs. For example, vacancies play an important role in dislocation climb. The atoms sitting on the edge of the extra half-plane forming a dislocation may move if there is a nearby vacancy. Planar (2D) defects (Figure 2) include solid (crystal) surfaces, block (domain) boundaries, stacking faults, and crystallographic shears. 2D defects range in area from 4 to 105 nm2 (grain boundaries, crystallographic shears). The difference in local environment between surface and bulk atoms and ions leads to a reduction in coordination number or distortion of coordination polyhedra in the surface layer. The Gibbs energy of surface atoms


141

is higher than that of bulk atoms. The surface energy of crystals of nonstoichiometric compounds is 0.5–2.0 J/m2. Crystals typically have a mosaic or domain structure, with a domain or block size of up to ~10000 Å. Mosaic blocks have a relatively perfect structure, but neighboring blocks differ in orientation. The misorientation angle may be very small, from a fraction of a second of arc to 1o. Regions between domains (blocks) are called block boundaries. They may be planar or curved, or may have the form of a crystal face. If the normal to a block boundary is perpendicular to the rotation axis relating the block orientations, the blocks are said to be separated by a tilt boundary. If the normal is parallel to the rotation axis, the blocks are separated by a twist boundary. A crystal consisting of several phases always contains interfaces with significant energies. An interface between two phases may be coherent, incoherent, or semicoherent. An interface is coherent if there is a perfect lattice match between the planes in contact. Such interfaces have a low energy (≤ 0.015 J/m2). One example of a coherent interface is the boundary of the MgFe2O4 spinel precipitated in magnesium oxide, MgO. The reason for this is that the oxygen atoms in both MgO and MgFe2O4 are close-packed, which allows the precipitate to maintain coherency with the parent phase. Semicoherent interfaces result from a sufficiently large lattice mismatch between phases in contact. They include so-called low-angle boundaries and have the form of a network of periodically arranged edge dislocations. Their energy depends on the relative orientation of the two grains. At large misorientation angles (>5o), the parts of a nonstoichiometric crystal under consideration are called crystallites or grains. A solid phase containing high-angle boundaries is called a polycrystal. A special case of a high-angle boundary is a twin. A twin boundary separates two regions of the crystal that are related by reflection. Twinning takes place in many minerals and is responsible for coprecipitation of, e.g., calcite and feldspars. Stacking faults are variations from a regular, e.g., cubic or hexagonal, stacking sequence of atomic layers in a crystal structure. A stacking fault is a thin, diatomic layer with identical structures on both sides. Such defects form during crystal growth. 2D defects also include intergrowths and crystallographic shears. Epitaxy and polytypism are examples of intergrowths along solid–solid interfaces. Epitaxy is of great technological interest because it offers the possibility of producing thin single-crystal semiconductor films on appropriate substrates. Such structures are used in integrated circuits, optoelectronic converters (lasers, photodetectors, and solar cells), electronic amplifiers, and other devices. Intergrowths of crystals may, in principle, be thought of as modulated structures in which the intergrowth boundary is a periodic disturbance. To form an intergrowth, two structures must be identical in atomic configuration along some crystallographic plane. One example of a periodic intergrowth structure is the family of AxWO3 (A = alkali metal, alkaline-earth metal, Bi) tungsten bronzes, in which WO3 slabs are intergrown with hexagonal bronze layers. The formation of intergrown bronzes seems to be related to particular growth conditions. Intergrowths may have periodic (ordered) or aperiodic (disordered) boundaries. Among the most important 2D defects are crystallographic shears—planes at which the coordination polyhedra of two ideal structures in contact are rearranged.

142


Several key features of 2D defects warrant attention. First, they have a high formation energy (>3 eV) and are kinetically stabilized nonequilibrium defects. The frozen-in state of 2D defects is responsible for their “memory” of the preparation history. Second, they produce no stoichiometry changes. Third, planar defects result from interactions between APDs and have a significant effect on the reactivity and physical properties of nonstoichiometric crystals. Bulk (3D) defects (Figure 2) extend over regions that are larger than the lattice parameter in the three dimensions. In fact, these are macroscopic structural imperfections forming during growth and subsequent processing. Bulk defects include individual blocks; mosaics (a set of many low- and high-angle boundaries); inclusions (microprecipitates), which result from phase transformations, e.g., decomposition of solid solutions; magnetic domains (regions of aligned spins or electric dipoles), Guinier–Preston zones (variously spaced, aligned platelets several unit cells in thickness, having the same composition as the crystal), pores, and cracks. Bulk defects can be thought of as resulting from defect association and ordering processes, e.g., vacancy association in the case of pores. In addition, bulk defects include tensile and compressive elastic stresses. There are also other types of defects: orientation disorderingand motion disordering. The former type appears in ferromagnets. At low temperatures, all of the magnetic moments in a magnetic material are parallel or antiparallel. With increasing temperature, the magnetic moments deviate from the preferred orientation. The deviations can be regarded as defects. Motion disordering (defects) is observed at T > 0, e.g., in ammonium halide crystals, where some polyhedra rotate out of phase with others.

4. DEFECTS IN SOLID NONSTOICHIOMETRIC COMPOUNDS WITH NARROW AND BROAD HOMOGENEITY RANGES To characterize a nonstoichiometric region, it is necessary to determine its width, the nature of the defects responsible for deviations from stoichiometry, and the defect structure of the crystal. The deviation from stoichiometry, i.e., the width of the homogeneity range, varies widely from system to system. It may be small, so that it can be only assessed by indirect physical methods (galvanomagnetic, optical, and others) and not by chemical means. At the same time, deviations from stoichiometry may be so large that defect interactions become significant, leading to defect ordering, clustering, superstructure formation, longrange ordering, and the formation of new nonstoichiometric phases differing in symmetry, energetics, and other aspects from the parent phase. In such systems, defects are intrinsic components of the crystal structure rather than being chance imperfections. Consider in detail the defect structure of crystals of nonstoichiometric compounds with narrow and broad homogeneity ranges.


143

4.1. Defects in Solid Nonstoichiometric Compounds aith a Narrow Homogeneity Range The homogeneity range of such compounds is less than 0.1 at % in width, and nonstoichiometry is due to APDs, which can be thought of as quasi-components. In solidstate chemistry, this approach was developed by Wagner and Schottky [8], Frenkel [9] and Kröger [10]. In the dilute solution approximation, in which activities are replaced by concentrations, the formation of point defects in nonstoichiometric AB1+δ crystals with a narrow homogeneity range can be described by a set of quasi-chemical reactions with appropriate equilibrium constants K:

" O" = VAx + VBx + H Sh

(7)

⎛Δ H ⎞ K Sh = [VAx ][VBx ] = exp(Δ r S/k)exp⎜ r Sh ⎟ ⎝ kT ⎠

(7.1)

VAx = VA' + h + + E a Ka =

[VA' ]p [VAx ]

(8)

⎛E ⎞ = exp(Δ r S/k)exp⎜ a ⎟ ⎝ kT ⎠

(8.1)

x =V' +e _ +E VB B b Kb =

(9)

⎛E ⎞ = exp(Δ r S/k)exp⎜ b ⎟ ] ⎝ kT ⎠

[VB' ]n [VBx

(9.1)

"O"= e _ + h + + E r

(10)

⎛E ⎞ K i = np = exp(Δ r S/k)exp⎜ i ⎟ ⎝ kT ⎠

(10.1)

1/2X 2 (g) = X Xx + VAx + H BV

(11)

2

K BV = 2

[1 − [VAx ]][VAx ] p1/2 B2

n + [ VA' ] = p + [VB⋅ ]

=

VAx p1/2 X2

⎛ H BV2 = exp(Δ r S/k)exp⎜ − ⎜ kT ⎝

⎞ ⎟ ⎟ ⎠

(11.1)

(12)

144


Here, “0” is the initial state of an ideal crystal; symbols x, ' and + refer to neutral, negatively charged, and positively charged vacancies, respectively; e − is an electron; h+ is a hole; X Xx is a neutral X atom on its own site; n and p are the electron and hole concentrations, respectively; square brackets represent the concentration of the species enclosed (fraction of the sites); {1–[ VAx ]} < 1 since [ VAx ]< 1; ΔH and E are energies; and ΔrS is the entropy of reaction. Reaction (7) describes the formation of neutral atomic defects through thermal disordering, and reaction (11) represents the formation of neutral defects owing to nonstoichiometry Reactions (8) and (9) represent the appearance of electrons and holes h+ via the ionization of atomic defects, and reaction (10) describes the generation of electrons and holes owing to intrinsic conduction, when electrons are excited to the conduction band, leaving holes in the valence band. The electroneutrality condition (12) corresponds to the minimum energy of the nonstoichiometric crystal. In deriving the system of Eqs. (7)–(12), we assume that the predominant defect species, ionization energies Ea and Eb, band gap Ei, degree of APD ionization, and partial vapor pressures of components ( p A(V) , p B2 (V) , p AB(V) ) over the nonstoichiometric crystal are known. According to the phase rule, a two-phase state (vapor + solid) of a binary system at T = const is described by one independent parameter, the partial pressure p B 2 , which determines the deviation from stoichiometry.

Figure 3. Defect diagram of an AB 1 + δnonstoichiometric crystal heat-treated in B vapor ( Ki > K S ): (I, V) SAB + V + L heterogeneous equilibria; (II–IV) SAB + V equilibrium. The diagram specifies the defect densities at points A–C.


145

Solving the system of six equations in six unknowns ([ VAx ],[ VBx ], [VA' ] , [VB⋅ ] , n, and p), one can readily find [10] defect densities [ ] as functions of p B2 and the product of equilibrium constants: [ ] = f( p B2 , ∏j Kj (T). Such plots are presented in Figure 3. Regions II, III, and IV correspond to electronic (n-type), intrinsic, and hole (p-type) conduction, respectively. In region III, the carrier concentration is only determined by the band gap Ei: n = p = exp(–Ei /kT), and is independent of the partial pressure and, accordingly, of nonstoichiometry δ. These relations can be verified in experiment by measuring the Hall coefficient and the concentration of majority carriers (n and p) in AB1+ δ crystals annealed at constant temperature and different partial pressures. If the experimentally determined slopes of lines in regions II and IV (Figure 3) coincide with those obtained using model solutions, the model under consideration [Eqs. (7)–(12)] is sufficiently accurate, and one can evaluate unknown constants. Measuring n and p as functions of and K at different temperatures, one can find temperature – dependent equilibrium constants,

⎛Δ Н⎞ K = exp(Δ r S/k)exp⎜ r ⎟ , ⎝ kT ⎠ and the corresponding thermodynamic parameters: entropy ΔrS and enthalpy ΔrH of quasichemical reactions involved in defect formation. If experimental data and calculation results disagree, the model can be corrected by taking into account additional defect species (interstitials, APD complexes, and others) and varying the degree of their ionization. On the other hand, a model of an imperfect nonstoichiometric phase can be refined by independent methods: by measuring the selfdiffusion coefficient [11] and galvanomagnetic and optical parameters as functions of composition and temperature or by comparing x-ray (calculated) and pycnometric (measured) densities [5, 12, 13]. As an example, Table 1 lists the enthalpies ΔrH and entropies ΔrS of formation for quasichemical defects in nonstoichiometric III–V compounds [3, 12, 13]. The dominant defect species in these compounds are metal vacancies and interstitials and nonmetal interstitials and vacancies . The defects were identified by measuring density, lattice constants, and galvanomagnetic and optical parameters, and also selfdiffusion coefficients as functions of temperature and partial pressures [5 – 13]. The results can be used to locate the homogeneity range of the compounds studied. As an example, Figure 4 presents data for GaAs. Knowledge of the properties of nonstoichiometric defects is critical for understanding and controlling the nonradiative recombination and degradation times in lasers and lightemitting diodes based on nonstoichiometric III–V compounds and the effect of heat treatment on carrier concentration. The dominant defect species and the thermodynamic functions of defect formation were also reported for other compounds: GaN [14], II–VI [15−17] and IV–VI [18−20]. Such data are needed for understanding the chemical properties of nonstoichiometric compounds, their oxidation and sintering behavior, phase transformations, etc. [10].

146


Point-defect equilibria can be described using not only the quasi-chemical approach but also statistical thermodynamics. In the latter approach, one makes up a total energy distribution function for a model of the defect structure. This function is used to derive an expression for the free energy of the system, which is then minimized to give equilibrium conditions [21]. The final result is the same as in the quasi-chemical approach: the density of nonstoichiometric defects as a function of partial nonmetal pressure and temperature. For example, the composition of the metal-deficient transition-metal monoxides M1– xO (M = Mn, Fe, Co, Ni) is a power-law function of oxygen partial pressure: x ∝ p О 2 metal vacancies ( VМx = VМ2- + 2h+) and x ∝ p О2

1/ 4

1/6

for doubly charged

for singly charged vacancies ( VМx = VМ- +

2h+). Table 1. Enthalpy ∆rH and entropy ∆rS of defect formation in III–V compounds


147

The thermodynamics of nonstoichiometry can also be analyzed using the relative partial Gibbs energy,

ΔG(O 2 ) = μ O 2 − μ oO = RTlnp O 2

(13)

2

where μ O 2 is the chemical potential of oxygen in solid M1– xO, μ 0O 2 is the standard chemical potential of oxygen, and p O 2 is the oxygen partial pressure in the system M1– xO(s) + vapor. Since

ΔG(O 2 ) = nRTlnx

(14)

ΔG (O 2 ) must be a linear function of lnx, with a slope n that characterizes the dominant defect species: n = 6 for doubly VМ2- charged vacancies, n = 4 for singly VМ- charged vacancies, etc. Plots of ΔG(O2) against lnx can be constructed using thermogravimetric or coulometric data.

Figure 4. Temperature dependences of APD densities for As-enriched (solid lines) and Ga-enriched (dashed lines) gallium arsenide.

Such plots for the system Fe1 – xO(s) + vapor (O 2 ) [22] are presented in Figure 5 which indicates n values for different defect models. As seen, n = 6 for x ≥ 0.09, which corresponds 2to VFe doubly charged vacancies. The value n = 5 corresponds to (VFeVFe)4− associates. The 22values n = 3 and 4 observed for x < 0.09 are attributabl to the [4 VFe −Fe 3i+ ]5− and [16 VFe –

148


5Fe 3i+ ]17− defect complexes, respectively. The formation of such defect complexes was confirmed by x-ray diffraction. These results highlight the importance of combined thermodynamic and structural characterization of nonstoichiometric compounds.

Figure 5. Composition dependences of the relative partial molar Gibbs energy Δ⎯G (O2 ) for Fe 1 – x O [22].

4.2. Problems in the Theory of Solid Nonstoichiometric Compounds with a Broad Homogeneity Range The approximation of randomly distributed, noninteracting APDs is of limited utility and is only applicable to nonstoichiometric compounds with a homogeneity range no broader than 0.1 at %, that is, to many oxides, chalcogenides, halides, and p-block pnictides. There are, however, many compounds, in particular transition-metal oxides, which have substantially broader homogeneity ranges. Characterization of such compounds by neutron diffraction, high-resolution electron microscopy (HREM), Mössbauer spectroscopy, coulometric titration, and other techniques demonstrates that their properties cannot be understood in terms of classical APDs. The behavior of structural defects in such compounds ranges from the point-defect regime, controlled by entropy, to enthalpy control, as in the case of the decomposition of crystals with a broad homogeneity range into discrete phases with narrow homogeneity ranges, or vacancy ordering accompanied by crystallographic shears. To develop an appropriate theory of nonstoichiometric compounds with a broad homogeneity range, it is


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necessary to address both the crystal-chemical and thermodynamic aspects of such compounds. The crystal-chemical aspect of nonstoichiometric compounds is related to the structure of imperfect crystals with a broad homogeneity range. The thermodynamic aspect involves evaluation of criteria for the stability of imperfect crystals with a broad homogeneity range. In light of this, we will scrutinize the concepts of existing stable and metastable phases, consider conditions leading to phase separation by virtue of the instability of a nonstoichiometric compound with a broad homogeneity range, and analyze the concepts of phase and two-phase region with application to homologous series of compounds with narrow homogeneity ranges.

4.3. Crystal-Chemical Aspects of Nonstoichiometric Compounds with a Broad Homogeneity Range In solid nonstoichiometric compounds with a broad homogeneity range, structural defects interact and undergo ordering (self-organization), forming superstructures. The behavior of defects ranges from the point-defect regime, controlled by entropy, to enthalpy control, as in the case of crystallographic shears. Large deviations from stoichiometry lead to the formation of new defect species (associates and clusters), influence their distribution over lattice sites, and may alter the lattice symmetry. A high degree of local ordering extends beyond the nearest neighbor environment, which implies that the “former” defects become structural elements and that the observed crystallographic and thermodynamic properties of nonstoichiometric phases are due to the loss of long-range order in the soloid. In connection with this, consider the key crystalochemical aspects of highly imperfect, nonstoichiometric compounds with a broad homogeneity range: (1) the concept of structural defect in such nonstoichiometric compounds; (2) structural rearrangement in response to changes in composition (nonstoichiometry) and temperature. If a crystal contains a high density (>10 at %) of randomly distributed APDs, it is difficult to ascertain on purely crystal-chemical grounds which atom sits on a normal lattice site and which occupies an interstice. As a result, the symmetry of a nonstoichiometric crystal may be difficult to identify. As an example, Figure 6 shows a schematic of a 2D lattice which may be thought of both as a primitive lattice containing 25% of vacant sites and as a cubic lattice with 25% of the interstices occupied. Such problems are encountered in crystal-chemical analysis of nonstoichiometric compounds in which the average number of atoms per unit cell differs from the number of available sites, and the cation or anion sublattice is deficient or enriched in atoms. Among such compounds are Ga2S3 and similar III2–VI3 chalcogenides, binary (AgI) and ternary (Ag2HgI4) iodides, solid phases in the Ni–Te system between NiTe (NiAs structure, B8) and NiTe2 (CdI2 layered structure), and many other transition-metal compounds. Atomic defects (vacancies) in such systems are structural elements to the same degree as occupied sites. The

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difference between basic vacancies (structural elements) and faulty vacancies (resulting from structural disordering) accounts, e.g., for the fact that the Ga2S3 structure contains many vacancies but dissolves only small amounts of excess gallium [10].

Figure 6. Schematic of (a) a 2D lattice containing 25% of vacant sites and (b) a diamond-type primitive lattice with 25% of the interstices occupied.

For crystals built from various structural units, it is reasonable to define the concept of ideal crystal and to analyze disordering relative to such a crystal. In an ideal crystal, all identical or different structural elements (atoms, vacancies, and others) are ordered on equivalent sites and are related by symmetry elements. In the simplest structures of binary compounds with the AB or AB2 stoichiometry, the A and B atoms occupy positions displaced relative to one another, and the crystal symmetry is determined by the long-range order. Such crystals are built up of simple components identical in structure, corresponding to one of the fourteen Bravait lattices, e.g., cubic (NaCl type) or hexagonal (NiAs type). At the same time, the structures of many compounds in multicomponent systems, including those of YBa2Cu3O7–δ and many other mixed oxides, consist of coherent intergrowths of different blocks, e.g., rock-salt (NaCl), fluorite (CaF2), and perovskite (CaTiO3) blocks, stacked in the direction of the largest unit-cell parameter. Necessary conditions for the formation of intergrowth structures consisting of alternating simple blocks are, first, that blocks differing in structure be lattice - matched in a certain plane, second, that the different metals involved be chemically compatible (electronic configuration and oxidation state) and similar in chemical bonding (overlapping of atomic orbitals) between the metal and oxygen atoms, and, finally, that the unit cell be electrically neutral [23]. If coherent boundaries in intergrowth structures become elements of the supercell, they should not be regarded as structural defects. Thus, from the crystal-chemical viewpoint, defect ordering in nonstoichiometric compounds with a broad homogeneity range alters the concepts of ideal crystal and defect. The resulting ordered groups or defect clusters should be thought of not as distortions of the ideal structure but as native structural elements of a new ideal crystal. Its state can be taken as a standard state, relative to which any deviation from the ordered arrangement of structural elements will be regarded as a defect.


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This situation is analogous to that in crystals of chemical compounds (binary, ternary, and more complex) built from coherent intergrowths of different blocks. The decomposition of high-temperature nonstoichiometric phases to a number of ordered phases with narrow homogeneity ranges may be caused by changes not only in composition (nonstoichiometry) but also in temperature. Consider a schematic of structural changes in an initially disordered system (Figure 7), illustrating the effect of nonstoichiometry on the nature of structural elements and their distribution. The topmost box in Figure 7 represents nonstoichiometric phases with narrow ( 0 and d2G/dxB2 > 0. At a lower temperature, T2 < Tc, the curve has two inflections (spinodal points), where d2G/dx2B = 0. Between these points, d2G/dx2B < 0. Any composition between the spinodal points is completely unstable since, in this range, any composition fluctuation reduces the Gibbs energy and is, therefore, irreversible and spontaneously propagating [6, 33−35]. The compositions of the disproportionation products (Figure, 13, points a, b) are defined by the tangency points of the tangent common to the two segments of the curve. Note that phase separation in a spinodal point covers large volumes, is initiated by small order and composition fluctuations, and is a continuous transformation, whereas nucleation of a new phase occurs at large composition and order fluctuations in a small volume and is, therefore, not a continuous but a jumplike process. Consequently, coexisting low-temperature phases and the phase stable above Tc must have topologically related structures. Nonstoichiometric phases with a critical temperature and structurally related (e.g., different ordering configurations) intermediate phases would be expected to be unstable to spinodal decomposition. An example is provided by the iron–oxygen system, whose G–xO diagram is shown schematically in Figure 14. Above 570 0C, wüstite, Fe1–xO, coexists with Fe and magnetite, Fe3O4. Below 5700C, the metastable, quenched wüstite decomposes into Fe-enriched and oxygen-enriched FeO phases. The decomposition occurs spinodally and involves no nucleation processes. One possible Fe-based spinodal decomposition product is stoichiometric FeO, which is also metastable with respect to the end products. The oxygenenriched decomposition product differs from the Fe3O4 spinel − whose formation requires nuclei − and seems to consist of ordered defect clusters, each comprising an Fe3+ interstitial and two VFe2− vacancies bound to it: (VFeFeiVFe)– (Figure 8). This configuration is more stable than an isolated vacancy and is a structural element of the Fe3O4 resulting from wüstite conversion above the critical Fe content. The discovery of crystallographic shear and block structures, and also of infinitely adapted structures [5−7] in TinO2n–1 with 4 ≤ n ≤ 10, in which the crystallographic shear plane rotates in its own zone from one stable direction to another, presents some difficulties as to the use of the phase rule and, particularly, the concept of chemical composition. To quantify chemical composition, one should specify, first, the structural constituents involved and, second, the unit of measure. As structural constituents, one can use not only atoms, APDs, etc., but also extended defects (clusters, shear planes, and others) that result from ordering processes and become constituent elements of the crystal. The somewhat arbitrary choice of structural constituents will not cause negative consequences if their amounts are consistent with chemical analysis data, do not disturb the electroneutrality of the system, and fit with the measured composition dependences of properties. Constituents are called independent, or


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components of the system if they meet the above requirements (are fully consistent with measured properties) and cannot form from one another (independence condition) [36]. Another unanswered question in this context is whether Wadsley defects (disordered crystallographic shear planes) and the homologous series TinO2n–1 (4 ≤ n ≤ 10) can be regarded as distinct phases [5]. The third question is whether the phases in the above homologous series are separated by two-phase regions. The answers to the last two questions are probably “yes”, since all of the above compounds meet Gibbs’ definition of a phase where x is the mole concentration of independent structural constituents, or components of the system. At the same time, such “weak” phases are characterized by small magnitudes of the Gibbs energy of formation ΔfG from neighboring coexisting phases. Characteristically, they have narrow G(x) curves lying on a convex broken G(x) line. The breaks in the broken line correspond to the Gibbs energies of such phases, and the linear portions correspond to the Gibbs energies of two-phase systems (Figure 12). Thermodynamic analysis of the existence and properties of such low-stability phases was carried out by Voronin [32]. The reason for the existence of two-phase regions is that there are complete instability boundaries of a homogeneous state, at which the parent phase decomposes into two new phases. As pointed out above such boundaries are formed by spinodals (Figure 13) of the parent and forming phases. For first order phase transitions, the spinodals of the two phases issue from the critical point and run downward in different directions, encompassing the phase-transition region from the two sides. Thus, the spinodals make up an inner boundary of the first-order phase-transition region, where only a two-phase state is stable.

Figure 12. Schematic composition dependences of Gibbs energy for (1, 2) stable and (3, 4) metastable phases in system A–B.

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Figure 13. Schematic composition dependence of Gibbs energy illustrating spinodal phase separation: (ac, db) metastable states, (cd) labile state; (a, b) compositions of stable phases.

Figure 14. Schematic composition dependence of Gibbs energy for the Fe–O system in the range 200– 350°C, illustrating spinodal decomposition and the formation of Koch clusters.

5. PHASE DIAGRAM AS A KEY TO SELECTING CONDITIONS FOR THE SYNTHESIS OF NONSTOICHIOMETRIC COMPOUND A major problem in materials research is the preparation of NONSTOICHIOMETRIC COMPOUNDS with predetermined composition and properties. Targeted synthesis of such compounds involves control over phase transformations. For this reason, to optimize synthesis parameters data on phase equilibria are needed. Geometrically phase equilibria in a two – component system with volatile component can be represented using a threedimensional pressure (P)- temperature (T)- composition (x) diagram or its two-dimensional


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T−x, P−T and P−x projections [10, 36 - 38]. Consider first the key features of a T–x (Figure 15) phase diagrams: the solidus, liquidus and vapor lines, difference in composition of solid nonstoichiometric compound SAB, liquid (L) and vapor (V) at the maximum melting max temperature Tm, AB , the invariant points of congruent melting, sublimation. The maximum max melting temperature Tm, AB is a temperature when a nonstoihiometric solid SAB appears to be

melted and above which can not exist . The solidus (S'S''), liquidus (L'L'') and vapor (V'Vmax V’') lines on Figure 15 represent the temperature dependence of the composition of solid, liquid and vapor phases which are in equilibrium . The homogeneity range of a solid SAB is limited by the solidus line. The homogeneity range may include the stoichiometric composition or not. At the maximum melting temperature coexisting phases have different compositions; xS ≠ xL ≠ xV [37]. The temperature where the compositions of the solid and liquid phases are identical (xS congr == xL) is called the congruent melting temperature Tm, AB of phase SAB. The temperature

where the compositions of the solid and vapor are identical t (xS = xV) is called the congruent congr max sublimation temperature Tsublcong . The compositions corresponding to Tm, AB , Tm, AB and

Tsublcong differ from the stoichiometric composition δ = 0 of the solid phase A1/2– δB1/2+δ (x = 1/2 + δ), where δ is the deviation from the stoichiometric composition AB). P–T projection of the P–T–x diagram is shown in Figure 15b. The line Q1 Tmс Q2 represents the equilibrium SAB + L + V and is of interest for the growing of nonstoichiometric solid AB (SAB) from the melt. The three-phase equilibrium is seen to be possible over a wide range of temperatures and pressures; but once P is given, T is fixed. The composition of solid AB liquid (L) and vapor (V) coexisting under various conditions of P and T varies, as shown by the solidus, liquidus and vapor lines in Figure 15a. The general the compositions of the various phasea are different. In the situation as given in Figure 15, two special points Tmс and

TSс occur, where the composition of two of the phases are identical: (1) at point Tmс the composition of the liquid is identical within that of the solid (xL =

x SAB ); (2) at a pont TSk the composition of the solid nonstoichiometric AB is equal to that of the vapor ( x SAB = xV). Whenever possible, the synthesis of solid AB will be carried out at or near congruent points

Tmс

or

TSс .

The concept of congruence is of importance in the synthesis of nonstoichiometric compounds because a difference in composition between the nutrient (N) (vapor or melt) and solid gives rise to flows of rejected material and the associated kinetic instability of the growth interface.

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Figure15. (a) T–x and (b) p–T projections of the p–T–x phase diagram of a binary system containing a chemical compound S AB.

It may well be, however, that the congruent points occur at a pressure or temperature too high to be reached ubder normal conditions. In this one can work at other parts of the threephase line where the solid is in equilibrium with liquid at lower temperatures and pressures. This has been applied, for instance, for the synthesis of nonstoichiometric InP: whereas the pressure near the maximum temperature is 60 atm, indium-rich melts have much lower vapor pressure [10] and therefore solid synthesis from such melts is much more convinient. At a fixed vapor pressure of the more volatile component, supersaturation is created by cooling or heating a three-phase system. The latter corresponds to the temperature range T < T2 in Figure 15. For example, cadmium telluride crystals can be prepared by heating cadmium- enriched melts [10]. Note that the composition of crystals grown by the vapor–


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liquid solid process always corresponds to the solidus line, that is, to the limit of the homogeneity range.

6. APPROACHES FOR CONTROLLING THE NONSTOICHIOMETRYOF SOLIDS The nonstoichiometry of inorganic compounds can be controlled using the following approaches: (1) (2) (3) (4) (5)

annealing of grown crystals at fixed partial pressures of their components; varying the partial pressures of vapor species during vapor or melt growth; chemical vapor transport; coulometric titration; deposition of films of nonstoichiometric compounds from solutions containing coordination compounds.

6.1. Control Over the Vapor Composition and the Nonstoichiometry of Solids Equilibria involving the vapor phase play an important role in crystal growth and nonstoichiometry control. The compositions that can be obtained by annealing solids in an vapor of constant composition (xV) fall within the stability regions in the T–x and p–T projections (Figure 15), where each point represents one composition x (nonstoichiometry δ) if the temperature and partial pressures pi of vapor species are maintained constant: x(δ) = f(T, pi). The resultant composition may lie within or on the boundary of the homogeneity range, which depends, according to the phase rule [37 ] , c = k + 2 − r − α where k is the number of components, 2 is due to the presence of two external fields (baric and thermal), r is the number of phases, and α is the number of independent constraints on the intensive parameters c . For example, in a binary (k = 2) system A–B, one can obtain any composition within the homogeneity range using the vapor–solid equilibrium (r = 2) and maintaining the annealing temperature and partial pressure (pA or pB ) constant. The choice of the component determining the compositions of the vapor phase and nonstoichiometric crystal is dictated by the condition: the applied pressure (pi)appl must exceed the pressure of that component corresponding to the congruent sublimation ( pI )congr of the compound: (pi)appl > (pi)congr. Otherwise, (pi)appl will be determined not by the “cold” point temperature but by the temperature of the solid being annealed, and the system will prove uncontrollable [10]. In the first and second approaches above, the vapor pressure of the major component can be controlled in both open and closed systems. 1. If the amount of a volatile component in a closed isothermal system is such that, at the experimental temperature, it vaporizes entirely, the pressure is proportional to temperature (Gay-Lussac law). This approach was used to grow nonstoichiometric gallium arsenide crystals [10].

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V. P. Zlomanov and A. Ju. Zavrazhnov 2. If the amount of a component in a closed isothermal system is such that, at the experimental temperature, it vaporizes only partially, the vapor pressure pi is related to temperature by pi = Aexp(–HV)/(RT). This approach was used to synthesize zinc oxide crystals with different deviations from stoichiometry [39]. 3. Most frequently, use is made of closed two-zone systems, as exemplified in Figure 16. Solid AB, whose stoichiometry is to be changed, is maintained at temperature TAB, and a pure volatile component B is maintained at a lower temperature TB: TAB > TB. Such systems were used to vary the nonstoichiometry of II–VI [16, 40], III–V [41, 42 ], IV–VI [43], and many other compounds. Instead of a pure component, one can use A + AB or AB + B solid mixtures. The vapor pressure pB is then only determined by temperature TB, but the composition of the end product corresponds to the boundary of the homogeneity range. This method was used to vary the nonstoichiometry of PbTe [44] and Nb2O5 [45].

Figure 16. Schematic of a two-zone system for varying the nonstoichiometry of AB 1+δ solid.

Figure 17. Procedures for controlling the S2 vapor pressure over (a) ZnS and (b) CdS at 1250 K in an H2S + O2 atmosphere [10].


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The partial pressure of a component can be controlled using one of its gaseous compounds that dissociate on heating. For example, an H2 + H2S mixture was used in open flow systems to produce an appropriate sulfur pressure, and H2 + H2O and CO + CO2 mixtures were used to maintain the required oxygen pressure. The procedures for controlling the vapor pressure p S2 over ZnS and CdS are illustrated in Figure 17 [10, 46, 47].

6.2. Nonstoichiometry Control during Solid Synthesis To control the nonstoichiometry of binary compounds during synthesis, one can use the system shown schematically in Figure 18. AB vapor is transported along the ampule owing to a temperature gradient, and component B is maintained at a lower temperature TB (“cold” end), which ensures the required partial pressure pB. The solid stoichiometry is controlled by varying the growth temperature TAB and accurately maintaining temperature TB. Such a procedure was used in the vapor growth of PbS and PbSe crystals with low (down to 1016 cm−3) carrier concentrations [48] and perfect CdTe and CdZnTe crystals [49]. In melt growth of nonstoichiometric compounds, use is commonly made of the Bridgman process and Czochralski pulling.

Figure 18. Schematic illustrating nonstoichiometry control during vapor growth of AB 1 +δcrystals.

In the former process, the boat shape is such as to select a single nucleus, and the vapor composition is determined by temperature TB. A more effective method for the crystal growth of gallium arsenide is the liquid-encapsulated Czochralski (LEC) process at a controlled pressure of the volatile component [50]. A crystal puller schematic is shown in Figure 19. The growth zone is made air-tight using a liquid B2O3 or Ga layer. The arsenic vapor source is maintained at 617°C, which ensures the optimum arsenic vapor pressure for the growth of dislocation-free GaAs crystals. The temperature gradient can then be substantially reduced, with no risk of surface decomposition of the growing crystal. This procedure enables the growth of GaAs single crystals 10 and 15 cm in diameter, with dislocation densities below 5 ⋅ 103 cm−2.

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Figure 19. Schematic of a liquid (B2O3) encapsulated CZ system for the crystal growth of GaAs at a controlled arsenic pressure: (1) B2O3 (or Ga) encapsulation layer, (2) heaters, (3) GaAs seed, (4) GaAs crystal (5) As vapor source at 617 C, (6) B2O3 flux, (7) GaAs melt.

Figure 20. Schematic of a three-zone system for varying the nonstoichiometry of crystals of an (A 1 – x B x) 1 – δ C 1 + δ ternary compound.

In ternary systems, nonstoichiometry can be controlled using three-zone annealing (Figure 20). The reservoirs containing B and C source materials are connected to the tube containing (A1–xBx)1–δC1+δ by capillaries, which prevents rapid transport of components B and C. Similar configurations can be used for melt or vapor growth of nonstoichiometric ternary compounds. At the same time, one can use two-component, two-phase mixtures, which ensure appropriate vapor pressures of both components at a constant temperature [19, 49].


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6.3. Nonstoichiometry Control Using Chemical Vapor Transport [51, 52] The nonstoichiometry of compounds containing a nonvolatile component can be varied using chemical vapor transport. The basic principle of the method is to introduce or remove such a component through selective chemical vapor transport (Figure 21). The sample, e.g., GaSe, is located at one end of an ampule and is maintained at temperature T2, and the Ga source (or getter) material is located at the other end, at temperature TB. The transporting agent is gallium triiodide, GaI3. Gallium transport from the sample to the Ga charge or in the opposite direction is due to the reversible reaction 2Ga(GaSe sample or charge) + GaI3(V) = 3GaI(V). The Ga transport direction and, hence, the nonstoichiometry of the GaSe single crystal depend on the Ga source (getter) temperature T1, GaSe sample temperature T2, and source (getter) composition x1. If metallic gallium is used as the charge, the sample composition x2 and nonstoichiometry depend on two operational parameters of annealing: T2 and T1. It is convenient to represent these conditions in a T2–T1 – x2 3D phase diagram or its T2 –T1 projection (Figure 22) showing the stability regions of the phases involved.

Figure 21. Schematic illustrating a vapor transport procedure for varying the nonstoichiometry of four GaSe samples; T2΄ is the GaSe temperature and T1 ΄, T1΄΄ T1΄΄΄ and T1 ΄΄΄΄ are the Ga source (getter) temperatures.

Figure 21 illustrates the procedure for varying the nonstoichiometry of GaSe1+δ. The composition of the resultant materials was evaluated by x-ray diffraction and cathodoluminescence spectroscopy. The results were used to construct a partial T–x projection of the p–T–x phase diagram of the Ga–Se system, which takes into account GaSe

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polytypism (Figure 23). To successfully control the nonstoichiometry of an inorganic compound using chemical vapor transport, the transporting agent should not dissolve in its crystals and should not form binary or ternary compounds with the second component (Se). Chemical vapor transport was used to vary the nonstoichiometry of gallium selenides and indium sulfides [51, 52 ].

Figure 22. T1–T2 phase diagram representing conditions for controlling the nonstoichiometry of GaSe and Ga 2 Se 3 using chemical vapor transport.

Figure 23. (a ) T - x phase diagram of the GaSe system; (b ) Homogeneity ranges of the two polytypes ε - GaSe and γ – GaSe.


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6.4. Nonstoichiometry Control Using Coulometric Titration Coulometric titration is an electrochemical analytical technique. Its basic principle is to evaluate the weight change of the sample from the quantity of electricity consumed. In coulometric titration, electrolysis is commonly carried out at a constant current since the concentration of the substance to be converted to the reagent can be sufficiently high to remain constant throughout “titration.” The quantity of electricity is then evaluated from the current and electrolysis time. The current can be determined potentiometrically from the voltage drop across a standard series-connected resistor. As an example, consider the cell

An applied voltage causes Ag+ ions and electrons to migrate to the right of boundary I and to the left of boundary II, respectively. Since AgI possesses no electronic conductivity, the electrons must remain in Ag2S. As follows from the electroneutrality condition, an equivalent amount of Ag+ also remains in Ag2S, resulting in transport of silver atoms to Ag2S. Their concentration can be determined from the quantity of electricity passed through the cell. Thus, the process offers the possibility of controlling the Ag2S nonstoichiometry. At the opposite current direction, silver atoms leave Ag2S owing to Ag++ transport through AgI and electron transport to the platinum electrode. Coulometric titration is conceptually similar to nonstoichiometry control via annealing of crystals in vapors of their components (pi). In both procedures, new phases − pure components or neighboring solid compounds − form when the potential E (µ = nFE) and partial pressure pi (µi = µio + RTlnpi) reach the boundary of the homogeneity range. At the same time, electrochemical titration has the advantages of high accuracy, simple equipment, and high sensitivity. The cell must offer 100% current efficiency for the substance to be processed, and the electrodes must possess only ionic conductivity. Coulometric titration was used to vary the nonstoichiometry of silver, copper, and lead chalcogenides [53−56]; Cd1+xCr2Se4 and Cu1+xCr2Se4 spinels [57] TiO2, NbO2 [ 58], MgFe2O4, NiFe2O4 [59 ] and other compounds.

6.5. Synthesis of Nonstoichiometric Compounds with a Broad Homogeneity Range Solid nonstoichiometric compounds with a broad homogeneity range are commonly synthesized at high temperatures by directional solidification, vapor phase processes, or solidstate recrystallization [60]. The composition of the growing solid depends on the synthesis temperature and nutrient composition. Given the broad homogeneity range (>1 at %) of the compounds in question, the appropriate charge is prepared by weighing the starting reagents. Since there are several coexisting phases during growth (S + L + V, S1 + S2, etc.), the

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composition of the grown crystals lies at one of the boundaries of the homogeneity range (the largest deviation from stoichiometry). Solid compositions falling within the homogeneity range can be obtained by vapor growth at appropriate constant partial pressures of the components [10, 43]. The preparation of solids with controlled nonstoichiometry is impeded by the facts that a high-temperature phase with a broad homogeneity range may decompose during cooling into a number of phases with narrow homogeneity ranges and that retrograde solubility may lead to precipitation of solid components and other phases. Nonstoichiometric compounds can be synthesized and characterized in different temperature ranges. At low temperatures, kinetic hindrances may prevent the system from reaching true equilibrium. Indeed, compositional homogeneity of such a phase can only be reached through diffusion, but diffusion coefficients drop with decreasing temperature and increase with increasing nonstoichiometry, as, e.g., in the iron sulfide Fe1–xS [61]. In other words, a sulfide containing ordered vacancies has a low self-diffusion rate. This seems to be responsible for the high stability of iron alloys toward corrosion in H2S atmosphere, which produces a continuous film of the ordered phase Fe9S8 or Fe7S8 [6, 62].

7. CRITERIA FOR EVALUATING THE HOMOGENEITY OF NONSTOICHIOMETRIC SOLIDS The Gibbs energy G of a solid is a statistical quantity related to a distribution function. The average G determines the most likely distribution of 0D, 1D, 2D, and 3D defects. Since there may be fluctuations about the average value, in a closed system (a solid of constant bulk composition at constant temperature) configuration fluctuations may have the form of compositional changes within a small region as a result of random motions of particles into or from a volume element. The question that arises in this context is what solid can be considered homogeneous? The inhomogeneity of a solid phase is characterized by a random distribution of constituent structural elements. Among such structural elements are constituent atoms sitting in normal lattice sites and various 0D, 1D, 2D, and 3D defects (Figure 2). Inhomogeneity can be quantified using three types of distributions: (1) distribution of structural elements (building blocks) within some measurable volume, (2) distribution of such volumes over the solid, and (3) distribution of characterization results and properties of the solid phase. A solid can be considered homogeneous if

C i − 1/N

N

∑C

i

≤σ

i =1

where σ is the confidence interval, and Ci is the concentration of structural elements in the ith microvolume. If this inequality is not fulfilled for at least one value of i, the solid should be considered inhomogeneous. For practical application of a material, those deviations of a property in a given volume from the weighted-average value for the entire system which fall


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beyond the confidence interval are of consequence. In this regard, an inhomogeneity can be thought of as a set of values of the property being measured which fall beyond the limits in question and are taken over all the microvolumes. Analysis of generalized homogeneity criteria with the use of an autocorrelation function was performed by Nikitina et al. [63 ]. Thermodynamic analysis of defect ordering and interpretation of the composition dependences of physical properties with allowance made for short- and long-range order in terms of the structural elements (cluster components) considered above were reported by Men’ et al. [64].

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Van Bueren, H.G., Imperfections in Crystals, New York: Interscience, 1961. Stavola, M., Semicond. Semimet., 1998, vol. 51A, p. 47. Handbook of Semiconductor Technology, Jackson, K.A. and Schröter, W., Eds., Weinheim: Wiley-VCH, 2000. Fistul’, V.I., Fizika i khimiya tverdogo sostoyaniya (Physics and Chemistry of Solids), Moscow: Metallurgiya, 1995. (in Russian). West, A.R., Solid State Chemistry and Its Applications, Chichester: Wiley, 1985. Rabenau, A., Problems of Nonstoichiometry, New York: North Holland, 1970. Rao, C.N.R. and Gopalakrishnan, J., New Directions in Solid State Chemistry: Structure, Synthesis, Properties, Reactivity, and Materials Design, Cambridge: Cambridge Univ. Press, 1986. Wagner, C. and Schottky, W., Z. Phys. Chem., 1930, vol. 11, p. 163. Frenkel, J., Z. Phys., 1926,j vol. 35, p. 652. Kröger, F.A., The Chemistry of Imperfect Crystals,2nd ed. Amsterdam: North-Holland, 1973. Atomic Diffusion in Semiconductors, Shaw, D., Ed., London: Plenum, 1973. Bublik, V.T. and Mil’vidskii, M.G., Materialovedenie, 1997, no. 2, p. 21.(in Russian). Bublik, V.T. and Mil’vidskii, M.G., Materialovedenie, 1998, no. 5, p. 16. ( in Russian). Li Jing-Bo and Tedenac, J.C., J. Electron. Mater., 2002, vol. 31, no. 4, p. 321. Fochuk, P., Korovyanenko, O., and Panchuk, O., J. Cryst. Growth, 1999, vol. 97, no. 3, p. 603. Kukk, P.L. and Altosaar, M., J. Solid State Chem., 1983, vol. 98, no. 1, p. 1. Berding, M.A., van Schiefgoarde, M., and Paxton, A.T., J. Vac. Sci. Technol., 1999, vol. 8, p. 1103. Novoselova, A.V. and Zlomanov, V.P., Curr. Top. Mater. Sci., 1981, vol. 7, p. 643. Zlomanov, V.P., Demin, V.N., and Gas’kov, A.M., J. Mater. Chem., 1992, vol. 2, no. 1, p. 31. Kuznetsov, V.L. and Zlomanov, V.P., Neorg. Mater., 1999, vol. 35, no. 4, p. 263 [Inorg. Mater. (Engl. Transl.), vol. 35, no. 4, p. 197]. Chebotin, V.N., Fizicheskaya khimiya tverdogo tela (Physical Chemistry of Solids), Moscow: Khimiya, 1982. (in Russian). Sörensen, O.T., Nonstoichiometric Oxides, New York: Academic, 1981, p. 271.

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[23] Abakumov, A.M., Antipov, E.V., Kovba, L.M., et al., Usp. Khim., 1995, vol. 64, no. 8, p. 769.( in Russian). [24] Buseck, P.R., Cocoley, J.V., and Eyring, L., High-Resolution Transmission Electron Microscopy and Associated Techniques, Oxford: Oxford Univ. Press, 1988, p . 371. [25] Eyring, L. and O’Keefe, M., The Chemistry of Extended Defects in Non-metal Solids, Amsterdam: North Holland, 1970, p. 380. [26] Wiesendanger, R. and Guntherodt, H.J., Scanning Tunneling Microscopy II, Springer Ser. Surf. Sci., 1992, vol. 28, p. 42. [27] Trushin, Yu.V., Fizicheskoe materialovedenie (Physical Principles of Materials Research), St. Petersburg: Nauka, 2000, p. 235. (in Russian). [28] Van de Valle, C.G. and Neugebauer, J., Phys. Rev. Lett., 2002, vol. 88, p.103. [29] Gudilin, E.A., Targeted Synthesis of Inorganic Superconductors Based on Rare-Earth Barium Cuprates, Doctoral (Chem.) Dissertation, Moscow: Moscow State Univ., 2003.(in Russian). [30] Kienle, L. and Simon, A., J. Solid State Chem., 2001, vol. 161, p. 385. [31] Voronin, G.F., Zh. Neorg. Khim., 1999, vol. 39, no. 11, p. 1763.( in Russian). [32] Voronin, G.F., Neorg. Mater., 2000, vol. 30, no. 3, p. 342 Inorg. Mater. (Engl. Transl.), vol. 30, no. 3, p. 271]. [33] Novikov, I.I., Termodinamika spinodalei i fazovykh perekhodov (Thermodynamics of Spinodals and Phase Transitions), Moscow: Nauka, 2000. (in Russian). [34] Gerasimov, Ya.I., Dreving, V.P., Eremin, E.N., et al., Kurs fizicheskoi khimii (A Course on Physical Chemistry), Moscow: Gostekhizdat, 1963, vol. 1, p. 367. (in Russian). [35] Cahn, J.W., Acta Metall., 1961, no. 41, p. 795. [36] Voronin, G.F., Osnovy termodinamiki (Principles of Thermodynamics), Moscow: Mosk. Gos. Univ., 1987. (in Russian) [37] Zlomanov, V.P. and Novoselova, A.V., P–T–x-Diagrammy sostoyaniya sistem metal– khal’kogen (P–T–x Phase Diagrams of Metal–Chalcogen Systems), Moscow: Nauka, 1987.(in Russian). [38] Storonkin, A.V., Termodinamika geterogennykh system (Thermodynamics of Heterogeneous Systems), Leningrad: Leningr. Gos. Univ., 1967, part 1.( in Russian). [39] Scharowsky, E., Z. Phys., 1953, vol. 135, p. 318. [40] Nishizava, Ex. J. and Oyama, Y., Mater. Sci. Eng., 1994, vol. 12, nos. 6–8, pp. 273– 426. [41] Nishizava Jun-ichi, I Int. Symp. on Point Defects and Nonstoichiometry, Sendai, 2003, p. 1. [42] Neubert, M. and Rudolph, P., Progr. Cryst. Growth Charact. Mater., 2001, vol. 43, p. 119. [43] Zlomanov, V.P. and Yashina, L.V., in Lead Chalcogenides: Physics and Applications, New York: Taylor and Francis, 2002, p. 37. [44] Brebrick, R.F. and Gubner, E., J. Chem. Phys., 1962, no. 36, p. 170. [45] Van Lierder, W. and de Jonghe, L., Solid State Commun., 1964, vol. 2, p. 129. [46] Van Gool, W., Principles of Defects Chemistry of Crystalline Solids, New York: Academic, 1966, p. 327. [47] Van Gool, W., Philips Res. Rep., Suppl., 1961, no. 3, p. 361. [48] Prior, A.C., J. Electrochem. Soc., 1961, vol. 108, p. 82.


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[49] Goldgirsh, A., Shusterman, S., Zilber, R., and Azouloy, M., Programme and Abstracts of Symposium Solid Solutions of the II–VI Compounds, Zakopane, 2002, p. 20. [50] Osvenskii, V.B., in Fundamental’nye problemy rossiiskoi metallurgii na poroge XXI veka (Critical Issues in Russian Metallurgy on the Threshold of the 21st Century), Moscow: Ross. Akad. Estestv. Nauk, 1998, vol. 4, p. 85. (in Russian). [51] Zavrazhnov, A.Yu., Turchen, D.N., Naumov, A.V., and Zlomanov, V.P., J. Phase Equilib., 2003, vol. 24, no. 4, p. 330. [52] Zavrazhnov, A.Yu., Zarzyn, I.D., Turchen, D.N., et al., Inorg. Mater., 2004, vol. 40, suppl. 2, p. 101. [53] Wagner, J.B. and Wagner, C., J. Chem. Phys., 1957, vol. 26, p. 1602. [54] Miyatani, S., J. Phys. Soc. Jpn., 1959, vol. 14, p. 750. [55] Mathieu, H.J. and Rickert, H., Z. Phys. Chem. (Frankfurt/ Main, Ger.), 1972, vol. 79, p. 315. [56] Leushina, A.P. and Simonova, M.V., Zh. Fiz. Khim., 1975, vol. 49, p. 1218. (in Russian). [57] Leushina, A.P., Kolesnikov, L.A., Makhanova, E.V., and Zlomanov, V.P., Trudy VII soveshchaniya “Fundamental’nye problemy ioniki tverdogo tela” (Proc. VII Conf. Fundamental Issues in Solid-State Ionics), Chernogolovka, 2004, p. 30. ( in Russian). [58] Alcock, C.B., Zador, S., and Steele, B.C.H., Proc Br. Ceram. Soc., 1967, vol. 8, p. 231. [59] Schmalzried, H. and Tretyakov, Yu.D., Ber. Bunsen-Ges. Phys. Chem., 1966, vol. 72, p. 180. [60] The Growth of Single Crystals; Crystal Growth Mechanisms: Energetics, Kinetics, and Transport, Laudise, R. and Parker, R., Eds., New York: Prentice-Hall, 1970. [61] Condif, R.H., Kinetics of High Temperature Processes, New York: Wiley, 1959, p. 97. [62] Herzog, F., Corros. Anticorros., 1959, vol. 7, p. 281. [63] Nikitina, V.G., Orlov, A.G., and Romanenko, V.N., in Protsessy rosta poluprovodnikovykh kristallovi plenok (Growth of Semiconductor Crystals and Films), Novosibirsk: Nauka, 1981, vol. 6, p. 204.(in Russian). [64] Men’, A.N., Bogdanovich, M.P., Vorob’ev, Yu.P., et al., Sostav–defektnost’–svoistva tverdykh faz. Metod klasternykh komponentov (Composition–Perfection–Properties of Solids: Method of Cluster Components), Moscow: Nauka, 1977. (in Russian).



Chapter 4

SEMICONDUCTING INTERMETALLIC COMPOUNDS ---WITH SPECIAL INTEREST IN SILICIDES AND RELATED COMPOUNDS Yoji Imai National Inst of Advanced Industrial Science and Technology (AIST) AIST Tsukuba Central 5, Higashi 1-1 Ibaraki 305-8565, Japan

1. INTRODUCTION Though intermetallic compounds composed of metallic elements may be expected to be metallic, there are several semiconducting intermetallic compounds composed of transition metals (Fe, Ru, Ir, etc) or alkaline earth elements (Mg, Ca, Sr, Ba) and p-block elements (Al, Ga, In; Si, Ge, Sn, Pb; As, Sb, Bi; Se, Te, etc.). Main advantages of them, especially of silicides, exist in capability of finer band gap tuning compared to the elemental semiconductors (Diamond, Si, Ge, alpha-Sn) and in abundance in natural resources and in less toxicity compared to the III-V compound semiconductors (GaAs, GaSb, etc). In this paper, our recent studies on semiconducting intermetallic compounds using firstprinciple electronic structure calculations based on the density-functional theory (DFT) are reviewed and the future prospects are described. The target of the studies includes transition metal silicides, alkaline earth metal silicides and pnictides, and transition metal aluminides and gallides. However, the main interest will be focused on silicides since there has been an increasing attention to the semiconducting silicides [1]. The reason of the recent interest in silicides exists in that, (1), they are composed of non- or less toxic and naturally abundant elements in the earth’s crust, and (2), some of their band gaps are favorable for applications to photoelectronic and thermoelectric devices. It should be pointed out that there exists a problem in predicting physical nature by the calculation using DFT employing local density approximation (LDA) or its improved methods. That is underestimation of the band gap of most semiconductors and insulators. One of the possible reasons was thought to be the inaccurate exchange-correlation functional.

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However, this can be improved by taking into account the charge density gradient, which has been used in most of the present calculations. Another possible reason for the incorrect prediction of the gap value is the fact that the Kohn-Scham eigenvalues are not the quasiparticle energies in the excited states. Although it is customary to interpret the difference between the highest occupied and the lowest unoccupied DFT eigenvalues as the true quasiparticle band gap (Eg), this differs in principle from the former (DFT gap) by Δ , the discontinuity in the exchange-correlation potential when an electron is added to the system. The discrepancy between the DFT gap and Eg is known to be large when the Coulomb repulsion of electrons is large as in the case of the transition metal oxides, Mott-Hubbard insulators. However, we present the results obtained by DFT calculations since the ground state properties, such as the lattice constants and relative stability of various phases, are well reproduced, as stated below.

2. SILICIDES, OVERVIEW Most of metal elements make various compounds with silicon. Many of these compounds have been synthesized by sintering the fine powder from a crushed massive material obtained by (1)direct fusion method of the metal and silicon, (2) high temperature reduction of mixed powder of metal oxide and SiO2 by carbon, or (3) reduction of metal oxide by silicon. Recently, thin films or needle-like single crystals have come to be obtained using vapor processes or liquid processes. The list of the known binary compounds of metals and silicon upto now is shown in Figure 1. Most of them are "metal" and some of them show excellent electronic conductivity and durability against high temperature oxidation, which is favorable for an electrode material in high temperature. They are also used as a coating material for the high temperature oxidation in the air of 1500 or more. However, there are several compounds which show semiconducting-like behavior with a monotonous decrease in electric resistivity. Though some of them are not real ‘band’ semiconductor and ’hopping conduction’ of electrons is considered as a cause of this semiconductor-like behavior, there are real band semiconductors such as -FeSi2, BaSi2 and so on. In the following sections, results of their electronic structure calculations will be described. Transition metal silicides and alkali-earth metal silicides will be described separately because of the following reason. In transition metal silicides, the electronegativity of metal and silicon is not different so much and the structural change can be roughly understood by considering the so-called “valence electron concentration (VEC)”, number of valence electrons per metal atom. The structures whose density-of-states (DOSs) at their Fermi level is the least would be an energetically stable among stoichiometrically possible structures in most cases. This suggests that metal silicides with the same group metal elements will have the same structure, or at least, will have nearly the same local configuration of atoms.

Semiconducting Intermetallic Compounds

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Figure 1. List of binary compounds of metal-Si. Chemical formulae of compounds described here are those conventionally used, but there is room for discussion. For example, ReSi2-x may be described as ReSi1.75 or Re4Si7. B14Si is often described as BnSi, because Si atoms replace part of boron atoms in boron frame found in pure β-boron and also occupy interstitial sites and it is a non-stoichiometric compound. α-Fe2Si5 is the compound usually described as α-FeSi2, the high-temperature modification of disilicides but is considered to have Fe vacancies and the stoichiometric ratio of Fe:Si is nearly equal to 2:5.

On the contrary, electronegativity of alkali (A) and alkali-earth (AE) metal is very weak compared to that of Si. They form silicides which have peculiar characteristics such as, 1)high melting point, sometimes significantly greater than the constituent elements, 2)narrow homogeneity width (i.e. line compounds), 3) high heat of formation, 4)poor conductivity, 5)greater brittleness, 6)most of them are diamagnetic. They have saltlike properties. AE silicides with high ratio of Si to AE are the typical examples of “Zintl” phases where AE donates its valence electron to Si so as to complete the various Si-network. The form of network depends on the size of metal atom to be accommodated in that network and therefore the structure varies with the promotion of the metal atom to the heavier elements. The structure is also affected by pressurization as will be expected.

3.TRANSITION METAL DISILICIDES Most of transition metal （TM） elements form disilicides, MSi2, where M denotes a transition metal. Correlation between the crystal structures of MSi2 and the location of M in the periodic table of the elements is shown in Figure 2.

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Figure 2. Correlation between the crystal structures of transition metal disilicides (MSi2) and the location of M in the periodic table of the elements.

As shown, the number of d-electrons in TM disilicides brings about their structural change from the TiSi2- or ZrSi2-type (disilicides of the 4th group metal), the CrSi2- or MoSi2type (the 5th and the 6th groups), the -FeSi2-type (the 8th group), to the CaF2- type (the 9th and 10th groups) structures. This structural change with increase in number of d-electrons can be roughly summarized as the change from stacking of MSi2 layers of nearly hexagonal arrangement found in the 4th , 5th , and 6th group elements to the nearly cubic coordination of M by Si found in 8th , 9th and 10th group elements, as described later. The 7th group elements (Mn, Tc, Re) do not form stable disilicides but form the compounds of MSi2-x. Among them, CrSi2 and 8th group element (Fe, Os) disilicides are known to be semiconducting. The 8th group element (Ru, Os) also form semiconducting sesquisilicides, M2Si3, as described later. Here, main emphasis will be placed on FeSi2 and the related compounds which are attracting recent attention for possible photoelectronic and thermoelectric devices.

3.1. FeSi2 The Fe-Si phase diagram is composed of five intermetallic compounds (Fe2Si, Fe5Si3, FeSi, FeSi2-low and FeSi2-high), and three solutions (A2 for random bcc, B2 for the CsCltype ordered structure, and DO3 for the BiF3-type ordered structure). Among them, FeSi and β-FeSi2, the lower temperature modification of FeSi2, are semiconductors. β-FeSi2 has attracting an increasing attention since this has a suitable band-gap for applications to photoelectronic devices, a band gap of ca 0.75eV, corresponding to the infrared region (1.65 μm) which is useful for optoelectronic devices integrated on wellestablished Si-technology [2]. It has also been investigated as a thermoelectric energy conversion device at mid temperatures (～500℃)[3] because of its relatively high Seebeck coefficient and stability in high-temperature oxidizing atmosphere.


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β-FeSi2 belongs to the space group of Cmca (No.64) with orthorhombic symmetry. There are two Wyckoff positions for Fe atoms, 8d (0.2146, 0, 0) and 8f (0, 0.8086, 0.1851), and also two Wyckoff positions for Si atoms, 16g (0.1283, 0.2746, 0.0512) and 16g (0.3727, 0.0450, 0.2261). Therefore, the unit cell contains sixteen formula units and the stoichiometric description of the unit cell is Fe16Si32. The unit cell of β-FeSi2 is shown in Figure 3(a) but can be reduced to the primitive cell composed of 24 atoms.

Figure 3. Crystal structures of β-FeSi2, γ-FeSi2 and α-FeSi2. Open circles and closed circles denote Si and Fe, respectively.

This crystal structure looks quite complex but can be regarded as a distorted CaF2-type structure[4]. The disilicides of the neighboring transition metal elements in the periodic table, Co and Ni, are known to have this CaF2-type structure, belonging to the space group of Fm3m with cubic symmetry, but FeSi2 with the CaF2-type structure can exist only in the ultrathin film on Si(111) [5]. This is sometimes referred to as γ-FeSi2 but is not present as an equilibrium phase. In Figure 3, crystal structure of γ-FeSi2 and α-FeSi2, the high temperature modification of FeSi2, are also presented.

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The local atomic configuration around Fe atoms in β-FeSi2 and γ-FeSi2 are compared in Figure 4. Both are surrounded by eight Si atoms; Fe atoms in γ-FeSi2 are located in the center of the cubic of Si but Fe atoms in β-FeSi2 are surrounded by an irregular hexahedron. The structure of α-FeSi2 is much different from β- and γ−FeSi2. The structure of α-FeSi2 is characterized by the presence of Si-Si bonding in the unit cell.

Figure 4. Local atomic configuration around Fe atoms （shown by closed circles）in γ-FeSi2 and βFeSi2 Open circles denote Si atoms.

Figure 5 shows the calculated band structures (BSs) along several high-symmetry lines in the Brillouin zone of β-FeSi2 near their Fermi levels (EF). The energies are shifted so that the top of the valence band is aligned with zero. Plotted in the BS Figure are the numbers which express the order counted from the bottom of the valence band. Because the reduced unit cell of β-FeSi2 contains eight Fe atoms and sixteen Si atoms, 128 valence electrons (eight electrons from each Fe atom and four electrons from each Si atom) are contained in the unit cell, and therefore, 64 bands are fully occupied because there is no overlap in energy between the 64th band (and below) and the 65th band (and above). The valence band maximum of β-FeSi2 is located at Y(-1/2 1/2 0) and a conduction band minimum is located between Γ (0 0 0) and Z (0 0 1/2). The indirect band gap between them was calculated to be 0.79eV which is close to the observed value [6]. The rather flat nature of the BS diagram especially at the conduction band edge was considered to be the reason of the relatively large effective masses. However, observed mobilities for holes and electrons in β-FeSi2 produced by conventional techniques is of the order of several tenths cm2/Vs for electron and of several cm2/Vs for hole at room temperature, much smaller than those expected from the BS diagram and this very poor mobility was regarded as the most important obstruction factor for the practical use of βFeSi2. Now, the reason is considered to be due to scattering by ionized impurities as well as strong electron-phonon scattering and recent elaborate preparation techniques have increased the mobility by magnitude of order of 2 or more [7] and the application has become hopeful.


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Figure 5. Band structure of β-FeSi2. The energies are shifted so that the top of the valence band is aligned with zero. Plotted in this and suceeding band structure (BS) diagrams are the numbers which express the order counted from the bottom of the valence band. The arrow in BS diagrams show transition from the top of the valence band to the bottom of the conduction band.

Comparison of the electronic energies of α-, β- and γ-FeSi2 is shown in Figure 6. The energies shown here were calculated using the density functional theory with the local density approximation with a norm-conserving nonlocal pseudopotential description of electron–core interactions. The calculations have been done for varied volumes of unit cells assuming, (a), the unchanged ratios of the lengths of the unit cell edges parallel to each reference axis, (b), the unchanged interaxial angles, and (c), the unchanged fractional coordinate of each atom, from the observed crystal structure of each phase. Among these phases, β- FeSi2 is correctly predicted to be the lowest in energy. The following is α-phase. The energy minimum is obtained at the equilibrium volume of β-FeSi2 (=37.6x10-3nm3/BaSi2). This is consistent with the phase diagram which shows that α-phase is stable at higher temperature, where entropy term becomes important in free-energy. The contribution of atomic configuration to the entropy term in β- FeSi2 with the complex

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structure will be smaller than that in α-FeSi2 with simpler structure in case the contribution of the lattice vibration are nearly the same.

Figure 6. Comparison of the electronic energies of α-, β- and γ-FeSi2：Variation of their electronic energies with the cell volume. The arrow in the Figure shows the equilibrium cell volume of β-FeSi2 (=37.6x10-3nm3/FeSi2).

The reason of the different total energies of FeSi2’s is demonstrated by Figure 7 which presents the densities of states (DOS) of these phases. In contrast to the semiconducting β-FeSi2, the Fermi level of γ-FeSi2 with the undistorted CaF2 structure is located at the local maximum in the DOS. In β-FeSi2, the gap has opened as a consequence of splitting of the peak of DOS of the fluorite–type structure; a Jahn-Teller distortion of the fluorite–type structure opened the gap [8]. DOS value of α-phase is also small at the Fermi level and electronic energy of α-phase will be lower than that of γ-FeSi2, the DOS of which has a sharp peak at the Fermi level.


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Figure 7. The densities of states of β-, α- and γ-FeSi2. The energies are shifted so that the Fermi level is aligned with zero.

The partial DOSs (PDOSs) calculated for Fe3d,4s,4p and Si3s,3p components for β-FeSi2 are shown in Figure 8. Since there are two inequivalent sites of Fe and Si in β-FeSi2, all the angular momentum projection (s, p, d,･･) on all the atoms are performed but the site dependence of the PDOS of the same kind of atoms can be roughly ignored. As shown in the Figure , the valence band and the conduction band are mainly composed of Fe3d state hybridized with the Si3p state. This can be compared to the alkaline-earth (AE) metal silicides stated later, where contribution of AE d-state to the bands near the Fermi level is smaller even if there is. From the DOS curve and the band structure diagram, β-FeSi2 is an intrinsic semiconductor. However, it is known that not intentionally doped β-FeSi2 is a p-type semiconductor. Therefore, defects in β-FeSi2 seems to play an important role on this nature. To elucidate the effect of defects on the type of conduction, the DOSs of non-stoichiometric β-FeSi2 was calculated.

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Figure 8. Total and partial DOSs of β-FeSi2.

The calculated DOS of β-FeSi2 with Si-vacancies and that with Fe-vacancies near the gap are shown in Figure 9 with that of stoichiometric β-FeSi2. As shown in the Figure s, the Fermi level, shown by the arrow, of Si-deficient β-FeSi2 (Fe32Si63 ) is located a bit higher than the top of valence-band, though some defect levels are formed between the gap. On the contrary, the Fermi level of Fe-deficient β-FeSi2 (Fe31Si64 ) is located at the defect levels formed between the gap. Thus, p-type conduction would be caused by Si-defects. However, the energetic evaluation of defect formation is left for future studies.


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Figure 9. DOS curve of β-FeSi2 with Si-vacancies （Fe32Si63), that with Fe-vacancies （Fe31Si64）, along with that of stoichiometric β-FeSi2. The arrows in the Figure indicate the position of the Fermi level in each.

Also left for future studies is the effect of intentional doping of β-FeSi2. The preliminary studies on the doping effect on the DOS curves are shown in Figure 10. It is known that replacement of Fe in β- FeSi2 by Cr or Mn gives p-type conduction and that by Co or Ni does n-type conduction [9]. These effects can be understood using the rigid band model, where the electronic structures are fixed and different degrees of electron filling are allowed in the band and DOS curves. Co or Ni substituting Fe will supply excessive electrons to fill the gap and will cause the n-type conduction. Substitution of Fe by Cr or Mn will supply deficient electrons to fill the gap and will cause the p-type conduction. However, the ‘ hydrogen-atom model ’ shown below gives the positions of the impurity level too close to the band edge.

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Figure 10. DOS curves of Cr-, Mn-, Co-, and Ni-doped β-FeSi2. The arrows in the Figure indicate the position of the Fermi level in each.

(m0/m*)・(ε-2)・13.6（eV） where m0 is the free electron mass, m* is the effective mass of electron or hole, andε is a static dielectric constant of the semiconductor matrix. If we assume the following values of


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m*≒1.0m0 [10] and ε =61.6 [11], the above terms mean the generation of impurity levels at about 4 meV higher than the top of the valence band or lower than the bottom of the conduction band. On the contrary, the predicted position of the Fermi level (and shrinkage of band gap accompanied by generation of impurity levels) is closer to the observed behavior [12] though calculated position depends on k-point sampling and has a rather arbitrary nature.

3.2. OsSi2 and Possible RuSi2 Osmium (Os), belonging to the 8th group as well as Fe, forms OsSi2 with the β-FeSi2 type structure which is a semiconductor with wider band-gap than β-FeSi2. Therefore, Os is a candidate doping material to widen the band-gap of β-FeSi2. However, the toxicity of Os limits its applicability. Instead, ruthenium (Ru) is expecting and the Ru-doped β-FeSi2 can be prepared by, for example, sputtering deposition method [13] but the electric properties have not been determined yet. From the viewpoint of band-gap engineering, perfect solid solution of FeSi2-RuSi2 will be hopeful but pure RuSi2 is not present in the Ru-Si system as an equilibrium phase. Ru2Si3 is present as an equilibrium phase, which will be described later. In the Ru-Si system, RuSi2 does not appear and Ru2Si3 is present. In the Fe-Si system, FeSi2 does appear and Fe2Si3 does not. In the Os-Si system, both of OsSi2 and Os2Si3 are present. These should be understood by considering the relative stability of MSi, M2Si3, and MSi with reference to M and Si, which will be published elsewhere.

3.3. TiSi2, CrSi2, MoSi2 and the 7th Group Element Defect-Disilicides TiSi2 has an orthorhombic symmetry, belonging to the space group F ddd (No.70) and a unit cell consists of 24 atoms (Ti8Si16). CrSi2 has a hexagonal symmetry, belonging to the space group P 6222 (No.180) and a unit cell contains 18 atoms (Cr6Si12). MoSi2 has a tetragonal symmetry, belonging to the space group I 4/mmm (No.139) and a unit cell contains 6 atoms (Mo2Si4). Though their structures shown in Figure 11 look complicated, these have a common structural feature, that is, nearly hexagonal M-Si2 layers, and they are generated by changing the stacking sequence of neighboring M-Si2 layers: The TiSi2–type structure contains four layers in an ABCD stacking sequence, the CrSi2 type structure contains three layers, ABC, and the MoSi2-type structure consists of two layers with AB stacking. Since their local atomic configurations are alike, their DOS curves may be nearly the same. The d-states of T, the transition metal atom, will be filled with 10 electrons and the sp state of the Si atoms will be filled by four electrons, 14 valence electrons per T atom (usually referred to as a ‘ valence electron concentration (VEC) ’ )are considered to be just enough to fill these bands when there is no overlap of bonding and antibonding states. If this idea is appropriate, CrSi2, MoSi2 and WSi2 will be semiconductors. However, the band structure calculation shows that CrSi2 is a real semiconductor while MoSi2 and WSi2 are not.

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Figure 11. Crystal structures of TiSi2, CrSi2, and MoSi2. Open circles and closed circles denote Si and Ti (or Cr or Mo), respectively. The solid lines connecting Si atoms show hexagonal arrangement of Si atoms.

Figure 12. Band structures of CrSi2 and MoSi2.

Figure 12 shows the band structure (BS) of CrSi2 and MoSi2. As is shown, there exists definite energy gap in the BS diagram of CrSi2 with the indirect nature, while energy dispersion curve of MoSi2 cross the energy zero (the Fermi level) near P (1/4 1/4 1/4).


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Therefore, MoSi2 is not a semiconductor. Since the calculated DOS curve has a minimum at the Fermi level, it will act as semimetallic conductor. In the end of this section, it should be mentioned here about the 7th group element silicides. Re was previously believed to form ReSi2 and considered to have the MoSi2-type structure. Recent structural investigation by Gottlieb [14] suggests that the stable phase has Si vacancies and that the composition should be described as ReSi1.75 or Re4Si7, which results in the valence electron concentration as (7x4+4x7)/4=14. The calculation showed that the Fermi level exist near the minimum of DOS curve if we assume the stoichiometric ratio of Re to Si is 1:1.75, though clear energy gap could not be obtained. If we take the random distribution of Si vacancy into account, the so-called Anderson localization of wavefunctions will occur and the electric conduction will be determined by variable range hopping of carriers. Semiconducting-like behavior of a monotonous decrease in resistivity with temperature would be observed. Mn is known to have a series of silicides with the formulae of MnSi2-x, which are described in the following section.

4. CHIMNEY-LADDER COMPOUNDS A family of compounds known as Nowotny chimney-ladder (CL) phases are characterized by the composition of TnXm ( m and n are integers with 2>m/n>1.25, T is a transition metal element belonging to the 4th to the 9th group such as Ti, V, Cr, Mo, Mn, Ru, Os, Rh, and Ir, which is in a tetragonal β-Sn arrangement(chimney). X is the 13th or 14th group elements such as Al, Ga, Si, Ge, and Sn) in a coupled helical arrangement (ladder). Compounds belonging to this family have been proposed as advanced thermoelectric energy conversion materials (TE materials) because they have low lattice heat conductivity because of their complex structures [15]. The ‘14 valence electron concentration (VEC) rule’ stated above is sometimes, but not always, valid for CL compounds for predicting semiconducting behavior as stated later. Though compounds with tetragonal symmetry are really CL compounds, compounds such as Ru2Si3 and Ru2Ge3 in low temperature modification with orthorhombic symmetry are also included in this category since their structure is closely related to the CL structure in that two unit cells of Ru2Sn3 placed side by side gives the unit cell of the Ru2Si3-type structure. Both have nearly the same position of the transition elements and the difference between them exists in the Si and Sn ( Ge) position[16]. The structural relationship between the tetragonal phase and orthorhombic phases can be seen, for example, in Figure 1 of the paper by Simkin et al [17]. The band structure Ru2Si3 is shown in Figure 13(a). Since the unit cell is composed of 16 Ru atoms and 24 Si atoms, 224 valence electrons (8 electrons from each Ru atom and 4 electrons from each Si atom) are contained in the unit cell. The gap is being formed between the 112th and the 113th bands, as shown in Figure 13(a). It is characterized by a direct transition at the Γ point of the Brillouin zone, but the conduction band minimum located at Y has neary the same energy and the difference between Γ113 and Y113 is quite small. As for the cases in the Ru2Sn3 type structure, which is properly grouped with the chimney-ladder structure, the unit cell contains 8 Ru atoms and 12 Sn atoms. 112 valence

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electrons (8 electrons from each Ru atom and 4 electrons from each Sn atom) are contained in the unit cell. The gap is being formed between the 56th and the 57th bands. The band structure of Ru2Ge3 in the high temperature modification, which belongs to this type of structure, is shown in Figure 13(b). As is revealed, the band gap is located at the Γ point. The energy band gap decrease in the heavier elements semiconductor results in the closure of the gap of Ru2Sn3. A small overlapping of the conduction band and the valence band at Γ would be responsible for the metallic character of Ru2Sn3 [18]. As for the 6th , 7th and 9th group elements, CL compounds are present which do not necessarily obey the 14 VEC rule. The 6th group elements (Cr and Mo) form CL compounds of Cr11Si19 and Mo13Ge23, the VECs of which are 12.9 and 13.1, respectively. Thus, the Fermi level would be located at a place before the gap of the DOS curve, as shown in Figure 14(b) and (c), and they are metallic. Mn, the 7th group element, forms a series of defect silicides of Mn11Si19 (MnSi1.727), Mn26Si45 （MnSi1.730）Mn15Si26 (MnSi1.722), and Mn27Si47 (MnSi1.741) and they are usually written as MnSi1.75-x. The unit cell of these Mn compounds can be represented as a chain of sublattices extended along the direction of the [001] axis. In all these sublattices the Mn atoms occupy the same position, whereas the coordinates of the Si atoms are of a variable nature.

Figure 13. Band structures of (a), Ru2Si3 and (b), Ru2Ge3 in the high temperature modification.


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Figure 14. DOS curve of Mn11Si19,(a), Cr11Si19, (b), Mo13Ge23, (c), Rh10Ga17, (d), and Rh17Ge22, (e). The energies are shifted so that the Fermi level is aligned with zero.

As shown in Figure 14(a), the Fermi level (EF) of Mn11Si19, is located just below the gap of about 0.7eV. Mn11Si19 is reported to be not a metal but behaves like a p-type

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semiconductor with the band gap of 0.4eV. [19]. Generation of localized energy levels between the gap and random distribution of Si defects would cause the localization of the wavefunction, which result in semiconductor-like conduction as in the case of rhombohedral boron. Iridium (Ir) in the 9th group form CL compounds with Ga and Ge, Ir3Ga5 and Ir4Ge5, the VECs of which are equal to 14. However, the BS diagram of Ir3Ga5 shown in Figures 15(a) and (b). We find intersections of the bands of Ir3Ga5 with the Fermi level, which indicates its whereas the metallic property. As for Ir4Ge5, the conduction band minimum exists at valence band maximum exists at a point between M and . Overlap of the valence and the conduction band is limited near these points, suggesting its semiconducting (or, at least, semimetallic) nature if tendency of underestimation of band gap by the present densityfunctional calculation is allowed. Rhodium (Rh) which also belongs to the 9th group forms Rh10Ga17 and Rh17Ge22 whose VECs exceed 14. The total DOS of these are shown in Figures 14(d) and (e). In contrast to the case of Mn11Si19, their Fermi levels are located at the place of the upward slope which is past the gap of the DOS curve. The value of the DOS at their Fermi levels are of the same order as Mn11Si19, and therefore they may display n-type semiconductor-like behavior if the energy levels near their Fermi levels are fully isolated. However, the experimental data have not been obtained to our knowledge.

5. TRANSITION METAL MONOSILICIDES 5.1. Monosilicides, Overview Most of transition metal elements form monosilicides, MSi, where M denotes a transition metal. Among them, FeSi and RuSi are known to be narrow-gap semiconductors and CoSi to be semimetallic. Crystal structures of transition metal monosilicides are either of five following types; the FeB-type, the CrB-type, the FeSi-type, the MnP-type, or the CsCl-type. The FeSi structure, usually referred to as a B20 structure, is described as a pairing distortion of a face-centered-cubic (fcc) structure (rocksalt structure) in which Fe and Si are displaced along the direction. This displacement reduce the space group symmetry from F m3m to P 213. Both the Fe and Si atoms are locate at the 4a-type sites in the simple cubic unit cell with position coordinates (u,u,u), (1/2+u, 1/2-u, u), (u, 1/2+u,1/2-u) and (1/2-u, u,1/2+u). For FeSi, u(Fe)=0.1358 and u(Si) =0.844 [20]. In passing I might mention that the atom-position parameters of rocksalt structure correspond to the value of u(Fe)=0.25 and u(Si)=0.75, respectively. The CrB-type and the FeB-type structure are characterized by (1)the silicon atoms form zig-zag chains, and (2)the metal atoms have six silicon neighbors and lie in octahedral symmetry. The zig-zag chain in the CrB- type and FeB-type exist on one plane, say the x-y plane. The difference exists in that the phase of the zig-zag chain is coherent in the alternate layer in the z direction in the CrB-type whereas a lag in the half-period exists in the alternate layer in the FeB-type structure.


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The MnP-type structure can be described as the distorted the NiAs-type structure. The transition metal atoms also have six silicon neighbors and lie in octahedral symmetry but the zig-zag chain formed by Si atoms does not exist on one plane. Correlation between the crystal structures of MSi and the location of M in the periodic table of the elements is shown in Figure 16. Monosilicides with the CrB- or the FeB- type structures appear in the earlier part of the transition element. Monosilicides with a MnP-type structure appear in the latter part of the transition metals Transition metals such as Cr, Mn, Fe, and Co, which have medium number of d-electrons, form monosilicides of the FeSi-type of structure. CsCl-type monosilicide appears as the high-temperature modification of RuSi. Their structural trend can be understood qualitatively from the principle that the ‘ DOS at Fermi level would be hopefully smaller in an energetically- favored structure ‘, as shown below. Figure 17 show the position of the Fermi level of the compounds, MSi, written on the DOS curve of the CrB-type, the FeB-type, the FeSi-type and the MnP-type structure, assuming that the ‘rigid band approach’ is valid. Underlined elements mean that the equilibrium structure of MSi has the corresponding structure. As shown, ScSi with the CrB type, TiSi with the FeB type, FeSi and CoSi with the FeSi type, and NiSi with the MnP-type structure have smaller DOS values at their Fermi level, compared to other types of structures. MnSi with the FeSi-type structure have relatively large DOS value but a calculation where the spin polarization is taken gives the split of the DOS curve at the Fermi level, though not shown here, and the system reduces the energy by ferromagnetic spin configuration, which can partly explain the helical spin structure observed.

Figure 15. Band structure of Ir3Ga5 and Ir4Ge5.

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Figure 16. Correlation between the crystal structures of transition metal monosilicides (MSi) and the location of M in the periodic table of the elements.

5.2. FeSi In the preivious section, the structure of FeSi was qualitatively discussed in comparison with other possible structures. The more quantitative analysis for FeSi is given in Figure 18. This presents the total energies of FeSi’s （ε−FeSi, hypothetical FeSi with the NaCl-type structure, and hypothetical FeSi with the CsCl-type structure） calculated using a normconserving nonlocal pseudopotential. Among these phases, ε-FeSi is correctly the lowest in energy. The following is hypothetical FeSi with the CsCl-type structure. The reason of the different total energy is clearly demonstrated by Figure 19 which presents the densities of states (DOSs) of these phases. FeSi wit undistoted NaCl type structure have definite value of DOS at its Fermi level but the distortion stated above cause the perfect split of DOS to open the gap and the shift of the Fermi level to just in the gap of DOS, to make FeSi semiconductor. CsCl-like configuration also makes gap of DOS and total energy of this structure is not so high compared to ε-FeSi. In fact, RuSi have this type of structure at elevated temperatures where entropy effect is more favorable for simpler atomic configurations. The band structure near the Fermi level for FeSi is plotted in Figure 20. Here, each band is two-fold degenerate. Forty-eight electrons per cell, eight from each Fe atom and four from each Si atom, are sufficient to fill the lowest 24 valence bands and the valence band maximum exits along the MΓ, ΓR, or at X, and the conduction band minimum at X , along MΓ or along ΓR. The minimum indirect gap is very close to the minimum direct gap occurs along ΓM.


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Figure 17. Position of the Fermi level of transition metal monosilisides on the DOS curve of the CrB-, FeB-, FeSi- and MnP- type structure assuming the regid band model. Underlined elements mean that the equilibrium structure of MSi has that structure.

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Figure 18. Variation of the electronic energies of FeSi with the ε−FeSi type, the hypothetical NaCltype, and the hypothetical CsCl-type structure with the cell volume. The arrow in the Figure shows the equilibrium cell volume of ε-FeSi (=22.6x10-3nm3/FeSi).

However, the band gap predicted here is much broader than the observed value(～0.05eV). The reason for that is not clarified but the value of the gap would be significantly changed when the spin-orbit coupling is taken into account, where the degeneracy above stated is lifted. FeSi is known to behave similary to the strongly correlated electron systems. Nevertheless, the ground sate properties such as lattice constants are wellreproduced by the band calculation here, as shown by arrows in Figure 18.

6. ALKALINE EARTH METAL DISILICIDES 6.1. Alkaline Earth Metal Disilicides,Overview Hereafter, we describe the results for alkaline earth (AE) metal silicides. Most of the AE disilisides crystallize in either of four structure types that differ characteristically in their silicon sublattices [21].


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A) Isolated Si-tetrahedra separated from each other by more than 1.5 times as large as Si-Si bond distance is the most prominent feature of the orthorhombic BaSi2 type structure (P nma, No.62). BaSi2 has this type structure at normal pressure. The unit cell of BaSi2 is shown in Figure 21 As shown, there are two crystallographically inequivalent sites for Ba (BaI, BaII) and three inequivalent sites for Si (SiIII, SiIV, and SiV). The unit cell contains eight formula units and the stoichiometric description of the unit cell is Ba8Si16. Atoms are distributed over 4 BaI, 4 BaII, 4 SiIII, 4 SiIV, and 8 SiV sites. BaSi2 transforms into the cubic SrSi2 type structure at higher pressure in low temperature below ca 1000 K.

Figure 19. Comparison of the densities of states of FeSi with the ε−FeSi type, the hypothetical NaCltype , and the hypothetical CsCl-type structure.

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Figure 20. Band structure of ε-FeSi. It should be noted that each band (for example, the 23rd and the 24th, the 25th and the 26th , is two-fold degenerate.

B) Three–dimensional (3-D)three－connected network of Si is found in SrSi2 type structure. All Si atoms have three equidistant neighbors in flat trigonal pyramids, but twisted against each other. SrSi2 have this structure (P 4332, No.212) at ambient condition. C) Corrugated layers of three-connected Si atoms with equidistance bonds and equal bond angles are found in this CaSi2 type structure (R 3m, No.166). This is composed of the alternative layer-by-layer packing of the hexagonal Ca layer and the Si layer. D) SrSi2 and CaSi2 transform into the tetragonal ThSi2 type structure (I 41/amd, No.141) at high pressure. Another type of Si network is found, where each silicon atom has three neighbors. They are in planar arrangement and the Si4 groups are twisted alternatively by 90°in the direction of the tetragonal c-axis


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These observed facts imply that the relative stability of these structures has close correlations with the atomic volume of these structures. Therefore, energy variation of these structures with the change of the atomic volume was calculated. The calculated total energy curves of CaSi2 with the CaSi2-type, ThSi2-type, SrSi2 type and BaSi2-type structures are shown in Figure 22 by squares, triangles, circles and crosses, respectively. The energy minima appear in the order of the ThSi2-type, SrSi2-type, CaSi2type, and BaSi2-type. The ThSi2- and SrSi2-type, (3-D network of Si atoms), are favorable for tight packing of the atoms. The layered structure in the CaSi2-type is the next and the BaSi2type, characterized by isolated Si-tetrahedra, is unfavorable to the dense packing of the atoms. This order of the volumes at energy minima is almost common to the other AE disilicides, as will be seen later. The value of the total energy is almost in the order of the BaSi2-, ThSi2-, SrSi2-, and CaSi2-type, though their dependences on the cell-volumes are different.

Figure 21. Crystal structure of BaSi2.

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The broken arrows in the Figure show the values of the volume experimentally determined for the structures of CaSi2-type at normal pressure (65.6x10-3nm3) and ThSi2-type at higher pressure (62.0x10-3nm3, prepared at 4GPa). These values are a bit larger than the volumes at energy minima of the total energy curves of each phase (about 63x10-3nm3 for CaSi2-type and about 60x10-3nm3 for ThSi2-type), as is consistent with general tendency that DFT calculation is likely to underestimate the cell volume. The energy of CaSi2-type structure has the largest negative value among the structures considered at that volume (65.6x10-3nm3, shown by a closed square), and this agrees with the fact that CaSi2 is the stable phase at normal pressure. On the contrary, the energy of ThSi2-type at the volume of 62.0x10-3nm3 shown by a closed triangle was about 0.05eV larger than CaSi2-type, which disagrees with the fact that ThSi2-type is stable at higher pressure.

Figure 22. Calculated variation of the electronic energy of CaSi2 with the CaSi2 type (□,■), ThSi2 type ( , ▲), SrSi2 type(○) and BaSi2 type(ｘ) structures. The arrows in the Figure show the values of the volumes experimentally determined for CaSi2-type structure at normal pressure and ThSi2-type at higher pressure (prepared at 4GPa, 1273 K ). The closed symbols mean the energies at the equilibrim volume experimentally determined.

However, it should be noted that the energy minimum of the ThSi2-type structure is located at the cell volume of about 60x10-3nm3 and the total energy of ThSi2-type at that cell volume is more negative than that of CaSi2-type. Small discrepancy between the predicted cell volume and the observed cell volume may lead to the erroneous conclusion in case such a small energy difference among the different crystal structures is the matter. Figures 23 and 24 give corresponding relation for SrSi2 and BaSi2, respectively. They give relatively reliable results for prediction of the phases which appear under ambient and high pressures, though the cell volumes predicted from the energy minima are a bit smaller than the experimental values.


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Figure 23. Calculated variation of the electronic energies of SrSi2 with the CaSi2 type(□), ThSi2 type ( , ▲), SrSi2 type(○, ●) and BaSi2 type(x) structures. The arrows in the Figure show the values of the volumes experimentally determined for SrSi2-type structure at normal pressure and ThSi2-type at higher pressure (prepared at 4GPa, 1273 K). The closed symbols mean the energies at the equilibrium volume experimentally determined.

Figure 24. Calculated variation of the electronic energies of BaSi2 with the CaSi2 type(□), ThSi2 type ( ), SrSi2 type(○, ●) and BaSi2 type(x) structures. The arrows in the Figure show the values of the volumes experimentally determined for the BaSi2-type structure at normal pressure and the ThSi2-type at higher pressure (prepared at 4GPa, 1273 K). The closed or bold symbol mean the energy at the equilibrim volume experimentally determined.

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6.2. BaSi2 and SrSi2 Figure 25 shows the band structures along several high-symmetry lines in the Brillouin zone of BaSi2 near their Fermi levels. Plotted in the BS Figure are the numbers which express the order counted from the bottom of the valence band.

Figure 25. Band structure of BaSi2. The energies are shifted so that the top of the valence band is aligned with zero.

Because the unit cell of this alloy contains eight Ba atoms and sixteen Si atoms, 80 valence electrons (two electrons from each Ba atom and four electrons from each Si atom) are contained in the unit cell, and therefore, 40 bands are fully occupied because there is no overlap in energy between the 40th band (and below) and the 41st band (and above).


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The valence band maximum of BaSi2 is between Γ (0 0 0) and Y (0 1/2 0) and a conduction band minimum is located at T (0 1/2 1/2). The indirect band gap between them was calculated to be 0.72eV, 60 % of the observed value (1.3 eV) and this is a typical example which indicate the underestimation of the gap by DFT calculation. Figure 26 shows the calculated total DOS of BaSi2 and its angular momentum projection to give the partial DOS(PDOS) near the Fermi level. The site dependence of the PDOS of the same kind of atoms can be roughly ignored. .As shown, the valence band edge is mainly composed of Si 3p .. The conduction band edge is mainly composed of Si3p hybridized with the Ba 5d.

Figure 26. Total and partial DOSs of BaSi2.

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Figure 27. Band structure of SrSi2.

BaSi2 thin film is expected as a good candidate for high-efficiency thin-film solar cells [22]. Its band gap value (Eg) is closer to the ideal value (ca 1.4eV) than silicon (Si, Eg is 1.1eV) which is now predominantly used for solar cell materials. In addition, BaSi2 has also much higher optical absorption coefficient than Si. The band structure of SrSi2 is shown in Figure 27. The top of the valence band, the 20th band, is located between Γ and X . The energy minimum of the lowest conduction band, the 21st band, is located between Γ and M . The unit cell (Sr4Si8) contains 40 valence electrons and, therefore, 20 bands are fully occupied. The energy difference between the top of the 20th band and the bottom of the 21st band was calculated to be 3meV, which is much lower than the observed value of 35meV [23], and again the gap is underestimated However, the


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decreasing tendency of the gap by pressurization [24] is known to be well reproduced by the calculations, though not shown here.

7. ALKALINE EARTH METAL HALF SILICIDES Though alkaline earth metal monosilicides (CaSi, SrSi and BaSi) are metallic, half silicides of Mg2Si, Ca2Si and Sr2Si.are semiconductors. Mg2Si has an anti-CaF2 type structure (F m3m, No.225) but Ca2Si and Sr2Si has the structure belonging to the space group of P nma, No.62 with orthorhombic symmetry. This structure is sometimes referred to as the Co2Si-type or the anti-PbCl2 type but we call this the Ca2Si-type here for simplicity.

Figure 28. Band structure of Mg2Si. The energies are shifted so that the Fermi level is aligned with zero.

Calculated band structures of Mg2Si and Ca2Si are presented in Figures28 and 29, respectively, in parallel with the DOS curves. As seen from the Figure s, Mg2Si is predicted to have an indirect band gap from Γ to X of 0.28eV, which is less than half of the observed value, 0.77eV. Ca2Si are predicted to have a direct band gap of 0.36eV., which is much less than observed value of 1.9eV. Again calculated values are much lower than the observed

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values but shows anyhow that Ca2Si is a semiconductor. Sr2Si, which has the same crystal structure with Ca2Si, has nearly the same band structure with Ca2Si and have a bit wider direct band gap of 0.402eV at Γ.

Figure 29. Band structure of Ca2Si.

8. ALKALINE EARTH METAL PNICRIDES Recently, Kajikawa et al. proposed that semiconducting Mg pnictides can be better thermoelectric (TE) materials than Mg2Si-Mg2Ge alloy, which has been investigated as a promising TE material, because they are composed of elements heavier than Si or Ge and would have lower lattice thermal conductivities [25]. Mg is known to form a series of intermetallic compounds with the 15th group elements (Pnicogens (Pn); N, P, As, Sb and Bi), the formulas of which are expressed as Mg3Pn2. Mg3Pn2 are known to have either the crystal structure of a), a cubic structure of the Mn2O3


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type or b), a hexagonal structure of the La2O3 type. The unit cell of the former is composed of 80 atoms, 48 Mg and 32 Pn, and belongs to the space group of I a3 (206), which can be reduced to the primitive cell composed of 40 atoms. The unit cell of the latter is composed of 5 atoms, 3 Mg and 2 Pn, and belongs to the space group of P 3m1 (164). Mg3N2 and Mg3P2 are known to have the Mn2O3-type structure. Mg3As2 also has this type of structure at ambient temperature, but changes to the La2O3-type structure at about 1323Ｋ. On the contrary, Mg3Sb2 has the La2O3-type structure below 1203 K, but has the Mn2O3-type structure above that temperature. Mg3Bi2 has also La2O3-type structure at the ambient temperature.

Figure 30. Band structure of Mg3Sb2.

Figure 30 shows the band structure (BS) of Mg3Sb2 along the high symmetry directions of the Brillouin zone near the Fermi level. The gap value is about 0.41eV. The bottom of the conduction band, the 9th band, is located at K. The band gap is indirect with the top of the valence band (the 8th band) at Γ. The gap value between them is about 0.41eV. There seems to be no recent measurements of the band gap of crystalline Mg3Sb2. However, Verbrugge and Zytveld [26] estimated the gap of the liquid phase of Mg3Sb2 as 0.8eV.

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The band structure of Mg3As2 in the high-temperature modification, not shown here, indicates that both of the top of the valence band and the bottom of the conduction band are located at Γ and the energy gap between Γ8 and Γ9 is estimated to be 1.1eV. However, the energy difference between the Γ, K and the state along the line M-L of the 9th band is about 0.05eV or less and it is difficult to state definitely that the gap is direct or indirect. In the band diagram of Mg3Bi2, we find contact of the valence band maximum and the conduction band minimum at Γ , and it is predicted to be a semimetal. Therefore, the turn of the band gaps of these are as follows: Mg3As2 > Mg3Sb2 > Mg3Bi2.

Figure 31. Band structure of low-temperature modification of Mg3As2. The energies are shifted so that the top of the valence band is aligned with zero.

Figure 31 shows their calculated band structure of Mg3As2 (low temperature phase) with the Mn2O3 type structure.


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As are shown, that is a semiconductors with the direct band gap of 1.57eV. The same can be said for Mg3N2and Mg3P2 with the gap values of 1.64eV (Mg3N2) and 1.73eV (Mg3P2). Reckeweg et al. [27] determined the energy gap of Mg3N2 to be 2.8eV using optical diffusereflectance spectra. Our result for Mg3N2 is about 60% of the observed value, as is often the case when using the density functional method. As for Mg3As2, our value calculated is about 70% of the observed value of 2.2eV [28]. There are no available data for the observed gap value of Mg3P2 as a comparison. One may assume that a monotonic shift for a band gap in the systematic calculations going from Mg3N2 to Mg3P2 and to Mg3As2 would be natural as in the case of Mg3Pn2 with the La2O3-type structure. The reason for the difference in the expected tendency and the calculated result is not clear at present, but there are several factors which may influence the gap value. For example, Larson et al.[29] carried out systematic calculations of the electronic structure of YNiPn where Pn is a pnicogen element. A decrease in the gap was observed as one goes from As to Bi. On the contrary, broadening of the band gap upon going to heavier elements is observed in the series of transition metal disilicides and sesqui-silicides, which may be caused by the enhanced effect of hybridization in the heavier elements for which the energy difference between higher orbitals is smaller. The apparent complex tendency of the gap broadening in the present case may be caused by these opposite factors. In addition, relativistic effect (massvelocity term and Darwin term) will predict complex effect on the band structures of the heavier element compounds [30] though the present calculations do not treat that explicitly but through the pseudopotentials.

9. IRON GROUP ALUMINIDES AND GALLIDES (FEGA3) The 8th group elements (Fe, Ru and Os) make semiconducting aluminides, Gallides and Indiumides. They are classified into two groups; chimney-ladder compounds which has been described above and compounds of the FeGa3-type structure. RuAl2 and RuGa2 belong to the former, which obey the 14 VEC rule. FeGa3, RuGa3, OsGa3, and RuIn3 belongs to the latter. Though they were considered to have the CoGa3-type structure and belong to the space group of P4n2 (No.118) [31,32], recent studies describe them as belonging to the space group of P 42/mnm ( No.136) [33. 34]. Energetic consideration supports the latter type of structure for semiconducting compounds [35]. Here, their band structures are described assuming that they have the latter crystal structure. Figure 32 shows the BS diagram of FeGa3. The valence band maximum occurs at A and the conduction band minimum occurs at a point between Z and Γ. The band gap of the FeGa3 structure is 0.496eV. The observed band gap by Häussermann et al. [36] is 0.3eV and that by Amagai et al. [37] is 0.26 eV Their value is smaller than the value predicted by the present calculation. It is contrary to the general tendency that DFT calculation will give narrower gap than the observed value. The reason is not clarified but study of the precise structure refinement of the prepared samples will be necessary since slight deviations from stoichiometric ratio due to defects or small amount of impurity would cause a shift of the Fermi level into the conduction band or the valence band and they can be the possible reason for the discrepancy between the calculated gap values and observed values.

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As for other compounds, OsGa3, RuGa3, and RuIn3, the band structure diagrams have almost the same features; the valence band maximum occurs at A or at a point near A between A and R or between A and Z. The conduction band minimum occurs at a point between Z and Γ. The gap values are calculated to be 0.68eV for OsGa3.,0.26eV for RuGa3, and 0.30eV for RuIn3.

Figure 32. Band structure of FeGa3.

12. SUMMARY In this paper, results on electronic structure calculation of intermetallic semiconductors have been presented. The compounds taken are transition metal silicides, chimney ladder compounds, alkaline earth metal silicides, alkaline earth metal pnictides, and iron group element aluminides and gallides. These are attracting since they have favorable band gaps and


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this gap can be controlled by alloying with the same group element, though little can be described here. Recent investigation clarified, for example, possibility of band gap tuning of BaSi2 by alloying with Sr to increase the efficiency of solar energy conversion. However, realization of these techniques is still in the early stage and there seems to be much room for investigation. In addition, there are many intermetallic semiconductors not included in this article such as a Half-Heusler alloy. This has the MgAgAs-type structure and composed of transitition metals and a sp metal such as Al and Sb. It has been clarified that the idea of valence electron concentration (VEC) is also important for judging its semiconductivity. Alloys with VEC=18 are attracting intention for thermoelectric materials to be used at relatively low temperature since this is a narrow band-gap semiconductor whose electronic properties can be changed by fine tuning of band gap using a partial substitution of constituent metal atoms. These examples show broad capability of intermetallic semiconductors.

REFERENCES [1]

International symposium on semiconductingt silicides have been performed since 1999 and the manuscripts presented there were published in Thin Solid Films Vol.381 (2001) 171-302 and in Vol. 461 (2004) 2-226, and will be in July 2007. [2-1] J.Derrien, J.Chevrien, V.Le Thanh, J.E.Mahan, Appl. Surface. Sci. 56 (1992) 382, and references therein. [2-2] E.Arushanov, E.Bucher, Ch.Kloc, O.Kulikova, L.Kulyk, A.Siminel, Phys. Rev., B52 (1995). [3] See, for review of thermoelectric behaviors of FeSi2, U.Birkholz, E.Gross, in “Thermoelectrics” ed. by M. Rowe, (CRC press, 1994) p.287. Also see many papers related to the thermoelectric energy conversion published in “International Conference on Thermoelectrics” held at Dresden in 1997, Nagoya in 1998, Baltimore in1999, Cardiff in 2000, Beijing in 2001, Long Beach in 2002, La Grande-Motte in 2003, Adelaide in 2004, Clemson in 2005, and Vienna in 2006. [4] P. Y. Dusausoy, J. Protas, R.Wandji, B.Roques, Acta Crystallogr. B27, 1209 (1971). [5] N. Onda, J. Henz, E. Muller, K. A. Mader, H. von Kanel, Appl. Surf. Sci., 56, 421 (1992). [6-1] C. A. Dimitriadis, J. H. Werner, S. Logothetidis, M.Stutzmann, J. Weber, R. Nesper, J. Appl. Phys. 68, 1726 (1990). [6-2] H. Lange, Phys. Stat. Sol. B201 (1997) 3 and references therein. [7] K. Takakura, H. Ohyama, K. Takarabe, T. Suemasu, F. Hasegawa, J. Appl. Phys., 97 (2005) Article No.093716. [8] N. E. Christensen, Phys. Rev. B 42: (1990) 7148. [9] M. Komabayashi, K. Hijikata, S. Ido, Jpn. J. Appl. Phys., 30 (1991) 331. [10] E.Arushanov, Ch. Kloc, E.Bucher, Phys. Rev., B50 (1994) 2653. [11] U. Birkholz, H. Finkenrath, J. Naegele, N.Uhle, phys. stat. sol., 30 (1968) K81. [12] D.Panknin, E.Wieser, W.Skorupa, W.Henrion, H. Lange, Appl. Phys., A62 (1996) 155. [13] T. Tsunoda, M. Mukaida, Y. Imai, Thin Solid Films, 381 (2001)296.

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[14] U. Gottlieb, B. Lambert-Anderson, F. Nava, M. Affronte, O. Laborde, A. Rouault., R. Madar., J. Appl. Phys. ; 78 (1995) 3902. [15] T. Caillat,.J. –P.. Fleurial , A. Borshchevsky, J. Alloys Compounds., 252 (1997) 12. [16] D. J. Poutcharovsky E. Parthe , Acta Cryst, B30 (1974) 2692. [17] B. A. Simkin, A. Ishida, N. L. Okamoto, K. Kishida, K. Tanaka, H. Inui, Acta Materialia, 54 (2006) 2857. [18] C. P. Susz, J. Muller, K. Yvon,E. Parthe, J. Less Common Met., 71 (1980) P1. [19-1] Nishida I, J. Mat. Sci.,;7(1972) 435. [19-2] Nikitin EN., Tarasov VI, Tamarin PV, Soviet Physics - Solid State, 11(1969) 187. [20] H.Watanabe, H.Yamazaki, K.Ito, J. Phys. Soc. Jpn, 18 995(1963) 13. [21] See, for example, Wells, A. F., “Structural Inorganic Chemistry” 5th ed., (1984, Oxford University Press, Oxford, UK) p.987-991. [22] Morita K. Inomata Y. Suemasu T. Thin Solid Films 508 (2006) 363. [23] Imai M, Naka T, Furubayashi T, .Abe H, Appl. Phys. Lett, 86 (2005) 32102. [24] M. Imai, T. Naka, H. Abe, T. Furubayashi, Intermetallics 15 (2007) 956. [25] T. Kajikawa, N. Kimura, T.Yokoyama, Proc. 22nd Int, Conf.Thermoelectrics, (2003) 305-308nd. [26] D. M. Verbrugge, J. B.Van Zytveld, J. Non-Crystalline Solids, 156-158 (1993) 736 [27] O. Recheweg, C. Lind, A. Simon, F. J. DiSalvo, Zeit fur Naturforschung B –J. Chem.. Sci., 58 (2003) 159. [28] K. Pigon, Helv. Phys. Acta 41 (1968) 1104. [29] P. Larson, S. D. Mobanti, Phys. Rev. B59 (1999) 15660. [30] See, for example, G. M. Fehrenback, H. Bross, Eur. Phys. J., B 9 (1999) 37. [31] K. Schubert, H. L. Lukas, H. –G. Meissner,S. Bhan, Zeit. Metallkunde, 50 (1959) 534. [32] C. Dasarathy , W. Hume-Rothery , Proc. Ｒoy Soc London Ser A, 286 (1965) 141. [33] C. Tao-Fan , L. Ching-Kwei , Chinese J. Phys, 22 (1966) 952. [34] S. S. Lu, L. Ching-Kwei, Chinese J. Phys., 21 (1965) 1079. [35] Y.Imai, A.Watanabe, Intermetallics 14 (2006) 722. [36] U. Häussermann, M. Boström, P. Viklund, ö. Rapp, T. Björängen, J. Solid State Chem., 165 (2002) 94. [37] Y. Amagai , A. Yamamoto,T. Iida, Y. Takanashi, J. Appl. Phys. 96 .(2004) 5644.



Chapter 5

DUCTILE, STOICHIOMETRIC B2 INTERMETALLICS Alan M. Russell∗ Materials Science and Engineering Department, and Materials Engineering Physics Program, Ames Laboratory, USDoE Iowa State University, Ames, IA, 50011, USA

ABSTRACT A growing number of B2 intermetallic compounds has been reported to exhibit high room temperature tensile ductility in the polycrystalline form when tested in normal room air at ambient temperature. These are noteworthy findings, since poor room temperature ductility and low fracture toughness are major impediments to wider engineering use of intermetallic compounds [1]. Most intermetallic compounds can achieve high tensile ductility at room temperature only by means of one or more “contrivances”, such as testing single crystals, testing in an ultra-dry atmosphere, testing specimens with a metastable disordered crystal structure, or testing compositions that are off-stoichiometry or to which third elements have been added. The first of these inherently ductile compounds, AgMg, was reported in the early 1960’s to have good room temperature tensile ductility without the need for any of these contrivances. A few years later, even greater room temperature ductility was reported for another B2 compound, AuZn. Within the past few years, similar reports have been made for B2 CoZr and a large family of rare earth B2 intermetallics (DyCu, YAg, YCu, and several others). Most of these compounds share several common characteristics: substantial differences in the atomic radii and electronegativities of the two constituent elements; existence in the binary equilibrium phase diagram as a Daltonide, linecompound with no perceptible deviation allowed from precise equimolar stoichiometry; the absence of stress-induced twinning or shape-memory-type phase transformations; and a positive temperature dependence of yield strength above room temperature. This chapter describes the experimental findings reported for these materials; the factors thought to contribute to their high ductility; the commonly observed yield strength maxima at elevated temperatures; the strain aging effects seen in some of these materials; the potential applications these materials may have; and the possibilities that “lessons

∗

E-mail: [email protected]

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Alan M. Russell learned” from their study may suggest ductilizing strategies that could be applied to other intermetallic compounds.

1. INTRODUCTION AND EXPERIMENTAL FINDINGS 1.1. Background Information on Ductility in Intermetallics As a general rule, intermetallic compounds have low tensile ductility and low fracture toughness at room temperature. If struck with a hammer, they shatter rather than dent. There are numerous exceptions to this rule, but these exceptions typically involve one or more special circumstances or contrivances that must be invoked to achieve ductility. These contrivances include: •

Tensile tests performed on single crystals – Tensile ductility in single crystal intermetallic compounds can be quite high, even in materials with little or no polycrystalline tensile ductility. If a material has even one active slip system and the tensile specimen is oriented to give a reasonably high Schmid factor for that slip system, dislocations can glide relatively unimpeded over long distances, resulting in substantial elongation before fracture occurs. For example, polycrystalline NiAl has at most 1 to 2% tensile elongation [2]. Yet NiAl single crystals have been reported to elongate as much as 16 to 28% in tension at room temperature; the larger elongations occur in crystals pre-strained in compression to clear dislocations from large subgrain regions [3,4].

The reason for the large disparity between polycrystalline and single crystal ductilities was described by von Mises 80 years ago. In a polycrystalline metal, shape changes are required in almost every conceivable direction in each deforming grain to prevent void generation at grain boundaries that leads to rapid fracture. In his seminal paper on ductility in polycrystalline metals [5], von Mises stated that five independent slip systems must operate in a plastically deforming polycrystalline metal to accommodate the complicated strain requirements imposed by grain boundaries. This requirement has come to be known as the von Mises criterion. In this context a slip system is defined to be independent of other slip systems if its operation changes the shape of the crystal in a way that cannot be duplicated by combinations of slip on the other slip systems [6,7]. Thus, by von Mises’ definition, an FCC crystal deforming by {111} slip possesses not just one slip system, but all five of the independent slip systems required (Table 1). In the case of NiAl, room temperature slip is restricted to only the directions; this means that the crystal cannot be directly elongated or compressed in a direction because the Schmid factors are all zero for such slip. As a result, NiAl possesses only three of the required five independent slip systems, and polycrystalline NiAl fractures after little or no tensile elongation. •

Compositions that are “off-stoichiometry” – Many binary intermetallics can maintain the crystal structure of the stoichiometric compound even when the composition deviates by several atomic per cent from stoichiometry. This is accomplished by substituting atoms of the “wrong” element on some lattice sites

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(anti-site defects) or by leaving some lattice sites vacant. For many compounds, tensile ductility increases sharply as composition deviates from stoichiometry. For example, polycrystalline Co3Ti, an L12 structure compound, will elongate 58% before fracture when the composition is Co0.80Ti0.20, but ductility approaches zero as composition approaches Co0.75Ti0.25 [8]. Several other intermetallics behave similarly. Table 1. Slip systems and independent slip systems as defined by von Mises, for B2 compounds [7] Slip Families {011} {011} {011} + {011} {100} {011} + {100} {011} {112} {111}

Number of Physically Distinct Slip Systems 6 6 12 6 12 12 12 12

Number of Independent Slip Systems (von Mises) 3 2 5 3 3 5 5 5

It might seem that the remarkable improvement in ductility sometimes seen in offstoichiometric intermetallics solves the brittleness problem, thereby permitting wider use of these materials in engineering applications. But, regrettably, some of the other properties that make intermetallic compounds so appealing to the design engineer (e.g., high strength and high creep resistance) degrade sharply as compositions depart from stoichiometry. •

•

Compositions that have a third element added – Ternary intermetallics often possess better ductility than binary intermetallics. For example, polycrystalline NiAl has near zero tensile elongation at room temperature, but addition of Fe, Co, or Cr substantially raises room-temperature tensile ductility by introducing a ductile FCC solid solution phase at the B2 grain boundaries [9]. Tensile tests performed in vacuum or ultra-dry atmospheres – A number of intermetallic compounds display much higher tensile ductility when they are tested in atmospheres devoid of H2O vapor. The so-called environmental embrittlement effect in intermetallics exposed to water vapor is believed to result from reactions on the material’s surface of the type: 2Al + 3H2O → Al2O3 + 6H

The H produced by this reaction is then thought to diffuse rapidly along grain boundaries, weakening them and causing intergranular fracture. For example, tests of two compositions (24 at.% Al and 23.5 at.% Al) of boron-free, recrystallized Ni3Al performed in air showed 2.5% tensile elongation, while tests of the same materials in ultra-dry oxygen produced 7-8% tensile elongation [10]. Fracture toughness also improves markedly in H20-free environments.

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KJmax values in off-stoichiometric iron aluminides more than double when tested in ultra-dry oxygen rather than in room air [11]. •

Specimens that have been quenched from high temperature to preserve a metastable, disordered crystal structure – The ordered crystal structures of intermetallics increase yield and ultimate strengths, improve creep resistance, and slow diffusion, but they also tend to lower ductility because dislocation motion is inhibited by the ordered structure. Many intermetallics have a transformation temperature, above which the ordered crystal structure is replaced by a random solid solution. Material quenched from above this transformation temperature can often retain its disordered structure as a metastable phase at room temperature, and such disordered alloys generally have greater ductility than material of the same composition with the equilibrium ordered structure.

The β−β’ transformation in Cu-Zn, for example, occurs at 460˚C. Above this temperature, β phase is a ductile, disordered BCC solid solution; below this temperature β' has the ordered B2 (CsCl-type) structure and is brittle at room temperature. Metastable β quenched to room temperature is ductile at 20˚C. •

•

Specimens tensile tested under high hydrostatic pressure to suppress fracture – The dominant failure mode for brittle intermetallics is Mode I crack propagation. Since large hydrostatic pressures act to push cracks closed, brittle intermetallics display greater tensile elongations if they are tensile tested under high hydrostatic pressure. For example, NiAl has almost no tensile ductility at ambient temperature and pressure, but when tensile tested at 20˚C under 300 MPa hydrostatic pressure the ductility increases to 4.6% elongation, and at 500 MPa pressure to more than 10% elongation [12]. This ductility increase is attributed to (1) pressure-generated formation of mobile dislocations at grain boundaries and second-phase boundaries, and (2) suppression of void nucleation and crack propagation by the applied external pressure. Materials that display superelasticity (i.e., shape memory effect) due to stressinduced transformations between two different crystal structures – A small number of intermetallic compounds have stress-induced phase transformations that allow them to deform extensively by transforming to another crystal structure. As soon as the stress is removed, however, the metal reverts to its original crystal structure and the geometry it had prior to deformation (the “shape memory effect”). The bestknown of these compounds is the NiTi compound (NITINOL), which has a B2 crystal structure at higher temperatures and a distorted tetragonal structure as the product of its stress-induced martensitic transformation [13]. NITINOL has seen numerous applications in eyeglass frames, stents, and related devices.


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1.2. Ductility in the B2 AgMg Intermetallic Compound Until recently, very few reports existed of intermetallics that are inherently ductile at room temperature without relying upon one of more of the above contrivances. The first such report was published by Wood and Westbrook in 1962 for AgMg [14]. AgMg is a B2 ordered compound at all temperatures below its congruent melting point (820˚C). It tolerates large deviations from stoichiometry, retaining a one-phase B2 structure by substitutional defects over the range of 41 to 53 at.% Mg at 300˚C. Wood and Westbrook reported [14] that AgMg deforms by dislocation glide between room temperature and about 400˚C, with solute-dislocation interactions (e.g., yield point drops, large strain rate sensitivity) becoming quite pronounced in the temperature range 150˚ to 350˚C. Tensile ductilities at fracture were not reported, but many specimens were strained to 8% elongation without fracture, which is a much greater elongation than would typically be observed for a polycrystalline, stoichiometric B2 material at room temperature. Measurements of the stored energy in AgMg specimens deformed at room temperature show greater amounts of stored energy in AgMg than would be seen in most other metallic materials. This is thought to result from the disordering effect of plastic deformation in AgMg [15]. Stoichiometric AgMg also displays substantial ductility in torsion at room temperature [16]; torsion strains of 0.045 are tolerated at room temperature in 50.1 at.%Mg-49.9 at.%Ag (torsion strain is expressed by the dimensionless parameter nd/L, where n is the number of turns of a wire specimen (360˚ of torsional rotation around the wire centerline being one turn), d is the wire diameter, and L is the gauge length deforming in torsion). The ductilebrittle transition in stoichiometric AgMg occurs near room temperature. Off-stoichiometry AgMg (44.2 at.%Mg-55.8 at.%Ag) is ductile at room temperature and also at cryogenic temperatures, tolerating a torsion strain of 0.045 at 195 K and 0.022 at 77 K. The degree of strain-induced disorder is estimated to be about 3% in stoichiometric AgMg cold-worked 4% [16]. Recovery in plastically deformed, stoichiometric AgMg is slow at room temperature, but can be completed in 15 minutes at 160˚C. Recovery is thought to begin by vacancy migration, but dislocation motion becomes an important contributor to removing disorder as recovery progresses. Recovery occurs gradually at room temperature in cold-worked 44.2 at.%Mg-55.8 at.%Ag, suggesting that room temperature deformation should be considered "warm-work" for that composition. The active slip system in AgMg was reported by Rachinger and Cottrell [17] to be {321}. In addition, {211} and {110} slip were reported by Westbrook and Wood [14]. These three slip systems, of course, are the slip systems active in simple BCC metals such as Fe, and slip satisfies the von Mises criterion for polycrystalline ductility. Mobile dislocations are consistent with high ductility, but they seem somewhat surprising in an intermetallic compound of Ag and Mg. Dislocation motion would either have to occur by dislocations with a full displacement for the Burgers vectors or by superdislocation pairs, which create an anti-phase boundary (APB) between two 1/2 dislocations gliding in tandem (Figure 1). Since dislocation line tension scales as the square of Burgers vector length, a full dislocation would be expected to have a much higher energy than dislocations moving in other slip directions, such as the more commonly seen {110} and {100} slip in B2 crystals. Ag and Mg differ appreciably in both electronegativity (eN=0.7 Paulings) and atomic radius (0.016 nm or 10%), so the APB energy

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associated with having atoms on the “wrong” sites might be expected to be significant in this material. However, that observation is seemingly contradicted by the large deviations AgMg tolerates from equi-molar stoichiometry, which Jena, et alia, report to be accommodated by anti-site substitutional atoms [16].

Figure 1. The B2 crystal structure with ½ and dislocation Burgers vectors marked. The {001} and {110} slip planes are shaded. (Atoms drawn disproportionately small for clarity).

Figure 2. Stress-strain plots at various temperatures for AgMg ( εÝ= 2(10-4) s-1) and NiAl ( εÝ= 1.4(10-3) s-1). Redrawn from [18] and [19].

The ductility of stoichiometric AgMg is clearly superior to that of most B2 intermetallics. However, room temperature appears to be near the ductile-brittle transition temperature of


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AgMg, and room temperature is 27% of AgMg’s 1093 K melting temperature. For comparison (Figure 2), the well-studied NiAl B2 intermetallic shows 4% tensile elongation when tested at 25% of its 1912 K melting temperature and 30% elongation when tested at 35% of its melting temperature [18]. It is noteworthy that none of the various papers on AgMg mechanical properties reported XRD results on the degree of ordering, which leaves open the possibility that the materials were not fully ordered. For these reasons, AgMg is considered an interesting ductile intermetallic, but its room temperature ductility is partially attributable to its somewhat low melting point, and it does not appear to be a “breakthrough” discovery in intermetallic ductility.

1.3. Ductility in the B2 AuZn Intermetallic Compound High room-temperature ductility was reported in 1970 for polycrystalline β'-AuZn, a compound with the B2 crystal structure at all temperatures below its congruent melting point (725˚C). Although room temperature is 30% of AuZn’s melting temperature, AuZn is ductile at less than 10% of its melting temperature, which defines a much lower homologous temperature ductility range than is seen in AgMg. AuZn tolerates significant deviations from stoichiometry, retaining a one-phase B2 structure by substitutional anti-site defects over the range of 47.5 to 52 at.% Au at 20˚C [20]. A study by Causey and Teghtsoonian [21] of the tensile ductility of various AuZn compositions reported high ductility in stoichiometric, polycrystalline AuZn over the temperature range 77 to 533 K (Figure 3). Room temperature ductility was 33% elongation, and even at liquid nitrogen temperature the tensile elongation was 13%. Failure occurred by intergranular fracture. Serrated yielding was observed in non-stoichiometric AuZn specimens at room temperature, but serrated yielding was not observed in the stoichiometric specimens. Deformation twinning is not seen in AuZn, which is consistent with theorists’ predictions [22] that such twinning is unlikely to occur in ordered compounds.

Figure 3. Tensile elongation of AuZn intermetallic at various temperatures ( εÝ= 1.6(10-3) s-1). Redrawn from [21].

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AuZn specimens display a high work hardening rate. The θ/G ratio (where θ is the work hardening rate and G is the shear modulus) is about 50 times greater for AuZn than for most ordinary metals. The high work hardening rate is attributed to dislocation intersections resulting from dislocation motion on two active slip systems. Deformation occurring by slip in both and directions would be expected to cause frequent dislocation intersections, which is consistent with the high work hardening rate observed. Study of single crystal AuZn [23] indicated that slip at room temperature occurs primarily in the direction, but that slip occurs on the {211} slip system when the specimen is oriented with the tensile axis nearly parallel to the direction, a "hard" orientation that produces small Schmid factors for slip. AuZn presumably slips mostly in the direction, but slip occurs near grain boundaries to provide many of the geometrically necessary dislocations to avoid intergranular fracture. This is supported by observations that wavy slip lines are most commonly seen near grain boundaries in plastically deformed polycrystalline AuZn [23]. The combination of {110}, {100}, and {211} slip satisfies the von Mises criterion and appears to explain the ductility. Although AuZn has long been known to be a shape memory material, its low martensitic transformation temperature (65K) [23-25] suggests that the shape memory effect is probably not the primary cause of AuZn's room temperature ductility. The AuZn B2 intermetallic involves two elements with substantially different electronegativities (ΔeN = 0.8 Paulings) and atomic radii (0.011 nm or 7.6%), so the presence of slip in AuZn poses the same questions about dislocation motion as were previously discussed for AgMg. It is perhaps significant that AuZn, like AgMg, accommodates deviation from equi-molar composition at equilibrium by creating anti-site defects in the B2 structure. This suggests that, notwithstanding differences in electronegativities and radii, these materials can tolerate the local disorder associated with an APB formed between superdislocation pairs with 1/2 Burgers vectors. In fact, as with the reports on the AgMg compound, none of the papers on AuZn mechanical properties reported XRD results on the degree of ordering, which leaves open the possibility that the materials were not fully ordered.

1.4. Ductility in B2 CoZr Intermetallic Compound In the 1970's the first reports of limited room-temperature tensile ductility were made for B2 CoZr. CoZr is a Daltonide (line) compound (i.e., no appreciable variation from equi-molar stoichiometry at equilibrium) with a melting point of 1670 K. CoZr’s room temperature ductility is greatly enhanced by Ni substitutions for Co to produce ternary alloys with the general formula Zr50Co(50-x)Nix [26]. Tensile elongation of 20% is observed when x = 4, and elongation reaches a maximum value of 34% at x = 12 [27]. However, early studies [26-27] reported only a few percent tensile elongation in binary CoZr. In 2005 Yamaguchi, Kaneno, and Takasugi at Osaka Prefecture University reported 7.5% tensile elongation at room temperature in polycrystalline CoZr [28]. At the time of publication, this value of tensile elongation was the highest reported for binary CoZr. Although it was the intent of this study to produce equi-molar, one-phase CoZr, it is difficult to achieve a completely single-phase specimen of a line compound. The material studied contained small amounts of dispersed C15-type Laves phase Co2Zr, indicating that it was


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slightly Co-rich. The arc-melted specimens were homogenized at 1100˚C for 24 hours, furnace cooled, hot rolled at 1000˚C to a 60% reduction, hot rolled at 700˚C to an additional 60% reduction, then annealed at 1000˚C for one hour. This thermomechanical process achieved hot breakdown of the arc melted grain structure and a recrystalled grain structure (average grain size 13 μm) containing second phase elongated dispersoids of Co2Zr aligned parallel to the rolling direction. The microstructure developed with this processing treatment presumably enhances ductility. The 7.5% tensile elongation of CoZr was somewhat difficult to explain since TEM analysis showed that the dislocations activated by room temperature deformation during tensile testing were mostly -type. Slip limited to the direction provides only three of the five independent slip systems required by the von Mises criterion. The authors speculated that one reason for the high ductility was the large number of "punch-out" dislocations at CoZr-Co2Zr interfaces that are present as plastic flow begins during the tensile test, a phenomenon previously observed in NiAl-based materials [29]. In 2007 Kaneno, et alia, reported a more detailed examination of the ductility of CoZr [30]. In this study, five compositions of CoZr were prepared containing 49.0, 49.5, 50.0, 50.5, and 51.0 at.% Zr. The equimolar composition had 20% tensile elongation at room temperature in normal room air. The fracture surfaces of these tensile specimens showed a mixture of the dimpled, transgranular fractures characteristic of ductile failure plus intergranular fracture surfaces. The equi-molar specimens tolerated 70% reduction by cold rolling without serious cracking. The off-stoichiometry compositions contained the expected Co2Zr or CoZr2 Laves phases, and these compositions were somewhat less ductile and slightly stronger than the equi-molar specimens. These materials had low yield strengths and high ultimate strengths (Figure 4), similar to the high work hardening rate behavior observed in AgMg and AuZn. In the 2007 report, TEM analysis of the dislocations in CoZr showed only -type Burgers vectors. By the von Mises criterion, polycrystalline material deforming only by dislocation motion would be expected to be brittle unless some other factor(s) act to enhance ductility.

Figure 4. Tensile stress-strain plots for equi-molar CoZr tested in vacuum at various temperatures ( εÝ= 1.6(10-4) s-1). Vacuum testing is necessary at the higher temperatures to avoid oxidation; CoZr does not display environmental embrittlement. Redrawn from [30].

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Such factors could include deformation twinning or a stress-induced phase transformation, but no evidence of either has yet been reported in CoZr. It is also conceivable, of course, that some other slip mode is actually operating in this material but was not detected in the TEM foils examined. Like most B2 compounds, CoZr is comprised of two elements with a significant difference in electronegativities (in CoZr, ΔeN = 0.4 Paulings) and atomic radii (in CoZr, 0.034 nm or 21%) [31]. Unlike AgMg and AuZn, CoZr is a line compound that will not accommodate any deviation from equi-molar composition at equilibrium. CoZr also differs from AgMg and AuZn in that no evidence has yet been reported for -dislocation motion in CoZr; thus, the source of its ductility remains undetermined.

1.5. Ductility in Rare Earth B2 Intermetallic Compounds Approximately 130 binary rare earth intermetallic compounds have the B2 structure. These compounds share the general formula RM (where R = a rare earth element, M = an element from Groups 2, 8-13). In 2003, Gschneidner, et alia, published the first of several reports on the mechanical properties of RM B2 compounds [32]. Fifteen RM compounds were examined and determined to have good room-temperature ductility; two (TbCu and YZn) were found to have little or no tensile ductility. DyCu, YAg, and YCu have been most extensively studied [33-35]; all three compositions display tensile ductility of 11 to 20% elongation (Figure 5). Some, but not all, specimens’ stress-strain plots show heavily serrated plastic flow that suggests a strain aging effect. The fracture toughnesses of these three compounds were measured and found to be quite high for intermetallics: 12.0 MPa√m for YCu, 19.1 MPa√m for YAg, and 25.5 MPa√m for DyCu [36]. For comparison, the fracture toughness of polycrystalline NiAl has been reported as 5.1 to 6.4 MPa√m [37]. Most RM compounds also display good tensile ductility at 77 K. Tensile tests performed on polycrystalline YCu at elevated temperatures revealed an ultimate-tensile-strength maximum at approximately 400˚C. Strain rate tensile jump tests have been performed on several RM compounds at both room temperature and 77 K; all these tests showed little or no strain rate sensitivity, which suggests that deformation is occurring by ordinary dislocation glide rather than diffusionbased processes. Slip trace analysis of single crystal RM compounds [34,35] show slip on {110} and {100}, two slip systems that together provide only three of the five independent slip systems required for tensile ductility in polycrystalline material. Some RM studies [32] report dislocations to be present, but these may not result from slip, but may instead be junction dislocations formed by the collision of two gliding -type dislocations. TEM examination of these same single-crystal specimens also showed smaller numbers of dislocations, but it was not until 2007 that slip traces caused by dislocations were reported [33]. Thus, at least some RM compounds appear to satisfy the von Mises criterion. Neutron diffraction experiments performed on YCu specimens during tensile and compression testing have found no mechanical twinning and no stress-induced phase transformations. The neutron diffraction experiments have, however, shown a peculiar effect in which all diffraction peaks increase in intensity as plastic deformation progresses. Since texturing effects cannot raise the intensity of all peaks simultaneously, this phenomenon has


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been attributed to an extinction effect resulting from a change in mosaic (subgrain) size as dislocation density increases during deformation.

Figure 5. Tensile stress-strain plots for DyCu, YAg, and YCu tested in room air ( εÝ= 2(10-4) s-1). Redrawn from [36].

Single-crystal tests also revealed a curious anomaly in the RM compounds; the yield strengths of these materials are often lower in polycrystalline specimens than in single-crystal specimens. Although other possible causes for the low yield strengths in polycrystalline specimens (e.g., interstitial and substitutional impurity differences between sample batches) need to be examined, it suggests the possibility that some sort of grain boundary dislocation source mechanism may be operating in these materials. TEM studies on DyCu, TbCu, and YCu showed that the specimens contain a few volume percent of an orthorhombic phase in the B2 matrix (Figure 6). Electron diffraction has shown that in DyCu this phase has lattice parameters of a0 = 0.38 nm, b0 = 1.20 nm, c0 = 0.40 nm. These lattice parameters do not correspond to any equilibrium phase in the Dy-Cu binary system. _ In DyCu, TbCu, and YCu, the orthorhombic–B2 interface has a _ (110)[111]B 2 || (111)[101]ORTHO orientation. Since plastically deformed and as-arc-melted material show similar amounts of the orthorhombic phase, it does not appear to be a stressinduced transformation product. The appearance of the orthorhombic phase does not change in TEM foils from cryogenic temperatures to 700˚C. There are some indications that this orthorhombic material may be a H-stabilized phase, but, whatever its source, it does not appear to be directly related to the high ductility since it has not been observed in the majority of RM materials, including YAg, the most ductile RM compound found to date. From the perspective of atomic radii differences, the ductility of RM compounds seems more surprising than do the ductilities of AgMg, AuZn, and CoZr. The RM compounds have atomic radii differences of 22% (for YAg) to 37% (for YCu and DyCu); these differences are greater than the differences between Ag and Mg in AgMg (10%), Au and Zn in AuZn (7.6%), and Co and Zr in CoZr (21%). The differences in atomic radii for these systems are consistent

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with the degree to which their B2 structures will tolerate equilibrium deviations from stoichiometry. Lattice strain from anti-site defects becomes severe when atomic radii differ greatly.

Figure 6. Orthorhombic second phase (darker regions) in DyCu after tensile testing to 5% elongation.

The AgMg and AuZn compounds, whose size differences are modest, maintain a singlephase microstructure over ranges of several atomic percent from exact equi-molar stoichiometry. By contrast, CoZr and RM compounds, whose size differences are large, are line compounds. If 1/2 dislocation motion is necessary forductility in these materials, then the material's ability to form APB's between 1/2 dislocation pairs becomes a key factor. Large atomic radii differences would seem likely to raise APB energies due to the lattice strain that occurs from juxtaposing like atoms in the B2 structure. From this perspective the RM compounds seem the least likely to be highly ductile because they seem poorly suited to forming low-energy APB's.

2. FACTORS CONTRIBUTING TO TENSILE DUCTILITY AND FRACTURE TOUGHNESS With the exception of CoZr, all the materials described in §1 have been observed to deform by slip systems involving slip directions that satisfy the von Mises criterion. No evidence has been reported for mechanical twinning, stress-induced phase transformations, or similar processes that might enhance the ductility of these materials. With the possible exception of CoZr, the ductility seems to originate from slip. Thus, there is a major difference in the slip systems active in the ductile B2 compounds compared to those in brittle B2 intermetallics, such as NiAl. Interest then naturally shifts to the question of why these materials allow slip at room temperature when most ordered intermetallics with substantial differences in the A and B atom sizes and electronegativities do not. To date, the ductility of the RM compounds has attracted the most attention from theorists.


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2.1. Anisotropy Effects One factor that has been suggested to explain the ductility in the RM compounds is the location of the RM B2 compounds on a plot of (anisotropy ratio)-1/2 vs. Poisson ratio of the type shown in Figure 7 that was introduced by Yoo, et alia [38]. The anisotropy ratio is defined by the elastic constants of the material: A = 2c44/(c11-c12) When A = 1, the material is isotropic, and the prospects for ductility are maximized; when A1/2 and the Poisson ratio deviate outside the bounds marked by the dashed lines on Figure 7, the material is predicted to be less ductile. The three RM compounds plotted in Figure 7 (DyCu, YAg, YCu) are all located near the elemental BCC metals, rather than with ionic or intermetallic compounds. Although the predictive value of this type of plot is imperfect, the location of the three RM compounds is interpreted to mean that the bonding in these RM compounds is more like that of metallic elements than ionic or intermetallic compounds.

Figure 7. Plot of the (anisotropy ratio)-1/2 vs. Poisson ratio for several B2 compounds. RM compounds are depicted with circles; note that they are located near elemental BCC metals such as W, Ta, and V. Redrawn from [32].

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The nearly isotropic behavior of the RM compounds' elastic constants also appears to facilitate dislocation motion in these materials. Chen and Biner [39] calculated the line tensions for screw dislocations in YAg, YCu, and YZn and found (Figure 8) that they have positive line tensions for all values of θ (θ = the angle between the dislocation's Burgers vector and the dislocation line) and that dislocations are stable for all θ values in these three materials. This contrasts with the behavior of B2 NiAl, which has unstable dislocations for 38˚

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