Sintering of Advanced Materials (Woodhead Publishing in Materials)

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Sintering of advanced materials

i © Woodhead Publishing Limited, 2010

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Related titles: High-energy ball milling: mechanochemical processing of nanopowders (ISBN 978-1-84569-531-6) Mechanochemical processing is a novel and cost-effective method of producing a wide range of nanopowders. The process uses a high-energy ball mill to produce nanopowders that are used in the production of ceramic and metallic components using sintering and other powder metallurgy techniques to produce net shape components. This important book will review the technique which is revolutionising the manufacture of many advanced materials. Topics covered include mechanism and kinetics of the mechanochemical process, mechanochemical synthesis of complex ceramic compounds, principles and application of soft mechanochemical synthesis and mechanochemical synthesis of titanium dioxide and its derivatives. Handbook of advanced dielectric, piezoelectric and ferroelectric materials: synthesis, properties and applications (ISBN 978-1-84569-186-8) This comprehensive book covers the latest developments in advanced dielectric, piezoelectric and ferroelectric materials. It presents current research from leading innovators in the field. Sections will cover topics under the general headings: High strain high performance piezo- and ferroelectric single crystals; Electric field-induced effects and domain engineering; Morphotropic phase boundary related materials and phenomena; High power piezoelectric and microwave dielectric materials; Nanoscale piezo- and ferroelectrics; Piezo- and ferroelectric films; Novel processing, new materials and properties. Solid-state hydrogen storage: Materials and chemistry (ISBN 978-1-84569-270-4) The next several years will see an emergence of hydrogen fuel cells as an alternative energy option in both transportation and domestic use. A vital area of this technological breakthrough is hydrogen storage, as fuel cells will not be able to operate without a store of hydrogen. The book focuses on solid state storage of hydrogen. Part I covers storage technologies, hydrogen containment materials, hydrogen futures and storage system design. Part II analyses porous storage materials, while Part III covers metal hydrides. Complex hydrides are examined in Part IV and Part V covers chemical hydrides. Finally, Part VI is dedicated to analysing hydrogen interactions. Details of these and other Woodhead Publishing materials books can be obtained by: • visiting our web site at www.woodheadpublishing.com • contacting Customer Services (e-mail: [email protected]; fax: +44 (0) 1223 893694; tel.: +44 (0) 1223 891358 ext.130; address: Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, UK) If you would like to receive information on forthcoming titles, please send your address details to: Francis Dodds (address, tel. and fax as above; e-mail: francis.dodds@ woodheadpublishing.com). Please confirm which subject areas you are interested in.

ii © Woodhead Publishing Limited, 2010

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Sintering of advanced materials fundamentals and processes Edited by Zhigang Zak Fang

Oxford

Cambridge

Philadelphia

New Delhi iii

© Woodhead Publishing Limited, 2010

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Published by Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21 6AH, UK www.woodheadpublishing.com Woodhead Publishing, 525 South 4th Street #241, Philadelphia, PA 19147, USA Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road, Daryaganj, New Delhi-110002, India www.woodheadpublishingindia.com First published 2010, Woodhead Publishing Limited © Woodhead Publishing Limited, 2010 The authors have asserted their moral rights. This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials. Neither the authors nor the publisher, nor anyone else associated with this publication, shall be liable for any loss, damage or liability directly or indirectly caused or alleged to be caused by this book. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming and recording, or by any information storage or retrieval system, without permission in writing from Woodhead Publishing Limited. The consent of Woodhead Publishing Limited does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from Woodhead Publishing Limited for such copying. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN 978-1-84569-562-0 (print) ISBN 978-1-84569-994-9 (online) The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp which is processed using acid-free and elemental chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. Typeset by RefineCatch Limited, Bungay, Suffolk, UK

iv © Woodhead Publishing Limited, 2010

Contents

Contributor contact details Introduction

xi xv

Part I Fundamentals of sintering

1

1

Thermodynamics of sintering

3

R. M. German, San Diego State University, USA

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13

Introduction The sintering process Surface energy Sintering stress Atomistic changes in sintering Sintering changes prior to interfacial energy equilibrium Microstructure gradients Chemical and strain gradients Thermodynamics, stages and mechanisms of mass flow Microstructure links to sintering thermodynamics Conclusion Sources of further information and advice References

3 4 5 9 13 15 16 18 20 26 29 31 31

2

Kinetics and mechanisms of densification

33

M. N. Rahaman, Missouri University of Science and Technology, USA

2.1 2.2 2.3 2.4 2.5 2.6 2.7

Introduction Solid-state sintering Viscous sintering Liquid-phase sintering Pressure-assisted sintering Effects of material and process variables Conclusions

33 35 44 45 47 53 61 v


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Contents

2.8 2.9

Sources of further information and advice References

3 Path and kinetics of microstructural change in simple sintering

61 61 65

R. T. DeHoff, University of Florida, USA

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

Introduction The description of microstructural evolution Path of microstructural change in sintering Cell structure visualization of the path The thermodynamics of sintering Kinetics of densification Discussion Conclusion References

65 66 68 71 74 76 82 84 85 86

4

Computer modelling of sintering: theory and examples

W. Niu and J. Pan, University of Leicester, UK

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

Introduction Sintering modelling at the atomic scale Sintering modelling at the particle level Sintering modelling at the component scale Multi-scale modelling of sintering Conclusion Acknowledgements References

86 87 90 96 103 106 107 107

5

Liquid phase sintering

110

S-J. L. Kang, Korea Advanced Institute of Science and Technology, Korea

5.1 5.2 5.3 5.4 5.5

Introduction Grain growth in a liquid matrix Densification during liquid phase sintering Summary References

6 Master sintering curve and its application in sintering of electronic ceramics

110 112 118 125 126 130

C. B. DiAntonio and K. G. Ewsuk, Sandia National Laboratories, USA

6.1 6.2 6.3 6.4

Introduction to electroceramics Sintering and densification of electroceramics Master sintering curve as applied to electronic ceramics Extending the master sintering curve to the third dimension


130 134 139 148

Contents

vii

6.5 Case study: Controlling electrical performance of ZnO varistors using a master sintering curve 6.6 Conclusion 6.7 Acknowledgements 6.8 References

149 156 158 158

Part II Advanced sintering processes

163 165

7

Atmosphere sintering

C. Blais, Université Laval, Canada

7.1 7.2 7.3 7.4 7.5

Introduction Types and sources of sintering atmospheres Thermodynamics aspects of atmosphere sintering Role of atmosphere in sintering References

165 165 168 178 187

8

Vacuum sintering

189

D. F. Heaney, The Pennsylvania State University and Advanced Powder Products, Inc., USA

8.1 8.2 8.3 8.4 8.5 8.6 8.7

Introduction Evaporation under vacuum Material purification Densification under vacuum Equipment configurations Practical processing References

9 Microwave sintering of ceramics, composites and metal powders

D. Agrawal, The Pennsylvania State University, USA

9.1 9.2 9.3 9.4 9.5 9.6

Introduction Microwave sintering of important materials Mechanisms to explain microwave–matter interactions Future trends Sources of further information and advice References

10 Fundamentals and applications of field/current assisted sintering

189 190 193 196 197 213 220 222 222 224 242 244 245 245 249

D. V. Quach and J. R. Groza, University of California, USA, A. Zavaliangos, Drexel University, USA and U. AnselmiTamburini, University of Pavia, Italy

10.1

Introduction

249


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Contents

10.2 Fundamentals of sintering under an external electrical field/current 10.3 Applications of field/current activated sintering 10.4 Conclusions 10.5 Acknowledgement 10.6 References

251 261 267 268 268

11 Photonic sintering – an example: photonic curing of silver nanoparticles

275

J. West, J. W. Sears, S. Smith and M. Carter, South Dakota School of Mines and Technology, USA

11.1 11.2 11.3 11.4 11.5 11.6

Introduction Background Experimental results Heat equation simulations of the photonic curing process Conclusions References

275 276 278 283 287 287

Part III Sintering of advanced materials

289

12

291

Sintering of aluminium and its alloys

M. Qian and G. B. Schaffer, The University of Queensland, Australia

12.1 Introduction 12.2 Aluminium P/M and its application 12.3 Green shape formation 12.4 Sintering atmosphere and dew point control 12.5 The surface of air-atomised aluminium powder 12.6 Disruption of the oxide film by powder compaction and amorphous-to-crystalline transformation 12.7 Sintering of aluminium in nitrogen 12.8 Mechanical properties of sintered aluminium alloys 12.9 Future trends 12.10 Acknowledgements 12.11 References

291 291 296 297 301

13

324

Sintering of titanium and its alloys

303 306 315 316 318 319

M. Qian and G. B. Schaffer, The University of Queensland, Australia and C. J. Bettles, Monash University, Australia

13.1 13.2 13.3

Introduction Titanium powder Powder compaction


324 325 332

13.4 13.5 13.6 13.7 13.8

Contents

ix

Sintering Mechanical properties and applications Future trends Acknowledgements References

336 346 349 350 351 356

14

Sintering of refractory metals

J. L. Johnson, ATI Engineered Products, USA

14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10

Introduction Refractory metals and alloys Refractory metal powders Sintering methods Solid-state sintering Activated sintering Liquid-phase sintering Future trends Sources of further information and advice References

356 356 358 362 363 377 379 381 382 382 389

15

Sintering of ultrahard materials

J. D. Belnap, Smith Megadiamond, USA

15.1 15.2 15.3 15.4 15.5 15.6

Introduction Thermodynamic and kinetic considerations High-pressure/high-temperature apparatus Microstructure development Future trends References

389 392 396 402 410 411

16

Sintering of thin films/constrained sintering

415

O. Guillon, Technische Universität Darmstadt, Germany, R. K. Bordia, University of Washington, USA and C. L. Martin, Laboratoire SIMAP, France

16.1 Introduction 16.2 Background 16.3 Densification kinetics of constrained films and coatings 16.4 Microstructural development 16.5 Numerical simulation of densification and microstructural evolution 16.6 Crack growth and damage evolution during constrained sintering 16.7 Conclusion and future trends 16.8 References


415 416 418 423 425 427 428 430

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Contents

17

Sintering of ultrafine and nanosized particles

434

Z. Z. Fang and H. Wang, University of Utah, USA

17.1 Introduction 17.2 Thermodynamic driving force for the sintering of nanosized particles 17.3 Kinetics of the sintering of nanosized particles 17.4 Grain growth during sintering of nano particles 17.5 Techniques for controlling grain growth while achieving full densification 17.6 Conclusion 17.7 References

434

474

Index


435 437 450 462 467 468

Contributor contact details

(* = main contact)

Editor and Chapter 17

Chapter 2

Z. Z. Fang* Department of Metallurgical Engineering University of Utah 135 S. 1460 E. Room 412 Salt Lake City UT 84112 USA

Professor M. N. Rahaman Department of Materials Science and Engineering Missouri University of Science and Technology 223 McNutt Hall 1400 N. Bishop Avenue Rolla, MO 65409-0340 USA

E-mail: [email protected]


Chapter 1 R. M. German Associate Dean of Engineering & Professor of Mechanical Engineering College of Engineering San Diego State University 5500 Campanile Drive San Diego, CA 92182-1326 USA E-mail: [email protected]

Chapter 3 R.T. DeHoff Professor Emeritus Department of Materials Science and Engineering University of Florida Gainesville FL 32611-6400 USA e-mail: [email protected]

xi © Woodhead Publishing Limited, 2010

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Chapter 4 W. Niu* Department of Materials Science and Engineering Chong-Qing University Chong-Qing 400044 China E-mail: [email protected]

Jingzhe Pan Professor Department of Engineering University of Leicester Leicester LE1 7RH UK

K. G. Ewsuk Sandia National Laboratories Advanced Microsystem Packaging Albuquerque, NM 87185-0352 USA e-mail: [email protected]

Chapter 7 C. Blais Professor Département de Génie des Mines De la Métallurgie et des Matériaux 1718-B Pavillon Adrien Pouliot Université Laval Quebec Canada G1K 7P4



Chapter 5

Chapter 8

Suk-Joong L. Kang Professor Department of Materials Science and Engineering Korea Advanced Institute of Science and Technology 335 Gwahak-ro, Yuseong-gu Daejeon 305-701 Korea

D. F. Heaney Associate Professor Department of Engineering Science and Mechanics The Pennsylvania State University 118 Research Building West University Park, PA 16802 USA E-mail: [email protected]


Chapter 6 C. B. DiAntonio* Sandia National Laboratories Materials Science and Engineering Center Advanced Prototyping S&T Albuquerque, NM 87185-0959 USA

President and Director of Development Advanced Powder Products, Inc. 301 Enterprise Drive Philipsburg, PA 16866 USA E-mail: [email protected]




Chapter 9

Chapters 12 and 13

D. Agrawal Director of Microwave Processing and Engineering Center Professor of Engineering Science & Mechanics 107 Materials Research Lab The Pennsylvania State University University Park PA 16802 USA

M. Qian* Division of Materials School of Mechanical and Mining Engineering The University of Queensland Brisbane QLD 4072 Australia


Chapter 10 J. R. Groza* Chemical Engineering/Materials Science Dept University of California 1 Shields Avenue Davis CA 95616 USA E-mail: [email protected]

Chapter 11 J.W. Sears Executive Director Quad City Manufacturing Laboratory Rock Island USA and IL Director Additive Manufacturing South Dakota School of Mines & Technology 501 E. St. Joseph St Rapid City SD 57701 USA

xiii


G. B. Schaffer Faculty of Engineering, Architecture & Information Technology The University of Queensland Brisbane QLD 4072 Australia E-mail: [email protected]

Chapter 13 C. Bettles Monash University ARC Centre of Excellence for Design in Light Metals Clayton, Victoria 3800 Australia E-mail: [email protected]. edu.au

Chapter 14 John L. Johnson ATI Engineered Products 7300 Highway 20 West Huntsville AL 35806 USA E-mail: [email protected]

E-mail: [email protected] © Woodhead Publishing Limited, 2010

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Chapter 15

C. L. Martin Laboratoire SIMAP, Grenoble-INP Groupe GPM2, Domaine Universitaire, BP 46 38402 Saint Martin d’Heres cedex, France

J. D. Belnap, Ph.D. Engineering Manager Smith Megadiamond 275 West 2230 North Provo, UT 84604 USA E-mail: [email protected]


Chapter 17

Chapter 16 O. Guillon Institute of Materials Science Technische Universität Darmstadt FB11, FG NichtmetallischAnorganische Werkstoffe Petersenstr. 23, Geb. 73a D-64287 Germany

H. Wang Department of Metallurgical Engineering University of Utah 135 S. 1460 E. Room 412 Salt Lake City UT 84112 USA

E-mail: guillon@ceramics. tu-darmstadt.de

R. K. Bordia* Professor Department of Materials Science and Engineering Roberts Hall Box 352120 University of Washington Seattle WA 98195 USA E-mail: [email protected]


Introduction

One of the first things we do when teaching sintering is to define what sintering is. Is it a process technology, a subfield of science, or a class of materials? The short answer is of course that it is primarily one category of manufacturing processes. However, those of us who study sintering will argue that the fundamentals of sintering involve all aspects of modern natural sciences, including physics, chemistry, mechanics, physical chemistry, surface science, thermodynamics, kinetics, and diffusion. On the one hand, sintering is a craft (called firing) that has been practiced since ancient civilizations for several thousand years in the form of pottery, bricks, and art. On the other hand, ever-increasing demands for near-perfect quality and high performance of modern sintered technical products place the competitive edges of a sintering practitioner squarely on his or her level of understanding of the science of sintering. Therefore, borrowing an expression from the book by Prof. Robert Cahn of Cambridge – The Coming of Materials Science – sintering is a ‘craft turned into science’. This book was initiated by Woodhead Publishing based on their marketing research that indicated needs for a book on recent advances in sintering. We were aware that there were already several excellent monographs on sintering available in libraries around the world, including most notably books by Professors R. German, M. Rahaman, and S.J. Kang. Therefore, the challenge is how a new book can serve the needs of readers by adding value to the existing books. We reckon that the unique characteristic of sintering is that it is at an ‘intersection’ of many sub-disciplines of materials science and engineering; hence it involves a large variety of vastly different techniques and a large family of completely different materials. It is usually difficult to find both fundamental science and sufficient specific technological information in one volume. The objective of the book was thus conceived and laid out to provide readers, in one book, not only with technical guides on advanced sintering technologies but also with the scientific fundamentals that form the common ground of all sintering techniques. The contents are divided into three parts: fundamentals, advanced processes, and advanced materials. The fundamentals include thermodynamics, kinetics, xv © Woodhead Publishing Limited, 2010

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Introduction

master sintering curve theory, microstructure evolution, liquid-phase sintering theory, and modeling-simulation of sintering. The selections of topics for advanced processes and materials are more difficult. It is obvious that we cannot include all the materials that are produced in industry by sintering or all the processes that are designed to sinter metals or ceramic powders. The emphasis was thus put on relatively new and advanced processes and materials. For instance, microwave sintering and spark plasmas sintering are examples of new processes that have become popular in the past two decades. The sintering of thin films and ultra-hard materials are examples of materials that have seldom been covered in any detail in the past. Regrettably, but inevitably, there are important processes and materials omitted from this book. For example, a large number of pressure-assisted sintering processes, including hot pressing and hot isostatic pressing (HIP), are widely practiced in industry today, but are not included. The sintering of cermet, including cemented tungsten carbide, which is perhaps the largest single family of sintered materials, is also not included. Fortunately, there are recent monographs on both topics (Hot Consolidation by A. Bose and Cemented Tungsten Carbide by G. Upadhyaya), to which readers are referred. Finally, I wish to thank all contributors to this book for their support and hard work. The essence of this book by design, I hope, is that the unique expertise of individual contributors in individual topics makes each chapter shine in its own right. I also thank the editorial staff at Woodhead Publishing (Mr Rob Sitton, Ms Lucy Cornwell, and Ms Nell Holden) whose professionalism, kind patience and persistence made this book possible. Z. Zak Fang University of Utah


Part I Fundamentals of sintering

1 © Woodhead Publishing Limited, 2010

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1 Thermodynamics of sintering R. M. German, San Diego State University, USA Abstract: Particles bond together when heated by a sintering process that is a combination of several atomic level events that include diffusion, creep, viscous flow, plastic flow and evaporation. Significant strengthening occurs in powder compacts due to sintering. Sintering consumes surface energy to build bonds between those particles. Small particles have more surface energy and sinter faster than large particles. Since atomic motion increases with temperature, sintering is accelerated by high temperatures. The thermodynamic driving force for sintering then is found in the surface area, interfacial energies and curvature gradients in the particle system. Actual atomic motion is by several transport mechanisms with concomitant microstructure changes. Key words: surface energy, surface area, diffusion, creep, viscous flow, plastic flow, particle size, interfacial energy, dihedral angle, contact angle, wetting, curvature.

1.1

Introduction

Sintering acts to bond particles together into strong, useful shapes. It is used to fire ceramic pots and in the fabrication of complex, high-performance shapes, such as medical implants. Sintering is irreversible since the particles give up surface energy associated with small particles to build bonds between those particles. Prior to sintering the particles flow easily while after sintering the particles are bonded into a solid body. From a thermodynamic standpoint sinter bonding is driven by the surface energy reduction. Small particles have more surface energy and sinter faster than large particles. Since atomic motion increases with temperature, sintering is accelerated by high temperatures. The driving force for sintering comes from the high surface energy and curved surface inherent to a powder. The initial stage of sintering corresponds to neck growth between contacting particles where curvature gradients normally dictate the sintering behavior. The intermediate stage corresponds to pore rounding and the onset of grain growth. During the intermediate stage the pores remain interconnected, so the component is not hermetic. Final stage sintering occurs when the pores collapse into closed spheres, giving a reduced impediment to grain growth. Usually the final stage of sintering starts when the component is more than 92% dense. During all three stages, atoms move by several transport mechanisms to create the microstructure changes, including surface diffusion and grain boundary diffusion. Sintering models include parameters such as particle size and surface area, temperature, time, green density, pressure and atmosphere. Further, the addition of a wetting liquid induces faster sintering. Accordingly, most sintering is 3 © Woodhead Publishing Limited, 2010

4


performed with a liquid phase present during the heating cycle. These basic thermodynamic attributes are treated in this first chapter.

1.2

The sintering process

Sintering is fundamentally a one-way event. Once sintering starts, surface energy is consumed through particle bonding, resulting in increased compact strength and often a dimensional change. Accordingly, the definition of sintering is as follows:1 Sintering is a thermal treatment for bonding particles into a coherent, predominantly solid structure via mass transport events that often occur on the atomic scale. The bonding leads to improved strength and lower system energy.

The bonding between particles is evident in the scanning electron microscope in terms of the newly formed solid necks between contacting particles. Figure 1.1 illustrates spherical bronze particles after sintering at 800 °C. Necks grow between the contacting spheres, providing strength and rigidity. Longer sintering gives a larger neck and usually more strength. The emergence of the necks between is driven by the system thermodynamics, while the rate of sintering depends mostly on the temperature. At room temperature, the atoms in a material such as bronze are not noticeably mobile, so the particles do not sinter. However, when heated to a temperature near the melting range, the atoms are very mobile. Atomic motion

1.1 Scanning electron micrograph of the sintering neck formed between 26 µm bronze particles after sintering at 800 °C.



5

increases with temperature and eventually this motion induces bonding that reduces the overall system energy. The energy changes in sintering are usually small, so the rate of change during sintering is slow. In the case of the 26 µm bronze powder shown in Fig. 1.1, which has a solid–vapor surface energy of 1.7 J/m2, the energy per unit mass stored as excess surface area is about 50 J/kg. But not all of this energy can be consumed during sintering, since the structure usually fails to sinter to full density and other interfaces emerge, such as grain boundaries, which add energy into the system. The total surface energy increases as the particle size decreases, so with nanoscale powders smaller than 0.1 µm there is a large driving force for sintering, meaning faster sintering or a lower sintering temperature. Early models for sintering realized that a sphere affixed to a flat plate presented a large energy difference, since the sphere has much more surface area and by implication more surface energy. Accordingly, early sintering studies measured the neck size between spheres and plates, and subsequently between contacting spheres. The two-sphere model considers two equal-sized spheres in point contact that subsequently fuse to form a single larger sphere with a diameter 1.26 times the starting sphere diameter, as sketched in Fig. 1.2. The rate of particle bonding during sintering depends on temperature, materials, particle size and several processing factors.2 Small particles are more energetic, so they sinter faster. Thus, the thermodynamics of sintering show the importance of smaller powders, while the kinetics of sintering emphasizes the importance of temperature. Sintering occurs in stages, as illustrated in Fig. 1.3. Without compaction a model powder system starts at a packing density of 64%, the dense random packing. In the initial sintering stage, the interparticle neck grows to the point where the neck size is less than one-third of the particle size. Often there is little dimensional change so at the most 3% linear shrinkage is seen in the initial stage. For loose spheres this generally corresponds to a density below 70% of theoretical. Intermediate stage sintering implies the necks are larger than one-third the particle size, but less than half the particle size. For a system that densifies, this corresponds to a density range from 70% to 92% for spheres. During the intermediate stage the pores are tubular in character and connected (open) to the external surface. The sintering body is not hermetic so gas can pass in or out during firing. Final stage sintering corresponds to the elimination of the last 8% porosity, where the pores are no longer open to the external surface. Isolated pores, associated with final stage sintering, are filled with the process atmosphere.

1.3

Surface energy

Surface energy is the thermodynamic cause of sintering. A model of a surface is generated by starting with an ideal crystal, such as shown in Fig. 1.4, where each atomic species occupies specific, repeating sites. Between atoms are bonds,


6


D

D

Initial point contact Spherical particle D = diameter

Neck

Grain boundary

Early stage neck growth (short time)

Late stage neck growth (long time)

1.26 D

Terminal condition fully coalesced (infinite time)

1.2 Two-sphere sintering model, where the two spheres grow a neck during sintering that grows to the point where the spheres fuse into a single sphere that is 1.26 times the diameter of the starting spheres.

represented by lines. If scissors were used to snip these atomic bonds, then the resulting surface would consist of broken bonds. These bonds provide the atomic interaction responsible for the surface energy. Figure 1.5 illustrates this concept, where the free surface is covered with broken bonds. Surface energy relates to the density of broken bonds (bonds per unit area), so it varies with crystal orientation. Also, since stronger bonding is associated with a higher melting temperature, surface energy is higher for high melting temperature materials.


Thermodynamics of sintering Loose powder

Initial stage

Intermediate stage

Final stage

7

1.3 Illustration of the sintering stages with a focus on the changes in pore structure during sintering.

1.4 An illustration of a perfect crystal where each atom is in a repeating position and atomic bonds are linking the atoms.


8


1.5 An illustration of how a free surface for a crystalline material results in disrupted atomic bonding; it is the dangling atomic bonds that give surface energy.

An atomic model for the grain boundary would be similar, where broken atomic bonds from the two crystal lattices only partly match. As illustrated in Fig. 1.6, some misorientations lead to more disrupted bonding and high grain boundary energies, while other misorientations lead to less disruption and lower grain boundary energy. Thus, depending on the misorientation between the two crystals, the grain boundary energy might be high (much disrupted bonding) or low (good bond matching). Some grain orientations are higher energy than others, so touching grains rotate or rearrange during sintering to reduce their grain boundary energy. In a sintering structure consisting of solid particles and pores, a variety of grain boundary configurations are possible between the randomly assembled particles. Further, a range of solid–vapor surface energies come from the range of crystal surface orientations. With a liquid, the inventory of surface energies increases to include grain boundary, solid–vapor, liquid–vapor, and solid–liquid combinations. All of these are distributed properties and not single-valued. Rather than dealing with this level of detail, sintering models rely on average values that reflect the millions of different combinations. For many engineering materials, the average solid–vapor surface energy is in the 1 to 2 J/m2 range, while grain boundary energies are even lower. For a single-phase solid, sintering is slow since the energy release on sintering is low. Similar to other chemical reactions, as the surface energy is consumed, then the driving force for continued sintering is diminished and the process continually slows.



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Grain boundary energy Surface Neck

Atoms

Grain boundary Misorientation angle

Misorientation angle

1.6 Grain boundary misorientation and the relative energy from the misorientation, such that during sintering the random particle to particle contacts result in a wide array of microstructure relations.

1.4

Sintering stress

The capillary stress arising from the surface energy acts to move surfaces during sintering. The neck between contacting particles is associated with a large change in curvature over distance. For example in Fig. 1.1, the base of the neck is concave. A concave surface acts to pull itself into a flat surface. On the sphere surface away from the neck, the curvature is convex with an opposite curvature. The Laplace equation gives the stress s associated with a curved surface as, σ=γ

(

)

1 1 + R1 R2

[1.1]

where γ is the energy associated with the curved surface (for example solid–liquid, solid–vapor, or liquid–vapor surface energy), and R1 and R2 are the radii of curvature for the surface. For a sphere, both radii are the same and equal to the radius of the sphere so the stress is uniform, but during sintering the two radii vary with position in the microstructure and often are opposite in sign. This is evident with the saddle surface seen in the sintering neck. The sintering microstructure consists of a mixture of convex and concave surfaces, and the shift from tension to compression occurs over distances smaller than the particle size. The natural tendency is to remove the gradients during sintering. Because the stress in the neck region is different from the neighboring region, the curvature gradient gives a thermodynamic gradient that drives mass flow during sintering. Atomic motion takes place to remove the gradient. When heated


10

Sintering of advanced materials Surface mass under compression Mass flow

Surface mass under tension

Convex surface Concave surface

1.7 The action of sintering is to remove concave and convex surfaces and to move toward flat surfaces, as schematically illustrated here. The mass from the convex transports to fill in the convex surface.

to where atomic motion occurs, the atoms naturally flow from the convex to concave surfaces. Atom motion is faster at higher temperatures and small particles have large gradients. Accordingly, particles sinter faster when they are small and heated to high temperatures. As sketched in Fig. 1.7, a concave solid surface tends to fill and a convex surface tends to flatten. In a powder compact consisting of a mixture of pores and particles, sintering acts to remove the curvature gradients – namely to smooth the pores. The convex particles represent mass sources and pores represent mass sinks that fill using mass from the convex regions. From the instantaneous pore-grain geometry it is possible to quantify these parameters and assess the sintering stress and its dissipation over time. As with many reactions, sintering goes more slowly as it progresses, simply because the action of sintering is to remove the gradients. In the initial stage of sintering, the saddle surface formed between particles has a sharp curvature at the root. Assuming isotropic surface energy and spherical particles, then for a small neck size a substitution into Equation 1.1 gives the sintering stress σ as follows:

[

]

σ = γSV - 2 + 4(D –2 X) X X

[1.2]

where X is the neck diameter, D is the particle (sphere) diameter, and γSV is the solid–vapor surface energy. This relation is valid in the initial stage of sintering when X/D < 0.3. This stress induces particle bonding as a natural part of sintering. Although surface energy is consumed as the neck grows, not all surface energy is available for sintering. For a crystalline solid, nearly every particle contact forms a grain boundary. The grain boundaries are defective regions with high atomic mobility. For most inorganic powders, diffusion along the grain boundary proves to be a dominant sintering mechanism. As the neck grows to remove surface



11

energy the grain boundary grows and adds interfacial energy, so sintering only continues as long as the rate of surface energy annihilation exceeds the rate of grain boundary annihilation. Heat stimulates the atomic motion that allows sintering to proceed. Most sintering processes are thermally activated, meaning that input energy is necessary for mass flow. For example, sintering by diffusion depends on the energy to create a vacancy and the energy to move an atom into that vacancy. The population of vacant atomic sites and the number of atoms with sufficient energy to move into those sites both vary with an Arrhenius temperature relation. The Arrhenius relation determines the probability that an atom has enough energy to move, as determined by the activation energy Q. For example, the volume diffusion coefficient DV is determined from the atomic vibrational frequency D0, absolute temperature T, universal gas constant R, and the activation energy Q, which corresponds to the energy required to induce atomic diffusion via vacancy exchange,

( )

DV = D0 exp -

Q RT

[1.3]

Sintering is faster at higher temperatures, because of the increased number of active atoms and available sites. Thus, temperature is a dominant parameter in defining a sintering cycle. Other important factors include the particle size, applied pressure, formation of a liquid phase, sintering time, heating rate, and process atmosphere. Another important source of sintering stress comes from wetting liquids. About 80% of all sintering occurs with a liquid or glassy phase. The liquid causes the powder to agglomerate since significant capillary stress is generated by a wetting liquid. Wetting refers to a liquid that spreads over a surface. We rely mostly on the contact angle to measure wetting. Also known as the wetting angle, the contact angle is formed at the intersection of liquid, solid, and vapor phases. When gravity is ignored, the contact angle θ is defined by the horizontal equilibrium of surface energies, as illustrated in Fig. 1.8. The general consensus is to measure the contact angle on a surface perpendicular to the gravity vector. Then ignoring gravity the horizontal solution is known as Young’s equation, γSV = γSL + γLV cos(θ)

[1.4]

where γSV is the solid–vapor surface energy, γSL is the solid–liquid energy, and γLV is the liquid–vapor surface energy. Wetting liquids are associated with contact angles near zero and nonwetting liquids are associated with contact angles over 90°. During spreading or retraction of a liquid over a solid surface, the contact is not in equilibrium. Further, various corrections exist for the effect of surface roughness, since finely textured solid surfaces will induce wetting even though the contact angle predicts nonwetting.


12

Sintering of advanced materials γLV

V-vapor γSL

θ

γSV

θ L-liquid S-solid θ = Contact angle

γSV = γSL + γLV cos (θ)

1.8 Contact or wetting angle definition based on a droplet sitting flat on a surface so the vertical forces are balanced.

φ Liquid

Solid

Solid Grain boundary

φ = Dihedral angle

φ

()

φ γSS = 2γSL cos _ 2

γSL

γSL

γSS

1.9 The dihedral angle is defined based on a solid–solid grain boundary energy intersecting a liquid or vapor phase.

Finally, the dihedral angle describes the grain boundary structure. The angle formed by a grain boundary where it intersects with another solid, pore, or liquid during sintering is described by a thermodynamic balance termed the dihedral angle. As illustrated in Fig. 1.9, it is determined by a vertical surface energy balance. For the case of a grain boundary in contact with a liquid during liquid phase sintering the vector balance gives,


Thermodynamics of sintering γSS = 2γSL cos

() ϕ 2

13 [1.5]

where γSS is the solid–solid interfacial energy (grain-boundary energy) and γSL is the solid–liquid interfacial energy. Alternatively,

( )

γ ϕ = 2 arccos 2γSS SL

[1.6]

In the case of a grain boundary in contact with the free surface, a thermal groove forms and the dihedral angle is determined by the solid–vapor surface energy γSV. In materials held at high temperature for a prolonged time the dihedral angle is evident at all surfaces and exposed grain boundaries. Grain boundary grooving on a free surface is a reflection of the dihedral angle. Since segregation changes grain boundary and surface energies, the dihedral angle exhibits a time dependence related to the diffusion of species to or from grain boundaries and free surfaces.

1.5

Atomistic changes in sintering

The surface stress associated with a curved surface gives a nonequilibrium vacancy concentration. A flat surface free of stress is at equilibrium. In sintering, microstructure curvature drives mass flow by taking both the concave and convex surfaces toward a flat state. Mass from the convex surface moves to fill in the concavity. The vacancy concentration C under a curved surface depends on the local curvature,

[ ( )]

C = C0 1 –

γ Ω 1 1 + kT R1 R2

[1.7]

where C0 is the equilibrium vacancy concentration associated with a flat surface at the same temperature, γ is the surface energy (either solid–liquid or solid– vapor), Ω is the atomic volume, k is Boltzmann’s constant, and T is the absolute temperature. The equilibrium concentration increases on heating. As shown in Fig. 1.10, two perpendicular arcs pass through at any point on the surface. These arcs have radii of curvature designated as R1 and R2. The more highly curved the surface, the smaller R1 and R2 and the departure from equilibrium. For a concave surface, the vacancy concentration is higher than equilibrium; for a convex surface it is lower; thus, atomic flow is from regions of vacancy deficiency – convex – to regions of vacancy excess – concave. When a radius of curvature is located inside the solid it is deemed negative while a radius located outside the solid is positive. A concave surface is a source of vacancies that works with a counter flow of atoms to fill the concavity. Atomic motion (volume diffusion) depends on atomic exchange with neighboring vacancies. For diffusion to occur, an atom must have sufficient energy QB to break existing bonds with neighboring atoms and then additional energy to exchange its position with a neighboring vacant site. The probability of


14


Curved surface

R2

R1

R1, R2 = Principal radii of curvature

1.10 The definition of surface curvature in terms of the radii of the two perpendicular arcs passing through a point on a curved surface.

a neighboring atomic site being vacant depends on the vacancy formation energy QN. In other words, volume diffusion requires both the formation of a vacancy and the provision of sufficient energy to break an atom free so that it can jump into the vacant site. As an approximation to the rate of atomic diffusion, the Arrhenius equation gives the relative number of active atoms NA compared with the total number of atoms N0 as follows:

(

NA = N0 exp -

QB + QN RT

)

[1.8]

where R is the gas constant and T is the absolute temperature. Most typically, the rate of atomic diffusion is termed the diffusivity, which depends on several parameters including the frequency of atomic vibration, crystal class, lattice parameter and similar factors. The resulting form for the diffusion coefficient is an Arrhenius equation given earlier as Equation 1.3. The activation energy Q is the sum QN + QB. In turn, for a given crystal structure both activation energies can be rationalized to



15

the number of atomic bonds that must be broken to form a vacancy and the number of atomic bonds that must be broken to move an atom. Many handbooks compile data diffusion data as D0 and Q, which allows calculation of D at any temperature. Similar to vacancy creation and annihilation at free surfaces, the grain boundaries are important to sintering. Diffusion on a grain boundary undergoes a rapid increase with a modest temperature increase. Further, impurities preferentially segregate to grain boundaries, so often the fast diffusion observed along the grain boundaries is a reflection of the segregated impurities. At very high temperatures the impurities are more soluble in the materials being sintered, so there is less effect. But at intermediate temperatures, segregation is more severe and leads to significant changes in sintering rates. This is true in systems such as tungsten doped with nickel, where low concentrations of nickel doped into the tungsten greatly lower the sintering temperature.3

1.6

Sintering changes prior to interfacial energy equilibrium

During sintering, shrinkage causes grains to come into contact with each other and form new sinter bonds, at times much delayed from the initial bonding. Grain rearrangement is observed due to the grain boundary torque.4 The motion of grains or particles into new and higher density packing positions is frequent in liquid phase sintering. During heating, the liquid spreads to wet the solid grains as soon as it forms, dissolving existing solid–solid necks. The resulting loose grain structure with a wetting liquid produces a capillary force that acts to pull the separated grains together. The individual rearrangement events happen very quickly when the liquid forms, so the grains literally jump into new positions. However, the formation of liquid requires heat transport through the porous compact, which tends to be a slow step.5 For this reason most powder compacts show a slow rearrangement step that is controlled by heat transport. Each individual bond undergoes rearrangement in a split second, but the thermal wave needed to form the liquid propagates through the compact over a few minutes. An especially important nonequilibrium transient occurs in liquid phase sintering. Newly formed liquid spreads, and if it has solubility for the solid, then it penetrates the solid–solid interfaces on liquid formation. This results in a dimensional change, usually swelling, where the amount of swelling varies with the liquid flow into the surrounding pores. The liquid flow is estimated as a function of hold time as follows: X2 =

dP γLVt cos θ 4η

[1.9]

where x is the depth of liquid penetration, dP is the pore size, γLV is the liquid– vapor surface energy, θ is the contact angle, t is the hold time, and η is the liquid viscosity. Several aspects of sintering are explained by this transient liquid penetration of grain boundaries. The solid skeleton formed during heating


16


dissolves, reducing compact rigidity, and in turn this allows for distortion. A second is that liquid can be stranded on grain boundaries, leading to what is termed a necklace microstructure. Finally, the dihedral angle and other equilibrium thermodynamic properties vary during sintering.

1.7

Microstructure gradients

A natural affinity exists between the pores and grain boundaries. Because of the solid–vapor surface energy, a pore contributes surface energy. At the same time a grain boundary has grain boundary energy. If the pore sits on the grain boundary, then the configurational energy is lower; effectively the pore-boundary combination is pinned. Thus, there is a high probability for a pore to attach to a grain boundary, even during grain growth. However, sintering works to minimize energy and this usually means a reduction in grain boundary energy through an increase in grain size. Thus, a dynamic exists where pores are attached to grain boundaries while at the same time grains are growing to reduce grain boundary area. Mobile pores remain with the moving grain boundaries and sintering progresses to full density. On the other hand, if the pores and grain boundaries separate, then a porous sintered body results. It is effectively impossible to shrink a pore that is removed from a grain boundary. At high sintered densities the pores are mostly associated with the largest grains. In final stage sintering the relation between grain size G, pore diameter dP, and fractional porosity ε is given as: G K = dP Rε

[1.10]

where R expresses the ratio of attached pores to randomly placed pores, and K is a geometric constant. Values of R range from 1.7 to 5.7 for various sintering materials.6 The degree of boundary-pore contact remains essentially constant during most of the sintering cycle. Consequently, grain size tracks with porosity during sintering; grain size increases, porosity decreases, and pore size initially decreases, but late in sintering might increase. In the initial stage of sintering the pores pin the grain boundaries to retard grain growth. If a grain boundary were to move then it must drag the pore and that is a slow event. In the intermediate stage of sintering the pores are smaller yet located on the grain edges. The pore surface area declines while the grain size enlarges, effectively making the pore diameter smaller and the pore length longer. Accordingly, a fundamental relation is observed where the grain size and solid– vapor surface area per unit volume SV tracks with the square of the porosity ε, and the grain size G tracks with the inverse of the remaining surface area [7, 8]: G≈

1 1 ≈ SV ε2

[1.11]



17

Of course this predicts an infinite grain size at full density. The terminal condition in sintering is a single crystal, or one grain, so this is not overly incorrect. As porosity declines the pore surface area that retards grain growth decreases, so grain growth occurs with decreasing impediment. Thus, grain size increases rapidly as full density is approached [1, 9]. As plotted in Fig. 1.11, the declining surface energy associated with pores diminishes grain boundary pinning, so there is little resistance to a rapid rise in grain size as full-density is approached. Typically the assumed grain geometry during late stage sintering is the tetrakaidecahedron, a 14-sided polyhedron consisting of squares and hexagons. Figure 1.12 shows a sketch of this grain shape. In intermediate stage sintering the pores exist as tubes on the grain edges and in the final stage of sintering the pores are spheres located at the grain corners. During intermediate stage sintering the pores form a tubular network that is attached to the grain boundaries. As densification occurs the pores shrink while simultaneous grain growth stretches the pores. As this continues, eventually the elongated and thinning pores pinch off into closed spherical pores, a process termed pore closure. Based on energy reduction, a calculation of the instability of a cylindrical pore of length l and diameter dP gives the critical condition for closure into separate pores as follows: l ≥ dP π

[1.12]

For a cylindrical pore occupying the edges of tetrakaidecahedron grains this instability occurs at a porosity of approximately 8%. In reality, due to distributions in initial particle sizes, the instability that induces pore closure occurs over a 12 Copper 8 µm powder

Final stage

8 Intermediate stage

Grain size, µm 4

Initial stage

Progressive sintering

0 0.6

0.7 0.8 0.9 Fractional sintered density

1.0

1.11 Grain size plotted as a function of porosity during the sintering of 8 µm copper powder to illustrate how rapid grain growth occurs as pores are removed with a reduction in the grain boundary pinning effect that retards grain growth at higher porosities.


18


1.12 The tetrakaidecahedron is a 14-sided polygon with 35 edges and 24 corners that packs to full density. It consists of six squares and eight hexagons, and pores then occupy the edges during intermediate stage sintering or the corners during final stage sintering.

broad range of densities from 85 to 95% and final stage sintering occurs with rapid grain growth and slow densification from that point.

1.8

Chemical and strain gradients

Sintering is a process where energy is consumed and the material is relaxed. If the powder is milled and has stored strain energy, then the release of that strain during sintering increases the sintering rate. Indeed, thermal stresses from rapid heating will improve the sintering rate, but often damage the component. Phase transformations are another means of including strains to alter the sintering rate. Adding energy to the material increases the sintering rate, so radiation and electromagnetic fields have beneficial effects. Chemical gradients are important to mixed powder sintering. For example, mixed powders are compacted and heated to form an alloy such as bronze or stainless steel. Most common is the formation of steel using mixed iron and graphite powder. During the sintering cycle the carbon goes into solution. Other examples include mixed copper and tin powders used to form bronze, and mixed silica and alumina used to form mullite. The number of combinations is large.



19

Mixed powder sintering is biased by the phase diagram thermodynamics. If an intermetallic is produced, typically it involves an exothermic reaction, such as NiTi, MoSi2, or Ni3Al. Some reactions are so strong that the system self-heats once initiated. Phase diagrams are equilibrium depictions of the phases that form versus temperature and composition, but mixed powders are not necessarily at equilibrium during heating. The tendency to react, swell, densify, or otherwise change traces to the phase diagram. For example, the iron-aluminum system shows solubility of aluminum in iron, but not the reverse solubility. Thus, during heating the aluminum melts and diffuses into the iron, leaving a pore behind at the prior aluminum particle sizes. Figure 1.13 is the Fe-Al phase diagram and the resulting microstructures below the phase diagram show images taken during heating as the core aluminum particle first melts, reacts, and then diffuses out to create a pore, giving compact swelling.

1600

1540

1500

L ?Fe2Al3ht

1400

1200

1160

1170

1155

700

660

0

Al

(Fe) rt

FeAl

800

FeAl2.8

Fe4Al13

900

Fe6.5Al11.5rt

1100

1000

600

1310 1230

1160

1100

(Al)

Temperature, ºC

1300

655

10

20

30

40

50

at. %

60

70

80

90

100

Fe

1.13 The pore evolution in sintering mixed iron and aluminum, showing the reaction around the aluminum particle to form an intermediate compound. The phase diagram shows that the intermetallic phases are very stable, thus the chemical reaction dominated sintering.


20


Other features of great importance to sintering can be identified from phase diagrams. These include solubility, dissolution, and liquid phase formation. Several of the important reactions are categorized elsewhere [1, 3, 10, 11]. One of the more difficult sintering tasks is to manage reactive systems, especially where a transient phase forms. Copper-tin is the most famous of these, where during heating tin melts, forms intermetallic compounds, and the compounds subsequently melt or dissolve. Although complicated, this system is fundamental to sintered oil-less bronze bearings and control of the events is crucial to successful functioning.

1.9

Thermodynamics, stages and mechanisms of mass flow

Transport mechanisms tell how mass flows to lower the system energy during sintering. There are two classes of sintering mechanisms: surface transport and bulk transport. Each is composed of several atomistic events that contribute to bonding. The pores are large accumulations of vacancies, so the sintering mechanisms describe vacancy motion and annihilation during heating. Vacancies and atoms move along particle surfaces (surface diffusion), across pores (evaporation-condensation), along grain boundaries (grain boundary diffusion), and through the lattice (viscous flow or volume diffusion). Also, vacancies couple with dislocations via plastic flow and dislocation climb. Surface transport processes give neck growth without a change in particle spacing (no shrinkage or densification) since the mass flow originates and terminates at the particle surface. The atoms are rearranged, but no annihilation of vacancies takes place. Surface diffusion and evaporation-condensation are two contributors to surface transport controlled sintering. Surface diffusion dominates the low-temperature sintering of many metals and ceramics, while evaporationcondensation is active when the vapor pressure is high. Bulk transport processes promote neck growth and shrinkage during sintering. For densification to occur, the mass must originate from the particle interior with deposition at the neck. The vacancy annihilation takes place on the grain boundary by particle rotation and rearrangement. Bulk transport mechanisms include volume diffusion, grain boundary diffusion, dislocation climb, plastic flow and viscous flow. Plastic flow is important during the heating period, especially for compacted powders where the initial dislocation density is high. Without rapid heating, surface tension stresses are generally insufficient to generate new dislocations and the dislocations are annihilated once they intersect a grain boundary or free surface. Thus, the role of plastic flow decreases as the dislocations are annealed out at high temperatures. In contrast, amorphous materials, such as glasses and polymers, sinter by viscous flow, where the particles coalesce at a rate that depends on the particle size and material viscosity. A form of viscous flow is also possible for metals with liquid phases on the grain boundaries. Grain boundary diffusion is fairly important to densification for most crystalline



21

materials, and appears to dominate the densification of many common systems. Volume diffusion is most active in cooperation with dislocation climb. Relative to the melting temperature, bulk transport processes are dominant at higher temperatures and surface transport processes are dominant at lower temperatures. The sinter bond between the contacting particles is the critical region. It is the point where atoms are deposited to reduce the surface energy. Generally all of the key sintering measures relate to the mass transport rates and how they influence neck growth and change the pores and grains. Models for solid–state sintering have subdivided the treatments into specific combinations of the sintering stage and mass transport mechanism, such as surface diffusion during initial stage sintering or grain boundary diffusion during intermediate stage sintering. Amorphous materials exhibit a decreasing viscosity (increased flow) as temperature increases. Under the action of an applied stress a viscous material flows. Both glasses and polymers densify by viscous flow. The lower the viscosity the more rapid the sintering process, so temperature is a key control parameter. If an external stress is applied, then the rate of sintering increases in proportion to the applied stress [1]. The two-particle sintering situation is different for amorphous materials when compared to crystalline solids, since amorphous materials lack grain boundaries. As neck growth occurs, amorphous materials reach a neck size ratio of approximately X/D = 2/3 where sintering often stops. In most cases the powder is fully densified by this point. Many early models of sintering associated viscous flow with creep and volume diffusion processes. The Stokes-Einstein relation effectively relates the volume diffusion coefficient to an effective viscosity, so such an idea is widely accepted. If a sintering body is measured for effective viscosity during periods of rapid sintering, the viscosity of 10 GPa-s is about the same as that of a viscous child’s toy known as Silly Putty®. Vapor transport during sintering leads to the repositioning of atoms located on the particle surface, without densification. Evaporation preferentially occurs from a convex surface and transport takes place across the pores to deposit mass on a nearby convex surface. The result is a reduction in the surface area as bonds grow between touching particles, but there is no change in the distance between particle centers. The fraction of atoms on surface sites decreases over time as the concave surfaces are filled using mass from the convex surfaces. Vapor pressure increases with temperature, following the Arrhenius behavior. Higher temperatures give a higher vapor pressure and more vapor phase transport during sintering. Because the vapor pressure changes with surface curvature, deposition occurs at the concave necks between particles where the vapor pressure is slightly below equilibrium. Materials with a large sintering contribution from evaporationcondensation include NaCl, PbO, TiO2, H2O, Si3N4, BN and ZrO2. All of these systems exhibit weight loss during sintering. In several situations the sintering atmosphere induces vapor transport, even when the vapor pressure of the material being sintered is low. Chemical species in


22


the sintering atmosphere (hydrogen, water, oxygen, carbon monoxide, chlorine and fluorine as examples) initiate considerable vapor phase transport, for both metals and ceramics. Sintering in vacuum stops vapor transport. No matter what the transport mechanism, once the neck size reaches a thermodynamic equilibrium dictated by the solid–vapor dihedral angle, further neck growth only occurs if there is grain growth. Neck growth occurs until the surface energy, dihedral angle and grain boundary energy attain a balance. From this point on, neck growth follows grain growth and generally both increase with the cube-root of time. In final stage sintering, closed pores become distorted by pore migration since pores try to stay on moving grain boundaries. As illustrated in Fig. 1.14, a migrating pore-boundary combination leads to a differential curvature between the leading and lagging faces. The corresponding vapor pressure gradient allows the pore to move with the grain boundary. Mass evaporates from the lower curvature surface and deposits on the higher curvature surface. Final stage

Grain boundary

Pore

Dihedral angle

1.14 Pore pinning of grain boundaries is possible if the pore has differing front and rear surface curvature gradients that enable transport in the pore to allow motion with the grain boundary.



23

densification critically depends on minimized grain growth and attachment of the pores to the grain boundaries. Vapor transport provides one of the means for this process. Surfaces of crystalline solids are usually not smooth, but consist of defects that include ledges, kinks, vacancies and adatoms. Surface diffusion involves the motion of atoms between the surface defects. The population of sites and the motion between sites are both thermally activated, meaning temperature has a significant influence on surface diffusion. Secondary consideration is given to the crystal orientation, since some orientations favor diffusion. A typical surface diffusion event involves three steps that might be rate controlling. The first is breaking an atom away from existing bonds, typically at surface defect. The population of kinks depends on both the surface orientation and temperature. Once dislodged, the atom moves with a random motion across the surface, usually as a fast step. Finally, the atom must reattach at an available surface site, possibly again at a kink. The populations of sites and the ease of motion determine the surface diffusion rate. There is an activation energy associated with the slowest step that is known as the surface diffusion activation energy, which often changes with temperature. Highly curved surfaces and high temperatures increase the defective site population, leading to more surface diffusion. Surface diffusion is active during heating to the sintering temperature. The activation energy for surface diffusion is less than that for other mass transport processes. Consequently, it initiates at a low temperature. Surface diffusion slows as the surface defect structure is consumed or as the available surface area is lost to sintering bonds. It does not produce shrinkage. For this reason surface diffusion works against densification, and rapid heating is one means to circumvent the problem. Surface diffusion is an initial contributor to the sintering of almost all materials. Boron and several covalent ceramics such as SiC exhibit surface diffusion dominance. Other examples include very small oxide powders at low temperatures and some metals when the particle size is small. Volume diffusion, or lattice diffusion, involves the motion of vacancies through a crystalline structure. The rate of volume diffusion depends on temperature, composition and particle size. In compounds, temperature and stoichiometry are the controlling parameters. There are three vacancy diffusion paths in sintering. One path is from the neck surface, through the particle interior, with subsequent emergence at the particle surface. A net result is deposition of mass at the neck surface. This is effectively transport from a surface source to a surface site so there is no densification or shrinkage. It is termed volume diffusion adhesion to distinguish it from the densification process. Although treated theoretically, there is little evidence for this occurring at significant levels in most sintering cycles. The second path is termed volume diffusion densification and involves vacancy flow to the interparticle grain boundary from the neck surface. This produces shrinkage and densification since effectively a layer of atoms moves in the opposite direction to the contact between the particles, allowing the centers to


24


approach as the sinter bond grows. A cooperative grain boundary accommodation step of rotation or slip is implied with this transport path. Dispersoids and phase boundaries are other interfacial vacancy sources that are important to the sintering of multiphase materials. Finally, the vacancies can be emitted or annihilated by dislocations, via a process termed dislocation climb. It involves cooperative action by both dislocations and vacancies. This process occurs during heating, and is especially active in compacted powders. The vacancy path is in the opposite direction to the atomic flux in each case. For compounds there is an additional factor beyond temperature that controls the vacancy population, that being stoichiometry. Off-stoichiometric ionic compounds contain excess vacancies to neutralize charge. The flux by volume diffusion is then the combined action of the thermally induced vacancies and those induced by the loss of stoichiometry. An excess of ionic vacancies associated with the slow-moving species accelerates sintering. The stoichiometric effect is accessible through the original compound formulation or through the process atmosphere or by chemical additions. For example, in sintering UO 2, a hyperstoichiometric oxygen level (2.02 oxygen atoms for each uranium atom), gives the highest sintered density. Sintering in a reducing atmosphere lowers the oxygen excess, resulting in retarded sintering. Alternatively, sintering in nitrogen preserves the oxygen excess and lowers the sintering temperature. Similar results are evident in other ionic materials, where small compositional changes result in large densification changes. Late in the sintering process, the remaining pores exist as nearly smooth, spherical collections of vacancies. A difference in size between neighboring pores leads to a vacancy concentration gradient. Consequently, large pores are vacancy sinks and small pores are vacancy sources, leading to progressive coarsening of the large pore and the eventual elimination of the small pore. It is important to sustain vacancy annihilation sites, such as grain boundaries, to avoid this form of pore coarsening during late stage sintering. Thus, attention is directed toward grain growth control and the coupling of pores to grain boundaries to achieve full densification. Although volume diffusion is active in most materials at high temperatures, it is often not the dominant mass transport process during sintering, especially for small powders. The activation energy for surface diffusion is typically lower, and in many cases grain boundary diffusion has an activation energy intermediate between surface and volume diffusion. Consequently, interfacial diffusion processes (surface and boundary diffusion) are generally more active. If the material has a small grain size or small particle size, then the effective transport via interfacial paths dominates sintering. Volume diffusion is a controlling process in the sintering of narrow stoichiometry compounds, such as BeO, CaO, Cr2O3, CuO, TiO2 UO 2 and Y2O3. Grain boundary diffusion is relatively important to the sintering densification of most metals and many compounds. Grain boundaries form in the sinter bond



25

between individual particles due to misaligned crystals as a collection of repeated misorientation steps. The defective character of the grain boundary allows mass flow along the boundary with an activation energy that is usually intermediate between surface diffusion and volume diffusion. The net impact depends on the grain size. As surface area is consumed and surface diffusion declines in importance, the simultaneous emergence of new grain boundaries increases the role of grain boundary diffusion. But grain growth reduces the importance of grain boundary diffusion. During sintering, transport also takes place between pores via the grain boundary, leading to pore coarsening. This is most active late in sintering when the grain boundary is an inefficient vacancy sink: Vacancy accumulation on a grain boundary requires motion of the boundary, and this is resisted by contacting neighbors. Grain boundary diffusion controlled sintering is most prevalent. It is well documented for metals, including Ni, W, Mo, Fe, Cu and various alloys. For compounds, a grain boundary segregant often acts to accelerate sintering; examples of this are in ZrO2 with Er2O3 additives, Ni3Al with small quantities of B, and Al2O3 with TiO2 additives. Dislocations play two roles in sintering: vacancy absorption (dislocation climb) and dislocation glide (slip). Dislocations participate in sintering during heating, especially if the powders were subjected to plastic deformation during compaction. Dislocations interact with vacancies during sintering to improve mass transport. The dislocations climb by the absorption of vacancies emitted from the pores, leading to annihilation of the vacancies and dislocation motion to a new slip plane. In this case, densification by volume diffusion does not require an efficient vacancy sink at the grain boundary. Unfortunately, one consequence of dislocation climb is that the dislocation population declines, thereby halting the process. Dislocation flow is restricted to the early stage of sintering near the neck surface for small powders. As the sintering neck enlarges, the shear stress declines below the flow stress and the process becomes inactive. Plastic flow contributions to sintering are transients that are favored by rapid heating (over 10°C/min), smaller particles (less than 100 µm), or pressure-assisted sintering. Dislocation motion can also be induced by phase transformations during heating, but this is restricted to polymorphic materials. Plastic flow has been observed during sintering for a variety of materials – Al2O3, Ag, CaF2, CoO, Cu, Fe, MgO, NaCl, Ni, Pb, ThO2, Ti, W and Zn. But in each case the contribution occurred during the application of a stress or during heating and was not sustained under isothermal conditions. There are several possible mass transport paths in sintering. The two main categories are surface transport and bulk transport. It is the latter which is responsible for densification during sintering. Both contribute to bonding. Evaporation-condensation and surface diffusion are the common surface transport processes. Materials with high vapor pressures or those that form a volatile


26


species by reacting with the sintering atmosphere are candidates for evaporationcondensation controlled sintering. A weight loss (beyond that normally encountered by evaporation of surface contaminants) is an indication of evaporation-condensation. For most materials the vapor phase transport contributions are small and can be ignored, but for low sublimation enthalpy compounds this is not true. In reactive atmospheres (including hydrogen, oxygen, halides and water) a high vapor pressure can be generated to sustain surface area loss during sintering, without densification. Surface diffusion also produces a loss of surface area during neck growth, but fails to induce shrinkage or densification. It is an initial contributor to the sintering and microstructure coarsening of many materials, especially those with a low activation energy for surface diffusion. Covalent ceramics exhibit surface diffusion controlled sintering so it is common to add grain boundary dopants to induce liquid phase sintering to attain sintering densification. Surface transport processes are involved in pore smoothing and migration during the latter stages of sintering densification.

1.10 Microstructure links to sintering thermodynamics Atomic motion during sintering is not directly visible, so various monitors are used, often based on the microstructure. However, studies have been able to image particles and necks during sintering [12–14]. Neck size and its change with time or temperature is the most important aspect of sintering. The neck-size ratio X/D, defined as the neck diameter X divided by the particle diameter D, is the fundamental monitor, as evident in Fig. 1.1. If the powder is irregular, compacted, or far from this ideal, still the conceptualization is valid. From the neck size ratio come many other measures, some of which are easier to measure. The surface area declines rapidly during sintering and is tracked with a dimensionless parameter ∆S/So (change in surface area normalized to starting surface area). Surface area is measured using microscopic analysis, gas adsorption, or gas permeability techniques. Also it is tracked based on quantitative microscopy. Related to the surface area are parameters such as thermal conductivity, electrical conductivity, corrosion behavior, and even catalytic activity. Many powder compacts change dimensions during sintering, as well as density, strength, hardness, and elastic modulus. A good example is illustrated in Fig. 1.15, showing the size of a teacup prior to and after sintering. Simple experiments can be performed using interrupted cycles where the component is cooled and measured for size or density. More preferred is dilatometry, where the sample size is measured in situ during a firing cycle. However, not all neck growth in sintering gives dimensional change and not all dimensional change is associated with neck growth. Thus, although convenient, shrinkage and dimensional change need to be used with caution in trying to identify the sintering mechanism. In a related manner, bulk properties are used to follow the sintering process, and show similar changes with temperature and time. Sintering shrinkage is coupled to density



27

1.15 A picture of two teacups, before and after sintering, to illustrate the shrinkage common to sintering.

changes and the elimination of pores. Shrinkage, ∆L/Lo, is the change in compact length divided by the initial dimension. Because of shrinkage, the compact densifies from the fractional green density ρG to the fractional sintered density ρS according to the relation,

ρS =

ρG 3 1 – ∆L Lo

( )

[1.13]

This is a mass-conservation equation that assumes no mass loss. In reality, powder compacts usually have contaminants and polymers that burn out during sintering, so the green density needs to be corrected for such mass loss. High green densities result in high final densities, even with small sintering shrinkages. Not all forms of sintering lead to densification and some lead to swelling. The latter is especially true for reactive systems where two powders undergo a dissolution or solvation event during heating. Porosity is the remaining void space. For filters the final porosity might be 25% and in some distended materials, such as sintered aluminum foams, the porosity might be 95%. Curiously, this material is formed by adding titanium hydride to the aluminum powder, and during heating the hydrogen evolved from the hydride blossoms many a gas pocket in the compact. This is an instance where the green density might be 80% of theoretical and the final density is 5% of theoretical, so obvious swelling has occurred.


28


Another parameter is densification Ψ, defined as the change in fractional density due to sintering divided by the fractional density change that is needed to attain a pore-free solid: Ψ=

ρS – ρG 1 – ρG

[1.14]

Densification, final density, neck size, surface area, and shrinkage are related measures of the particle bonding and pore elimination during sintering. Although densification is associated with many sintering cycles, it is not a guarantee that the pores will shrink. Porosity might decline as the pore size increases, with a concomitant decrease in the number of pores. As a rough guide, a pore size less than half the grain size is needed to sustain densification in most materials. Consequently, broad pore size distributions, due to agglomeration or poor consolidation, lead to sintering difficulties. The narrow distribution associated with a high packing density inhibits grain growth and allows rapid densification. Thus, smaller pores, higher green densities, and narrow pore size distributions are precursors to rapid sintering densification and high final densities; consequently, narrow particle size distributions (which usually give a narrow range of pore sizes) prove easier to sinter to full density [15]. As sintering progresses the individual particles are blurred and the grain structure becomes evident. Not all grains are the same size or shape. Most sintered materials are assessed for grain structure using two-dimensional sections. Larger grains will have more faces, but the average will be between four and six in two dimensions and 13 to 15 faces in three dimensions. As noted earlier, the tetrakaidecahedron is commonly assumed as the best model for the grain shape during sintering, where pores occupy the corners of this polyhedron with 14 faces, 36 edges, and 24 corners. Figure 1.16 shows an example of such a grain. The sintered grain structure is not random, since smaller grains tend to cluster. Pores tend to collect on grain faces when the grain is growing and on corners when the grain is shrinking. The grain size distribution for sintered materials follows an exponential distribution function. In the cumulative form this is a Weibull distribution given by F(G) = 1 – exp[− ln(2) (G/Gm)M], where F(G) is the cumulative fraction of grains up to size G, where Gm is the median size corresponding to half of the grains being smaller, and M is an exponent that is 2 for two-dimensional grain size measures and M = 3 for three-dimensional grain size measures. Early work suggested an exponential probability density function given by a related function where P(G) is the probability of finding grains of size G [1]:

[ ( ) ]

P(G) = PM exp -α

 G

2

GM – 1

[1.15]

where PM is the peak in the frequency distribution (the amount at the mode size), G is the grain size, GM is the mode grain size, and α is typically between 2 and 6.



29

200 μm

1.16 Scanning electron micrograph of the polyhedral grains associated with sintering. Compare these actual grains with the idealized tetrakaidecahedron shown earlier.

Since sintering produces a self-similar distribution (shape of the distribution is the same, only shifting by the location of the size scale) the mode is usually 17% larger than the median size. This model works for both solid and liquid phase sintered materials. Both broad and narrow initial particle size distributions result in similar grain size distributions after sintering to full density [16]. Hence, sintering is a process that moves the microstructure toward a normalized condition, independent of the starting attributes. Figure 1.17 plots several grain size distributions measured in two dimensions for liquid phase sintered materials with a normalization to show how similar these distributions become. There are big differences in the ease of sintering various powders, but the morphological attributes of the sintered product tend to converge. This convergence is often termed ‘self-similar’ in that no matter where we start in microstructure, the thermodynamics of the sintering system seem to be attracted toward the same final state. Of course the time to reach this point is long, so most sintered materials represent only partial marches along the natural sintering trajectory.

1.11 Conclusion Sintering concepts are best developed for the case of loose, monosized spherical powders sintering by solid-state diffusion. In this case, the thermodynamic driving force is well understood and the stages are easily identified. Unfortunately, only a


30

Sintering of advanced materials 100

W-Ni-Fe

Cumulative percent

80

TiC-Mo-Ni BaTiO3-TiO2 60

VC-Ni Fe-Cu Co-Cu Sn-Pb

40

1 – exp(–0.7 L2) 20

0 0.1

0.2 0.4 0.6 1 Relative intercept size, mm (L = G/G50)

2

3

1.17 Cumulative grain size distributions for several liquid phase sintered materials to show how the normalized distributions become self-similar when the size is normalized to the median grain size, each follows a Weibull distribution with M = 2.

small portion of sintering practice relies on solid-state sintering of loose, monosized spheres. More common is to start with multiple phases, nonspherical particles, and broad particle size distributions, where one of the ingredients forms a liquid during the heating cycle. Further, an external pressure might be added to enhance densification. Although much of the effort here relates to engineered products, the reader must realize that sintering is pervasive and occurs for example in nature during the transformation of snow into glaciers and the transformation of certain mineral phases in the presence of magma melts. Indeed, the microstructures seen in geological and glacial samples are identical to those seen in products formed in the materials laboratory. Single phase, solid-state sintering is applicable to pure substances such as nickel, ice, alumina, or copper. Usually, faster sintering is induced by adding phases that form liquids between the solid particles, usually by wetting the grain boundaries. If there is solid solubility in the liquid, then significant increases in mass transport rates are possible with a further benefit from capillary forces pulling the particles together in a manner that is similar to the role of an external pressure. Over 70% of the sintered products are formed using a liquid phase and they constitute 90% of the commercial sintered product value. The most important application is in the fabrication of hard materials also known as cemented carbides, such as WC-Co, TiC-Fe, and mixtures such as WC-TaCTiC-Co. Other examples are encountered in almost all areas of engineering, and include stainless steels, superalloys, Si3N4– based compositions, steel and



31

bronze, intermetallics such as silicides and aluminides, tool steels, many electronic compositions, most carbides, oxides, borides, nitrides, and a wide variety of composites such as AlN-Y2O3, TiC-Fe, ZnO-Bi2O3, WC-Co, Fe-P, Mo-Cu, W-Ag, Al-SiC, and W-Ni-Fe. Sintering is critical to many industries and contributes significantly to the advanced materials area. As the sintering process is mastered, we find the products being tailored for a wide range of engineering property combinations – literally from high-temperature rocket nozzles forming hafnium carbide to low-temperature copper-based solders for electronic circuits. In turn the applications range from mundane bathroom fixtures to magnetic recording devices, cutting tools, home appliances, wristwatches, musical instruments, sporting equipment, bearings, filters, heat sinks, hard disk drives, hand tools, rechargeable batteries, and electrical capacitors. Some of these devices require high surface areas, so it is desirable to obtain sintered strength without densification. In other cases, sintering is performed under conditions where near full density is obtained. In the latter cases, sintering requires a high temperature, small particles, a liquid phase, or external pressure to ensure densification. Such processing flexibility is unparalleled in materials science.

1.12 Sources of further information and advice J. R. Blackford, ‘Sintering and Microstructure of Ice: A Review,’ Journal of Physics D: Applied Physics, 2007, vol. 40, pp. R355–R385. E. A. Olevsky, V. Tikare, and T. Garino, ‘Multi-Scale Study of Sintering: A Review,’ Journal of the American Ceramic Society, 2006, vol. 89, pp. 1914–22. R. M. German, Sintering Theory and Practice, John Wiley and Sons, 1996, New York, NY. R. M. German, P. Suri, and S. J. Park, ‘Review: Liquid Phase Sintering,’ Journal of Materials Science, 2009, vol. 44, pp. 1–39. S. J. L. Kang, Sintering Densification, Grain Growth, and Microstructure, Elsevier, Oxford, United Kingdom, 2005. Z. A. Munir, U. Anselmi-Tamburini, and M. Ohyanagi, ‘The Effect of Electric Field and Pressure on the Synthesis and Consolidation of Materials: A Review of the Spark Plasma Sintering Method,’ Journal of Materials Science, 2006, vol. 41, pp. 763–77. A. P. Savitskii, Liquid Phase Sintering of the Systems with Interacting Components, Russian Academy of Sciences, Tomsk, Russia, 1993. N. J. Shaw, ‘Densification and Coarsening During Solid State Sintering of Ceramics: A Review of the Models, I. Densification,’ Powder Metallurgy International, 1989, vol. 21, no. 3, pp. 16–21. B. Uhrenius, J. Agren, and S. Haglund, ‘On the Sintering of Cemented Carbides,’ Sintering Technology, R. M. German, G. L. Messing and R. G. Cornwall (eds.), Marcel Dekker, New York, NY, 1996, pp. 129–39.

1.13 References 1. R. M. German, Sintering Theory and Practice, John Wiley and Sons, 1996, New York, NY.


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2. P. W. Lee, Y. Trudel, R. Iacocca, R. M. German, B. L. Ferguson, W. B. Eisen, K. Moyer, D. Madan, and H. Sanderow (eds.), Powder Metallurgy Technologies and Applications, vol. 7 ASM Handbook, ASM International, Materials Park, OH, 1998. 3. A. P. Savitskii, ‘Relation between Shrinkage and Phase Diagram,’ Science of Sintering, 1991, vol. 23, pp. 3–17. 4. G. Petzow, and H. E. Exner, ‘Particle Rearrangement in Solid State Sintering,’ Zeitschrift fur Metallkunde, 1976, vol. 67, pp. 611–18. 5. A. Belhadjhamida, and R. M. German, ‘A Model Calculation of the Shrinkage Dependence on Rearrangement During Liquid Phase Sintering,’ Advances in Powder Metallurgy and Particulate Materials – 1993, vol. 3, Metal Powder Industries Federation, Princeton, NJ, 1993, pp. 85–98. 6. Y. Liu and B. R. Patterson, ‘A Stereological Model of the Degree of Grain BoundaryPore Contact During Sintering,’ Metallurgical Transactions, 1993, vol. 24A, pp. 1497–505. 7. Y. Liu and B. R. Patterson, ‘Grain Growth Inhibition by Porosity,’ Acta Metallurgica et Materialia, 1993, vol. 41, pp. 2651–6. 8. O. Blaschko, R. Glas, G. Krexner and P. Weinzierl, ‘Stages of Surface and Pore Volume Evolution During Sintering,’ Acta Metallurgica et Materialia, 1994, vol. 42, pp. 43–50. 9. R. L. Coble and T. K. Gupta, ‘Intermediate Stage Sintering,’ Sintering and Related Phenomena, G. C. Kuczynski, N. A. Hooton and C. F. Gibbon (eds.), Gordon and Breach, New York, NY, 1967, pp. 423–41. 10. R. M. German, ‘The Identification of Enhanced Sintering Systems Through Phase Diagrams,’ Modern Developments in Powder Metallurgy, vol. 15, E. N. Aqua and C. I. Whitman (eds.), Metal Powder Industries Federation, Princeton, NJ, 1985, pp. 253–73. 11. K. G. Nickel and G. Petzow, ‘Phase Diagrams – Key to Advanced Ceramics Development,’ Sintering ’91, A. C. D. Chaklader and J. A. Lund (eds.), Trans Tech Publ., Brookfield, VT, 1992, pp. 11–22. 12. A. Vagnon, J. P. Riviere, J. M. Missiaen, D. Bellet, M. Di Michiel, C. Josserond, and D. Bouvard, ‘3D Statistical Analysis of a Copper Powder Sintering Observed In Situ by Synchrotron Microtomography,’ Acta Materialia, 2008, vol. 56, pp. 1084–93. 13. P. Lu. J. L. Lannutti, P. Klobes, and K. Meyer, ‘X-Ray Computed Tomograph and Mercury Porosimetry for Evaluation of Density Evolution and Porosity Distribution,’ Journal of the American Ceramic Society, 2000, vol. 83, pp. 518–22. 14. M. Nothe, K. Pischang, P. Ponizil, R. Bernhardt, and B. Kieback, ‘3D Analysis of Sinter Processes by X-Ray Computer Tomography,’ Advances in Powder Metallurgy and Particulate Materials – 2002, Metal Powder Industries Federation, Princeton, NJ, 2002, pp. 13.176–13.184. 15. A. Petersson and J. Agren, ‘Sintering Shrinkage of WC-Co Materials with Bimodal Grain Size Distributions,’ Acta Materialia, 2005, vol. 53, pp. 1665–71. 16. Z. Fang and B. R. Patterson, ‘Influence of Particle Size Distribution on Liquid Phase Sintering of W-Ni-Fe Alloy,’ Tungsten and Tungsten Alloys Recent Advances, A. Crowson and E. S. Chen (eds.), The Minerals, Metals and Materials Society, Warrendale, PA, 1991, pp. 35–41.


2 Kinetics and mechanisms of densification M. N. R ahaman, Missouri University of Science and Technology, USA Abstract: This chapter discusses the kinetics and mechanisms of densification in solid-state, liquid-phase, and pressure-assisted sintering. Theoretical approaches used to analyze the densification process are outlined, and their limitations for describing the sintering of real powder systems are discussed. The effects of key material and sintering parameters not commonly taken into account in the idealized models, such as particle packing, particle and pore shape anisotropy, gaseous atmosphere, and non-isothermal sintering, are described. Key words: sintering models; kinetics of densification; sintering mechanisms; sintering process variables.

2.1

Introduction

The major processes that occur during sintering are densification and grain growth (Fig. 2.1). This chapter is devoted to a treatment of the kinetics and mechanisms of densification. The thermodynamics of sintering are considered in Chapter 1. An analysis of sintering must also consider how the microstructure of the porous material evolves (Chapter 3). In sintering, both the grains and the pores often increase in size while decreasing in number. The term coarsening is used to describe this process of grain growth coupled with pore growth. Densification and coarsening often occur concurrently, and both lead to a reduction in the energy of a porous polycrystalline material. Coarsening decreases the driving force available for densification and it increases the diffusion distance for matter transport, leading to a marked reduction in the densification rate. As a result, sintering is sometimes said to involve a competition between densification and coarsening (or grain growth). The three categories of sintering are solid–state sintering, liquid–phase sintering, and viscous sintering. For some systems, densification achieved by any of these categories of sintering may be inadequate. A common solution to this problem is the application of an external pressure during heating, giving the method of pressure-assisted sintering, of which hot pressing and hot isostatic pressing (HIP) are common examples. To distinguish it from pressure-assisted sintering, sintering performed without the application of an externally applied pressure is referred to as conventional sintering. The kinetics of densification are commonly described in terms of the density or shrinkage of the material as a function of time (isothermal sintering) or temperature (constant heating rate sintering). The bulk density, defined as the mass divided by 33 © Woodhead Publishing Limited, 2010

34


2.1 Micrographs of tungsten powder during solid-state sintering, showing the decrease in porosity (black regions), and grain growth. (From German, R. M. (1996), Sintering theory and practice, New York, Wiley, 1996; p. 72.)

the external volume of the body or, more commonly, the relative density ρ, defined as the bulk density divided by the theoretical density of the solid, is used as the density parameter. Relative density and total porosity P of a solid are related by

ρ = 1 – P

[2.1]

The linear shrinkage is defined as ∆L/Lo, where Lo is the original length, L is the length at a given time or temperature, and ∆L = L – Lo (a negative quantity). If the shrinkage is isotropic, then:

ρ=

ρo (1 + ∆L/Lo)3

[2.2]

where ρo is the initial relative density. Measurement of ρ or DL/Lo is easy to perform and provides substantial information about the rate of sintering. The



35

densification rate, defined as (1/ρ)(dρ/dt), where t is the time, is equivalent to a volumetric strain rate.

2.2

Solid-state sintering

The driving force (the reduction in surface free energy) provides a motivation for sintering (Chapter 1), but the actual occurrence of sintering requires transport of matter. In crystalline solids, matter transport occurs by diffusion of atoms, ions, or molecules along definite paths that define the mechanisms of sintering. Viscous flow is the dominant sintering mechanism in glass (or amorphous materials).

2.2.1 Mechanisms of solid-state sintering Sintering of crystalline materials can occur by at least six mechanisms or paths: vapor transport (evaporation/condensation), surface diffusion, lattice (volume) diffusion, grain boundary diffusion, and plastic flow. Figure 2.2 shows a schematic representation of the matter transport paths for two sintering particles. A distinction is commonly made between densifying and non-densifying mechanisms. Vapor transport, surface diffusion, and lattice diffusion from the particle surfaces to the neck lead to neck growth and coarsening of the particles without densification. The densifying mechanisms, grain boundary diffusion, lattice diffusion from the grain boundary to the neck, and plastic flow cause neck growth as well as densification (shrinkage). When the non-densifying mechanisms dominate, coarsening leads to the production of a porous article, whereas a dense article is favored under conditions when the densifying mechanisms dominate.

2.2 Schematic representation of the sintering mechanisms for a system of two particles.


36


Grain boundary diffusion and lattice diffusion are important densification mechanisms in metals and ceramics. Plastic flow, by dislocation motion in response to the sintering stress, plays essentially no role in the sintering of ceramics because of the low dislocation density. The occurrence of plastic flow during the sintering of metals is controversial, but most likely dislocations participate in the initial stage of sintering. Finite element analysis (Ogbuji, 1986) and experiments (Morgan, 1973; Brett and Seigle, 1963) indicate that plastic flow by dislocation motion is inactive in the intermediate and final stages of sintering.

2.2.2 Effects of grain boundaries Because of the presence of grain boundaries in polycrystalline materials, the energy decrease due to elimination of free surface area does not go totally into driving the densification process. Part of the energy decrease goes into driving the grain growth process, leading to a reduction in the driving force for densification. The presence of the grain boundaries also dictates the equilibrium shapes of the pores (and the grains), which can influence matter transport during sintering. Taking a hypothetical pore surrounded by grains (Fig. 2.3), the forces must balance at the junction where the surfaces of the pores meet the grain boundary. At the junction, the tension γsv in the solid–vapor interface is tangential to that interface, while that in the grain boundary, γgb, is in the plane of the boundary. The balance of forces leads to

γgb = 2γsv cos (ψ/2)

[2.3]

where ψ is the dihedral angle. A high dihedral angle indicates a low grain boundary energy, making continued densification favorable. On the other hand, a low dihedral angle can lead to inhibition of densification because the replacement of free surfaces by grain boundaries during sintering becomes unfavorable.

2.3 Pore shape and pore stability are determined by the dihedral angle and the pore coordination number. (a) The pore with the concave surfaces will shrink while (b) the pore with the convex surfaces will grow (or become metastable).



37

2.2.3 Theoretical analysis of solid-state sintering A comprehensive theory of sintering should be capable of describing the entire sintering process: densification, as well as the evolution of the microstructure. However, in view of the complex nature of the sintering process, it is unlikely that such a theory will be developed. A common approach is to develop an understanding of the densification and coarsening processes separately, and explore the consequences of their interaction. Several theoretical approaches have been used to analyze solid-state sintering (Table 2.1). The analytical models played a key role in developing an understanding of sintering, but they have been criticized because the drastic simplifications assumed in the models (uniform packing of monosize spheres, isothermal sintering, and no grain growth) limit their ability to quantitatively predict the densification of real powder compacts. The analytical models provide only a qualitative understanding of sintering. Numerical models offer a powerful tool for gaining insight into some of the complexities of sintering, and the technique is increasingly being used.

Table 2.1 Main approaches used for the theoretical analysis of solid-state sintering Approach

Comments

Selected references

Scaling law Not dependent on specific Herring, 1950a geometry effects of change of scale on the rate of single mechanism derived. Analytical models Oversimplified geometry. Analytical Frenkel, 1945; Kuczynski, equations for dependence of sintering 1949; Kingery and Berg, rate on primary variables derived for 1955; Coble, 1958; Coble, single mechanism. 1961; Johnson, 1970; Beeré, 1975 Numerical Equations for matter transport solved Nicholls and Mullins, 1965; simulations numerically. Complex geometry and Bross and Exner, 1979; concurrent mechanisms analyzed. Svoboda and Riedel, 1995; Zhang and Schneibel, 1995 Topological Analysis of morphological changes. Rhines and DeHoff, 1984 models Predictions of kinetics limited. More appropriate to microstructural evolution. Statistical models Statistical methods applied to the Kuczynski, 1976 analysis of sintering. Simplified geometry. Semi-empirical analysis. Phenomenological Empirical or phenomenological Tikkanen and Makipirtti, equations derivation of equations to describe 1965; Ivensen, 1973 sintering data. No reasonable physical basis.


38


Analytical models of solid-state sintering The analytical models assume a relatively simple, idealized geometry for the powder system, and for each mechanism, the mass transport equations are solved analytically to provide equations for the sintering kinetics. The drastic change in the microstructure during the sintering of real powder compacts is approximated by dividing the process into three idealized stages, referred to as initial, intermediate, and final. Each stage is assumed to have an idealized geometry (Fig. 2.4) which approximates the microstructure of real powder compacts (Coble, 1961).

2.4 Idealized models for the three stages of sintering: (a) initial stage: model structure represented by spheres in tangential contact; (b) near the end of the initial stage: spheres have begun to coalesce; (c) intermediate stage: dark grains have adopted the shape of a tetrakaidecahedron, enclosing white pore channels at the grain edges; (d) final stage: pores are tetrahedral inclusions at the corners where four tetrakaidecahedra meet. (From Coble, 1961.)



39

For the two-sphere geometry assumed for the initial stage, equations for neck growth (X/a) and, for the densifying mechanisms, shrinkage (∆L/Lo), have been derived for each mechanism (Frenkel, 1945; Kuczynski, 1949; Kingery and Berg, 1955; Coble, 1958). The equations can be expressed in the general form

( ) ( )

X m H = n t a a ∆L Lo

m/2

[2.4]

= – mH n t 2 a

[2.5]

where X is the neck radius, a is the sphere radius, t is the time, m and n are numerical exponents that depend on the mechanism of sintering, and H is a function that contains the geometrical and material parameters of the powder system. Plausible values for m, n, and H are summarized in Table 2.2 (Exner, 1979; Coblenz et al., 1980). Since m is dependent on the mechanism of sintering, it might seem that the measurement of m could be used to determine the mechanism. However, the limitations of these initial stage equations for describing the sintering of real powder compacts are well recognized. For the intermediate and final stage models (Fig. 2.4), the non-densifying mechanisms are inactive. Equations for the intermediate and final stages of Table 2.2 Plausible values for the constants appearing in Equation 2.4 and Equation 2.5 for the initial stage of sintering Mechanism

m

n

Surface diffusiona 7 4 Lattice diffusion from the surfacea

4 3 Vapor transporta

Hb 56Dsδsγsv Ω kT 20Dl γsv Ω kT

3 2

3poγsvΩ (2πmkT)1/2kT

Grain boundary diffusion

96Dgbδgbγsv Ω kT

6

4

Lattice diffusion from the grain boundary 5

3

80πDl γsv Ω kT

Viscous flow 2 1

3γsv 2η

a Denotes

non-densifying mechanism, i.e., shrinkage ∆L/Lo = 0. Dl, Dgb, diffusion coefficients for surface, lattice, and grain boundary diffusion. δs, δgb, thickness for surface and grain boundary diffusion. γsv, specific surface energy; po, vapor pressure over a flat surface; m, mass of atom; k, Boltzmann constant; T absolute temperature; η, viscosity. b D , s


40


sintering by lattice and grain boundary diffusion have been developed (Coble, 1961). The equations for the densification rate, (1/ρ)dρ/dt, can be expressed in general form

( )

1 dρ H1DΩφ(m – 1)/2 αγsv = ρ dt GmkT r

[2.6]

where H1 is a numerical constant that depends on the assumed geometry of the model and on the sintering mechanism, D is the appropriate diffusion coefficient (D = Dl for lattice diffusion, and D = Dgbδgb for grain boundary diffusion), Ω is the atomic volume of the rate controlling species, G is the grain (or particle) size, r is the pore radius, k is the Boltzmann constant, T is the absolute temperature, φ is a density-dependent term, referred to as the stress intensification factor (discussed later), which relates the neck diameter to the grain size, α is a parameter that depends on the stage of sintering, and m is an exponent that depends on the mechanism of sintering. Values of the parameters are summarized in Table 2.3. Equation 2.6 predicts that for an equivalent microstructure, the densification rate increases almost exponentially with T (due to the Arrhenius dependence of D on T ), and has a strong dependence on the grain size G (or the particle size). For example, if the pore radius is assumed to scale as the grain (or particle size), the rate of densification by grain boundary diffusion is predicted to vary as 1/G4. Reduction in particle size provides a key method for enhancing the densification rate, reducing the sintering time, or reducing the sintering temperature. For the same densification rate predicted by Eq. 2.6, the relationship between particle size a and sintering temperature T for two systems (designated 1 and 2) is given by

() ( )

mln

a2 Q 1 1 – a1 ≈ R T1 T2

[2.7]

where Q is the activation energy (per mole), and R is the gas constant. As an example, for coarse-grained ZnO with a sintering temperature of 1200 °C, if the particle size were reduced by a factor of 10 then, according to Eq. 2.7, the same densification rate is achieved by sintering at ~750 °C, assuming that densification occurs by grain boundary diffusion (m = 4), and Q ≈ 250 kJ/mol. Although the Table 2.3 Plausible values for the constants appearing in Equation 2.6 for the intermediate and final stages of sintering by diffusional mass transport Mechanism Lattice diffusion Grain boundary diffusion

Intermediate stage H1 40/3 95/2

m 2 3

Final stage α 1 1

H1 40/3 15/2


m 2 3

α 2 2


41

reduction in practical sintering temperatures is lower than the predicted values, often due to inhomogeneous particle packing and coarsening, the benefits of small particle size are significant. A lower sintering temperature is particularly beneficial in some materials, such as those that evaporate or decompose at higher temperatures. Nanoscale powders (particle size less than 50–100 nm) show large reductions in the sintering temperature. For tungsten with a particle size of 16 nm, the onset of sintering was detected at 725 °C, which is only ~0.25 of the melting temperature (3683 K), far lower than the range observed for conventional tungsten powders. Figure 2.5 shows data for the sintering of three nickel powders, where the finest powder shows the lowest temperature for sintering to high density (Andrievski, 1994). However, nanoscale powders can also suffer from processing difficulties, such as larger sintering shrinkage due to lower packing density of the green article and greater contamination due to the larger surface area. Herring’s scaling law The scaling law (Herring, 1950a) does not assume a specific geometrical model. Instead, it assumes that the geometrical changes during sintering remain similar. The law considers the effect of change of scale (e.g., particle size) on the rate of

2.5 Relative density vs. sintering temperature for three nickel powders with the average particle sizes shown.


42


matter transport for individual mechanisms. The time ∆t to reach geometrically similar microstructural changes in two systems (designated 1 and 2) which differ only in particle size a is predicted to be

()

a m ∆t2 = 2 ∆t1 a1

[2.8]

where m is an exponent that depends on the mechanism of matter transport. In the case of lattice diffusion, m = 3, whereas m = 4 for grain boundary diffusion, which agrees with the strong grain size dependence predicted by the analytical models. Because of the general approach used in its derivation, the scaling law might be expected to have some advantage over the analytical models that assume a specific geometry. A problem is that the requirement of geometrical similar microstructural change is not easy to achieve for real powder compacts, so the law has not found wide applicability in sintering. Numerical modeling In practice, more than one mechanism operates during sintering. Numerical simulations have been used to examine some of the complexities of sintering, such as use of more realistic geometries (Nicholls and Mullins, 1965; Bross and Exner, 1979) and sintering with concurrent mechanisms (Svoboda and Riedel, 1995; Zhang and Schneibel, 1995; Bouvard and McMeeking, 1996; Pan et al., 1998). The approaches include finite element analysis, finite difference solutions, and Monte Carlo simulations. Figure 2.6 shows the predictions of a numerical model for the normalized neck radius (X/a) vs. normalized time for sintering of spherical particles by the simultaneous occurrence of grain boundary diffusion and surface diffusion for a dihedral angle ψ = 120 ° (Svoboda and Riedel, 1995). While the analysis confirms a power-law dependence of the neck radius on time, an interesting prediction is that the exponent m (see Eq. 2.4) increases from 11/2 for high values of Ds /Dgb to 7 for low Ds /Dgb values, where Ds /Dgb is the ratio of the surface diffusion coefficient to the grain boundary diffusion coefficient. This trend in the value of m is opposite to that predicted by the analytical models (Table 2.2). Sintering maps Sintering maps have been constructed to show the dominant mechanisms as a function of the temperature and density (Ashby, 1974; Swinkels and Ashby, 1981). The construction employs the sintering equations derived for the analytical models and data for the material parameters in the equations. Because of the inadequacy of the database and the drastic simplifications of the models, the applicability of the maps is limited. Nevertheless, they have served a useful function in visualizing conceptual relationships between the various



43

2.6 Results of numerical simulations for the normalized neck radius vs. reduced time for sintering of two spherical particles by the simultaneous occurrence of surface diffusion and grain boundary diffusion. (From Svoboda and Riedel, 1995.)

mechanisms and changes in the sintering behavior under different sintering conditions. Phenomenological sintering equations Empirical equations have been developed to fit densification data. Whereas they provide little help in developing a deeper understanding of sintering, they may serve a useful function in numerical models that require the use of a densification equation. A simple expression that is found to be successful for fitting many sintering and hot pressing data is

ρ = ρo + K ln (t/to)

[2.9]

where ρo is the density at an initial time to, ρ is the density at time t, and K is a temperature-dependent parameter. Some theoretical justification can be developed for this semi-logarithmic expression (Coble, 1961). Other empirical equations in the sintering literature include one due to Tikkanen and Makipirtti (1965) and Ivensen (1973). It is often found that more than one empirical equation can provide a good fit to any given set of sintering data, so the choice of any one of the equations can be somewhat arbitrary. The semi-logarithmic relationship (Eq. 2.9) has the advantage of simplicity and is successful in fitting much sintering and hot pressing data (Fig. 2.7).


44


2.7 Semi-logarithmic dependence of the density on time during the hot pressing of high purity MgO. (From Vieira and Brook, 1984.)

2.3

Viscous sintering

Densification of glass occurs by viscous flow. Viscous sintering models based on an energy balance concept (Frenkel, 1945) provide an excellent description of the sintering of glass. Models for viscous sintering have been developed for the initial stage (Frenkel, 1945), intermediate stage (Scherer, 1977), and the final stage (Mackenzie and Shuttleworth, 1949). Despite a large difference in geometry between the Scherer and the Mackenzie and Shuttleworth models, significant differences between the predictions of the models occur only when the relative density ρ falls below ~0.2. Unlike the case of polycrystalline materials, the densification of glass appears to be insensitive to structural details. For the Mackenzie and Shuttleworth model, consisting of a spherical pore of radius r in a concentric shell of dense glass (viscosity = η), the densification rate can be expressed as

( )( )

1 dρ 3 1 – ρ 2γsv =– ρ dt 4 ηρ r

[2.10]

According to Eq. 2.10, at any given density, the densification rate caries as 1/r. If the pore radius is taken to be proportional to the starting particle size, then the densification rate is inversely proportional to the particle size, which shows a much weaker dependence on particle size when compared to the sintering of polycrystalline materials (Eq. 2.6).


2.4


45

Liquid-phase sintering

In many sintering processes, a liquid phase is commonly used to enhance densification, lower the sintering temperature, achieve accelerated grain growth, or to produce specific grain boundary properties (Chapter 5). After the formation and redistribution of the liquid, liquid-phase sintering is generally regarded as proceeding in a sequence of overlapping dominant stages (Fig. 2.8): (1) rearrangement of the solid phase driven by capillary stress gradients, (2) densification and grain shape accommodation of the solid phase involving solution–precipitation, and (3) final stage densification driven by residual porosity in the liquid phase in which Ostwald ripening dominates the microstructural evolution. Despite the use of several theoretical and experimental approaches (Kingery, 1959; Huppmann and Riegger, 1975; Fortes, 1982; Kang et al., 1984), the analysis of rearrangement in a randomly-packed array of particles is a difficult problem, and an understanding of the process in real systems is limited. Computational approaches to rearrangement have also been used (Lee et al., 1999). Kingery (1959) used an empirical approach in which the surface tension forces driving densification are balanced by the viscous forces resisting rearrangement, and derived a simple kinetic relationship for the variation of the shrinkage with time t: ∆L 1 + y ~t Lo

[2.11]

where y is a positive number less than one. While Eq. 2.11 does not appear to be unreasonable, experimental verification has not been convincing.

2.8 Schematic evolution of a powder compact during liquid-phase sintering. The three dominant stages overlap significantly.


46


Two models have been put forward to describe densification in the solutionprecipitation stage (Fig. 2.9). Densification by ‘contact flattening’ was described by Kingery (1959) for a model consisting of two spherical particles of radius a, separated by a liquid layer of thickness δL. As a result of the compressive capillary force of a wetting liquid, the chemical potential of the atoms at the contact points between the particles is higher than at other solid surfaces. This difference in chemical potential (and, hence, solubility) leads to matter transport away from the contact points, and to the formation of a flat contact zone. If diffusion is the ratecontrolling step in the solution–precipitation process, the shrinkage ∆L/Lo as a function of time t is predicted to be –

(

)

∆L 6k1DLδLCoΩγlv = Lo a4kT

1/3

t1/3

(a)

(b)

2.9 (a) Two-sphere model for densification by contact flattening; (b) schematic diagram illustrating densification accompanied by Ostwald ripening.


[2.12]


47

where k1 is a geometrical factor, DL is the diffusion coefficient of the solute atoms in the liquid, Co is the solute concentration over a flat surface, Ω is the atomic volume, γlv is the tension in the liquid–vapor interface, k is the Boltzmann constant, and T is the absolute temperature. If the phase boundary reaction (solution or precipitation) is the rate-controlling step, then –

(

)

∆L 2k1k3CoΩγlv = Lo a2kT

1/2

t1/2

[2.13]

where k3 is a reaction rate constant. Another model is based on observations by Yoon and Huppmann (1979) for liquid-phase sintering of the W–Ni system in which shrinkage occurred concurrently with Ostwald ripening. While theoretical analysis of the shrinkage is difficult, one estimate based on diffusion-controlled Ostwald ripening gives –

(

)

∆L 48DL CoΩγlv = Lo a3kT

1/3

t1/3

[2.14]

Most experimental data often show reasonable agreement with the predicted dependence of the shrinkage on the one-third power of time, which is taken to indicate a diffusion-controlled solution-precipitation mechanism (Kingery and Narasimhan, 1959; Huppmann and Riegger, 1977). However, because of the overlap with the rearrangement stage, fitting the data to determine the time dependence of the shrinkage can sometimes involve some degree of arbitrariness. In view of the initially high capillary forces exerted on small grain contacts, it appears reasonable that Kingery’s contact flattening model is initially important. The model can also account for the phenomenon of grain shape accommodation. On the other hand, observations with real powder systems, which normally have a distribution of particle sizes, show that densification correlates with the onset of coarsening in the solution-precipitation stage. Kingery’s model assumes no grain growth, so it cannot account for this observed coarsening.

2.5

Pressure-assisted sintering

2.5.1 Kinetics and mechanisms The application of an external pressure enhances the densification rate in solidstate, liquid–phase, and viscous sintering. The chemical potential of the atoms under the contact surface (neck or grain boundary) is enhanced by the application of an external pressure, when compared to atoms under the pore surface, which leads to an increase in the driving force for densification (Coble, 1967; 1970). The driving force for densification, DF, can be expressed as DF = pe + γsvK


[2.15]

48


where pe is the effective stress at the contact surface, and K is the curvature of the pore surface. Using a force balance argument, the applied stress pa leads to a higher effective stress pe on the grain boundary because of the porosity. The relation is assumed to be pe = φpa

[2.16]

where φ is referred to as a stress intensification factor, to be defined in more detail later. Coble (1970) developed equations for pressure-assisted densification by diffusional mass transport by modifying equations for the creep of dense solids. In these creep models, matter transport is assumed to occur from the grain boundaries under compression to those under tension by lattice diffusion (Nabarro, 1948; Herring, 1950b), or by grain boundary diffusion (Coble, 1963). In densification, matter transport occurs from the grain boundaries to the pore surfaces, but this difference in path length should only affect the geometrical constants in the hot pressing equations. The densification rate equations for hot pressing can also be obtained by replacing the driving force term in the sintering equations by Eq. 2.15. The densification rate in hot pressing by grain boundary or lattice diffusion is predicted to be

(

)

αγ 1 dρ H1DΩφ(m – 1)/2 = pa φ + sv ρ dt GmkT r

[2.17]

where the parameters and geometrical constants are given in Table 2.3. It should be remembered that pa in Eq. 2.17 is the hydrostatic component of the applied stress. Pressure-assisted sintering of metallic materials can involve densification by plastic flow, particularly in the case of hot isostatic pressing (HIP), as well as by diffusion. At sufficiently high applied pressure and sintering temperature, the stress concentration at the particle contacts can exceed the yield strength, leading to instantaneous plastic flow, followed by diffusional mass transport. For plastic flow by dislocation motion, sometimes referred to as power-law creep, an empirical equation that is successful for describing much experimental data is

( )

1 dρ ADlµb paφ n = ρ dt kT µ

[2.18]

where A is a material constant, µ is the shear modulus, b is the Burgers vector, and n is a stress exponent (n ≥ 3) that depends on the mechanism of dislocation motion. Superplastic flow is achieved in some pressure-assisted sintering cycles, and it is found that the deformation strain rate is related to stress by an exponent n = 2. According to Eq. 2.17, at any given density, the ratio of the densification rate in hot pressing (HP) to that in conventional sintering (CS) is . ρ paφ + αγsv /r HP [2.19] . = αγ / r ρ CS sv which indicates that hot pressing is less effective for very fine powders, particularly when they are well compacted prior to hot pressing, because the driving force for



49

sintering of these powders can be greater than the pressure that the hot pressing die can tolerate. However, benefits may still be derived when the applied pressure serves to enhance the rearrangement process or assists in the collapse of large pores. A comparison of Eq. 2.17 and Eq. 2.18 indicates a different dependence of the densification rate on applied stress. For diffusional mass transport, the densification rate increases linearly with applied stress (n = 1), whereas a power-law relation is predicted for plastic flow by dislocation motion (n ≥ 3). The dependence of the densification rate on applied stress provides a reliable method for distinguishing between diffusion and plastic deformation as the rate-controlling mechanisms in pressure-assisted sintering. There is a strong grain size dependence of the densification rate for diffusion mechanisms, whereas densification by plastic deformation is independent of grain size. Therefore, diffusion mechanisms are expected to provide a major contribution to densification at smaller particle sizes and lower applied stresses. The application of an external pressure can activate or enhance mechanisms that are limited or absent during conventional sintering. Particle rearrangement is expected to contribute to densification during the early stage of hot pressing, but it is difficult to analyze theoretically. Grain boundary sliding is necessary to accommodate the diffusion-controlled shape changes in the intermediate and final stages of hot pressing. The stress exponents, grain size dependence, and appropriate diffusion coefficients for the pressure-assisted densification mechanisms are summarized in Table 2.4.

2.5.2 Pressure sintering maps Constitutive equations have been developed to describe densification during pressure-assisted sintering for the various mass transport mechanisms (Swinkels et al., 1983; Arzt et al., 1983; Helle et al., 1985). Using computer calculations and material data (such as surface energies, diffusion coefficients, yield strength, etc.), the constitutive equations were used to generate maps showing the relative contributions of the different mechanisms to densification. Figure 2.10 shows one type of map for HIP of Al2O3 (particle size = 2.5 µm) and for tool steel Table 2.4 Hot pressing mechanisms and the associated exponents and diffusion coefficients (where applicable) Mechanism

Lattice diffusion Grain boundary diffusion Plastic deformation Viscous flow Grain boundary sliding Particle rearrangement a D l

Grain size exponent, m

Stress exponent, n

Diffusion coefficienta

2 3 0 0 1 –

1 1 ≥3 1 1 or 2 –

Dl Dgb Dl – Dl or Dgb –

= lattice diffusion coefficient; Dgb = grain boundary diffusion coefficient.


50


(a)

(b)

2.10 Hot isostatic pressing (HIP) map for (a) Al2O3 powder (particle size = 2.5 µm), and (b) tool steel powder (particle size = 50 µm) at 1200°C. (From Arzt et al., 1983.) © Woodhead Publishing Limited, 2010


51

(particle size = 50 µm) at 1200 °C. The relative density is plotted vs. the applied pressure for isothermal times of ¼, ½, 1, 2, and 4 h. The boundary lines indicate points where two mechanisms make equal contributions to densification. At 1200 °C, densification of both materials is dominated by diffusion. A different plot, density vs. temperature for a constant applied stress of 100 MPa, showed that densification of the tool steel at temperatures lower than 1200 °C was dominated by plastic flow by dislocation motion (Arzt et al., 1983).

2.5.3 Stress intensification factor and sintering stress The stress intensification factor φ in Eq. 2.16, which relates the effective stress pe at the grain boundary to the applied stress pa, is geometrical in origin and should depend on the porosity and the dihedral angle. Several expressions have been proposed for φ (Table 2.5) and, depending on the powder characteristics and packing, one of these relations may be appropriate for fitting pressure-assisted sintering data. A plot of φ vs. ρ for these expressions (Fig. 2.11) shows large differences between the values (Dutton et al., 1995). Except for the model based on monosize spheres, the predicted values for φ can be well fitted by an exponential function of porosity. According to Eq. 2.17, the densification rate during pressure-assisted sintering can be written

Table 2.5 Stress intensification factors for various powder geometries Stress Density range Model intensification factor φ

Reference

1 – ρo ρ2(ρ – ρo)

Arzt et al., 1983

ρ < 0.90 Monosize spherical powder

(1 – ρ)2 ρ < 0.90 ρ(ρ – ρo)2

Monosize spherical powder, including neck growth due to diffusion

Arzt et al., 1983; Helle et al., 1985

1 ρ > 0.90 ρ

Random distribution of isolated pores

Coble, 1967; Coble, 1970

exp[α(1 – ρ)] ρ < 0.90

Free energy minimization for Beeré, 1975; equilibrium shapes of Vieira and Brook, continuous pores 1984

3 – 2ρ ρ < 0.95 ρ

Cubic array of intersecting cylindrical particles

1 ρ < 1.0 ρ5/2

Empirical equation developed Shima and to fit sintering data of spherical Oyane, 1976 Cu particles


Scherer, 1979

52

Sintering of advanced materials 1 dρ H1DΩφ(m + 1)/2 (pα + Σ) = ρ dt GmkT

[2.20]

where Σ is the sintering stress, defined as the equivalent externally applied stress that has the same effect on sintering as the curved surfaces of the pores and grain boundaries. The formulation of the driving force for sintering in terms of a fictitious externally applied stress is advantageous in the analysis of sintering where mechanical stress effects arise, such as in pressure sintering and constrained sintering. It also provides a conceptual basis for designing experiments to measure the driving force for sintering. The sintering stress has been measured experimentally by a zero-creep technique (Gregg and Rhines, 1973; Aigeltinger, 1975), loading dilatometry (Rahaman et al., 1986), and sinter forging (Venkatachari and Raj, 1986). The sintering stress varies inversely as the starting particle size, and has values of ~ 1 MPa for particles with a size of ~1 µm. Figure 2.12 shows data for S vs. ρ for Cu wire (particle size = 30 µm), measured by a zero-creep technique (Gregg and Rhines, 1973). The increase in Σ with increasing values of ρ up to ~0.95 can be attributed to a decrease in pore size, and it is likely that rapid coarsening of the microstructure caused the decrease in Σ above ρ ≈ 0.95.

2.11 Stress intensification factor vs. relative density for various idealized powder geometries given in Table 2.5 and for the data of Shima and Oyane (1976).



53

2.12 Data for the sintering stress vs. relative density for copper particles, determined by the zero-creep technique.

2.6

Effects of material and process variables

The analytical models provide only a qualitative understanding of the densification of real powders. Theoretical and experimental densification rates can differ widely, in large part due to the many simplifications assumed in the models (Exner et al., 1973). Deviations from the model assumptions should be recognized in order to understand how they influence the sintering of real powders.

2.6.1 Particle size distribution and particle packing The use of mixtures of discrete particle sizes or a wide distribution of particle sizes often results in an increase in the packing density of the green article, so the shrinkage required for complete densification is reduced. This reduction in shrinkage is important in industrial sintering of large objects. For the same average particle size, an increase in the width of the particle size distribution leads to an increase in densification of in the earlier stage of sintering (Yeh and Sacks, 1990), presumably due to the presence of the fine particles, as well as fine pores. Densification in the later stage of sintering depends critically on the particle packing. Heterogeneous packing often leads to differential densification and enhanced grain growth (due to the enhanced driving force arising from size difference), so the attainment of high density can be difficult. On the other hand, for homogeneous packing resulting in fine pores with a narrow size distribution, a high final density can be achieved regardless of the width of the initial particle size distribution. For enhanced sintering rates and the attainment of high density, the particles should be homogeneously packed with a high packing density. These packing


54


characteristics produce fine, uniform pores with a small pore coordination number (Fig. 2.3a). Furthermore, the number of particle contacts is maximized, providing many grain boundaries and short diffusion paths for rapid matter transport into the fine pores. Heterogeneous packing leads to a fraction of large pores with a large coordination number (Fig. 2.3b). These large pores are difficult to sinter, and may remain as residual porosity in the final article (Chapter 1). A clear demonstration of these principles was provided by Rhodes (1981). Using a fine Y2O3-stabilized ZrO2 powder (crystallite size ~ 10 nm), Rhodes prepared a suspension and allowed the agglomerates to settle. The fine particles in the supernatant were then used to prepare compacts by gravitational settling in a centrifuge, resulting in homogeneous packing with high packing density (0.74 of the theoretical density). Sintering for 1 h at 1100 °C produced almost complete densification (Fig. 2.13). In comparison,

2.13 Effect of particle packing on the sintering of Y2O3-stabilized ZrO2 powder compacts after 1 h at various temperatures. The compact with the more homogeneous microstructure (formed by centrifugal casting of fine, agglomerate-free particles) reached a far higher density than a compact formed by die-pressing the agglomerated, as-received powder. (From Rhodes, 1981.)



55

compacts prepared by die-pressing of the as-received, agglomerated powder reached a relative density of only 0.95 after sintering for 1 h at 1500 °C. The merits of ‘ordered’ packing vs. ‘random’ packing have been the subject of some discussion. Barringer and Bowen (1982; 1988) developed a processing approach based on the uniform packing of monodisperse, spherical particles. While rapid sintering was achieved at considerably lower temperatures, the compacts could not be sintered to full density (residual porosity ≈5%). A problem is that the uniform consolidation of monodispere particles leads to the formation of small regions with three-dimensional, ordered packing (typical of the packing in crystals), referred to as domains, which are separated by packing flaws (voids) at the domain boundaries. The faster sintering of the ordered regions, when compared to the domain boundaries, leads to differential stresses that cause enlargement of the voids, resulting in residual porosity. Liniger and Raj (1987) suggested that dense random packing of particles with a distribution of sizes may provide an alternative ideal packing geometry for enhanced sintering. When compared to the ordered packing of monodisperse particles, the random structure would be less densely packed than the domains but fluctuations in density should be less severe, leading to homogeneous sintering and the reduction of flaw generation due to differential sintering. Homogeneously packed Al2O3 green bodies formed by colloidal processing of fine powders have in fact been sintered to almost full density at temperatures as low as ~ 1200–1300 °C (Cesarano and Aksay, 1988; Yeh and Sacks, 1990), well below the sintering temperature of compacts formed from similar powders by die-pressing.

2.6.2 Anisotropic sintering shrinkage Anisotropic shrinkage during sintering makes dimensional control of the final article difficult. With proper conditions (e.g., no large temperature gradient in the furnace or friction between the sintering article and the substrate), the sintering process itself is capable of producing very uniform final dimensions. Often, the powder characteristics and the method used to form the powder into the green article provide the major sources of anisotropic shrinkage (density variations in the green article, anisotropy in the pore shape, and alignment of non-equiaxial particles). Thus, when anisotropic sintering occurs, the most useful approach is to identify the causes and, whenever possible, reduce or eliminate them. In cases where it is not possible to eliminate anisotropic shrinkage, the magnitude of the shrinkage anisotropy should be determined and compensated for in the final dimensions. Even when the starting particles have equiaxial (or spherical) shapes, compacts formed by methods such as uniaxial die-pressing can exhibit anisotropic shrinkage. Die-compacted powders often have a pore shape difference between the pressing direction and perpendicular to the pressing direction. The pore shape difference is most pronounced in materials such as metals, polymers, and spray-dried ceramic granules which exhibit plasticity during compaction. Generally, the pore, which is


56


elongated in the direction perpendicular to the pressing direction, tends to shrink more in the direction of elongation, leading to a reduction in the pore shape anisotropy with longer sintering time or temperature (Fig. 2.14) (Exner and Giess, 1988). The effect of pore shape on the shrinkage anisotropy during sintering was modeled by Olevsky and Skorokod (1993), who considered the powder compact to be a linear viscous continuum containing uniformly distributed elliptical pores of the same size. A model for the sintering of uniformly distributed elliptical pores with the same size in a polycrystalline material was developed by Ch’ng and Pan (2005). Both models predict that elongated pores lead to anisotropic shrinkage, and that the shrinkage is greater in the direction of the long axis of the pores. Anisometric or non-equiaxial particles can lead to anisotropic shrinkage if they become aligned or oriented during the forming of the green article (Krug et al., 2002; Shui et al., 2002; Patwardhan and Cannon, 2006). Generally, the shrinkage perpendicular to the direction of alignment is greater than that parallel to the alignment direction. This can be taken to result from faster or preferential matter transport into the pores from the grain boundaries oriented in the direction of the particle alignment. Powder matrices containing anisometric inclusions, such as short fibers, whiskers, or platelets, can also suffer from marked anisotropic shrinkage if the inclusion phase

2.14 Shrinkage anisotropy factor α, equal to the ratio of the axial shrinkage to the radial shrinkage (∆H/Ho)/(∆D/Do), as a function of relative volume shrinkage for two fractions of spheroidized glass particles of size 6 µm and 13 µm, compacted uniaxially at 75 MPa. The data for jagged particles of size 3.5 µm are shown by the dashed curve. (From Exner and Giess, 1988.)



57

becomes oriented during forming of the green body (Hoffmann et al., 1989; Stedman et al., 1993; Roeder et al., 1997). Generally, the shrinkage in the direction of orientation is lower than that perpendicular to the direction of orientation. Numerical models have been developed to simulate the anisotropic shrinkage of a polycrystalline system of elongated particles in two dimensions. For a system of uniformly-packed, elliptical particles, the shrinkage was predicted to be higher in the direction perpendicular to the long axis of the particles (Raj et al., 2002). Another model, which takes into account densification by grain boundary diffusion, grain growth driven by differences in grain boundary curvature, and pore migration by surface diffusion, suggests that the direction of higher (or lower) shrinkage may depend on the particle packing arrangement, as well as on the particle and pore characteristics (Tikare et al., 2005). For a system of aligned, elongated particles of random size and shape (Fig. 2.15a), the shrinkage was predicted to be higher in the direction perpendicular to the elongation (Fig. 2.15b). The shrinkage rate and the anisotropy in the shrinkage rates were found to decrease with time as the grains grew and the microstructure became more isotropic.

(a)

(b)

2.15 (a) Initial, two-dimensional model microstructure of randomlypacked elongated particles with random size and shape, oriented in the X-direction. (b) Shrinkage in the X-direction (parallel to orientation) and Y-direction (perpendicular to orientation) obtained from numerical simulation of sintering. (From Tikare et al., 2005.)


58


2.6.3 Sintering atmosphere Although not considered explicitly in the models, the sintering atmosphere can also have a marked influence on densification rates. When the non-densifying mechanisms dominate, a porous microstructure is favored, whereas the domination of the densifying mechanisms leads to a dense microstructure. A demonstration of these principles is provided by the work of Readey (1990), who studied the sintering of several oxides in oxidizing and reducing atmospheres. As an example, HCl gas in the atmosphere reacts with Fe2O3 to produce gaseous species that enhance vapor transport, and a reduction in the densification rate (Fig. 2.16). In the final stage of sintering, when the pores are isolated, a gas trapped in the pores from the sintering atmosphere (or from reactions within the pores) can limit the final density, and can even lead to pore growth and swelling of the sintering compact. This is particularly the case for an ‘insoluble’ gas which has a low diffusivity through the solid material. Coble (1962) found that that MgO-doped Al2O3 can be sintered to theoretical density in vacuum or in an atmosphere of H2 or O2, which diffuse out to the surface of the solid, but not in He, Ar, or N2 (or, therefore, air), which have a limited solubility in Al2O3. For the case of sintering in an insoluble gas, Eq. 2.6 can be modified to give

(

)

1 dρ H1DΩφ(m – 1)/2 2γsv – pi = ρ dt GmkT r

[2.21]

where pi is the pressure of the gas in the pores. Sintering stops when pi = 2γsv/r, so the compact reaches a limiting porosity Pf given by

2.16 Shrinkage versus time for Fe2O3 powder compacts sintered at 1000°C in different partial pressures of HCl. (From Readey, 1990.)


Kinetics and mechanisms of densification Pf = Po

( ) poro 2γsv

3/2

59 [2.22]

where po is the pressure of the sintering atmosphere, ro is the radius of the pores when they become isolated, and Po is the porosity (~0.10) when the pores become isolated. According to Eq. 2.22, the limiting porosity is controlled by po and ro. In practice, sintering in a vacuum (where applicable) and homogeneous packing of fine particles (giving fine pores) can improve the final density. After the limiting density has been reached, upon further sintering, grain growth and pore coalescence can lead to swelling of the compact (Fig. 2.17), as observed for several ceramic and metal powders (Gupta and Coble, 1968; Amato, 1971; Bose and German, 1988).

2.6.4 Non-isothermal sintering The models commonly assume isothermal sintering but, in practice, most sintering studies are either performed at a constant heating rate or include a significant portion of constant heating rate sintering. According to Eq. 2.17, the densification rate during sintering is 1 dρ H1DΩφ(m + 1)/2S = ρ dt GmkT

[2.23]

where the temperature dependence for the densification process is incorporated in the diffusion coefficient given by

( )

D = Do exp –

Qd RT

[2.24]

where Do is a constant, R is the gas constant, and Qd is the activation energy for the densification process. Experimentally, Σ is only weakly dependent on ρ (Rahaman

2.17 Schematic diagram showing the densification of a powder compact with an insoluble gas in the pores. The density goes through a maximum with time, as a result of coarsening with the trapped gas in the pores.


60


et al., 1986), and for a powder compacted to a given green density, G is dependent on the density only, so a rearrangement of Eq. 2.23 gives (Chu et al., 1991): k H1DoΩΣ

∫

ρ ρo

Gm(ρ)

t

ρφ(m + 1)/2(ρ)

dρ = ∫ t

1

oT

( )

exp –

Qd

RT

dt

[2.25]

The integral on left-hand side of Eq. 2.25 contains density-dependent terms only and can be taken to quantify the effects of the microstructure on densification, whereas the right-hand side depends only on Q and the temperature–time schedule. Putting F(ρ) =

k H1DoΩΣ

and

Gm(ρ)

∫ ρo ρφ(m + 1)/2 (ρ) dρ ρ

( )

Q t Θ(T, t) = ∫t 1 exp – d dt oT RT

[2.26]

[2.27]

then Eq. 2.25 can be written F(ρ) = Θ(T,t)

[2.28]

The relationship between ρ and F(ρ) is referred to as the master sintering curve. Using the equality in Eq. 2.28, the master sintering curve can be constructed from a series of sintering experiments for different times or temperatures. Each experiment gives the measured value of ρ and the corresponding value of Θ(T,t)

2.18 Master sintering curve for ZnO constructed from constant heating rate sintering data for the heating rates shown. (From Su and Johnson, 1996.)



61

found by performing the integration shown in Eq. 2.27 for the temperature–time schedule if Q is known or can be approximated. The most economical method of generating the master sintering curve is to perform constant heating rate sintering experiments at 4 or 5 heating rates using a dilatometer (Chu et al., 1991). Figure 2.18 shows the master sintering curve determined from constant heating rate sintering data for ZnO (Su and Johnson, 1996). Once the master sintering curve has been determined for a particular powder system, it can be used to predict the sintering behavior of similar powder compacts under arbitrary temperature–time schedules. In this way, it can serve a useful function for designing sintering schedules to reach a required final density. However, the limitations of the procedure should be recognized. The procedure should be applied only to compacts of the same starting powder which have been consolidated to the same green density by the same forming method. Furthermore, it is assumed that the grain size and geometrical parameters are dependent on the density only and that one diffusion mechanism dominates in the sintering process.

2.7

Conclusions

The factors that control the densification kinetics of porous single-phase materials have been reviewed. Because of the simplified assumptions, the theoretical models provide only a qualitative understanding of the effects of particle size, temperature, and applied pressure on the densification rates of real powder compacts. Numerical simulations are being used increasingly to examine some of the complexities of sintering, such as use of more realistic geometries and sintering with concurrent mechanisms. The effects of key variables not considered explicitly in the theoretical models, such as particle packing, particle size distribution, anisotropy in densification, sintering atmosphere, and non-isothermal sintering, were discussed.

2.8

Sources of further information and advice

German, R. M. (1996), Sintering theory and practice, New York, Wiley. Rahaman, M. N. (2007), Sintering of ceramics, Boca Raton, FL, CRC Press.

2.9

References

Aigeltinger, E. H. (1975), ‘Relating microstructure and sintering force’, Internat J Powder Metall Powder Technol, 11, 195–203. Amato, I. (1971), ‘The effect of gas trapped within pores during sintering and density regression of ceramic bodies’, Mater Sci Eng, 7, 49–53. Andrievski, R. A. (1994), ‘Compaction and sintering of ultrafine powders’, Internat J Powder Metall, 30, 59–66. Arzt, E., Ashby, M. F., and Easterling, K. E. (1983), ‘Practical applications of hot isostatic pressing diagrams’, Metall Trans, 14A, 211–21.


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Ashby, M. F. (1974), ‘A first report on sintering diagrams’, Acta Metall, 22, 275–89. Barringer, E. A. and Bowen, H. K. (1982), ‘Formation, packing, and sintering of monodisperse TiO2 powders, J Amer Ceram Soc, 65, C199–201. Barringer, E. A. and Bowen, H. K. (1988), Effect of particle packing on the sintered microstructure. Appl Phys A, 45, 271–75. Beeré, W. (1975), ‘The second stage sintering kinetics of powder compacts’, Acta Metall, 23, 139–45. Bose, A. and German, R. M. (1988), ‘Sintering atmosphere effects on tensile properties of heavy alloys’, Metall Trans, 19A, 2467–76. Bouvard, D. and McMeeking, R. M. (1996), ‘Deformation of interparticle necks by diffusion-controlled creep’, J Am Ceram Soc, 79, 666–72. Brett, J. and Seigle, L. (1963), ‘Shrinkage of voids in copper’, Acta Metall, 11, 467–74. Bross, P. and Exner, H. E. (1979), ‘Computer simulation of sintering processes’, Acta metall, 27, 1013–20. Cesarano, J., III and Aksay, I. A. (1988), ‘Processing of highly concentrated aqueous α-alumina suspensions stabilized with polyelectrolytes’, J Amer Ceram Soc, 71, 1062–67. Ch’ng, H. N. and Pan, J. (2005), ‘Modeling microstructural evolution of porous polycrystalline materials and a numerical study of anisotropic sintering’, J Comput Phys, 204, 430–61. Chu, M.-Y., Rahaman, M. N., De Jonghe, L. C., and Brook, R. J. (1991), ‘Effect of heating rate on sintering and coarsening’, J Am Ceram Soc, 74, 1217–25. Coble, R. L. (1958), ‘Initial sintering of alumina and hematite’, J Am Ceram Soc, 41, 55–61. Coble, R. L. (1961), ‘Sintering crystalline solids. I. Intermediate and final stage diffusion models’, J Appl Phys, 32, 787–92. Coble, R. L. (1962), ‘Sintering of alumina: effect of atmosphere’, J Amer Ceram Soc, 45, 123–27. Coble, R. L. (1963), ‘A model for boundary diffusion controlled creep in polycrystalline materials’, J Appl Phys, 34, 1679–82. Coble, R. L. (1967), ‘Mechanisms of densification during hot pressing’, in Sintering and related phenomena, Kuczynski, G. C., Hooton, N. A., and Gibbon, C. F., Eds., New York, Gordon and Breach, pp. 329–47. Coble, R. L. (1970), ‘Diffusion models for hot pressing with surface energy and pressure effects as driving forces’, J Appl Phys, 41, 4798–807. Coblenz, W. S., Dynys, J. M., Cannon, R. M., and Coble, R. L. (1980), ‘Initial stage solid state sintering models. A critical analysis and assessment’, in Sintering processes, Mater Sci Res, Vol. 13, Kuczynski, G. C., Ed., New York, Plenum Press, pp. 141–57. Dutton, R. E., Shamasundar, S., and Semiatin, S. L. (1995), ‘Modeling the hot consolidation of ceramic and metal powders’, Metall Mater Trans A, 26, 2041–51. Exner, H. E. (1979), ‘Principles of single phase sintering’, Rev Powder Metall Phys Ceram, 1, 7–251. Exner, H. E. and Giess, E. A. (1988), ‘Anisotropic shrinkage of cordierite-type glass powder cylindrical compacts’, J Mater Res, 3, 122–5. Exner, H. E., Petzow, G., and Wellner, P. (1973), ‘Problems in the extension of sintering theories to real systems’, in Sintering and Related Phenomena, Kuczynski, G. C., Ed., New York, Plenum Press, pp. 351–62. Fortes, M. A. (1982), ‘The kinetics of powder densification due to capillary forces’, Powder Metall Internat, 14, 96–110. Frenkel, J. (1945), ‘Viscous flow of crystalline bodies under the action of surface tension’, J Phys (Moscow), 5, 385–91.



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Gregg, R. A. and Rhines, F. N. (1973), ‘Surface tension and the sintering force in copper’, Metall Trans, 4, 1365–74. Gupta, T. K. and Coble, R. L. (1968), ‘Sintering of ZnO: II, density decrease and pore growth during the final stage of the process’, J Am Ceram Soc, 51, 525–8. Helle, A. S., Easterling, K. E., and Ashby, M. F. (1985), ‘Hot isostatic pressing diagrams: new developments’, Acta Metall, 33, 2163–74. Herring, C. (1950a), ‘Effect of change of scale on sintering phenomena’, J Appl Phys, 21, 301–3. Herring, C. (1950b), ‘Diffusional viscosity of a polycrystalline solid’, J Appl Phys, 21, 437–45. Hoffmann, M. J., Nagel, A., Greil, P., and Petzow, G. (1989), ‘Slip casting of SiC-whiskerreinforced Si3N4’, J Am Ceram Soc, 72, 765–9. Huppmann, W. J. and Riegger, H. (1975), ‘Modeling rearrangement processes in liquidphase sintering’, Acta Metall, 23, 965–71. Huppmann, W. J. and Riegger, H. (1977), ‘Liquid-phase sintering of the model system W–Ni’, Internat J Powder Metall Powder Technol, 13, 243–47. Ivensen, V. A. (1973), Densification of metal powders during sintering, New York, Consultants Bureau, 1973. Johnson, D. L. (1970) ‘A general model for the intermediate stage of sintering’, J Am Ceram Soc, 53, 574–7. Kang, S.-J. L., Kaysser, W. A., Petzow, G., and Yoon, D. N. (1984), ‘Elimination of pores during liquid-phase sintering of Mo-Ni’, Powder Metall, 27, 97–100. Kingery, W. D. (1959), ‘Densification during sintering in the presence of a liquid phase, I. Theory’, J Appl Phys, 30, 301–6. Kingery, W. D. and Berg, M. (1955), ‘Study of the initial stages of sintering solids by viscous flow, evaporation – condensation, and self-diffusion’, J Appl Phys, 26, 1205–12. Kingery, W. D. and Narasimhan, M. D. (1959), ‘Densification during sintering in the presence of a liquid phase, II. Experimental’, J Appl Phys, 30, 307–10. Krug, S., Evans, J. R. G., and ter Maat, J. H. H. (2002), ‘Differential sintering in ceramic injection molding: particle orientation effects’, J Europ Ceram Soc, 22, 173–81. Kuczynski, G. C. (1949), Self-diffusion in sintering of metal particles, Trans AIME, 185, 169–78. Kuczynski, G. C. (1976), Statistical theory of sintering, Z Metallkunde, 67, 606–10. Lee, S. M., Chaix, J.-M., Martin, C. L., Allibert, C. H., and Kang, S.-J. L. (1999), ‘Computer simulation of particle rearrangement in the presence of liquid’, Met Mater, 5, 197–203. Liniger, E. and Raj, R. (1987), ‘Packing and sintering of two-dimensional structures made from bimodal particle size distributions’, J Amer Ceram Soc, 70, 843–9. Mackenzie, J. K. and Shuttleworth, R. (1949), ‘A phenomenological theory of sintering’, Proc Phys Soc (London), 62, 833–52. Morgan, C. S. (1973), ‘Material transport by dislocation motion in sintering’, Phys Sintering, 5, 31–40. Nabarro, F. R. N. (1948), ‘Deformation of crystals by the motion of single ions’, in Report of a conference on the strength of solids, London, Physical Society, 75–90. Nicholls, F. A. and Mullins, W. W. (1965), ‘Morphological changes of a surface of revolution due to capillary-induced surface diffusion’, J Appl Phys, 36, 1826–35. Ogbuji, L. U. J. T. (1986), ‘Finite element analysis of sintering stress’, Sci Sintering, 18, 21–31. Olevsky, E. A. and Skorokod, V. (1993), ‘Deformation aspects of anisotropic-porous bodies in sintering’, J de Physique IV, 3, 739–42. Pan, J., Le, H., Kucherenko, S., and Yeomans, J. A. (1998), ‘A model for the sintering of particles of different sizes’, Acta Mater, 46, 4671–90.


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Patwardhan, J. S. and Cannon, W. R. (2006), ‘Factors influencing anisotropic sintering in tape-cast alumina: effect of processing variables’, J Am Ceram Soc, 89, 3019–26. Rahaman, M. N., De Jonghe, L. C., and Brook, R. J. (1986), ‘Effect of shear stress on sintering’, J Am Ceram Soc, 69, 53–8. Raj, P. M., Odulana, A., and Cannon, W. R. (2002), ‘Anisotropic shrinkage during sintering of particle-oriented systems – numerical simulations and experimental studies’, Acta Mater, 50, 2559–970. Readey, D. W. (1990), ‘Vapor transport and sintering’, Ceramic Trans, 7, 86–110. Rhines, F. N. and DeHoff, R. T. (1984), ‘Channel network decay in sintering’, in Sintering and heterogeneous catalysis, Materials Science Research, Vol. 16, Kuczynski, G. C., Miller, A. E., and Sargent, G. A., Eds., New York, Plenum Press, 49–61. Rhodes, W. W. (1981), ‘Agglomerate and particle size effects on sintering of yttriastabilized zirconia’, J Amer Ceram Soc, 64, 19–22. Roeder, R. K., Trumble, K. P., and Bowman, K. J. (1997), ‘Microstructure development in Al2O3-platelet-reinforced Ce-ZrO2/Al2O3 composites’, J Am Ceram Soc, 80, 27–36. Scherer, G. W. (1977), ‘Sintering of low-density glasses: I, theory’, J Am Ceram Soc, 60, 236–9. Scherer, G. W. (1979), ‘Sintering of inhomogeneous glasses: application to optical waveguides’, J Non-Cryst Solids, 34, 239–56. Shima, S. and Oyane, M. (1976), ‘Plasticity theory for porous metals’, Int J Mech Sci, 18, 285–91. Shui, A., Uchida, N., and Uematsu, K. (2002), ‘Origin of shrinkage anisotropy during sintering for uniaxially pressed alumina compacts’, Powder Technol, 127, 9–18. Stedman, S. J., Evans, J. R. G., Brook, R. J., and Hoffmann, M. J. (1993), Anisotropic sintering shrinkage in injection-molded composite ceramics’, J Europ Ceram Soc, 11, 523–32. Su, H. and Johnson, D. L. (1996), ‘Master sintering curve: a practical approach to sintering’, J Am Ceram Soc, 79, 3211–17. Svoboda, J. and Riedel, H. (1995), ‘New solutions describing the formation of interparticle necks in solid-state sintering’, Acta Metall Mater, 43, 1–10. Swinkels, F. B. and Ashby, M. F. (1981), ‘A second report on sintering diagrams’, Acta Metall, 29, 259–81. Swinkels, F. B., Wilkinson, D. S., Arzt, E., and Ashby, M. F. (1983), ‘Mechanisms of hot isostatic pressing’, Acta Metall, 31, 1829–40. Tikare, V., Braginsky, M., Olevsky, E., and Johnson, D. L. (2005), ‘Numerical simulation of anisotropic shrinkage in a 2D compact of elongated particles’, J Am Ceram Soc, 88, 59–65. Tikkanen, M. H. and Makipirtti, S. A. (1965), ‘A new phenomenological sintering equation’, Internat J Powder Metall, 1, 15–19. Venkatachari, K. R. and Raj, R. (1986), ‘Shear deformation and densification of powder compacts’, J Am Ceram Soc, 69, 499–506. Vieira, J. M. and Brook, R. J. (1984), ‘Kinetics of hot pressing: the semilogarithmic law’, J Am Ceram Soc, 67, 245–9. Yeh, T. S. and Sacks, M. D. (1990), ‘Effect of green microstructure on sintering of alumina’, Ceramic Trans, 7, 309–31. Yoon, D. N. and Huppmann, W. J. (1979), ‘Grain growth and densification during liquidphase sintering of W-Ni’, Acta metall, 27, 693–98. Zhang, W. and Schneibel, J. H. (1995), ‘The sintering of two particles by surface and grain boundary diffusion – a two-dimensional numerical study’, Acta Metall Mater, 43, 4377–86.


3 Path and kinetics of microstructural change in simple sintering R. T. D eHoff, University of Florida, USA Abstract: Simple sintering is here defined as the process by which a loose stack of chemically unchanging powder is transformed toward a fully dense block by heating at temperatures below the melting point. The microstructural description of the process is described in terms of the evolution in the geometry of two feature sets: the pore phase and the grain boundary network. The analysis is carried as far as possible without simplifying geometric assumptions, an approach which F. N. Rhines described as ‘microstructological’, and which leads to a description of the kinetics of densification which is free of simplifying geometric assumptions. Key words: sintering, kinetics, microstructure, stereology.

3.1

Introduction

The sintering process is traditionally viewed as occurring in three stages. The first stage begins with the formation of contacts in a loose powder stack which become interparticle welds that grow with time at the sintering temperature. In the second stage the pore network gradually disconnects itself as channels achieve unstable shapes and close. At the onset of the third stage the pore network has completed its disconnection and only isolated pores remain. In the third stage, these isolated pores shrink and disappear. All three stages are accompanied by densification, i.e., the macroscopic shrinkage of the body. This evolution is characteristic of the simplest of sintering processes, and can exhibit significant variations if, e.g., there is a second phase present that forms a liquid, or there is an insoluble atmosphere that is trapped in isolated pores and may in fact lead to swelling in the third stage, or if vapor transport makes an important contribution to moving atoms in the system. The focus of this presentation is upon simple sintering of a single phase crystalline solid. A crucial aspect of this evolution in a crystalline system is the simultaneous formation and evolution of a grain boundary network. The interaction of the pore and grain boundary networks plays a key role in the path of microstructural evolution, particularly in the late stages of the process. In this presentation the approach taken to the description of this process is based upon a viewpoint which F. N. Rhines called ‘microstructology’. In his view a microstructural state, or a sequence of states in a process, is described in terms of geometric properties that have unambiguous meaning for real three dimensional microstructures, and are also measurable with stereological techniques. 65 © Woodhead Publishing Limited, 2010

66


This approach leads to a visualization of the overall evolution in terms of a cell structure, in which each particle and its associated porosity constitute a cell in a space-filling tessellation of the system. In this visualization the three stages of sintering evolve seamlessly in a single continuous description of the process. The kinetics of the process is then formulated in terms of a second, imbedded cell structure, also space filling, in which each face in the primary cell structure is associated with a bipyramid cell, with the face as its base, that encompasses the part of the volumes of the two particles and their associated porosity that define the face in which all of the transport occurs that is responsible for local evolution. The underlying ‘microstructology’ philosophy in this approach dictates that it be formulated as far as possible without geometric simplification or idealization.

3.2

The description of microstructural evolution

The quantitative description of microstructural evolution begins with the description of individual microstructural states along the path. A microstructural state is first described qualitatively, with a list of the features – points, lines, surfaces and volumes – that are known to exist in the structure. This state is then made quantitative by assigning, and then measuring, geometric properties to each of the classes of features on the list. In the case of simple sintering the feature list is: • Volumes: Solid phase, α Pore phase, p • Surfaces: Pore solid interfaces, pα Grain boundaries, αα • Triple lines: Lines of intersection between grain boundaries and the pore-solid surface, ααp Triple lines in the grain boundary network, ααα • Quadruple points: Quadruple points in the grain boundary network, αααα Quadruple points where grain edges intersect the pore surface, αααp. In each case the notation reflects the nature of the volume entities (pore ore solid) whose incidence forms the feature. On a section through the structure volumes appear as areas (α and p), surfaces appear as line traces (pα and αα), and triple lines appear as triple points (ααα and ααp). Quadruple points cannot be observed on a sectioning plane, but nonetheless play an important role in the evolution of the structure. These feature classes are illustrated for a typical two-dimensional section in Fig. 3.1.


Path and kinetics of microstructural change

67

3.1 Two-dimensional section through a three-dimensional partially sintered structure illustrating the associated feature sets.

Quantitative information can be obtained by applying stereological methods to each of these feature classes.1 Each of the feature classes listed above has associated geometric properties which are unambiguously defined (Table 3.1). Volume, V, surface area, S, and line length, L are all familiar measures of extent of three, two and one-dimensional features in three-dimensional space. Number N and connectivity C are topological properties of the three-dimensional pore network; N is the number of disconnected parts of the pore network, while C is the number of extra connections within the network. Connectivity is particularly important in the sintering process, since the entire second stage is characterized by a decrease in the connectivity of the pore network from its initial value in the loose powder stack toward zero, which marks the beginning of the third stage. The integral mean curvature, M, is related to the distribution of mean surface curvature values, H, on the pore_solid interface,1 H≡

( )

1 1 1 + 2 r1 r2

[3.1]

where r1 and r2 are the local principle normal curvatures at any point on the surface, and


68


Table 3.1 Stereologically accessible geometric properties of feature classes in simple sintering Feature

Symbol Property

Solid phase, α Pore phase, p Pore-solid surface, p#ba Grain boundary surface, αα Triple line, ααp Triple line, ααα Quadruple point, αααp Quadruple point, αααα

VVα VVp CVp NVp SVpα MVpα pα SVαα LVααp LVααα NVαααp NVαααα

Volume fraction Volume fraction (= 1 – VVα) Connectivity per unit volume Number per unit volume Surface area per unit volume Integral mean curvature per unit volume Average mean surface curvature (= MVpα/SVpα) Surface area per unit volume Length of line per unit volume Length of line per unit volume Number of quadruple points per unit volume Number of quadruple points per unit volume

M ≡ ∫ ∫S H dS

[3.2]

is defined by the integral of H over pore_solid surface area. This somewhat abstruse property is included because: • It is one of four properties of three-dimensional features called the Minkowski functionals (V, S, M and C) that have unambiguous geometric meaning; • It is measured by the classic counting measurements of stereology;1 • It is related to the local mean curvature H, which in thermodynamics is the local geometric property determining the mechanical effects that control processes, such as sintering, that are driven by ‘capillarity’ effects.2 The average mean surface curvature may be defined to be ≡

∫ ∫S H dS = ∫ ∫S dS

M

[3.3]

S

Microstructural evolution for any process can be quantitatively described in terms of: • The path of microstructural change, which is the sequence of geometric states through which the system passes, and • The kinetics of traverse of that path.

3.3

Path of microstructural change in sintering

In the case of the sintering process, individual microstructural states are quantitatively characterized to be the set of measurables shown in Table 3.1. One of these variables is chosen as a measure of the extent of the process; in sintering



69

the obvious variable is the volume fraction, VVp, of the pore network, which has an initial value in the loose powder stack and proceeds monotonically to zero at full density. The path of microstructural change may then be represented by a series of plots of each of the variables versus the volume fraction.3 Measurements of connectivity and number of pores3 have shown that in a typical loose stack of equiaxed narrow size distribution powder the initial volume fraction of porosity is about 0.35. The transition to second stage occurs at slightly less than 0.25, and the third stage begins at about 0.08. The first stage is characterized primarily by the growth of the initial particle contacts into saddle-shaped necks between particles that spread over the particle surfaces. The path of microstructural change is described by the changes in properties with volume fraction during this stage: N p CVp

the number of separate parts of the pore network remains at 1. the connectivity increases slightly from its loose stack value as densification brings more particles into contact. pα SV the surface area per unit volume of the pore-solid interface also increases slightly as densification brings more particles into a given volume (the surface area per gram of powder changes very little as saddle-shaped neck surfaces replace convex particle surface). MVpα the integral mean curvature of the pore-solid interfaces is positive in the loose stack (surface elements are convex with a positive mean curvature) and decreases as spreading saddle-shaped necks, which have a negative mean curvature, replace convex particle surface elements. pα the average mean surface curvature of the pore-solid interfaces has the initial value of the convex loose powder particles and decreases as M decreases. SVαα the surface area per unit volume of grain boundaries in the system is initially zero, assuming the particles are single crystals. Grain boundaries form at points of contact and lengthen radially at the roots of interparticle necks as they grow. LVααp the ααp triple line circles the grain boundary edge in the interparticle necks and increases as the necks grow. There are no grain edges (ααα) or quadruple points (αααp and αααα) formed in the first stage of sintering. The second stage is characterized primarily by the disconnection of the pore network as channels in the network achieve a shape instability and close. The path of microstructural change during this stage: N p CVp SVpα

the number of separate parts of the pore network remains at 1. the connectivity decreases precipitously from its essentially loose stack value toward zero as channels in the pore network pinch off. the surface area per unit volume of the pore-solid interface decreases rapidly and linearly with volume fraction.


70


MVpα

the integral mean curvature of the pore-solid interface initially continues to decrease, then passes through a minimum toward the end of the second stage. pα the average mean surface curvature of the pore-solid interfaces has become negative early in the second stage as saddle surface elements outweigh convex elements and concave surface elements form at closed channel ends, and continues to increase in a negative direction. SVαα the surface area per unit volume of grain boundaries continues to increase as necks grow and the grain boundary network begins to form. ααp LV the ααp triple lines occur where grain boundaries intersect the pore surface. Their length initially increases, then passes through a maximum in the second stage. LVααα channels in the network typically result from the arrangement of three or more interparticle necks around an axis of a channel. When the channel closes, the grain boundaries at the associated necks become incident and react to form one or more ααα triple lines. Thus, the length of these lines increases as channels close during the second stage. αααp NV αααp quadruple points form at the intersection of ααα line segments and the pore surface. Initially each new ααα triple line segment formed as a result of channel closure processes forms two αααp quadruple points, one at each end of the line. Although, to the author’s knowledge, this property has never been measured for any evolving pore structure, it is likely that this number increases during the early part of the second stage. Its value must eventually pass through a maximum since at full density, this number is zero. αααα αααα NV quadruple points are an integral part of the grain boundary network in a fully dense polycrystal formed by the incidence of four ααα triple lines. Each vertex on a grain in such a structure is an αααα quadruple point. In a partially sintered structure an αααα quadruple point may form as a result of the encounter of two αααp quadruple points as the structure evolves. As grain growth occurs the decrease in the number of grains in the structure carries with it a decrease in the number of αααα quadruple points. As the second stage ends, a sufficient fraction of channels have closed to begin to isolate small pores from the network. The second stage ends when the connectivity of the remaining network reaches zero and all of the porosity is in the form of isolated pores. These may shrink and disappear during the third stage. Alternatively, if the pores contain insoluble gases, they may undergo a coarsening process and the attainment of full density is elusive. Assuming the former case, the path of microstructural change is: Np

the number of separate parts of the pore network increases, passes through a maximum and goes to zero at full density.



71

CVp SVpα

the connectivity remains at zero. the surface area per unit volume of the pore-solid interface decreases toward zero. MVpα the integral mean curvature of the pore-solid interface remains negative but increases toward zero. pα the average mean surface curvature of the pore-solid interfaces becomes increasingly negative as the pores shrink. SVαα the surface area per unit volume of grain boundaries decreases as the now fully formed grain boundary network allows grain growth (coarsening) to occur. LVααp provides an indicator of the extent to which the pores lie on grain boundaries; the length decreases to zero as the porosity disappears. LVααα decreases gradually as the grain boundary network coarsens. NVαααp must decrease toward zero as porosity shrinks. NVαααα must decrease as grains grow.

3.4

Cell structure visualization of the path

Overall evolution through the three stages may be visualized in terms of a tessellation of the structure into cells, each containing at the outset one particle and its associated porosity. Consider a loose powder stack and its associated connected pore network. A medial axis surface transform4 identifies the locus of points within the pore phase that are locally equidistant from the solid surface. These points form a set of surfaces that intersect at triple lines in the pore phase which themselves consist of points that are equidistant from three solid surfaces; these triple lines intersect at quadruple points that are equidistant from four solid surfaces. Taken together, these elements form a tessellation of three-dimensional space – a construction that divides it into polyhedral cells – such that • Each cell contains one particle; • A cell face passes through each point of contact. In a stack of more or less equal sized, equiaxed particles it has been shown that there are about six contacts per particle. Analyses of tessellations of threedimensional space generated with some random component (e.g., studies of naturally occurring cell structures like grains is a polycrystal) show that the average number of faces per cell is typically between thirteen and fourteen. Thus about half of the faces in the initial tessellation are equidistant from particle pairs that are not (yet) in contact. The qualitative path of microstructural change in sintering may be followed by focusing on the changes that occur in a typical cell in this tessellation. An individual cell showing a particle and its associated pore volume is sketched in Fig. 3.2a; Fig. 3.2b shows this cell imbedded in the neighboring structure. Evolution of this cell structure is sketched in Fig. 3.3. In the first stage, points


72


3.2 A single cell in the tessellation of a three-dimensional partially sintered structure used to visualize the sintering process: (a) the separated cell; (b) the cell embedded in the structure.

3.3 Evolution of the microstructure during simple sintering visualized for a typical cell in the tessellation. Grain boundaries (a) spread over the cell faces (b) and (c), touching the edges when channels close o produce aaa triple lines (d), eventually forming isolating pores (e) which shrink (f) as full density is approached.



73

of contact form grain boundaries which extend radially over their cell face as the contacts grow. The second stage begins when three adjacent necks come into contact at a cell edge, a triple line in the tessellation. This event is associated with the closure of the channel between the three particles, Fig. 3.4, forming the first element of ααα triple line and producing αααp quadruple points at the ends of the lines. Channels incident upon four or more particles (and thus four or more interparticle necks) will achieve shape instability and close later in the process. Closure of a fourth channel produces two ααα triple lines, four αααp quadruple points and a new αα face between two grains not previously in contact. Throughout the first and second stages grain boundaries continue to spread over the surfaces of the tessellation as the structure densifies. Eventually all of the triple lines in the tessellation are involved in the formation of ααα line segments, indicating that all of the channels have closed and the connectivity has dropped to zero. In the simplest ideal scenario the pores are isolated at the cell corners where they ultimately shrink and disappear. This simple picture may be complicated by grain growth.

3.4 Contacts between particles (a) grow (b) and (c) until they touch along a channel (d). Closure of a channel between three particles is accompanied by the incidence of three grain boundaries to form an aaa triple line.


74


In a single-phase polycrystal grain growth, or more aptly grain coarsening, is evidenced by an increase in the average grain volume and, since the grain structure is space filling, a decrease in the number of grains. This latter is a topological process usually associated with the shrinkage and disappearance of small tetrahedral grains, sometimes designated as a type I topological process.5 In order to maintain the supply of tetrahedral grains two other topological processes, type II (grain encounter) and type III (grain separation), must occur throughout grain growth. Type II processes, initially involving αααp quadruple points, are responsible for producing new faces in the grain boundary network and grain boundary quadruple points, αααα. If there is a second phase in the microstructure (porosity in the case of sintering) a broad spectrum of paths of microstructural evolution may result, ranging from ‘normal’ grain growth in which the size distribution of grains simply coarsens, to ‘abnormal’ to ‘exaggerated’ grain growth, in which a few grains grow comparatively rapidly at the expense of the others. The selection of the path for a given system is controlled by ‘Zener pinning’6 derived from the interaction of the pore-solid and grain boundary surfaces in the system and depends upon the relative interfacial energies and the geometry (volume fraction, size distribution, spatial distribution) of the second phase. Grain growth plays an important role in the evolution of the pore structure in the late stages of sintering. Densification results from the transfer of vacancies from the pore-solid interface to the grain boundaries where their annihilation produces displacements that result in the change in volume of the system. If the pores remain on the grain boundary network then the vacancy sources (pore-solid interface) and sinks (grain boundaries) remain close and diffusion length scales are short. If the grain boundaries move away from the pores communication between source and sinks is more restricted. Thus, grain growth is to be minimized if the goal of processing is full density.

3.5

The thermodynamics of sintering

The macroscopic ‘driving force’ for simple sintering is the reduction in surface energy associated with the decrease in the pore-solid surface area. This driving force manifests itself locally at each element of surface on the interface as a shift in the chemical potential of each component from the value it has for a flat interface in the same system. The magnitude and direction of this shift is shown in thermodynamics to be proportional to the value of the local mean curvature, H, at the surface element. Assuming local equilibrium exists at each interfacial element, the chemical potential of vacancies in a volume element adjacent to a curved surface element is given by2 µv(H) = µv0 + 2 γ VH

[3.4]

where µv0 is the chemical potential of vacancies adjacent to a flat surface at the temperature and external pressure of the system, γ is the specific interfacial free



75

energy and V is the molar volume of the solid phase. Since vacancies form a dilute solution, this shift in chemical potential translates to a shift in the molar concentration of vacancies cv(H) from the value in the same system with flat interfaces cv02 (i.e. a system with a flat surface for which H = 0): cv(H) = cv0 –

2 γ V cv0 H k T

[3.5]

where k is Boltzmann’s constant and T is the absolute temperature. Thus it is shown that the distribution of vacancy concentrations in volume elements adjacent to the pore-solid interface is determined by the distribution of local mean curvature values on the surface. For convex surface elements where the local stress state is compressive cv(H) < cv0; for concave surface elements where the local stress state is dilatational cv(H) > cv0; for saddle elements, for which H may be positive or negative, cv(H) may be larger or smaller than cv0. If there are elements on the saddle surface where H = 0 (curvatures are equal but opposite signs) cv(H = 0) = cv0. In the vicinity of ααp lines, where the negative principle curvature on the surface is larger, H is negative, and the local vacancy concentration is higher than the bulk value. Proceeding away from the triple line one encounters a linear boundary on the surface where the negative and positive principle curvatures become equal and the mean curvature H = 0. At this locus of points throughout the structure the surface concentration equals the bulk value. Further away from the triple line, where the negative principle curvature is smaller or positive, the local vacancy concentration is lower than the bulk value. Further still one encounters a line in the surface where the negative principle curvature passes through zero; this is the boundary of saddle surface in the system. Beyond this boundary the surface is convex with both curvatures positive. This distribution of vacancy concentrations provides part of the boundary conditions for the distribution of vacancy flows in the system. Surface elements on one side of the boundary lines defined by H = 0 are thus sources for vacancies; elements on the other side are sinks, as are the grain boundaries in the system. Vacancies in the flow pattern delivered to the grain boundaries produce densification; those delivered to other pore-solid surface elements produce only surface rounding. In simple sintering a crucial additional influence on the vacancy flow pattern is provided by the grain boundaries in the system, which generally act as sinks. Indeed it is the annihilation of vacancies at grain boundaries that is entirely responsible for densification of the system. In the development of a description of the kinetics of densification it will be necessary to identify the subset of surface elements with negative mean curvature (sources, lying between the curve defined by H = 0 and the ααp triple lines) that communicate with the grain boundaries in the system. The total area of these surface elements, Sδαp, is a crucial parameter in the development.


76


3.6

Kinetics of densification

A variety of mechanisms has been proposed as controlling the sintering process: • • • • •

Volume diffusion Grain boundary diffusion Surface diffusion Vapor transport Plastic deformation.

Each may have a role to play in any given system. Plastic deformation control is thought to make a negligible contribution since the stresses generated by surface tension are too small. Vapor transport may dominate if the solid phase has a high vapor pressure; however, vapor transport cannot produce densification since both sources and sinks are on the pore surface. Where this operates the initial network may smooth out, then coarsen without a change in volume. (Coarsening to produce an increase in the scale of a connected network is an interesting scenario in microstructural evolution which, to the author’s knowledge, has not been explored.) The same limitation applies to surface diffusion. Only volume diffusion and grain boundary diffusion may result in densification, i.e., a decrease in the volume of the structure. Densification is defined to be a decrease in the volume of the pore-solid network. This shrinkage occurs more or less uniformly throughout the system. Locally this process is due to the annihilation of vacancies at grain boundaries. In the cell structure visualization a part of the total area of faces in the tessellation is covered by grain boundaries. The local concentration of vacancies in the vicinity of grain boundaries has some distribution of value, cvb, that lies somewhere within the range of values for the pore-solid interface. Local flow patterns may be expected to flow vacancies from regions near ααp triple lines on the surface (where H is large and negative and vacancy concentrations are high) to the nearby grain boundaries, where the incoming vacancies may be annihilated. These annihilation events, spreading more or less uniformly over the grain boundary surfaces in the tessellation, smoothly and progressively remove layers from between particles and allow their centers to approach one another. This process has been described as painting the grain boundary areas with vacancy annihilation events. It must occur from early first-stage sintering, where a relatively few annihilation events in small necks produce significant shrinkage, through the third stage where the volume change approaches the volume of vacancies annihilated. Presumably the system adjusts the distribution of these rates of annihilation to be more or less uniform over the grain boundaries to maintain continuity, because at sintering temperatures the system cannot support the development of mechanical stresses. Consideration of the cell structure visualization shows that the removal of a layer of thickness dp from a face between a pair of particles requires the



77

annihilation of a volume of vacancies equal to Abdp, where Ab is the area of the grain boundary on the face. However, this process is accompanied by a change in volume equal to Afdp, where Af is the area of the entire cell face. Faces that do not contain grain boundaries also contribute to the volume change as the centroids of the non-contacting particle pair that produces this face move towards each other by an amount dictated by the shrinkage associated with nearby faces that do have grain boundaries. Thus, in the early stages of sintering where the grain boundaries occupy a small fraction of the cell faces, the vacancy annihilation process is very efficient; as grain boundaries spread over the faces, the efficiency drops off. A description of this behavior may be couched in terms of a second tessellation of the structure constructed within the original cell structure. Focus on a given face in the cell structure and the particle pair which gives rise to it. Identify the centroids of the particle pair. Construct a pyramid in each particle with the face as the base and the centroid as the apex, as in Fig. 3.5. Such a bypyramid cell may be constructed for each face in the cell structure, so that it is also space filling. For a given face, let p1 and p2 be the altitudes of these pyramids and Af the area of the base; Ab is the area of the grain boundary in the face. Let n˙A be the local rate of annihilation of vacancies at an element of area dA on the grain boundary (vacancies/cm2-sec). This annihilation has some distribution of values over the grain boundary. In some small time interval, dt, the number of vacancies annihilated at this area element, is n˙A dAdt. The volume associated with the lattice sites lost is

3.5 A bipyramid cell typical of those visualized for each face in the particle tessellation: (a) the bipyramid in the context of the pair of particles that produce it; (b) the separated bipyramid cell; (c) associated geometric entities including Af, the area of the cell face, Ab, the area of grain boundary in that face and p1 and p2, the vertical distances from the cell face to the particle centroids.


78

Sintering of advanced materials dp dA = – Ω n˙AdA dt

where Ω is the volume of one lattice site. The local normal dimension lost, dp, may be expressed as p˙dt where p˙ is the local normal rate of shrinkage at dA. Thus, p˙ dA dt = – Ω n˙A dA dt The total volume of lattice sights annihilated in time dt may be defined as an integral over the grain boundary area Ab in the tessellation: Ω ∫A

b

∫ n˙A dA dt = ∫Ab ∫ p˙ dA dt

[3.6]

Or, defining averages over the grain boundary area in the whole structure, bAb = – Ω Ab Thus b = – Ω

[3.7]

This result is free of simplifying geometric assumptions. Vacancy annihilation rates must be nearly constant (have a narrow distribution) over the grain boundary network. As layers of lattice sites are removed from the grain boundary network, the structure pulls itself together. Let dp be the local normal linear shrinkage at any point on the faces in the cell structure, including regions of cell faces not occupied by grain boundaries. Again define p˙ = dp/dt to be the corresponding local shrinkage rate. The volume decrease associated with an element of area of the face is dp dA = p˙ dA dt The total volume change for the structure in time dt is the sum over the total area Af of the faces in the cell structure: dV = ∫ ∫ dpdA = ∫ ∫ p˙ dA dt Af

Af

Overlaps at the cell edges are higher order differentials in dp and are negligible. The rate of change of volume of the structure may be written dV = ∫ ∫ p˙ dA = A [3.8] f f dt Af where f is the average local normal lineal shrinkage rate, averaged over the domain of the total area of cell faces in the tessellation, Af . Introduce a plausible assumption: the average local lineal shrinkage rate over the grain boundary area in the system is identical to that over the whole cell face area: f = b

[3.9]

With this assumption, the shrinkage rate may be expressed in terms of the average rate of annihilation of vacancies on grain boundaries in the system:



79

dV = f Af = b A f = – Ω Af dt Multiply and divide by the grain boundary area in the structure:

()

dV = – Ω  Af  A b A dt Ab Define the efficiency ratio, f, for the system to be f≡

Af Ab

=

SVcf

[3.10]

SVαα

where SVcf is the surface area per unit volume of cell faces. This quantity is actually the ratio of the volume change of the structure as a whole to the volume of lattice sites annihilated. The value of f is very large at the outset and descends slowly toward 1 as the structure densifies. With this definition, the rate of volume change is dV = – Ω f Ab dt

[3.11]

Visualization of the description of the microstructure in terms of the cell structure thus yields a simple yet general result for the rate of densification in terms of the average rate of annihilation of vacancies on grain boundaries. The flow pattern of vacancies in the vicinity of a grain boundary between particles is sketched in Fig. 3.6. The number of vacancies supplied to the solid volume of the system by an element of surface dS at the pore-solid interface may be expressed in terms of the local flux of vacancies in the solid at the surface, JL (vacancies per cm2 per sec), defined to be positive if flow is into the system: JL  d S dt JL is positive at surface elements that are sources and negative at those that are sinks. The sign of the flux at a surface element is determined by the sign of H. Focus on surface elements that operate as vacancy sources, for which H is negative. In the flow pattern sketched in Fig. 3.6 a subset of these surface elements connects with flow lines to the local grain boundary and contributes to densification. The remaining source elements connect with sink elements elsewhere on the surface and contribute to surface rounding, but do not contribute to densification. At some time t, let Sδαp be the area of elements that are communicating with grain boundaries in the system. Assume there is negligible accumulation of vacancies within the volume of the solid. The total number of vacancies supplied to the system from these surface elements in time dt is then equal to the number annihilated at grain boundaries in this time interval:

∫ ∫ n˙AdAdt = ∫ αp ∫ JL  dSdt

Ab

Sδ


[3.12]

80


3.6 Flow pattern of vacancies in the vicinity of a grain boundary. The negative pressure associated with a negative mean curvature at the surface gives rise to an increased concentration of vacancies which flow to the grain boundary where they are annihilated to produce densification.

The rate of annihilation of vacancies is simply related to the rate of densification (Equation 3.11): dV = – Ω f A = – Ω f A b dt

∫ ∫ JL dS

Sδα p

[3.13]

The flux of vacancies at an element of surface can be formulated from Fick’s first law: JL = – Dv (∇cv)S = – Dv

cv0 – cv(H) λ

[3.14]

where Dv is the diffusivity of vacancies in the system, (∇cv )S is the local concentration gradient of vacancies in the volume adjacent to the surface element. The second equation in this result defines λ, a local diffusion length that varies from element to element on the surfaces. This is a property of the distribution of vacancy concentrations in the flow pattern and is essentially defined by Equation 3.14. Its distribution could be evaluated in principle from a simulation of the process. Until such a simulation can be developed, only an estimate of an average value for λ can be made from stereological measurements as described in the discussion section. In the microstructological approach, λ is one of those properties that can be defined with rigor, but practically, can only be estimated.



81

Assuming local equilibrium at the surface, recall that this concentration difference may be evaluated thermodynamically (Equation 3.5): 2 γ V cv0

cv(H) – cv0 = –

kT

H

Insert this relation into Equation 3.14. The vacancy diffusion flux at the pore surface may be written: JS = – Dv

1 2 γ Vcv0 H = – KD 1 H λ kT λ

[3.15]

where KD contains the thermodynamic and kinetic factors in the equation. KD = Dv

2 γ Vcv0 kT

[3.16]

For elements for which H is negative, JS is positive and vacancies flow into the solid on the way to the nearby grain boundary or surface sinks. The rate of densification is related to the integral of this flux over the part of the pore surface that communicates with grain boundaries (Equation 3.13): dV = – Ω f dt

∫∫

αp Sδ

JS dS = – Ω f

∫∫

αp Sδ

– KD 1 H dS λ

[3.17]

Rewrite this equation:

dV = Ω f K D∫ dt

∫

αp Sδ

1– H dS = Ω f K D λ

1 H dS αp λ

∫ S∫ δ

∫ ∫ H dS αp

∫∫

H dS

αp

Sδ

Sδ

Define the ‘mean curvature weighted harmonic mean of diffusion length scales in the structure’ to be:

〈1λ〉

1 H dS αp λ

∫∫ H

≡

Sδ

∫∫

[3.18]

H dS

αp

Sδ

Again, the definition of this quantity is rigorous, but in practical terms, it can only be estimated from stereological measurements. From the definition of the integral mean curvature of the pα surface (Equation 3.2): Mδpα ≡ ∫

∫

H dS

αp

Sδ


[3.19]

82


Thus, the rate of densification in simple sintering is given by dV = Ω fK 1 M αp D λ H δ dt

〈〉

[3.20]

where Mδαp is the integral mean curvature of those αp surface elements that supply vacancies to the grain boundaries. The densification rate is negative (the pore volume is shrinking) because H for the surface elements contributing vacancies to the grain boundaries is negative and thus Mδαp is negative. This parameter is not accessible to direct measurement, but may be sought in simulations of the process. It is some fraction of Mαp, the integral mean curvature of the whole αp surface, which can and has been determined stereologically.2# Sometime early in the second stage of sintering the surface rounding process (transfer of vacancies from surface sources with negative H to surface sinks with positive H ) fades and Mδαp ⇒ Mαp the total curvature of the αp surface in the system. For the rest of the densification process the rate is given by dV = Ω fK 1 M αp D λ H dt

〈〉

3.7

[3.21]

Discussion

An attempt has been made to develop this theory in the mode of microstructology as envisioned by Rhines. The analysis has been carried forward as far as possible without simplifying geometric assumptions. The result is typical of this approach in that the final equation contains geometric parameters that can be defined with some rigor, but cannot be measured stereologically. The integral mean curvature of the sp surface, Mαp, has been measured in a few systems3 and can be estimated stereologically without simplifying assumptions. However, the integral mean curvature of those surface elements that communicate with grain boundaries, required in the application of the theory in the first and early second stages, can only be defined in the context of a description that includes the flow patterns, i.e., in a simulation of the process. The efficiency factor, f, defined in Equation 3.10, contains the grain boundary area, Ab, which can be measured, SVαα in Table 3.1. Probably a very good estimate of Af, the surface area of the cell faces, SVcf in stereological notation, may be obtained by using image processing to perform a medial axis transform on twodimensional sections, and applying the line intercept count in stereology to the resulting two-dimensional cell structure, accepting it as a valid section through the three-dimensional tessellation. Then cf

f=

SV SVαα

[3.22]



83

Most problematic of the parameters unearthed in Equation 3.21 is the ‘curvature weighted harmonic mean of the diffusion length scales’ defined in Equation 3.18. A rigorous evaluation of this property can only be accessible through a realistic simulation of the process. Alternatively, an estimate of an average diffusion length scale may be undertaken, recognizing at the outset that the reciprocal of the average length scale is not the same as the average of the reciprocal. The diffusion distances in the structure extend from the pore solid interface, mostly in the vicinity of ααp triple lines, where curvatures are sharpest and surface vacancy concentration highest, to points on the grain boundary area in the neighborhood. Uniform annihilation of vacancies over the grain boundary area requires that those points be distributed uniformly over the entire grain boundary area. An average distance between triple lines ααp and points in the grain boundary may be expected to scale with the mean lineal intercept of grain boundary surfaces, λb. This property may be estimated stereologically by visualizing the cell tessellation surface area as a two-dimensional structure partially occupied by grain boundary surface. The mean lineal intercept of a phase in a two-dimensional two-phase structure may be shown to be 2D = π

AA LA

[3.23]

where AA is the area fraction of the phase of interest and LA is the length of the boundary of the phase. The fraction of the tessellation surface area occupied by grain boundary is AA =

Sαα V cf SV

[3.24]

where SVαα is the surface area per unit volume of grain boundaries and SVcf is the surface area of cell faces. The perimeter of the boundaries on the cell face area is LA =

Lααp V SVcf

[3.25]

p where L αα V is the length of ααp triple line per unit volume. Insert these evaluations into Equation 3.22:

S Vαα

gb = π

AA LA

=π

S Vcf

S Vαα

LV

L Vααp

=π ααp

SVcf

[3.26]

It seems reasonable to assume that the diffusion length scales in the system scale with this parameter, though this is by no means a rigorous relationship. Assume as a first approximation


84


〈1λ 〉

H

≅

ααp 1 1 LV = π αα gb SV

[3.27]

Inserting this estimate into the densification rate equation (3.21) and normalize by dividing both sides by the total volume of the system gives p

ααp dVV S cf 1 LV M αp = Ω Vαα KD π S αα V dt SV V

[3.28]

This result contains: KD the physical factor containing the thermodynamic and kinetic properties of the system. Svcf the surface area of cell faces in the tessellation. Lvααp and Svαα which together report the diffusion length scales in the system, and Mvαp which contains the thermodynamic driving force. This result is typical of kinetic equations in that it contains a phenomenological physical factor, KD, a direct proportionality to a measure of the ‘driving force’ contained in the integral mean curvature, Mvαp, and an inverse proportionality to a measure of the diffusion length scales in the system. The microstructological results, embodied in equations 3.20 and 3.21, provide rigorous, if perhaps elusive, evaluations of these measures. These results may provide guidance for geometric properties that may be the focus of simulations of the sintering process.

3.8

Conclusion

Microstructural evolution in simple sintering involves the interplay of two network structures: • Pore network • Grain boundary network This evolution can be described by a sequence of microstructural states that define a path. The states, and the path, can be quantified by applying stereological methods to estimate the properties defined in Table 3.1. The evolution from start to finish can be visualized with the aid of a tessellation of the structure in which individual cells initially contain one particle and its associated porosity. Grain boundaries initially form at points of contact between particles and gradually spread over the faces of the cell structure. The encounter of spreading grain boundaries with cell edges in the tessellation corresponds to channel closure in the pore network and the formation of a grain edge (triple line) in the grain structure. Continued spreading of the grain boundaries over the cell faces eventually isolates pores on the grain boundary network. Subsequent evolution of the pore/grain structure is governed by the complexities of Zener pinning.



85

Analysis of the kinetics of the process is facilitated by visualizing a second cell structure, consisting of bipyramids erected at each face in the cell tessellation. This cell structure introduces the efficiency factor, f, which is useful in connecting global densification to local vacancy annihilation rates. If the vacancies are delivered by volume diffusion, then the densification rate is given by 1 dV Mαp = Ω f KD dt λH

〈〉

which identifies the geometric, thermodynamic and kinetic factors that operate in simple sintering.

3.9

References

1. R. T. DeHoff and J. C. Russ, Practical Stereology, Klewer Academic/Plenum Publishers, New York, (2000). 2. R. T. DeHoff, Thermodynamics in Materials Science, Second Edition, Taylor & Francis, Inc., Boca Raton, FL, (2006) Chapter 12. 3. E. A. Aigeltinger and R. T. DeHoff, Met. Trans., 6A (1975) 1853. 4. S. Bouix and K. Siddiqi. Divergence-based medial surfaces. In Sixth European Conference on Computer Vision, Trinity College, Dublin, Ireland (2000). 5. R. T. DeHoff, Grain Growth in Polycrystalline Materials II, H. Weiland, B.L. Adams and A.D. Rollett, Eds, TMS, Warrendale, PA, (1998) 225–30. 6. C. S. Smith, TransAIME, 175 (1948) 47.


4 Computer modelling of sintering: theory and examples W. Niu and J. Pan, University of Leicester, UK Abstract: The sintering process has been widely used in producing powder metallurgy parts and ceramic components. At present, the industry obtains the proper processing parameters mainly by trial and error. Compared with the actual sintering trials, computer simulation can save cost and provide more valuable references or guidance for real production. This chapter presents existing sintering models at different length scales, i.e. models at atomic, particle and continuum scales respectively. The multiscale model strategy is also discussed. At each length scale, sintering theories and numerical techniques for the computer simulation are briefly outlined and some typical examples are provided to demonstrate the potential usefulness of the models. Key words: sintering, modelling, finite element method, virtual power principle.

4.1

Introduction

Sintering was originally used in the firing of pottery. In the modern era, it has been used in the fabrication of sintered parts of all kinds, including bulk ceramic components and powder metallurgy parts. Sintering aims to produce sintered parts with reproducible and, if possible, designed microstructure through control of sintering variables. The sintered parts are normally quite small, and some typical examples include shock absorber pistons, belt pulleys, small helical gears, drive gears for chainsaws, and automotive pump gears. Because they are moulded, sintered parts can have extremely complex shapes, and do not require machining. The toughness and high strength properties of sintered parts make them especially good for many high-technology systems. Basically, sintering processes can be divided into three types: solid state sintering, liquid phase sintering and viscous sintering, which are all widely used in the industry. The driving force of sintering is the reduction in the total interfacial energy, which occurs via densification and grain growth. An external pressure or force is sometimes applied to accelerate the process. One difficulty for sintering is that, when a part is sintered, its size and shape change non-linearly with sintering time. The final dimensions have to be controlled carefully by the designer of the unfired piece. At present, the most practical way of achieving this is by trial and error. While this may be acceptable for very high-volume items, it is not cost-effective for small batches. 86 © Woodhead Publishing Limited, 2010

Computer modelling of sintering

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Many works have been carried out in developing computer models for sintering in order to understand the sintering process with the ultimate aims of guaranteeing the performance of the products, developing robust processes to provide high tolerance and net shape and reducing the rejection rate significantly. Starting in the 1940s Fenkel, Kuczynski, Coble, Kingery and Herring pioneered a series of sintering models. These early models aimed to find out the underlying mechanisms during the sintering process. These fundamental theories are well reviewed in a recent book by German (1996). Since then major progress has been made. A wellknown contribution is the sintering mechanism maps constructed by Ashby and his co-workers (Ashby, 1990) which collected all the previous sintering models together. Accompanying Ashby’s work was the development of the full constitutive laws for the finite element analysis of sintering, which have been reviewed by Cocks (1994b) and Olevsky (1998) respectively. Moreover, the development of computer simulation techniques for sintering at the particle scale makes it possible to consider coupling between different sintering mechanisms and more realistic microstructures. Cocks et al. (1999) provided a comprehensive review of a variational technique for the computer simulation. The development of molecular dynamic provides the opportunity to simulate the sintering process atom by atom. Pan (2003) made a comprehensive review of sintering models at different scales. The purpose of this chapter is to provide an update on the review. The chapter follows a similar structure to the previous review and collects seven different case studies to demonstrate the state of the art of the sintering models.

4.2

Sintering modelling at the atomic scale

4.2.1 General description of the model Sintering of nanoparticles has aroused some significant attention in research and industry. The main challenge is to avoid coarsening during the sintering process so that the nanostructure can be maintained. To understand the fundamental mechanisms of nanoparticle sintering, computer simulation offers a convenient way to investigate the phenomena at this small scale. There have been many attempts to model sintering of nanoparicles using molecular dynamics (MD) simulation. In MD modelling, each particle is modelled as an assembly of a large number of atoms. Unlike sintering models at the particle or continuum level, the chemical composition and atomic structure of each particle is explicit in an atomistic simulation. The material’s details, including the inter-atomic potential, are the input of the simulation, and the output is the trajectory of all the atoms from which further results, like neck growth with time, can be obtained. In addition, the thermodynamic and kinetic properties, and the phenomenological sintering mechanisms, can be revealed by analysing the atomistic trajectory. The atomistic simulations can provide a fundamental understanding of the sintering process.


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4.2.2 Molecular dynamics (MD) Although atomistic scale modelling has been widely used in many fields, like medicine, chemistry, materials science and nanotechnologies, the basic principle of the molecular dynamics is rather straightforward. In the numerical model, each atom interacts with its neighbours through inter-atomic forces. The force fi experienced by the i-th atom is usually expressed as the gradient of a so-called inter-atomic potential Φ with respect to the position of the i-th atom ri ,  riΦ(rij) fi = Σ ∇  j>i

[4.1]

in which rij is the distance between two atoms i and j. The velocity vi and position ri of the i-th atom are updated at each time step of the simulation using Newtonian mechanics: f v i (t + ∆t) = v i (t) + mi ∆t, [4.2] i f ri (t + ∆t) = ri (t) + v i (t)∆t + 1– mi ∆t2, [4.3] 2 i in which ∆t is the timestep length and mi is the mass of the i-th atom. The simple Newtonian mechanics can be modified in a variety of ways to maintain the system at a constant temperature or constant energy (Rafii-Tabar, 2000).

4.2.3 Example A – the role of particle reorientation on sintering Ding et al. (2009) used molecular dynamics and explored the possible difference between molecular dynamics and continuum diffusional models at the particle scale. The fundamental information that a continuum model does not have is the crystalline orientation of the particles. The MD results show that if the particles align perfectly at the beginning of the sintering process, they will stay this way during the whole process; otherwise, the particle can make a quick adjustment (reorientation) at the beginning of the sintering process as shown in Fig. 4.1. This phenomenon had been observed by other researchers both experimentally (Rankin and Sheldon, 1995) and in MD simulations (Zeng et al., 1998). However, its consequence for the sintering behaviour was not realized. The reorientation is driven by the minimization of the grain-boundary energy and may even eliminate some grain-boundaries from a particle system under certain conditions. The reorientation leads to different types of inter-particle boundaries in a particle system, some of which are perfectly aligned while others are normal grainboundaries. Ding et al. (2009) showed that large angle of initial misalignment between the particles, big particle size and higher sintering temperature are helpful to form a stable grain-boundary. The different boundaries then sinter by varying different matter transportation mechanisms. Figure 4.2 shows an example of one small particle in contact with two big neighbours sintering at 63% of the melting



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4.1 Particles with initial misaligned crystal orientations. The small particle reorients itself at the very beginning of the sintering process; only half of the particles are shown to reveal their relative rotation (Ding et al., 2009).

4.2 MD simulation of one small and two large particles sintering at T = 0.26ε/kB. (a) t = 500t*; (b) t = 50000t*; (c) t = 200000t*; (d) t = 500000t* (Ding et al., 2009).

temperature. As soon as the particles come into contact with each other, the small particle quickly aligns with the lower large particle to form a single crystal while a grain-boundary is formed between the small particle and the upper large one. The upper neck grows by grain-boundary diffusion while the lower one grows by surface diffusion. The grain-boundary also migrates into the small particle. It is


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obvious that the existence of a grain-boundary accelerates significantly the neck growth at the upper neck. Ding et al. (2009) found that if a continuum diffusional model takes the correct matter transportation mechanism, then its prediction of neck growth actually agrees very well with the MD model. Figure 4.3 compares the neck sizes versus sintering time predicted by the continuum and MD models respectively. Logarithmic scales are used for both axes. The solid line is the results of the continuum model assuming grain-boundary diffusion as the dominating sintering mechanism while the discrete dots were obtained from averaging several independent MD simulations of a particle system which have the same macroscopic states but different microscopic states, and all sintered by grain-boundary diffusion. Although the particles are very small, made of only about 10 000 atoms in the MD model, the continuum model works reasonably well. A challenge to the particle scale models is therefore how to deal with the uncertain initial condition of the inter-particle boundaries.

4.3

Sintering modelling at the particle level

4.3.1 General description of the model Sintering models at the particle level are the most mature among models in the three scales. All the early models belong to this category. The typical input data are the particle size, the specific energies and the diffusion coefficient. The models are typical in the form of rate equations for neck-growth and particle approaching. A major weakness of the early models is that they assumed simple geometry of

4.3 Neck size divided by initial particle radius as a function of time predicted by the MD model (discrete dots) and continuum model (solid line) for the sintering of two particles of the same size. Grain-boundary diffusion is the dominant mechanism for matter redistribution. Logarithmic scales are used for both axes (Ding et al., 2009).



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the particles. For example, the initial particles are assumed as perfectly uniform spheres or tetrakaidecahedron grains. The sintering process is often divided into three distinctive stages, i.e. contact formation, shrinkage and coarsening. Each stage is dominated by a single mechanism. The over-simplification of the microstructure had led to misunderstanding or even error in our understanding of the sintering behaviour as demonstrated in Example B. Over the last two decades, major progress has been made on computer simulation of the microstructure evolution, which allows us to drop the assumptions about particle and pores geometry in the classical sintering models and to examine the full interactions between the various underlying sintering mechanisms. Computer simulations also allow us to study sintering through a range of different mechanisms simultaneously.

4.3.2 Virtual power principle and finite element solution The driving force for sintering is the reduction in the total free energy associated with the particle surfaces. In general the total free energy comes from the chemical (bonding) energy, interfacial energy and elastic strain energy and can be written as

E=

∫(µ + e)dV +

grains

∫γdA

[4.4]

interface

in which µ, e and γ represent the specific chemical, strain and interfacial energies respectively. The microstructure evolves to reduce E. If a mechanical force is applied, the process is further accelerated and the microstructure evolves to reduce the total potential energy of the system, which is given by

E* =

∫(µ + e)dV + ∫γdA – ∫p ·u dA

grains

interface

[4.5]

boundary

in which p is the distributed force and u is the displacement of the component boundary where the distributed force is applied. Letting χ i represent the statistically averaged atomic velocity describing the i-th matter redistribution mechanism, and Fi represent the corresponding thermodynamic driving force for χ i, the virtual power principle can be stated as that the virtual variation of the time rate of the total potential energy must be balanced by the virtual power of all the thermodynamic driving forces: . dV = 0 δE * + [4.6] ∫ Fi ·δχ i — Ω i

Σ

particles

in which Ω is the atomic volume. This is simply a statement of energy conservation over a virtual (small and imaginary) change in the velocities. For the energy conservation to be valid, the virtual change of the kinetic velocities, i.e. δχi, cannot violate matter conservation. If we assume a linear relationship between χ i and Fi (for an example of using nonlinear kinetic law, see Pan, 2004):


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χ i = Mi Fi

[4.7]

in which Mi represents kinetic mobility and strongly depends on the temperature. The virtual power principle is then given by . 1 χ · δχ dV = 0. δE * + [4.8] i i ∫ M —– i iΩ

Σ

particles

The virtual power principle can be rewritten as δ Π = 0, and . 1 χ · χ dV. Π = E* + 1– ∫ —– [4.9] 2 i Mi Ω i i That is, among all the possible kinetic fields which satisfy matter conservation, the true ones make Π stationary. This is a powerful statement as it immediately leads to a systematic approach to determine the kinetic fields. One can assume a set of possible kinetic fields which already satisfy matter conservation but contain unknown parameters:

Σ

 i, j Nj (r ) χ i = Σ A j

[4.10]

in which A i,j represents the unknown parameters and Nj the assumed functions of a location vector r. Substituting Eq. 4.10 into Eq. 4.9, δ Π = 0 leads to ∂Π = 0.  i, j ∂A

[4.11]

This is a set of linear simultaneous equations from which Ai,j can be solved. Equations 4.9 to 4.11 form a general framework for modelling the sintering process. Details of the numerical method can be found in Ch’ng and Pan (2005), Ch’ng and Pan (2004) and Pan et al. (1997).

4.3.3 Example B – sintering kinetics of powder compacts containing large pores It is commonly believed that a large pore does not shrink during sintering. Here ‘large’ is defined by the number of grains surrounding a pore, which is known as the coordination number. A classical textbook theory (Kingery and Francois, 1967) predicts that a pore will shrink only if its coordination number is less than a critical value. It follows that grain-growth can be used as a means to eliminate large pores. There has been increasing experimental evidence contradicting the theory. For example, Elliott and Frederick (1992) showed that densification is controlled by the characteristic diffusion distance, rather than the co-ordination number. Flinn et al. (2000) showed that artificially introduced pores as large as 60 µm in diameter in an alumina powder compact shrink continuously. Using computer simulations, Pan et al. (2005) showed that the critical coordination number theory is a consequence of the over-simplistic assumption about the microstructure (that a



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pore is always surrounded by identical grains during sintering). Figure 4.4 shows the computer simulation of the sintering of two large pores embedded in a matrix of irregular grains. There is no exchange of matter across the boundary. Coupled grain-boundary and surface diffusion is assumed as the mechanism for matter redistribution. The grain-boundary network acts as the source while the pore surfaces act as the sinks for the diffusing atoms. It can be observed that the pores continuously shrink despite their large coordination numbers. As the material is being removed from the grain-boundary network and deposited into the pore surface, the total size of the system shrinks, reflecting the densification of the entire material. Pan et al. (2009) showed that the densification rate of the large pores is, however, extremely slow compared with small pores, and one should not expect

(a)

(b)

4.4 Computer simulated microstructure evolution of two large pores in an irregular grain matrix. The pores shrink continually despite their large co-ordination number.


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(c)

(d)

4.4 Continued.

that the large pore can be eliminated by extended sintering. The merit of the computer simulations is to show that the sintering behaviour of large pores is not decided by the coordination number. Consequently, grain-growth is always harmful to the elimination of the pores as grain-growth increases the characteristic diffusion distance to achieve densification.

4.3.4 Example C – sintering of particles with orientation dependent surface energy Many powder materials have anisotropic surface energy. This can be taken into account by using an orientation dependent expression for the surface energy in Eq. 4.4. Ch’ng and Pan used an expression for surface energy following (Zhang and Gladwell, 2003, 2007) 1 cos(4ϕ) γ = 1+ — [4.12] 15 © Woodhead Publishing Limited, 2010


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in which ϕ is the surface orientation angle, and studied the effect of anisotropic surface energy on the sintering behaviour of two particles. They considered surface diffusion and grain-boundary diffusion as the underlying matter transportation mechanisms. Figure 4.5 shows the computer simulated evolution of the two particles sintering. The initial configuration of two particles is shown in Fig. 4.5 (a). It is apparent that the sintering behaviour is very different when the two particles are placed into contact at different directions. To minimize the total energy of the system, four corners are formed while the neck grows continually to reduce the free surface. In the final stage, an equilibrium dihedral angle is achieved between the free surface and grain boundary as shown in Fig. 4.5 (c).

4.5 (a)–(c) The evolution of particles with anisotropic surface free energy. © Woodhead Publishing Limited, 2010

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4.4

Sintering modelling at the component scale

4.4.1 Finite element calculation of sintering deformation The finite element method can be used to model the sintering process of a component. In such a model, density and average grain size, which are the functions of time and location, are used to characterize the microstructure. The input data for a finite model include: • • • • • • • •

sintering constitutive law and its parameters grain-growth law and its parameters initial average particle size initial density field initial residual stress field after compaction initial geometry of the green powder compact sintering temperature and boundary conditions including applied forces.

The finite element analysis predicts the entire time history of • stress and strain fields • density and grain-size fields • shape and dimension of the component. Not all the input data are straightforward to obtain. For example, the residual stress and initial density field are difficult to measure; they may have to be modelled by another finite element analysis of the compaction process. The material information of the finite element analysis is contained in the constitutive and grain-growth laws. The constitutive law is a relationship between the strain . rates ε ij and the stresses σij which can be presented using a strain rate potential (Cocks, 1994a), Φ,

. εij = ∂ [Φ(d,D,T,σe,σm – σs)]. ∂σij

[4.13]

The potential Φ is a function of grain-size d, relative density D, sintering temperature T, von Mises effective stress σe, mean stress σm and sintering potential σs. The sintering potential is defined as

σs ≡ ∂F = σs (γs, γgb, D, d ), ∂Vpore

[4.14]

in which F is the total free energy of the solid and Vpore is the total volume of the pores in the solid. In general the sintering potential depends on the specific energies of the free surface and the grain-boundary, γs and γgb, the grain-size d and the relative density D. The constitutive law is completed by a grain-growth law,



97

which relates the grain-growth rate to the temperature, relative density and grain-size, . . d = d (T, D, d) [4.15]

4.4.2 Calculating sintering deformation using densification data Predicting the sintering deformation of ceramic powder compacts is very useful to manufacturing ceramic products. However, the finite element method is not widely used in the industry because currently it is perhaps more expensive to calibrate the constitutive laws than making a product by trial and error. This is because a force has to be applied to the sintering sample at the sintering temperature in order to measure the parameters in the constitutive law. To overcome this difficulty, Pan and his co-workers developed a reduced finite element method (Kiani et al., 2007, Huang and Pan, 2008, Pan and Huang, 2009), in which the densification data are used instead of the full constitutive laws. Their method is briefly outlined here. Under the framework of continuum solid mechanics, sintering deformation must satisfy four conditions: (a) compatibility, (b) equilibrium, (c) boundary conditions and (d) constitutive law. The reduced method developed by Pan and his co-workers satisfies conditions (a), (b) and (c) fully and (d) partially. The velocity field is used as the basic variable in a finite element formulation, and the compatibility condition is guaranteed by representing the velocity field using appropriate shape functions and by calculating the strain rates from the velocity field using the relationship . . . ∂u ∂uj εij = 1– —i + — , [4.16] 2 ∂xj ∂xi . . in which εij is the strain rate tensor, ui the velocity field and xi the Lagrange co-ordinate. The velocity boundary conditions are ensured by setting the nodal velocities on the boundary to their prescribed values. The equilibrium condition is equivalent to the principle of virtual power, which is . [4.17] ∫ σij · δεij dV = 0, v . in which σij is the stress tensor and δεij the virtual variation of the strain rates which must satisfy the compatibility and the velocity boundary conditions. The integration is over the entire sintering body. For simplicity, a linear constitutive law is assumed: sij σm σs . εij = —– + —– δ – —– δ , [4.18] 2ηs 3ηB ij 3ηB ij in which σm is the mean stress, σs the sintering potential, ηS the shear viscosity, ηB the bulk viscosity, δij the Kronecker delta function, and sij the devitoric stress tensor which is defined as

[

]


98

Sintering of advanced materials sij = σij – σmδij ·

[4.19]

In Eq. 4.18 the first term represents the shear deformation, the second term represents the volume change due to the mean stress and the third term represents the volume change due to the sintering potential. A uniform compact of any shape shrinks according to the third term if it is unconstrained and not subject to any external force. Therefore this term as a whole can be determined from free sintering experiment using uniform samples according to . . σs D εexp = – —– = – —–, [4.20] 3ηB 3D in which D represents the relative density and can be measured as a function of . time in the experiment. Alternatively εexp can also be calculated from a master sintering curve (Kiani et al., 2006) using Eq. 4.20 if such a curve is available. The difficulty in measuring the constitutive law experimentally is to separate the sintering potential σs from the bulk viscosity ηB. To avoid this difficulty, Kiani et al. (2007) assumed that σm = 0 and therefore dropped the second term from Eq. 4.18. The constitutive law then becomes sij . . εij = —– + εexpδij · 2ηS

[4.21]

Using Eq. 4.21 in Eq. 4.17 gives

.

.

.

∫ ηS(εij – εexpδij)δεij dV = 0.

[4.22]

V

It is difficult to measure ηS experimentally. Kiani et al. (2007) further assumed that the shear viscosity is uniform within a powder compact so that it is eliminated from Eq. 4.22. The virtual power principle can then be written as ∫ (ε.ij – ε.expδij)δε.ij dV = 0, subject to velocity boundary conditions. [4.23] V . Equation 4.23 is the reduced formulation which requires only εexp as material input. Using the standard finite element procedure (Zienkiewicz and Taylor, 1989), the velocity field u. i is represented using a set of shape functions, and the . strain rates εij are calculated using Eq. 4.16. Writing the results in the matrix form gives . . [ε]e = [B][u ]e [4.24] in which e indicates that the matrixes are defined for the e-th element, [B] is a matrix calculated from the shape functions, and [u. ]e contains the velocities of all the nodes on the e-th element. Substituting expression 4.24 into 4.23 leads to . . δ [u ]eT {[K]e [u ]e – [F]e} = 0 [4.25] elements

Σ



99

in which

and

[K]e = ∫ [B]T [B]dV

[4.26]

. . . [F]e = ∫ [B]T [εexp εexp εexp 0 0 0]dV

[4.27]

Ve

Ve

. For Eq. 4.25 to be true for arbitrary δ [u ], we must have . [K]e [u ]e = [F]e

Σ

elements

Σ

elements

[4.28]

Equation 4.28 is a set of linear simultaneous equations which can be solved using a standard solver to give the velocity field of the sintering deformation. It can be . seen that the material data, εexp, enters the force matrix (Eq. 4.27) while the usual material matrix in the viscosity matrix of Eq. 4.26 is simply unity. Therefore the reduced analysis can be readily implemented using a commercial finite element package (which provides an option of linear viscous material with large deformation) by setting the material matrix as unity and calculating the force matrix using Eq. 4.27. The validity of the reduced method (DFEM) can be tested by comparing the solution obtained using the reduced method with the solution obtained using the full constitutive law, or by comparing the prediction with experimental data directly.

4.4.3 Example D – warping of a bi-layer film Huang and Pan (2008) considered a thin film made of two layers with different initial relative densities, as shown in Fig. 4.6. Each layer is uniform and perfect bounding is assumed for the interface between the two layers. During sintering the film warps because the two layers have different shrinkages. This example is a good validity test of the reduced method because a small difference in the

4.6 A film consisting of two porous layers of different initial densities is sintered as the temperature rises from 30°C to 1000°C and is held at 1000°C. Only half of the film is modelled due to symmetry. Plane stress condition is assumed (Pan and Huang, 2009).


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velocity field can lead to a large difference in the displacement at the free end. Figure 4.7 shows the comparison between the reduced solution and the solution obtained using full constitutive law by Du and Cocks (1992). Figure 4.8 shows the similar comparison between the reduced solution and the solution obtained using full constitutive law by Olevsky (1998). It can be observed from the two figures that the reduced method works very well in both cases.

4.4.4 Example E – sintering deformation of a component with heterogeneous density distribution Kiani et al. (2007) provided two cases of direct comparison between the predictions of the reduced method and experimental measurement of the sinter deformation. Figure 4.9 shows a quarter of the specimen used by Kim et al. (2002), who obtained the full constitutive law for the powder compact and used it in their finite element analysis of the sintering deformation. Figure 4.10 (p. 102) shows the comparison between the reduced solution and the experimental measurement. The comparison is performed on the L-shaped section of the specimen. The thicker solid line shows the initial profile of the section, the thin solid line shows the experimentally measured final shape of the section and the dashed line shows

4.7 Comparison between the DFEM and FEM solutions obtained by using the constitutive laws by Du and Cocks (1992) (Pan and Huang, 2009).



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4.8 Comparison between the DFEM and FEM solutions obtained by using the constitutive laws by Olevsky (1998) (Pan and Huang, 2009).

4.9 A quarter of the alumina powder compact used by Kim et al. (2002) in their numerical and experimental study of sintering. The two L-shaped sections are the planes of symmetry (Pan and Huang, 2009).

the reduced solution. The agreement between the reduced solution and experimental measurement is as good as that achieved by the full constitutive law. However, the reduced method only requires the densification data. The second case studied by Kiani et al. (2007) was for a sintering experiment using a ceramic body which has a composition similar to porcelain. The dominating


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4.10 Comparison between the experimentally measured (Kim et al., 2002) and numerically predicted (Kiani et al., 2007) profiles of the L-shaped section as shown in Fig. 4.9. The outer thick frame shows the initial shape of the section (Pan and Huang, 2009).

4.11 A quarter of the specimen used by Kiani et al. (2007) in their numerical and experimental study of sintering deformation. The disc has three regions of different density. The two vertical cross-sections are the plane of symmetry (Pan and Huang, 2009).

sintering mechanism for this powder compact is liquid phase sintering. Figure 4.11 shows a quarter of the disc-like specimen. The density was deliberately designed to have three different values in three different zones of the sample to induce nonuniform deformation during sintering. Figure 4.12 shows the comparison between the measured and predicted profiles. The outer frame shows the initial shape of the green body before sintering. The inner solid line presents the measured profile of the



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4.12 Comparison between the experimentally measured (inner solid line) and numerically predicted (dashed line) profiles of the vertical cross-section shown in Fig. 4.11. The outer frame shows the initial (green) shape of the section (Pan and Huang, 2009).

sintered specimen while the dashed line is the predicted profile by the reduced method.

4.5

Multi-scale modelling of sintering

The strategy of crossing and linking models at different scales in materials modelling to enhance the predictability of the models has begun to make an impact on sintering modelling. A framework has emerged to link models at the particle scale with those at the component scale. This section provides two examples.

4.5.1 Example F – a two-scale model for simultaneous sintering and crystallization of tissue engineering scaffold made of Bioglass® Bioglass® based glass-ceramic foams have been recently developed as highly porous, mechanically competent, bioactive and degradable scaffolds for bone tissue engineering (Laurencin et al., 2002; Jones and Hench, 2003). However, the material development so far has been based on a trial-and-error approach and the existing materials are far from being optimized. Recently, Chen et al. (2006) used a foam replication technique to fabricate a 45S5 Bioglass® scaffold. Their experimental results indicated that there is a transition temperature for densification and crystallization. If the sintering temperature is lower than 900oC, then neither crystallization nor densification will occur. If the sintering temperature is too high, then crystallization can turn the bioactive glasses (in particular the composition 45S5 Bioglass® (Clupper and Hench, 2003) into an inert material (Li et al., 1992). Therefore there is an optimum sintering condition at which the foam can densify to give the required mechanical properties and to produce fine crystals of Na2Ca2Si3O9, but not deteriorate glass bioactivity too much.


104


The Bioglass® based foams have microstructures at two different scales, i.e. the foams are consisted by glass struts which contain fine glass particles. Huang et al. (2008) developed a two-scales model to predict the sintering behaviour as shown in Fig. 4.13. The sintering process of the struts was divided into two stages. The models by Frenkel (1945) and by McMeeking and Kuhn (1992) are combined for the early stage of sintering, and the model by Mackenzie and Shuttleworth (1949) was used for the later stage of sintering. The effect of crystallization was introduced into these models using the theory developed by Prado and Zanotto (2002). At the foam scale, a representative cell is considered as shown in Fig. 4.13 and the model by Scherer (1991) was modified to predict the sintering deformation of the glass form. Further details of the model can be found in Ref. (Huang et al., 2008). Figure 14 shows the predicted relative density D of the strut material as a function of time at 950 °C. For comparison, the case without crystallization is presented using the dashed line. It can be seen that the model without considering crystallization predicts larger shrinkage, which contradicts the experimental observation. By contrast the model considering crystallization predicts the same tread as observed by Chen et al. (2006). At 950 °C, extensive shrinkage and densification are obviously suppressed by the crystallization as shown in Fig. 4.14.

4.13 A schematic representation of the two-scale model for the Bioglass® foam (Huang et al., 2008).



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1.00 0.95 0.90

D

0.85 0.80 0.75 0.70 950°C without crystallization 950°C with crystallization

0.65 0.60 0.00

0.05

0.10

0.15 0.20 (t-t0)/tε

0.25

0.30

4.14 Predicted relative density for the strut material with crystallization (solid line) and without crystallisation (dashed line) (Huang et al., 2008).

4.5.2 Example G – a two-scale model for sintering damage in powder compact containing inert inclusions Although mechanical properties can be improved significantly by adding a second phase of hard particles into a ceramic matrix, the sinterability of the composite is poor compared with a single-phase powder compact. Understanding the effects of the inclusions on densification is crucial to control the microstructure of the composite and mechanical properties of the component. It has been noted that a very small volume fraction of inert phase could significantly retard the densification behaviour of a powder composite (De Jonghe et al., 1986). This influence depends on the volume fraction, average size and shape of the inclusions. It was also observed that damage typically occurs near pre-existing cracks in the early stage of constrained sintering (Lange, 1983, 1989; Bordia and Jagota, 1993). Therefore it is necessary to develop models to predict the effects of the inert inclusions and preexisting cracks during the sintering in particle reinforced ceramic composites. Huang and Pan (2007) developed a model to predict the damage development during the sintering of ceramic matrix containing inert inclusions. The basic concept of this model is similar to non-linear problems like contact mechanics (Conry and Seireg, 1971; Byung and Byung, 1984). The constitutive response of the powder compact containing damage depends on the strain state (whether it is compression or tension) of the material point under consideration. It cannot therefore be determined independently from the finite element analysis. Huang and Pan (2007) introduced a damage parameter into the particle scale model originally developed by McMeeking and Kuhn (1992) and Cocks et al. (1999). A variational


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4.15 Density distribution on a quarter of the eight inclusions structure (Huang and Pan, 2007).

principle is formulated for the problem of a sintering matrix containing hard inclusions using the damage parameter as a controlling parameter. The variational problem is discretized using the finite element method and solved using a sequential quadratic programming (SQP) algorithm (Bazaraa et al., 1993). The details of the model and numerical examples can be found in Huang and Pan (2007). Figure 4.15 shows a quarter of a representative unit of a powder matrix containing eight equiaxed inclusions. The distribution of the relative density after a period of sintering is shown in the figure. When several inert inclusions are placed close enough, i.e. if the distance between inclusions is less than the typical size of the inclusions, it is observed that enhanced densification occurs in the gap between the inclusions. This leads to a dense network which deters the densification of matrix enclosed by the network as reported by Sudre et al. (Sudre and Lange, 1992; Sudre et al., 1992). The differential shrinkage leads to further damage nucleation. It was also observed that networks behave as a non-deformable entity producing localized porous zones and that the local porosity often exhibits crack-like morphology.

4.6

Conclusion

With the development of computer simulation techniques, modelling has become more and more useful in understanding and optimizing the sintering process. At the atom level, the MD method makes it possible to model each particle by an assembly of atoms. The material details are explicit in such models. The major problem of MD



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simulation is its short time and length scales, which are usually a few nanoseconds and nanometres respectively. At the particle level, detailed microstructural evolution can be simulated during the whole sintering process. An important omission in this chapter for models at the particle scale is the discrete element model (DEM), which has become a very useful tool in understanding the early stage of the sintering process. At the continuum level, the finite element method is used to predict the sintering deformation, density distribution and grain size during sintering. However, the constitutive laws are expensive and difficult to calibrate experimentally. The densification-based method offers an effective solution but it is only valid if no external load is applied and the effect of gravity can be ignored. Sintering behaviour is affected by almost all the steps in the manufacturing process. Powder chemistry, die filling, film printing in some applications, powder compaction, drying or binder burn-out, heating rate, sintering atmosphere, etc., all have an effect on the final quality of a sintered piece. The multi-scale strategy promises to move the modelling capacity a step closer to taking these factors into consideration.

4.7

Acknowledgements

The authors are grateful to the following colleagues and students who have contributed to the work presented in this chapter: Alan Cocks (Oxford University), Julie Yeomans (University of Surrey), Ruslan Davidchack, H.N Ch’ng, Ruoyu Huang and Lifeng Ding.

4.8

References

Ashby, M. F. (1990) HIP6.0 Background Reading. Engineering Department, Cambridge University, UK. Bazaraa, M. S., Sherali, H. D. and Shetty, C. M. (1993) Nonlinear Programming: Theory and Algorithms, New York, John Wiley and Sons. Bordia, R. K. and Jagota, A. (1993) Crack growth and damage in constrained sintering films. Journal of the American Ceramic Society, 76, 2475–85. Byung, C. L. and Byung, M. K. (1984) A computational method for elastoplastic contact problems. Computers and Structures, 18, 757–65. Ch’ng, H. N. and Pan, J. (2004) Cubic spline elements for modelling microstructural evolution of materials controlled by solid-state diffusion and grain-boundary migration. Journal of Computational Physics, 196, 724–50. Ch’ng, H. N. and Pan, J. (2005) Modelling microstructural evolution of porous polycrystalline materials and a numerical study of anisotropic sintering. Journal of Computational Physics, 204, 430–61. Chen, Q. Z., Thompson, I. D. and Boccaccini, A. R. (2006) 45S5 Bioglass®-derived glassceramic scaffolds for bone tissue engineering. Biomaterials, 27, 2414–25. Clupper, D. C. and Hench, L. L. (2003) Crystallization kinetics of tape cast bioactive glass 45S5. Journal of Non-Crystalline Solids, 318, 43–8. Cocks, A. C. F. (1994a) Overview no. 117. The structure of constitutive laws for the sintering of fine grained materials. Acta Metallurgica et Materialia, 42, 2191–210.


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Cocks, A. C. F. (1994b) The structure of constitutive laws for the sintering of fine grained materials. Acta metallurgica et materialia, 42, 2191–210. Cocks, A. C. F., Gill, S. P. A. and Pan, J. (1999) Modelling microstructure evolution in engineering materials. Advances in Applied Mechanics, 36, 81–162. Conry, T. F. and Seireg, A. (1971) A mathematical programming method for design of elastic bodies in contact. ASME Journal of Applied Mechanics, 2, 387–92. De Jonghe, L. C., Rahaman, M. N. and Hsueh, C. H. (1986) Transient stresses in bimodal compacts during sintering. Acta Metallurgica, 34, 1467–71. Ding, L., Davidchack, R. L. and Pan, J. (2009) A molecular dynamics study of sintering between nanoparticles. Computational Materials Science, 45, 247–56. Du, Z. Z. and Cocks, A. C. F. (1992) Constitutive models for the sintering of ceramic components – I. Material models. Acta Metallurgica et Materialia, 40, 1969–79. Elliott, B. S. and Frederick, F. L. (1992) Densification of Large Pores: I, Experiments. Journal of the American Ceramic Society, 75, 2498–508. Flinn, B. D., Bordia, R. K., Zimmermann, A. and Rodel, J. (2000) Evolution of defect size and strength of porous alumina during sintering. Journal of the European Ceramic Society, 20, 2561–68. Frenkel, J. (1945) Journal of physics (USSR), IX, 385. German, R. M. (1996) Sintering Theory and Practice, New York, John Wiley & Sons. Huang, R. and Pan, J. (2007) A two-scale model for sintering damage in powder compact containing inert inclusions. Mechanics of Materials, 39, 710–26. Huang, R. and Pan, J. (2008) A further report on finite element analysis of sintering deformation using densification data – Error estimation and constrained sintering. Journal of the European Ceramic Society, 28, 1931–9. Huang, R., Pan, J., Boccaccini, A. R. and Chen, Q. Z. (2008) A two-scale model for simultaneous sintering and crystallization of glass-ceramic scaffolds for tissue engineering. Acta Biomaterialia, 4, 1095–103. Jones, J. R. and Hench, L. L. (2003) Regeneration of trabecular bone using porous ceramics. Current Opinion in Solid State and Materials Science, 7, 301–7. Kiani, S., Pan, J. and Yeomans, J. A. (2006) A New Scheme of Finding the Master Sintering Curve. Journal of the American Ceramic Society, 89, 3393–6. Kiani, S., Pan, J., Yeomans, J. A., Barriere, M. and Blanchart, P. (2007) Finite element analysis of sintering deformation using densification data instead of a constitutive law. Journal of the European Ceramic Society, 27, 2377–83. Kim, H., Gillia, O., Dor Mus, P. and Bouvard, D. (2002) Near net shape processing of a sintered alumina component: adjustment of pressing parameters through finite element simulation. International Journal of Mechanical Sciences, 44, 2523–39. Kingery, W. D. and Francois, B. (1967) The sintering of crystalline oxides. I. Interaction between grain boundaries and pores. In Kuczynski, G. C., Hooton, N. A., Gibbon, G. F., Goedon and Breach (Eds.) Sintering related phenomena. Goedon and Breach, New York, pp. 471–96. Lange, F. F. (1983) Processing-Related Fracture Origins: I, Observations in Sintered and Isostatically Hot-Pressed Al2O3/ZrO2 Composites. Journal of the American Ceramic Society, 66, 396–8. Lange, F. F. (1989) Densification of powder rings constrained by dense cylindrical cores. Acta Metallurgica, 37, 697–704. Laurencin, C. T., Lu, H. H. and Khan, Y. (2002) Processing of polymer scaffolds: polymer– ceramic composite foams. In Atala, A. L. and Lanza, R. P. (Eds.) Methods of tissue engineering. Academic Press, San Diego.



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Li, P., Yang, Q., Zhang, F. and Kokubo, T. (1992) The effect of residual glassy phase in a bioactive glass-ceramic on the formation of its surface apatite layer in vitro. Journal of Materials Science: Materials in Medicine, 3, 452–6. Mackenzie, J. K. and Shuttleworth, R. (1949) A phenomenological theory of sintering. Proceedings of the Physical Society. Section B, 62, 833–52. McMeeking, R. M. and Kuhn, L. T. (1992) A diffusional creep law for powder compacts. Acta Metallurgica et Materialia, 40, 961–9. Olevsky, E. A. (1998) Theory of sintering: from discrete to continuum. Materials Science and Engineering: R: Reports, 23, 41–100. Pan, J. (2003) Modelling sintering at different length scales. International Materials Reviews, 48, 69–85. Pan, J. (2004) Solid-state diffusion under a large driving force and the sintering of nanosized particles. Philosophical Magazine Letters, 84, 303–10. Pan, J., Ch’ng, H. N. and Cocks, A. C. F. (2005) Sintering kinetics of large pores. Mechanics of Materials, 37, 705–21. Pan, J., Cocks, A., Del, J., Rödel, J., Huang, R. and Ch’ng, H. N. (2009) Densification of powder compact containing large and small pores. Journal of the American Ceramic Society, 92, 1414–18. Pan, J., Cocks, A. C. F. and Kucherenko, S. (1997) Finite element formulation of coupled grain-boundary and surface diffusion with grain-boundary migration. Proceedings of the Royal Society, 453, 2161–84. Pan, J. and Huang, R. (2009) Finite element calculation of sintering deformation using limited experimental data. Materials Science Forum, 606, 103–18. Prado, M. O. and Zanotto, E. D. (2002) Glass sintering with concurrent crystallization. Comptes Rendus Chimie, 5, 773–86. Rafii-Tabar, H. (2000) Modelling the nano-scale phenomena in condensed matter physics via computer-based numerical simulations. Physics Reports, 325, 239–310. Rankin, J. and Sheldon, B. W. (1995) In situ TEM sintering of nano-sized ZrO2 particles. Materials Science and Engineering A, 204, 48–53. Scherer, G. W. (1991) Cell models for viscous sintering. Journal of the American Ceramic Society, 74, 1523–31. Sudre, O. and Lange, F. F. (1992) Effect of inclusions on densification: I, Microstructural development in an Al2O3 matrix containing a high volume fraction of ZrO2 inclusions. Journal of the American Ceramic Society, 75, 519–24. Sudre, O., Bao, G., Fan, B., Lange, F. F. and Evans, A. G. (1992) Effect of Inclusions on Densification: II, Numerical Model. Journal of the American Ceramic Society, 75, 525–31. Zeng, P., Zajac, S., Clapp, P. C. and Rifkin, J. A. (1998) Nanoparticle sintering simulations. Materials Science and Engineering: A, 252, 301–6. Zhang, W. and Gladwell, I. (2003) Evolution of two-dimensional crystal morphologies by surface diffusion with anisotropic surface free energies. Computational Materials Science, 27, 461–70. Zhang, W. and Gladwell, I. (2007) The effect of imposing a corner condition on the evolution of two-dimensional crystal morphologies by surface diffusion with anisotropic surface free energies. Computational Materials Science, 40, 57–65. Zienkiewicz, O. Z. and Taylor, R. L. (1989) The finite element method. London: McGraw-Hill.


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5 Liquid phase sintering S-J. L. Kang, Korea Advanced Institute of Science and Technology, Korea Abstract: This chapter describes the fundamentals of grain growth and densification, and related microstructural evolution during liquid phase sintering (LPS). Two different types of grain growth behavior, stationary (conventionally called normal) and nonstationary in terms of the relative grain size distribution, and their theoretical treatments are described. Particular emphasis is placed on the prediction of nonstationary grain growth with the suggestion of general principles of microstructural evolution during LPS. Fundamental differences between the two densification mechanisms, contact flattening and pore filling, are described and their validities discussed. Model calculations of densification kinetics by pore filling theory are also provided. Key words: stationary and nonstationary grain growth, abnormal growth of faceted grains, pore filling theory, calculations of coarsening and densification, microstructural evolution during liquid phase sintering.

5.1

Introduction

When a compact of a powder mixture is sintered above the solidus line, sintering proceeds in the presence of a liquid phase – liquid phase sintering (LPS). The liquid phase sintering system has usually been idealized as a system where the solid grains and a liquid are in chemical equilibrium. In real systems, however, solid state sintering usually occurs during heating to the liquid phase sintering temperature and reactions among different powders also occur during heating and at the beginning of LPS. The solid state sintering and the reactions in the system govern the initial state of LPS in real systems. Figure 5.1 shows typical densification curves of LPS [1]. In this particular case of W-Ni-Fe samples with different W particle sizes, the densification in the solid state is remarkable during heating, particularly in the sample with fine W powder. Figure 5.2 shows the microstructural evolution during LPS of a W-Ni-Fe sample of 5mm W powder. As sintering proceeds, grain growth and densification occur simultaneously. Densification and grain growth are the two fundamental phenomena occurring in LPS, as in the case of solid state sintering. The two fundamental phenomena are not independent of each other but affect each other, as explained later in this chapter. This chapter describes the fundamentals of densification and grain growth and the resultant microstructural evolution during LPS of samples in chemical equilibrium. Grain growth in a liquid matrix will be described first; a discussion of densification and microstructural evolution will follow. Effects of individual 110 © Woodhead Publishing Limited, 2010


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5.1 Densification curves of 98W-1Ni-1Fe(wt%) samples with different W powder sizes (1 µm and 5 µm) during heating to and isothermal annealing at 1460 °C for liquid phase sintering [1]. (Reprinted with permission of Springer Verlag.)

5.2 Microstructures of 98W(5 µm)-1Ni-1Fe(wt%) samples sintered at 1460 °C for various periods of time [1]. (Reprinted with permission of Springer Verlag.)


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parameters on LPS are not discussed in detail. They are treated in more extended descriptions of LPS, such as reference 2. Other phenomena, such as chemical reactions among particles and solid state diffusion, which may occur in practical systems at the early stage of sintering, are also not considered.

5.2

Grain growth in a liquid matrix

5.2.1 General phenomena and current issues Grain growth in a liquid matrix is referred to as ‘Ostwald ripening’. The driving force for Ostwald ripening is the capillary energy of the system and appears as the differences in chemical potential of atoms in grains of different sizes, which originate from the difference in capillary pressure of the grains. The capillary pressure ∆P of a spherical grain* with a radius of a is expressed as the Young-LaPlace equation: ∆P = Ps – Pl =

2γsl a

[5.1]

where s and l stand for solid and liquid, respectively, and γsl is the solid/liquid interfacial energy. The capillary pressure of a faceted grain* with a distance hi from the center of the grain to a facet surface i with an interfacial energy γi takes a form similar to Eq. 5.1 and is expressed as (Wulff theorem): ∆P = Ps – Pl =

2γi hi

[5.2]

Irrespective of the equilibrium shape of the grains, each grain is under its own capillary pressure expressed as Eq. 5.1 or Eq. 5.2. The capillary pressure increases the molar free energy of the solid and, therefore, the solubility of solute atoms in the liquid, as schematically shown in Fig. 5.3. Thermodynamically, the increase in solubility of the solute in a liquid is expressed as the Gibbs-Thompson (or Thompson-Freundlich) equation: Cal – C∞l =

2γslVmC∞ RTa

[5.3]

where Cal and C∞l are the solubilities of the solute atom (A in Fig. 5.3) in the liquid for a grain with radius a and for a grain with an infinite size, respectively, Vm is the molar volume, R the gas constant (8.314J/K·mol) and T the absolute temperature. Therefore, the highest solubility is for the smallest grain and the lowest solubility is for the largest grain. The average solute solubility in the liquid is determined by the contributions of all the grains and can be denoted as the solubility of a critical sized grain which neither grows nor shrinks at the moment

* Spherical or faceted grain means that the equilibrium shape of the grain is spherical or faceted.



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5.3 Schematic molar free energy vs. composition diagram showing the change in solute (A) solubility, Cl, of a grain with radius a in a liquid.

of observation. The smaller or larger grains, having higher or lower solubilities than that of the critical sized grain, dissolve or grow, respectively, resulting in an increase of the average sized grain. Theoretical treatments and experimental observations of Ostwald ripening have been made in many investigations [3–11]. Lifshitz and Slyozov [3], and Wagner [4] analyzed rigorously the grain growth controlled by the diffusion of atoms in the liquid for a model system with an infinitesimal fraction of grains in a liquid matrix. For the same model system, Wagner [4] also analyzed the grain growth controlled by reaction at the solid/liquid interface. In contrast to general acceptance of the Ostwald ripening theory (LSW theory) [3,4] for diffusion control, the validity of the theory for interface reaction control has been questioned [12,13]. A fundamental problem with the theory is related to its basic assumption that the interface reaction rate (growth rate) is simply proportional to the driving force. This assumption is valid only for systems with invariable interface mobilities with respect to the driving force, as schematically shown in Fig. 5.4(a). According to crystal growth theories and experimental observations [14–18], the constant mobility assumption is justified only for a spherical grain with a rough (atomically disordered) interface for which the migration is governed by diffusion of solute atoms in the liquid. For a faceted


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5.4 Schematics showing the growth and dissolution rates of a (a) spherical and (b) faceted grain with respect to the driving force.

grain with atomically ordered interfaces, the assumption does not hold. The growth of a faceted grain is governed either by interface reaction for driving forces smaller than a critical value or by diffusion for those larger than a critical value, as schematically shown in Fig. 5.4(b). The interface reaction-controlled growth of a faceted grain is, therefore, not linearly proportional to the driving force, unlike Wagner’s assumption.

5.2.2 Stationary and nonstationary grain growth Grain growth during LPS has conventionally been categorized into two types: normal and abnormal. Normal grain growth (NGG) has been considered to follow the diffusion-controlled LSW theory of Ostwald ripening and to exhibit an invariant (stationary) relative size distribution with annealing time. Abnormal grain growth (AGG) has been characterized by a bimodal size distribution of grains, where a few or some very large grains are embedded in a matrix of fine grains. This phenomenological classification of grain growth behavior considers only two extreme cases. In real systems, grain growth behavior which is neither normal nor abnormal is often observed. The most prominent characteristic of NGG is an invariant relative size distribution with annealing time. In this respect, grain growth behavior may be categorized into stationary and nonstationary in view of the variation of relative grain size distribution with annealing time. Stationary grain growth The growth or shrinkage of a grain in a liquid matrix can be idealized as a result of the interaction between the grain concerned and an imaginary grain of a critical



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size which neither shrinks nor grows at the moment of observation (mean field concept). When diffusion-controlled growth or dissolution occurs, the changing rate of the size of the grain is expressed as D(Cal – C -al ) da =– dt a =

2Dγsl C∞l Vm RTa

( )

1 1 –- – – a a

[5.4]

where Cal and C -al are the solubilities of the solute in the liquid for the grain with radius a and the critical sized grain with radius -a, respectively, and D is the diffusion coefficient of the solute in the liquid. (a- is, in fact, the radius of an average sized grain in diffusion-controlled Ostwald ripening.) Equation 5.4 indicates that the growth or dissolution rate of a grain is linearly proportional to the driving force (Fig. 5.4(a)). It also shows that each grain has its own growth or dissolution rate. Using Eq. 5.4, Lifshitz and Slyozov [3], and Wagner [4] analytically deduced a kinetic equation (referred to as the cubic law) for an infinitely dispersed system as follows a- 3t – -a30 =

8DγslC∞ Vm 9RT

t

[5.5]

Here, -at and -a0 are the average radii of grains at times t=t and t=0, respectively. They also showed that, irrespective of the initial grain size distribution, the relative grain size distribution becomes invariant on extended annealing (stationary - For systems with a finite grain growth) with the size of the largest grain amax=1.5a. liquid volume fraction, the growth kinetic is similar to Eq. 5.5 except for the proportionality constant, as a number of models and theories have shown [6, 8, 11]. With a reduction of liquid volume fraction, the proportionality constant increases because of the reduction of diffusion distance. Another notable feature of the effect of the reduction in liquid volume fraction is the broadening of the grain size distribution. If the mean field concept is adopted, as in the case of the LSW theory, the grain size distribution becomes that of Wagner’s interface reaction-controlled growth [6]. If the effect of neighboring grains predominates in grain growth, i.e. the communicating neighboring concept is valid, the distribution is different from the distribution of Wagner’s interface reaction control. For real systems, it was reported that the measured grain size distributions best fit the Rayleigh distribution function [10]. Nonstationary grain growth When there is any deviation from the relationship between the growth/dissolution rate by diffusion control and the driving force in a system being liquid phase sintered, as schematically shown, for example, in Fig. 5.4(b), the grain growth


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behavior is non-normal, i.e. nonstationary in terms of the relative size distribution with annealing time. According to crystal growth theories [14, 15, 17, 18], the growth of a faceted grain is governed either by diffusion or interface reaction for driving forces larger or smaller than a critical value, respectively. This is a consequence of serial processes of diffusion and interface reaction for crystal growth, where the slower process governs the overall kinetics. The dissolution rate of a faceted grain, however, is believed to be governed only by diffusion because there is no energy barrier for dissolution at the corner of the faceted crystal and the dissolution occurs over multi-atomic layers [18–20]. The growth rate of a faceted grain governed by interface reaction depends on the type of the defect present on the facets: defects (atomic steps) formed by twodimensional nucleation, a line defect (notably screw-dislocations) or a planer defect (twins). When the growth occurs via two-dimensional nucleation and growth or with the assistance of a surface twin, the growth rate da/dt takes a functional form as [15, 18, 21]

(

)

2 da ∝ exp – σ s dt kTh∆gv

[5.6]

When the growth occurs with the assistance of a screw dislocation, the growth rate takes a functional form as [14, 17] da h2 ∆g2v ∝ dt σsγsl

[5.7]

Here, σs is the step free energy (also called edge free energy), k the Boltzmann constant (1.38×10223J/atom·K), T the absolute temperature, h the step height, and ∆gv the driving force for growth. When the growth rate predicted by Eq. 5.6 or Eq. 5.7 is higher than that by diffusion, the overall growth rate is governed by diffusion as the straight line above the critical value in Fig. 5.4(b) shows. The transition between interface reaction control and diffusion control can be characterized as the critical driving force ∆gc for appreciable growth. In the case of two-dimensional nucleation and growth, ∆gc is expressed as [14, 22] ∆gc =

πσ2s (lnK)21 kTh

[5.8]

where K is a constant that includes the diffusion coefficient at the interface and the number of nuclei per unit area. The step free energy σs, which is the energy per unit length of the edge of a nucleus formed on a flat surface with a step height h, governs the equilibrium shape of grains [23]. For σs ≥ hγsl, the equilibrium shape of a crystal is a fully faceted polyhedron; when σs is smaller than hγsl but larger than zero, the equilibrium shape is a round-edged polyhedron, as schematically shown in Fig. 5.5(a). When σs=0, the equilibrium shape is a sphere. According to



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some recent investigations [24–26], the growth of partially faceted grains is also governed by the growth of facet planes. This indicates that the critical driving force for appreciable growth of a partially faceted grain is governed by the step free energy of the facet planes. Various types of nonstationary grain growth can appear depending on the contribution of the nonlinear region with respect to the driving force to the overall growth in the system. The contribution of the nonlinear region can be characterized by the value of the critical driving force, ∆gc, relative to the maximum driving force, ∆gmax, which is the driving force for the largest grain. The functional form of the nonlinear region is different for different mechanisms, as Eq. 5.6 and Eq. 5.7 show. However, two-dimensional nucleation and growth (2-DNG) may be considered as the controlling mechanism, for simplicity, because 2-DNG can govern the crystal growth even in the presence of screw dislocations [27]. Under growth by 2-DNG, various types of microstructural evolution have been predicted [20, 28], as Fig. 5.5 shows for systems with the same particle size and distribution but with different values of ∆gc. For the calculation, the values used in reference 20 were utilized. When the critical driving force is zero with zero step free energy (Fig. 5.4(a)), the average grain size increases continuously with calculation time steps following the cubic law of Ostwald ripening. For ∆gc  ∆gmax (with σs = 0.20hγsl), the growth behavior is quite normal within the calculation time steps (pseudo-normal grain growth, PNGG). For ∆gc ≈ ∆gmax (with σs = 0.49hγsl), abnormal grain growth occurs but grain growth is suppressed after impingement of abnormal grains, showing stagnant grain growth. For ∆gc  ∆gmax (with σs = 0.90 hγsl),

5.5 (b) Calculated changes in average grain size with calculation time steps for samples with different critical driving forces (step free energies, σs) shown in (a). The initial condition was taken to be the average powder radius of 0.5 µm and the standard derivation of 0.05 µm. The frequency plot of grains in (a) (dotted curve) is for a system with σs = 0.49hγsl. Schematic equilibrium shapes of a grain for different σs are also shown in (a). For the calculation, the data used in reference 20 were utilized. [in Chap. 7 of Ceramic Science and Technology, Vol. 3 (R. Riedel and I.-W. Chen (eds), 2010. Reprinted with permission of Wiley-VCH Verlag.]


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essentially no grain growth occurs (stagnant grain growth, SGG). Although the above calculation and prediction were made for a system with 2-DNG control, similar results, although not as distinctive as those of the above case, can be obtained for a system with screw dislocation-assisted growth [29]. The value of ∆gc relative to ∆gmax can also vary with a change in ∆gmax. As ∆gmax is governed by the initial powder size and distribution, various types of growth behavior can appear in the same faceted system with varying powder size. For a fine powder compact with ∆gmax  ∆gc, the growth behavior must appear quite normal (PNGG). As the powder size increases, AGG and SGG can appear. If the fine powder compact is annealed for a long period of time, grain growth behavior can change from PNGG to AGG and SGG, as a result of the reduction in ∆gmax with grain growth. Such a time variant growth behavior is typical of nonstationary grain growth. In the case of WC-Co, where the step free energy of WC is high, AGG and SGG of WC were observed with an increase in powder size [30, 31]. In the Na1/2Bi1/2TiO3-5BaTiO3 (mol%) system, where the step free energy is low, as the round-edged shape of the grains shows, PNGG and AGG appeared successively with increasing annealing time [26]. A recent investigation on the TiC-WC-Co system [32] demonstrated shape dependent growth behavior in the same liquid matrix: stationary (normal) for spherical Ti(W)C grains and nonstationary for WC grains. The faceted WC grains exhibited abnormal, incubated abnormal and stagnant growth with increasing initial WC powder size, in agreement with the prediction based on the theory of nonlinear growth behavior of faceted grains with respect to the driving force. The type of grain growth, either stationary or nonstationary, is therefore governed by the mechanism of grain growth, either the diffusion-control mechanism or mixed-control mechanism (diffusion and interface reaction), which is, in turn, related to the equilibrium shape of grains, either spherical or faceted. Many other experimental observations [33–39] also support the above theory and prediction of grain growth behavior in terms of ∆gmax relative to ∆gc, validating the general principles of grain growth in two-phase systems. Additional readings on this subject may be found in recent reviews [40, 41].

5.3

Densification during liquid phase sintering

5.3.1 Microstructural features of densification during LPS To understand the densification mechanism and phenomena during LPS, it may be useful to consider first the microstructural change during the thermal cycle of LPS. When a compact of a powder mixture of two phases with a low and a high melting point is heated, solid state reactions and sintering can occur before the formation of a liquid. At this stage, grain boundaries can form among particles and densification can occur. As a liquid phase forms above the eutectic temperature or the melting point of the low melting point powder, the formed liquid penetrates into fine



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capillaries between particles with a high melting point, leaving behind pores at their sites when the size of the low melting point powder is comparable with that of the high melting point powder [1, 42, 43]. This would be the initial state of LPS. During liquid penetration (liquid flow), solid particles may move and/or may be more closely packed (particle rearrangement), if the solid skeleton is not rigid. This process has, in general, been considered to enhance the densification. The particle movement with liquid flow and its contribution to densification, however, is different from system to system, but experimental observations in a number of the conventional LPS systems, suggest that the densification by liquid flow may not be considerable because there is no appreciable densification with the formation of liquid, as the densification curves in Fig. 5.1 show. In Fig. 5.1, the shapes of the curves for the two samples are similar, except the temperature range for rapid densification, suggesting that the rapid densification in the sample with 5µm W powder is not due to the formation of a liquid phase. A model calculation [44] also suggests that the densification with liquid formation is insignificant even in a system with spherical particles with a zero dihedral angle. When particle movement is possible with liquid formation, pores of a size larger than the original ones can also form [44, 45]. After the formation of a liquid, the interactions between solid grains and the formed liquid, such as dissolution of solid into liquid, occur more rapidly. According to a recent investigation [46], this process can enhance the packing of solid grains, hence the densification. The contribution of the dissolution of solid grains into liquid to densification, however, must be system dependent and its validity is uncertain for systems where grain boundaries form between solid particles. Densification with solid dissolution can be significant with the application of an external pressure [47, 48]. The external pressure effect would be related to the reduction of the rigidity of the solid skeleton with the formation of liquid and the dissolution of solid grains into liquid. The initial state of LPS may be represented by a compact containing uniformly distributed solid grains and pores in a liquid matrix, which is in chemical equilibrium with the solid. The pores are eliminated and considerable grain growth occurs during subsequent LPS, as typified in Fig. 5.2. After full densification, the microstructure consists of uniformly distributed grains in a liquid matrix. This microstructure can be idealized as grains of an equal size with regular packing in a liquid matrix. With the reduction of liquid volume fraction, the grain shape becomes increasingly anhedral. For a system under given experimental conditions, such as a given dihedral angle and a given liquid volume fraction, there exists an equilibrium shape of grains, which is determined by the condition of the minimum interfacial energy of the system [49]. Densification is, therefore, a process of attaining this microstructure via elimination of pores in the compact. The pressure in the liquid, Pl, in a solid/liquid two-phase system is expressed as Pl = Pout –

2γlv r

[5.9]


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where Pout is the external atmospheric pressure, γlv is the liquid/vapor interfacial energy, and r the radius of the liquid meniscus. Because the pressure in the liquid is lower than the external pressure, the compact is in compression, which can be considered as an effective pressure on the surface of the compact, if the contribution of the liquid/vapor surface tension is neglected. The force acting on each grain due to the effective pressure is balanced with a sphering force of the grain [49], and, hence, an equilibrium shape of grains is defined for given experimental conditions, such as liquid volume fraction and dihedral angle.

5.3.2 Densification models and theories The classical densification model [50] and theory [51] consider the sintering states from right after liquid formation to the completion of densification. The possible rearrangement of particles and resultant densification due to the flow of liquid were considered to be the characteristics of the initial stage of LPS. As explained in the preceding section (§5.3.1), the densification by liquid flow appears to be inconsiderable in pressureless LPS, unless a mass flow of solid grains and liquid occurs. In this respect, the liquid flow stage will not be discussed further. Reactions between solid and liquid on densification will also not be considered, although they may contribute to densification. After redistribution of liquid via liquid flow, the microstructure is characterized by a fairly uniform distribution of grains and pores in a liquid matrix. The grains will tend to achieve their equilibrium shape for a given liquid volume fraction, although many of them are also in contact with pores. A theoretical calculation [52] and an experimental observation [53] suggest that the grain shape change to an equilibrium shape is achieved mainly by grain growth. As the equilibration reactions and grain growth occur rapidly at the beginning of LPS, the shape of grains after liquid flow may be considered to be an equilibrium shape. Figure 5.6(a) [54] shows a schematic microstructure after liquid flow. For such a microstructure with grains and pores of different sizes, two densification mechanisms have been proposed: (a) contact flattening [51] and (b) pore filling [42, 54]. These two mechanisms have very different views of densification during LPS in terms of the material transport mechanism and may need to be discussed in detail, as in a previous description [13]. The contact flattening mechanism is based on the fact that the pressure in the liquid is lower than that of the atmospheric pressure outside the sample, following Eq. 5.9. Because of the lower pressure in the liquid, the grains are under compression. If a liquid film is present between grains and the film can transfer the compressive stress, the chemical potential of atoms at the contact region between grains is higher than that of the off-contact region. As a result, material dissolves at the contract region and the dissolved material transfers to the offcontact region, resulting in a change of grain shape (grain shape accommodation) and in pore shrinkage. This process assumes the presence of a difference in the chemical potential of atoms between the contact area and the off-contact area.



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5.6 Schematic microstructures showing the densification by pore filling: (a) and (b) just before and right after the liquid filling of small pores (Ps), (c) grain shape accommodation by grain growth and homogenization of microstructure around the liquid pockets and (d) just before the liquid filling of a large pore (P1) [54]. For the purpose of demonstration, the grains in (c) are drawn as extremely anhedral. ρi: radius of liquid meniscus; li: specimen length; LP: liquid pocket. (Reprinted with permission of Wiley-Blackwell.)

This assumption, however, is not justified for most of the time period of densification because the grain shape tends to become an equilibrium shape from the very early stage of LPS for a given liquid volume fraction. When the grains achieve their equilibrium shape for a given liquid volume fraction, there is no difference in the chemical potential of atoms from region to region and, therefore, no driving force for grain shape change. A pore in the compact, which is, in fact, an internal surface like the external sample surface, behaves like an insoluble second phase particle before its elimination. This understanding indicates that there is essentially no driving force for material transport from the contact area to the off-contact area in a sample containing pores. The contact flattening mechanism is valid only in a system where grains do not have their equilibrium shape, such as at the very early stage of LPS, or in a system with a very small volume fraction of liquid such that the liquid is present only in the neck region between particles. A model calculation suggests that contact flattening can be an important mechanism only at the initial stage of sintering and that its contribution decreases with increasing particle size [52]. © Woodhead Publishing Limited, 2010

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5.7 Schematic changes at the sample and pore surfaces showing the mechanism of pore filling: (a) stable state of a pore, (b) critical moment for pore filling (complete wetting of the pore surface) and (c) liquid filling immediately after the critical moment [56]. P: pore; ρ: the radius of liquid meniscus (ρ1< ρ2, ρ2≤ ρ3). (Reprinted with permission of Wiley-Blackwell.)

The pore filling mechanism is based on experimental observations of liquid filling of natural as well as artificially formed large pores [1, 42, 43]. The driving force for pore filling is the difference in liquid pressure between the regions of the sample surface and the pore surface, which arises right after a critical moment of pore wetting [55]. Figure 5.7 [56] schematically depicts the microstructures at the sample and pore surfaces with the wetting angle of zero degrees, for simplicity, to explain the pore filling process and its driving force. As the grains grow, the radii of liquid menisci at the sample surface and at the pore surface increase in proportion, if the gas pressure in the pore is the same as the external atmospheric pressure [57]. The pressure in the liquid is the same everywhere (hydrostatic pressure) (Fig. 5.7(a)). At this stage, the chemical potential of atoms in a grain is the same everywhere and there is no driving force for grain shape change. As the radius of the liquid meniscus becomes equal to the pore radius as a result of grain growth, the pore is completely wetted (Fig. 5.7(b)). With further growth of grains, the radius of the liquid meniscus at the sample surface increases while that at the pore surface is limited to the pore radius. Because of the difference in radius of



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liquid menisci between the sample and the pore surface, a pressure difference arises between the two surfaces, following Eq. 5.9, and the liquid flows from the regions of the sample surface and other intact pore surfaces towards the pore (Fig. 5.7(c)). Although the pore filling mechanism is explained for a system with spherical pores, it is also applicable to a system with irregular shaped pores because an irregular shaped pore is coagulated spherical pores of different sizes. The pore filling mechanism indicates that the pore filling, i.e. the densification, occurs as a result of grain growth. It further indicates the size of pores that can be filled with liquid to be linearly proportional to the radius of the liquid meniscus and hence the average grain size. The densification during LPS is, therefore, induced by grain growth (grain growth-induced densification), when pore filling is the dominant mechanism of LPS. Depending on the availability of the two mechanisms, contact flattening and pore filling, the expected microstructural development is different. When contact flattening is predominantly operative, the average pore size must decrease and grains must become increasingly anhedral with densification. In addition, the time needed for densification is expected to be similar for samples of different porosity but with the same pore size distribution. These expected microstructural changes and sintering kinetics have never been observed in real systems, indicating that the contact flattening mechanism is not a dominant mechanism of densification during LPS. According to the pore filling mechanism, however, the smaller pores disappear earlier and the larger pores later with grain growth. The time needed for densification increases with increasing porosity. These expected microstructural changes are observed in real systems, suggesting that the pore filling mechanism is the dominant densification mechanism of LPS. Figure 5.6 depicts schematically the microstructural change during LPS of a powder compact containing pores of different sizes (pore filling model of LPS) [54]. With grain growth, small pores disappear by liquid filling of pores and the density of the compact measured by the Archimedes method increases (Fig. 5.6(b)). As the pore filling is, in fact, the suction of a fraction of the liquid by the pores, the effective volume fraction of liquid in other dense regions decreases and the grain shape tends to become more anhedral during subsequent growth in the dense region, as observed in a model experiment with a reduction of liquid volume fraction during sintering [53]. Then, shrinkage results (Fig. 5.6(c)). With microstructural homogenization around the formed liquid pockets, the grains tend to restore their equilibrium shape and subsequent filling of larger pores occurs with grain growth. In real systems with a size distribution of numerous pores, these processes occur continuously and concomitantly. Densification and shrinkage occur concomitantly, not separately. The shape of grains for the given liquid volume fraction must also be effectively invariable during grain growth and densification. The pore filling theory [58, see also the computer program at http://milab.kaist. ac.kr], which was developed based on the pore filling model [54], allows us to


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estimate the effects of various processing parameters, such as the initial particle size, liquid volume fraction, wetting and dihedral angle, porosity and pore size distribution, on densification kinetics. The effect of liquid volume fraction fl is more pronounced than that of porosity Vp. The densification kinetics is approximately proportional to ( fl)23 and (Vp)2 for a system where grain growth is governed by diffusion. According to the pore filling theory, it is possible to predict the microstructural development in terms of relative density vs. average grain size. Figure 5.8 is an example showing the effects of liquid volume fraction (a) and wetting angle (b) [59]. As the liquid volume fraction increases, the radius of liquid meniscus increases for a given grain size. The average grain size necessary for densification decreases and the sintering time is greatly reduced. The wetting angle also considerably affects the densification kinetics. As the wetting angle increases, the complete wetting of the pore surface, the critical moment of pore filling, is retarded. As a result, the densification is also retarded. With an increased dihedral angle for a fixed wetting angle, however, the densification is enhanced because the radius of the liquid meniscus increases as the dihedral angle increases. The system we have considered so far consists of spherical or rounded grains where the radius of the liquid meniscus is linearly proportional to the average grain size. For a system with faceted grains, such as WC-Co, where nonstationary grain growth occurs (§5.2.2), the radius of the liquid meniscus may not be linearly proportional to the average grain size. It is, however, certain that the radius of the liquid meniscus increases with grain growth. The densification is, then, expected to be enhanced by increasing the grain size, if the pore size and distribution are the same. Figure 5.9(a) plots the densification curves of WC-Co powder compacts with different WC powder sizes [60]. The green densities of the compacts were

5.8 Microstructure development maps (relative density vs. grain size trajectories) showing the effects of (a) liquid volume fraction and (b) wetting angle [59]. Ko: rate constant in diffusion-controlled grain – – growth equation, G3t – G30 = Ko t; Vp: pore volume; fl: liquid volume fraction. (Reprinted with permission of Carl Hanser Verlag.)



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5.9 (a) Densification curves of 88WC-12Co (wt%) powder compacts with WC powders of different sizes during heating to and liquid phase sintering at 1350 °C. At the beginning of liquid phase sintering, the relative densities of samples with different WC powder sizes were the same. (b) Calculated densification curves using the computer program of the pore filling theory. The data points show measured densities [60]. (Reprinted with permission of Wiley-Blackwell.)

different; however, at the beginning of LPS, the densities and the pore size distributions of the compacts were similar. According to this result, the densification is enhanced by increasing the powder size, in agreement with the pore filling theory prediction. The densification curves calculated using the pore filling theory (Fig. 5.9(b)) also agree well with the measured data, considering possible differences in grain size distribution among samples as a result of nonstationary grain growth. This result also suggests that pore filling is the major densification mechanism of LPS for faceted systems.

5.4

Summary

This chapter has described the fundamentals of grain growth and densification during liquid phase sintering (LPS). Grain growth behavior is either stationary or nonstationary depending on the equilibrium shape of grains, either spherical or faceted. The grain growth behavior during LPS can be predicted in terms of the value of the maximum driving force for growth (∆gmax) relative to the critical driving force for appreciable growth (∆gc), which is largely governed by the step free energy. When ∆gc=0, stationary (normal) grain growth results. On the other hand, when ∆gc≠0, various types of nonstationary grain growth result: pseudo-normal grain growth for ∆gmax  ∆gc, abnormal for ∆gmax ≈ ∆gc, and stagnant for ∆gmax  ∆gc. Many experimental observations support the prediction and theory, validating the general principles of grain growth in terms of ∆gmax relative to


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∆gc. For densification, there are essentially two mechanisms available: contact flattening and pore filling. The validity of contact flattening can be found in a system where the grain shape is not at an equilibrium shape in the liquid. The mechanism can, therefore, be valid at the very early stage of LPS with point contacts of particles. It can also be valid in a system with a very small volume fraction of liquid so that the liquid is present only in the neck region between particles and the growth of particles is suppressed. The pore filling mechanism is justified for most of LPS where the grain shape can be considered to maintain an equilibrium shape. The microstructural evolution observed in real systems supports the pore filling mechanism rather than the contact flattening mechanism. The author acknowledges Dr. John G. Fisher for reading this manuscript, and Dr. Sung-Min Lee for providing the pore filling theory calculation program of LPS.

5.5

References

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6 Master sintering curve and its application in sintering of electronic ceramics C. B. D iAntonio and K. G. Ewsuk, Sandia National Laboratories, USA Abstract: The ability to optimize and tailor the properties of an electroceramic is one of the most challenging capabilities that an electroceramist must develop. Due to the fact that such a strong link exists between the microstructure of an electroceramic and its macroscopic electrical properties, significant efforts need to be made to control the factors and parameters that influence the characteristics of the microstructure. This chapter discusses the construction, utilization, and implementation of master sintering curves as specifically applied to electroceramics. The findings presented here demonstrate that a systematic approach to design, predict and control sintering of electroceramic systems is possible through the implementation of the master sintering curve. Key words: master sintering curve, electroceramic, sintering, densification.

6.1

Introduction to electroceramics

For many thousands of years ceramics have been used by people for a wide variety of applications. Archaeological sites in numerous areas have unearthed some of the oldest artifacts that reveal pottery was being used not only for everyday things, including the storage of food, but for use in the communication of information, such as correspondence on fired clay tablets. The word ‘ceramic’, derived from the Greek word, keramos, for potter’s clay or ware made from clay and fired, is based on clay and other siliceous minerals that are fired around 1000 °C. The meaning of the word ‘ceramic’, though, has broadened significantly with the evolution of ‘pottery’ to what are typically referred to as ‘advanced ceramics’. It now tends to describe ‘… solid articles which have as their essential component, and are composed in large part of, inorganic non-metallic materials’,1 although this description has also become quite limited, as amorphous materials, metallics, organics and single crystals are important components of many polycrystalline, inorganic, non-metallic and multiphase ceramics. Thus, in a broad sense, a ceramic is typically defined as a polycrystalline aggregate of particles which are typically consolidated and fused into a material through the sintering process. The parameters involved in sintering a ceramic are often controlled to eliminate porosity introduced from the forming process used to make a ‘green’ body. It is a feature of ceramic processing that careful control is used in sintering so that, although significant linear dimensional shrinkage may be realized, the overall shape remains substantially unchanged unless by design. In the case of pottery or 130 © Woodhead Publishing Limited, 2010

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porcelain, constituents are added that result in a liquid phase that sinters the aggregate particles together. As a property of many siliceous materials, their stability when exposed to extremes of weather and the high electrical resistivity led to the first use of ceramics in the electrical industry and the eventual development of electroceramics. Thus the methods developed for pottery were refined for the production of insulating bodies, for use in carrying and isolating electrical conductors, leading to applications in power lines, cores bearing wire wound resistors, electrical fire elements, etc.2 Since the end of the twentieth century ceramics have come to play an increasingly significant and important role in the electronics circuit and systems research, development and industry. The applications of ceramics in the electronics industry or ‘electroceramics’ can be broadly divided into two groups: • Materials for interconnection and packaging for semiconductor circuits. • Functional or active electroceramics, discrete components performing a function – e.g. capacitors, sensors, etc. The first half of the twentieth century was dominated by ceramics used for electrical applications based on their characteristic high degree of chemical stability and high electrical resistivity. It also became evident with time that the possible range of properties for ceramic-based electronic materials was extremely wide, as listed in Table 6.1. Table 6.1 Listing of electroceramic materials, use, approximate introduction timeframe, characteristics of interest, and applications Material/Use/ Introduction timeframe

Characteristics of interest

Application

Magnetite, ‘lodestone’ (Early 20th century)

Electrical conductivity, magnetic properties, chemical inertness

Anode in the extraction of halogens from nitrates

Lanthanide oxide doped zirconia (Early 20th century)

High temperature with applied current

Nernst filament, effective source of white light

Fast-ion conductors (Early 20th century)

Electrical conductivity through ion transport

Fuel cells, batteries, sensors

Ferrites (1910s), nickel-zinc High resistivity and and manganese zinc susceptibility to eddy ferrites currents

Choke and transformer core materials (frequencies up to and beyond 1 MHz)

Barium Ferrite, magnetic ceramic powders, gamet type structure (1930s)

Ferromagnetic

Permanent magnets, recording tapes, computer memory, toroids, microwave technology

Conductive ceramics (1920s)

Electrical conductivity

Silicon carbide heating elements (Continued)


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Table 6.1 Continued Material/Use/ Introduction timeframe

Characteristics of interest

Application

Negative temperature coefficients of resistivity ceramics (1920s)

Resistivity as a function of temperature

Temperature indicators

Porous ceramics, numerous compositions (1920s)

Resitivity as a function of local atmosphere (moisture content and oxidation potential)

Detectors for toxic or flammable components

Dielectrics (1930s), multilayer structures, low-temperature co-fired ceramics (1980s)

Relative permittivity, low sintering temperature, co-sintering

Capacitors, electronics packaging, substrates

Piezoceramics, lead zirconatetitanate composition family

Ferroelectricity, piezoelectricity, electrostriction, pyroelectricity, electrooptic behavior

Actuators, sensors, transducers, transformers, sonar, ultrasonics, infrared detectors

High positive temperature coefficient resistors (PTC), doped Barium Titanate

Resistivity as a function of temperature

Thermostatic heaters, current controllers, degaussing devices, fuel-level indicators

Superconductors, Yttrium, Barium, Copper Oxide (YBCO)

Superconductivity at high transition temperatures

Electrical power distribution, permanent magnets

Porous ceramics, numerous compositions (1920s)

Resistivity as a function of local atmosphere (moisture content and oxidation potential)

Detectors for toxic or flammable components

Varistors, silicon carbide and zinc oxide based ceramics (1950s)

Unique and sensitive behavior of the electrical resistivity to the applied electrical field strength

Transient electrical surge suppression, Spark suppression at relay contacts

Glass-ceramics (1950s)

Electrical resistivity, thermal expansion dimensional stability

Electrical insulators, electronic packaging technology

As one of the largest industry-based areas of the ceramics field, ‘Advanced Ceramics’ as they are categorized and of which the electroceramics industry is typically considered a sub-category, have favorable performance characteristics that have enabled growth into applications such as capacitors, cutting tools, membranes and orthopedic joint implants. Accounting for nearly half the advanced ceramics market demand in recent years, the use of advanced ceramics is highly dependent on the health of the electronic components and electrical equipment industries.



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Table 6.2 Application of advanced electroceramics as classified by the applied electronic function Electroceramic materials

Application

Insulation – Al2O3, BeO, MgO Integrated circuit, wiring, resistor, and electronics interconnection substrates, packaging, etc.

Ferroelectrics – BaTiO3, SrTio3 Ceramic capacitors Piezoelectrics – PZT, PLZT Transducers, ultrasonic devices, oscillators, filters, spark generators, etc.

Semiconductors – BaTiO3, SiC,

Negative temperature coefficient ZnO-Bi2O3, V2O5, transition thermistors – temperature sensors and metal oxides compensation, etc. Positive temperature coefficient thermistors – heater elements, switches, temperature compensation, etc. Critical temperature resistor thermistors – heat sensor elements Thick-film sensors – infrared sensors Varistors – noise suppression, surge current absorber, lightning arrestors, etc. Sintered CdS – solar cells SiC heater elements

Ionic conductors – β-Al2O3, ZrO2 Solid electrolytes, oxygen sensors, pH meters, fuel cells

Table 6.2 lists the applications of advanced electroceramics as classified by the applied electronic function. The United States electronic components industry is projected to remain sluggish, as Asia tends to dominate this area. However, growth opportunities still exist due to materials substitution as ceramics gain use over alternatives. For example, permanent magnets and capacitors will benefit from an increase in the production of small, economical and energy efficient automobiles. Unreinforced ceramics cast directly into final form, or ‘monolithic ceramics’, represent the largest and best-established segment of the advanced ceramics industry. By far the dominant monolithic product, accounting for half of the total monolithic ceramics demand recently, are ceramics for electrical equipment and electronic components. Although produced from numerous materials, these advanced ceramics are typically manufactured from materials with very high purity levels and are sintered under strictly controlled profiles and conditions, unlike the more traditional ceramic products such as flooring, wall tiles, pottery, china, refractory brick, etc. This results in specifically tailored microscopic/macroscopic properties, e.g., conductivity, resistivity, permittivity, ferroelectricity, etc., which are critical to the proper performance of the component in application. The final macroscopic properties therefore are intimately tied to the chemical composition of the material (based on the intrinsic properties), atomic structure, ceramic fabrication techniques and


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6.1 Illustration depicting the intimate tie of the chemical composition, atomic structure, ceramic fabrication parameters, and microstructure to the macroscopic properties of a material.

microstructure of the polycrystalline ceramic, as illustrated in Fig. 6.1. At present an enormous factor in the industry is associated with rising production costs, as seen in energy and machining costs. These costs could be addressed and possibly even reduced through more exact product forming by employing near-net shape techniques and improved sintering control, prediction and modeling.

6.2

Sintering and densification of electroceramics

Ceramics can densify by solid-state,3–6 liquid-phase,7 and viscous8 sintering. Overall, the reduction in surface energy as the free surfaces of initially individual and discrete particles coalesce is the major ‘driving force’ for densification in a polycrystalline ceramic. Specifically, polycrystalline ceramics sinter as a result of the thermodynamic driving force to minimize the Gibbs’ free energy, G, of a system,9–13 including minimizing the volume, interfacial, and surface energy in the system. This reduction in energy is accomplished by atomic level diffusion processes. These processes result in either densification of the ceramic body (internal grain matter is transported to the pores), coarsening of the microstructure (rearrangement of matter from various locations on pore surfaces with none to minimal decrease in pore volume), or a complex combination of all mechanisms. The sintering process encompasses permanent chemical and physical changes in a ceramic body that are occurring in harmony with changes in the porosity and density. Excess free energy, in a consolidated powder body, is primarily present in the form of the surface or interfacial energy (i.e., liquid–vapor and/or solid–vapor © Woodhead Publishing Limited, 2010


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interfaces) associated with porosity. Atoms migrate to thermodynamically more stable positions under the influence of elevated temperature and/or pressure during sintering. The chemical potential difference that exists between surfaces of dissimilar curvature within the system is what essentially drives material transport. As viewed from the center of a particle out, for a particulate system, atoms or ions move from convex particle surfaces to concave particle surfaces to decrease the curvature and chemical potential gradients in the system. The transport of material can occur by solid-state (material transfer by solid state diffusion), liquid-phase (material transfer by solubility and precipitation in the liquid phase), and/or vapor-phase (material dissolution into and diffusion through the liquid, followed by reprecipitation) mechanisms. This transport commonlyoccurs as ions diffuse through the volume, along grain boundaries (i.e., particle-particle intersections), and on particle surfaces, as depicted in the simplified ‘two-sphere model’ illustration in Fig. 6.2. Material transport occurs through the process of diffusion, the movement of atoms/ions, sometimes referred to as atom jump. Diffusion can occur along a number of paths including, but not limited to, grain boundaries or through the grain itself (lattice diffusion). Additionally, ions can vaporize from particle surfaces and subsequently re-condense onto more energetically favorable particle surfaces (i.e., evaporation-condensation). In general, when material transport occurs in such a manner that allows particle centers to approach during sintering, a ceramic body

6.2 Schematic representation of a generic ‘two-sphere’ model showing the simplified distinction between coarsening (non-densifying) and densification processes that result from atom movement (diffusion) during ceramic sintering.


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will undergo volume contraction and densify (volume and grain boundary material transport mechanisms can result in densification). If the active and dominant material transport mechanisms only change the geometry of the system without densification then only coarsening of the microstructure will result. Coarsening can occur when material is transported by volume diffusion, surface diffusion and/or evaporation/condensation. The most prevalent form of coarsening during the sintering process tends to be grain growth.

6.2.1 Densification and microstructure development It is in the sintering stage of the overall ceramic fabrication route that the ceramic body develops the desired microstructure. Interparticle pore shrinkage, grain boundary formation, a decrease in the total volume of the system through densification and an increase in the average size of the particles that make up the ceramic system through grain growth is how, from the aspect of the microstructure, material transport manifests itself during sintering. As sintering progresses, the surface area and free energy of the system decrease as porosity is eliminated and the overall curvature in the system decreases. Three basic stages have been defined for the ‘ideal’ sintering process: initial, intermediate and final stage sintering.3,6 In the initial stage, necks form between adjacent particles as material is transported from convex particle surfaces to the poregrain boundary intersection. The grain boundaries grow to create a three-dimensional array of approximately cylindrical, interconnected and continuous pore channels at three grain junctions. The intermediate stage of sintering is characterized as the decrease in the diameter of these pore channels. The channels eventually pinch off, due to Rayleigh instability (critical ‘cylinder’ length to diameter ratio), to approximately spherical and isolated (closed) pores at four grain junctions in the ceramic microstructure. The final stage of sintering is marked with the radial shrinkage of these closed pores and the growth of larger grains at the expense of smaller ones. Depending on the complexity of the starting materials, the changes occurring during sintering may be fairly complex in nature. The complex nature of the process has led to its analysis through a combination of theoretical analyses in terms of modeling (in many cases idealized modeling) combined with experimental investigations. The understanding of the sintering process/mechanisms therefore has matured considerably in the past half century. The major conceptual advances have originated, to a significant extent, from the advances in researchers’ ability to observe, characterize and quantify the sintering and densification mechanism(s) involved in the process. For the majority of electroceramic materials sintering is achieved either by solid state or liquid phase sintering mechanism(s), at least in the absence of an appreciable amorphous or glassy phase. A major constituent in tableware and electrical porcelain is the formation of a glassy phase that mainly develops from the presence of fluxes (feldspathic minerals). The glassy phase forms and wets the surfaces of the solid phase and a large fraction of the porosity is filled with glass © Woodhead Publishing Limited, 2010


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as the surface tension forces pull the mass of particles together. In almost all cases some of the initial porosity gets trapped in the microstructure as the gas cannot escape quickly enough through the vitreous phase. The glassy phase also tends to form a continuous network in the microstructure, resulting in modified electrical properties. This manifests itself in a tailored dielectric loss based on the application and intended use, so that electrical porcelain is used for adequate electrical insulation as the major requirement. In the absence of this glassy phase densification can be achieved by solid state or liquid phase sintering mechanism(s) or some complicated combination of these mechanisms.

6.2.2 Solid state sintering For solid state sintering to initiate, the ions that comprise the ceramic must have sufficient mobility in the microstructure. This is typically not achieved until the temperature of the ceramic is greater than approximately 80% of the melting temperature. In the early stages of solid state sintering the microstructure undergoes significant changes. One of the dominant diffusion mechanisms in this early stage can be attributed to the surface diffusion of ions from convex surfaces, to the concavities at particle contact points, reducing the curvature and lowering the free energy of the system. This mechanism, however, does not contribute to any densification as this process results only in mass transport by vacancy diffusion in regions close to the surface of a pore, changing the shape of the pore. The vacancy concentration in these regions of the microstructure is high relative to the equilibrium concentration in the bulk of the ceramic. Overall, densification occurring by solid-state diffusion controlled material transport refers to the process of ‘solid–state’ sintering. As higher energy solid–vapor interfaces, porosity, are replaced by lower energy solid–solid interfaces (grain boundaries), densification can occur. The densification is driven by the change in free energy associated with the elimination of this porosity. The grain boundaries act as vacancy sinks by virtue of their intrinsic disorder to facilitate pore shrinkage and densification. Following the elimination of pore surfaces and completion of densification, the free energy of the system can be further reduced by reducing the amount of high-energy solid–solid interfacial area through grain growth. The grain growth is driven by the change in free energy associated with the elimination of particle–particle interfaces. Therefore densification occurs via the reduction in size of thermodynamically unstable porosity. It is, however, kinetics that limit the shrinkage of pores trapped within grains, intra-granular porosity and pores larger than a ‘critical’ size.14–16

6.2.3 Liquid-phase sintering In liquid-phase sintering, conditions of temperature and composition are chosen so that a quantity of liquid, usually on the order of a few volume percent or less, is formed between the grains of the ceramic. Traditional liquid-phase sintering © Woodhead Publishing Limited, 2010

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involves heating and melting crystalline solids to form a eutectic liquid during sintering.7 Ion mobility is assisted by the formation of small quantities of the liquid. It is important for liquid-phase sintering that the crystalline phase has a limited solubility in this liquid to control the dissolution processes. In this case a ‘solution precipitation’ process, where ions dissolve at high-energy sites and precipitate at lower energy sites, produces mass transport (one of the most common liquid-phase sintered electroceramic components is the alumino-silicate based compositions used in high-temperature co-fired ceramics). Transport of dissolved grain material through the liquid allows closer packing of the grains and densification of the material as the grains are reshaped. As the material cools the liquid crystallizes or forms a glass and can yield a dense solid ceramic body. Therefore, for liquid-phase sintering, the requirements include that the liquid wets the solid particles, there is sufficient liquid present, and the solid is soluble in the liquid. As the temperature is increased above the eutectic temperature there is an increase in the concentration of the liquid and the solubility of the solid in the liquid or an increase in the reactivity. Overall, if it is energetically favorable to replace the liquid–vapor, solid–solid and solid–vapor interfaces during sintering, then densification will proceed. The process of densification during liquid-phase sintering can be described in a series of stages. Initially the liquid forms at particle intersections and begins to redistribute itself through the ceramic matrix due to the influence of capillary action. Particle rearrangement, typically resulting in improved particle packing, occurs due to shear stresses that have developed from the capillary pressure imbalance on the individual particles (each having a particular size and morphology) and contributes to the initial stage densification. The microstructure continues to mature into an intermediate stage where solution-precipitation controls the densification. Material located at convex particle surfaces starts to dissolve and can now migrate to pore surfaces where it precipitates out of solution to lower the system free energy. It is at this point where individual grains can actually change shape to fill in void space (porosity). This process is often referred to as ‘grain accommodation’. A rigid three-dimensional skeletal structure starts to form and densification continues by solution-precipitation. When closed pores are formed the transition to the final stage of liquid phase begins and, as with solid-state sintering, is characterized by the shrinkage of isolated pores and grain growth. Due to the fact that such a strong link exists between the microstructure of a ceramic and its macroscopic electrical properties, significant efforts need to be made to control the factors that influence the characteristics of the microstructure, including the grain size distribution, grain boundary characteristics, porosity, etc. Optimized conditions, initial particle sizes, tailored sintering schedules, and specific chemical compositions need to be determined based on the macroscopic property needs for a particular application or use. In some cases the differences in grain growth and densification kinetics could be exploited to produce a desired



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and optimized macroscopic property. It should also be mentioned that not in all cases involving the sintering of electroceramics is it always possible to obtain a minimal porosity body by ‘pressureless sintering’, sintering at atmospheric pressure, as just discussed. In some situations an optimized microstructure may require the complete elimination of porosity and the maintenance of a discrete grain size or grain size distribution. Hot pressing, hot forging, spark plasma (field assisted) sintering and/or isostatic hot pressing is typically employed as a sintering technique to achieve these results. These techniques can provide more control over densitication relative to coarsening during sintering as the pressure and/or applied electric field now provides a major part of the driving force to eliminate porosity and densify the microstructure as desired.

6.3

Master sintering curve as applied to electronic ceramics

The ability to optimize and tailor the properties of an electroceramic is challenging for the electroceramist. This ability requires having a basic understanding of the range of properties, including but not limited to the conductive, dielectric, optical, piezoelectric and magnetic properties and how they are intimately interrelated in the ceramic. Fundamental scientific understanding can be exploited to optimize the desired properties through the design of the material composition and the tuning of the microstructure and texture. The additional objectives of significantly reducing sintering temperature and simplifying the manufacturing to fabricate a ceramic component often make property optimization extremely difficult. Conventional microcrystalline powders present problems due to agglomeration, surface contamination, undesired grain coarsening and exaggerated grain growth, etc. this makes reproducible ceramic processing of homogeneous materials, that retain the highly desirable features after sintering, a challenge. The cost-effective manufacture of reliable ceramic components is critical for advanced ceramic component manufacturing and is typically manifested in robust and reproducible ceramic processing. The processes used to manufacture ceramic components has historically been developed from empirical engineering, but this alone cannot provide the necessary fundamental understanding for consistent, reproducible material processing. The integration of a fundamental understanding into a sciencebased processing technology that can be applied to more fully understand and control ceramic powder processing and sintering is one approach.17–24 The driving force for densification and microstructure evolution, and the mechanisms and paths for material transport during sintering6,25–27 are reasonably well understood (Note: the provided references are in no way exhaustive of the numerous literature sources available but are only intended to provide a starting point for exploration into the enormous subject of the sintering of ceramics; the additional chapters in this book also provide extensive information on these topics). The practical application of this fundamental sintering science and the link to a set of desired


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properties, though, remains a challenge. Over the years researchers have developed and used processing and sintering maps to design and interpret sintering experiments in an effort to gain a better understanding of how specific thermal profiles affect the sintering behavior and the resultant ceramic microstructure.28–34 These maps aid in simplifying the analysis of sintering results and have the potential to enable practical applications of the fundamental science of sintering theory in ceramic manufacturing. Recently another promising and practical approach to predict, control and tailor sintering has been introduced and is based on the concept of a master sintering curve (MSC).35–45 The MSC provides a characteristic measure of the densification of a material, within the boundary conditions of a specific density range, as determined through experimentation. It is an empirical curve and unique for a given material processed in a specific manner. By constructing an MSC for a given system the density and densification rates of a ceramic body can be predicted. The construction of the curve requires a few basic dilatometric sintering experiments, providing the necessary sintering behavior to allow predictions for almost any combination of sintering time and temperature, within the boundary conditions. Comparisons of the predicted, experimentally measured and modeled sintered densities of numerous ceramic systems have provided overwhelming verification of the predictive power of the master sintering curve concept.44,46,47 Although originally developed and demonstrated for traditional microcrystalline solid-state sintering ceramic systems, with isotropic sintering behavior, the concept of the master sintering curve has been extended to encompass systems exhibiting anisotropic, liquid phase, viscous phase and nanocrystalline sintering behavior.47 To construct and implement a master sintering curve the parameters in the sintering rate equation that governs it are separated, with terms related to the development of the microstructure and terms related to the temperature realized by the body, to opposite sides of the equation. The two sides of the equation are then related to each other experimentally. In most cases, for ceramic powder systems and ceramic processing and forming techniques, the geometric parameters of the microstructure are independent of the thermal sintering path, making this generalization possible and coherent. Although a general concept, the formulation and construction of an MSC are derived from the combined stage sintering model.27 The instantaneous linear shrinkage rate and equivalent isotropic densification rate as described by this model is given as: 2

dρ γΩa dL = = Ldt 3ρdt kBT

(

)

δDbΓb DΓ + v3v 4 G G

ρ = density of the ceramic body (g/cm3) γ = specific surface free energy Ωa = atomic volume kB = Boltzmann constant G = mean grain diameter


[6.1]


141

δ = grain boundary thickness (thickness of the region of enhanced diffusion at the grain boundary) Db = grain boundary diffusion coefficient Dv = volume diffusion coefficient αCkCb [6.2] Γb = geometric factor for grain boundary diffusion = Cλ Ca Ch Γv = geometric factor for volume diffusion =

αCkCv Cλ Ca Ch

[6.3]

This model extends the analysis of sintering beyond the secluded segments proposed by models that only account for individual sintering stages. Sintering models have been sought for since the earliest quantitative sintering studies were performed, with the typical objective being to gain a deeper understanding of the mechanisms involved in densification and to acquire the ability to relate sintering rate to the particle characteristics, ‘as-formed’ ceramic body characteristics, atmosphere and thermal profile. In many cases simplified geometries were used to identify sintering driving forces, mass transport paths, and geometric factors. As sintering proceeds the geometric factors continuously change and can be understood based on the DeHoff model,48 where each of these factors in Eq. 6.2 and Eq. 6.3 relates the mean grain diameter to a particular geometric factor for sintering, according to: αK ∇µ = = gradient in chemical potential λ λ = C2 G = maximum distance of diffusion C K = 2 k = curvature at the pore or neck surface G δLb/2 = δGCb = area for grain boundary diffusion Av = CvG2 = area for volume diffusion Sb = CaG2 = grain boundary area at the base of the pyramid h = ChG = height of the pyramid Note: In this model each grain is considered to be an irregular polyhedron defined by the grain boundaries between the grain and its nearest neighbor, where the polyhedron consists of pyramids with a common apex at the center of the grain, and the bases are defined at the grain boundaries. By extending the polyhedron into the pores the total volume of the body is included in the sum of all the polyhedra. Thus the grouped scaling parameters, Γ, relate the instantaneous shrinkage rate to the diffusion coefficient and other material parameters and mean grain diameter. Unless significant exaggerated grain growth or excessive surface diffusion occurs, during sintering these experimentally determined values are dependent on the density of the body but are independent of the thermal profile. Recognizing that


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both the mean grain diameter, G, and the scaling parameters, Γ, will evolve with density, and assuming that densification during sintering is a thermally activated process and controlled by a single dominant diffusion mechanism (i.e. typically grain boundary diffusion for fine grain size ceramics), it was proposed35 that Eq. 6.1 be rearranged, integrated and simplified to: t

∫0

1 exp(- Q ) dt = k RT γ ΩDo T

ρ

∫ρo

(G(ρ))n dp 3ρΓ(ρ)

[6.4]

where Q is the apparent activation energy (Joules/mol), R is the gas constant, Do = (Dv)o and n = 3 for volume diffusion, Do = (δDb)o and n = 4 for grain boundary diffusion. The much easier determined processing parameters of sintering time and temperature are now intentionally isolated from the more difficult to measure microstructure and material property parameters. The master sintering curve equations are now derived as: θ(t, T(t)) ≡ ∫ Φ(ρ)

k γ ΩDo

( )

1 exp - Q dt RT T

t 0 ρ

∫ρo

(G(ρ))4 dρ 3ρΓb(ρ)

[6.5] [6.6]

Equations 6.5 and 6.6 are then related to one another experimentally by the instantaneous sintered density, ρ(t), and the master sintering curve can be constructed empirically from a plot of ρ(t), for a specific sintering time and temperature as a function of log θ(t, T(t)) for the same time and temperature. A sintering process model is essentially derived from the data and it should be noted that no assumption is made about the dependence of temperature on time. Providing the boundary conditions under which the MSC was determined are not violated, the sintering characteristics can now be predicted for arbitrary temperature-time excursions. A commonly used method for obtaining the necessary data for the construction of the master sintering curve for a particular material is to employ a dilatometer and perform a series of constant heating rate sintering experiments on the as-formed samples. The final densities of the samples are measured following the experiment and the density, at various times during the thermal profile, is calculated from the linear shrinkage data. An example of the results from this type of sintering characterization for a low-temperature co-fire ceramic (LTCC) system is shown in Fig. 6.3. In this case an anisotropically densifying low-temperature co-fire ceramic (LTCC), DuPont low-temperature co-fire dielectric tape, 951 Green Tapetm, has had its sintering behavior characterized as a function of several constant heating rate experiments (5, 10, 15, 20, 25 and 30 °C/min). Low-temperature co-fire ceramic (LTCC) packaging technology is being used to produce advanced electronic components (e.g. for wireless communications). The ability to predict and carefully control sintering shrinkage is of critical importance in LTCC manufacturing. The



143

6.3 Linear shrinkage (%) as a function of temperature for constant heating rate experiments (5, 10, 15, 20, 25 and 30 °C/min) for a Dupont low-temperature co-fire dielectric tape, 951 Green Tapetm, (a) transverse to the plane direction (Z-direction), (b) in-plane direction (X,Y-direction), and the linear shrinkage results collapsed onto (c) density as a function of temperature for each heating rate.

goal of this study was to evaluate the master sintering curve (MSC) as a tool to predict and control LTCC sintering. Dilatometer sintering experiments were designed and completed to characterize the anisotropic sintering behavior of the DuPont 951 Green Tapetm, and the MSC was modified to account for the anisotropic sintering behavior. Due to the anisotropic densification of the LTCC it was necessary to characterize both the transverse (Fig. 6.1, A) and in-plane (Fig. 6.1, B) linear shrinkage and then collapse these into one density trajectory as a function of temperature (Fig. 6.1, C) plot for the material. Once this density trajectory, as a function of a few constant heating rates, was determined the master sintering curve was constructed from a computation of the master sintering curve parameter, θ, as a function of time and temperature. It is at this point that a known, assumed or calculated value of the apparent activation energy (Q) is necessary. The value of the apparent activation energy for densification during sintering can be determined using several techniques (Note: assuming valid and consistent results, each of these techniques should yield approximately equivalent values): • Minimization of residuals between the constructed master sintering curve and a fit curve, residual difference between the MSC predicted values and the fit curve values (Note: the results from this technique are dependent upon the type of curve fitting function used). 

The dispersion is best assessed quantitatively, where each individual constant heating rate experiment is ignored and the data is lumped into a


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Sintering of advanced materials single data set. A function is then fit to the data set and the mean square residual is computed from the predicted density of the MSC and the fit function at each data point. The fit curve functions can be polynomial fits, a sigmoidal curve fit, etc., each function having advantages and disadvantages based on the characteristics of the data set and the preferences of the user. The following equation provides an example for a sigmoidal curve fitting function that can be used: ρ = ρo + a / [1 +exp( – (log(θ) – log(θo)) / b))]c

[6.7]

ρ = density ρo = initial density (lower asymptote) θ = master sintering curve parameter θo = value of at the point of inflection of the fit curve a = difference between the upper and lower asymptotes b = curve shape parameter c = curve shape parameter • Minimization of residuals from the empirical construction of the MSC – mean square residual from the difference between the constant heating rate experiments for each θ value. An example of the output plot and mean residual squares equation from this minimization technique, for the LTCC sintering analysis, is shown in Fig. 6.4. • Experimentally determined using the time, temperature and density data from the constant heating rate sintering experiments, and the following expression:49,50

6.4 Example of the output plot and mean residual squares equation from the minimization of residuals from the empirical construction of the master sintering curve, (difference between the constant heating rate experiments for each θ value), for the DuPont low-temperature co-fire dielectric tape, 951 Green Tapetm.



(

ln T

)

Q dT dρ =– + ln[f(ρ)] + ln A – n ln dG RT dt dT

145 [6.8]

where T is the absolute temperature, t is time, R is the gas constant, f(ρ) is a function of density, G is the grain size (grain diameter), n is the grain size power law exponent (depending on whether the densification rate is controlled by volume (lattice) diffusion, n = 3, or by grain-boundary diffusion, n = 4) and A is a material parameter (constant) that is insensitive to G, T and ρ. The formulation was derived from a general sintering rate equation that separates the temperature dependent, grain size dependent and density dependent quantities:

(

Q

exp 2 dρ RT =A dt T

A=

)

f(ρ) dn

CγV23 R

[6.9] [6.10]

dρ is the instantaneous rate of densification, d is the grain size, γ is the dt surface energy, V is the molar volume, R is the gas constant, T is the absolute temperature, Q is the activation energy, f(ρ) is a function only of density and C is a constant. The apparent activation energy, Q, is determined using natural logs to put Eq. 6.8 in the more general form, y = mx + b. It is possible then to construct an Arrhenius plot dT dρ of ln T versus 1/T of the variations of the constant rate sintering data and dt dT determine Q for a specific sintered density ( f(ρ)), following the assumption that the grain size is dependent only on the sintered density. This apparent activation energy for densification, at a given density, can then be determined from the slope (m) of a linear least squares fit to the sintering data, where Q = 2mR. This relationship for the LTCC is shown in Fig. 6.5 and for a submicrometer-sized calcined alumina (A16) (α-Al2O3, Alcoa Industrial Chemicals, Pittsburgh, PA), in Fig. 6.6. As long as the temperature as a function of time is known from the beginning to the end of the thermal profile, the master sintering curve can be generated from the measured and calculated densities as a function log θ(t, T(t)) (Note: it may be important to include the early stages of cooling if significant densification is still occurring). A master sintering curve was obtained for the 951 Green Tape™, and the apparent activation energy for sintering was determined to be approximately 346kJ/mol (317 ± 38kJ/mol). The constructed master sintering curve for this system is shown in Fig. 6.7. The density for an arbitrary temperature-time excursion can now be predicted from the master sintering curve. The resultant master sintering curve not only characterizes the densification behavior of this LTCC material but it also provides a means to predict green tape density as a function of sintering time and temperature (Fig. 6.8), and allows one to assess lot-to-lot (materials) and run-to-run (process) Here,

(

)


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6.5 Arrhenius plot of ln (T dT/dt dρ/dT) versus 1/T of the variations of the constant rate sintering data and determination of the Q for a specific sintered density (f(ρ)) for the DuPont low-temperature co-fire dielectric tape, 951 Green Tapetm.

6.6 Arrhenius plot of ln (T dT/dt dρ/dT) versus 1/T of the variations of the constant rate sintering data and determination of the Q for a specific sintered density (f(ρ)) for submicrometer-sized calcined alumina (A16) (α-Al2O3, Alcoa Industrial Chemicals, Pittsburgh, PA).



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6.7 Master sintering curve for the DuPont low-temperature co-fire dielectric tape, 951 Green Tapetm.

6.8 Density versus the master sintering curve parameter showing how eleven unique thermal profiles were predicted by the master sintering curve for the DuPont low-temperature co-fire dielectric tape, 951 Green Tapetm.

variability in LTCC manufacturing (Fig. 6.9). Figure 6.8 shows a series of eleven separate and unique thermal profiles, independent of those thermal profiles used to construct the master sintering curve, that were used to sinter the LTCC material. It also shows how the resultant Archimedes determined density values compared to the predicted density from the master sintering curve. It is apparent from the graph in this figure that all final densities were predicted accurately, within experimental error, based on the constructed master sintering curve. The comparison of lot-tolot variability, in the graph of Fig. 6.9, is an example of how a master sintering curve can be utilized in product quality control/quality assurance where the densification behavior of three separate lots of LTCC material was compared against the predicted MSC values utilizing two separate thermal profiles. © Woodhead Publishing Limited, 2010

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6.9 Density versus the master sintering curve parameter for Dupont low-temperature co-fire dielectric tape, 951 Green Tape™, indicating how the master sintering curve can be utilized to assess lot-to-lot (materials) and run-to-run (process) variability in LTCC manufacturing.

It should also be noted that, as useful as the concept of the mater sintering curve is, since certain conditions must be satisfied, not all sintering is expected to be described by a master sintering curve. The samples used to construct the curve must be consistent in powder characteristics, forming process and overall green density. Also, under the conditions of interest, a ‘single’ or ‘average’ apparent activation energy must govern the sintering dynamics. In its purest form the master sintering curve has two critical assumptions imbedded in the theory. One, a single mechanism dominates densification and, two, G and Γb (the microstructure evolution) are dependent only on density. It will be observable in the master sintering curve results if deviations from a single dominant diffusion mechanism with a single apparent activation energy exist. For example, a mechanism such as surface diffusion could result in extensive microstructure coarsening and consumption of the sintering driving force without any significant densification of the body. The coarsening due to surface diffusion, at the cost of densification, may be anticipated for slower heating rates and at lower densities, particularly during the initial sintering stage. This would be evidenced, however, by a change in the master sintering curve parameter and a possible change in the apparent activation energy for densification.

6.4

Extending the master sintering curve to the third dimension

The concept of the master sintering curve, due to the intimate link established between ceramic processing, density, microstructure and the master sintering curve parameter, θ, can be taken a step further. It is possible to generate what can © Woodhead Publishing Limited, 2010


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be referred to as ’master sintering curve surfaces’ or ‘master processing optimization maps’ by effectively incorporating the materials property or parameter of interest, based on the intended application or a specific processing feature, as an additional variable in the construction of the master sintering curve. The MSC could be extended into the third dimension of, for example, green density or hot pressing pressure.51 Figure 6.10 provides SEM images of the microstructure variation as a function of the final density, for the LTCC system, based on thermal profiles along the master sintering curve trajectory. It is at least qualitatively apparent from these images of the development of the microstructure as a function of density and the thermal profile as linked through the master sintering curve parameter. Thus, if a specific and tailored microstructure is crucial to obtain a desired property or behavior for a particular electronic ceramic application, as is often the case, a ’master processing optimization map’ would be highly desirable. This is generically shown in Fig. 6.11.

6.5

Case study: Controlling electrical performance of ZnO varistors using a master sintering curve

6.5.1 Background The nonohmic ZnO based ceramics have been widely used as varistors for voltage stabilization and transient surge suppression in electronic circuits and electric power systems since the late 1960s. This type of varistor is a ceramic semiconductor based on zinc oxide, ZnO, and various dopant elements resulting in a component having a

6.10 Qualitative microstructure trajectory as a function of the density and the master sintering curve parameter, based on a specific thermal profile, for the Dupont low-temperature co-fire dielectric tape, 951 Green Tapetm.


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6.11 Generic representation of extending the mastering sintering curve into a third dimension and constructing ‘master sintering curve surfaces’ or ‘master processing optimization maps’.

highly nonlinear current–voltage relationship.52,53 The electrical characteristics of ZnO varistor materials are determined by their detailed microstructure, where three main microstructural features are especially important for determining their performance: 1. ZnO grain size, grain size distribution, and morphology 2. Grain boundary character 3. Intergranular network of bismuth rich phases These features constitute the functional microstructure which is a result of the synthesis and forming techniques used for component fabrication and develop into maturity during sintering and densification. This case study was concerned with investigating the development of this functional microstructure and how, through implementation of the master sintering curve, a link could be established from synthesis and forming through sintering to final electrical performance. The objective then was to be able to predict and control the electrical performance of a ZnO varistor material through the construction and implementation of a master sintering curve and to establish a link between processing, sintering, microstructure and the macroscopic electrical behavior (current–voltage relationship).

6.5.2 Functional microstructure As for most ZnO varistor compositions, the composition used in this study, as listed in Table 6.3, resulted in a microstructure containing ZnO grains, zinc silicate grains, spinel grains, and various bismuth-rich phases, as revealed through X-ray diffraction and SEM-EDS spectral mapping analysis and shown in Fig. 6.12. © Woodhead Publishing Limited, 2010


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Table 6.3 Additives and dopants used in this ZnO-based varistor composition for tailoring the microstructure and the component electrical behavior Material

Compositional role

Mol%

Weight%

ZnO Bi2O3 CoO MnO2 Sb2O3 Cr2O3 SiO2 NiO H3BO 3 BaCO 3 Al

Conductive grains Non-linearity inducer Non-linearity enhancer Non-linearity enhancer Non-linearity enhancer Non-linearity enhancer Grain growth retardant Stability enhancer Stability enhancer Stability enhancer ZnO conductivity enhancer

81.45 2.43 0.87 0.45 3.04 0.79 9.84 0.78 0.13 0.21 0.01

82.61 0.43 0.43 0.43 1.01 0.43 13.51 0.86 0.17 0.09 0.03

In this case the spinel grains are considered electrically insulating and do not directly contribute to the electrical characteristics. The microstructural components that have a direct influence on the electrical characteristics,52,53 or the functional microstructure, consist of: • Doped ZnO grains – responsible for the conductivity in the material, especially in the ‘p-turn’ region of the current–voltage behavior. • Interfaces between the ZnO grains – provide barriers to electrical conduction, produce the nonlinear properties. 



The breakdown voltage of each individual interface depends on the microstructure of that interface. The electrical characteristics are based on the type of interfaces and the grain size (grain size distribution) as this determines the number of barriers to conduction.

• Three-dimensional network of bismuth rich phases – located along the multiple ZnO grain junctions (triple junctions and their intersections at quadruple points). 



The bismuth rich phases form a network that contributes an additional current path. This path circumvents the barriers at the ZnO grain interfaces and can contribute significantly to the conductivity in the pre-breakdown region where the network conductivity is determined by its internal microstructure.

The samples prepared for this case study were dry pressed discs that all had a similar initial microstructure and an ‘as-pressed’ density of 2.85 ± 0.02g/cm3. A series of sintering/densification curves were constructed from the dilatometric characterization of the samples’ displacement behavior as a function of constant heating rate experiments at 1, 3, 5, 10, 15 and 20 °C/min. The constructed


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6.12 (a) Powder X-ray diffraction and (b) SEM-EDS spectral mapping analysis of ZnO varistor material revealing the two major phases of ZnO and ZnSiO4 and the intergranular bismuth network.



153

densification curves as a function of temperature for each constant heating rate are shown in the plot in Fig. 6.13. The characterization results of the dilatometric behavior of the samples and the constructed densification curves were used to build a master sintering curve and determine an apparent activation energy for this ZnO varistor composition sintered under these conditions, the results of which are shown in Fig. 6.14. An apparent activation energy was determined to be ~394 kJ/mole from the mean square residuals fit of the data (Fig. 6.14 inset). Based on these results and the development of a master sintering curve for this system three distinct thermal profiles were chosen to verify and establish the link between the matured functional microstructure, the master sintering curve parameter and the electrical behavior of the material based on the functional microstructure. The goal was to prove the underlying hypothesis that the electrical behavior of the material, voltage–current relationship in the ‘pre-breakdown’ and ‘breakdown’ region, is a direct function of the final functional microstructure as predicted through the master sintering curve parameter. The three sample sets, the chosen thermal profiles, percent of theoretical density of the ‘as-sintered’ samples, and average grain size information and representative SEM images of the microstructure for each sample set (SS#1 – sample set #1, SS#2 – sample set #2, and SS#3 – sample set #3) are shown in Fig. 6.15.

6.13 The constructed densification curves as a function of temperature for 1, 3, 5, 10, 15, and 20 °C/min constant heating rates for the ZnObased varistor composition samples.


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6.14 The constructed master sintering curve for a ZnO based varistor composition using 5, 10, 15, and 20 °C/min constant heating rate dilatometer results. (Inset shows the mean square residual analysis performed to estimate the apparent activation energy for sintering.)

6.15 Information and results for the three sample sets chosen for linking the functional microstructure through the master sintering curve parameter to the electrical behavior (including the thermal profiles, percent of theoretical density, and the average grain size results) and representative SEM images of the microstructure for each sample set (SS#1 – sample set #1, SS#2 – sample set #2, and SS#3 – sample set #3).

The thermal profiles for sample sets labeled SS#1 and SS#2 were each unique; however, they were chosen based on the master sintering curve prediction to produce similar microstructures. The thermal profile for SS#3 was chosen to produce a distinctively different microstructure from SS#1 and SS#2. The results



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in Fig. 6.15 verify that SS#1 and SS#2 have these similar characteristics and are unique from those determined for SS#3. Therefore, if the electrical behavior is intimately tied to the functional microstructure, then SS#1 and SS#2 should show nearly identical electrical behavior and SS#3 should be unique. The electrical behavior for each sample set was characterized in the ‘pre-breakdown’ and ‘breakdown’ regions for the voltage–current relationship. The results from this analysis are shown in Fig. 6.16. It is apparent that the current–voltage behavior is nearly identical for SS#1 and SS#2, each having a breakdown voltage value of approximately 48kV/cm and an alpha value of approximately 19, and unique for SS#3, breakdown voltage of approximately 28kV/cm and an alpha value of

6.16 Electrical behavior results for the three sample sets chosen for linking the functional microstructure through the master sintering curve parameter to the electrical behavior (SS#1 – sample set #1, SS#2 – sample set #2, and SS#3 – sample set #3), including the calculated breakdown voltage and alpha values for each sample set.52–53


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6.17 Generic processing optimization map constructed from establishing a link between the functional microstructure and the electrical behavior through the development of a master sintering curve for a ZnO varistor material.

approximately 21. These results establish and verify the link between the master sintering curve parameter, functional microstructure and electrical properties and thus demonstrate the ability to predict the electrical behavior from the master sintering curve. It has been shown, through this case study, that the detailed microstructure of the ZnO varistor material is strongly dependent upon the fabrication variables, in particular the sintering profile. The functional microstructure, established based on the sintering profile, directly influences the electrical properties of these materials. Therefore a process optimization map can be constructed through proper utilization of a master sintering curve, as depicted generically in the schematic in Fig. 6.17.

6.6

Conclusion

For advanced ceramic component manufacturing, reproducible processing, sintering and densification of ceramic systems intended for application as electronic ceramics are critical for the cost-effective manufacture of reliable electronic ceramic components. Empirical engineering has historically been used



157

to develop the techniques to manufacture these components. This alone, however, cannot provide the fundamental understanding necessary to design new electronic ceramic products, process new electronic ceramic materials and properly sinter and densify these materials to the desired requirements to produce components with the necessary electronic properties tailored to a specific application. Master sintering curve theory, although a relatively young concept, can provide the electroceramist with a characteristic measure of the sinterability of a ceramic body. It results in a single empirical densification curve that is, by design, independent of the heating history. It takes advantage of the parameters used in the sintering rate equation by separating those relating microstructure and time– temperature terms to opposite sides of an empirical equation. The formulation and construction of the master sintering curve has its roots in and is derived from the combined stage sintering model where the analysis of sintering has been extended beyond the segments described by the individual stage models that incorporate idealized geometric considerations that fail to properly represent the entire sintering process. A master sintering curve parameter and the equations used in constructing the curve are then developed through a subsequent rearrangement of this combined stage sintering model and are governed by a series of assumptions. The first is that a single dominant diffusion mechanism exists in a system where grain boundary or volume diffusion dominates the sintering process. Although a master sintering curve may not be entirely applicable in systems where surface or vapor transport are the active and dominate diffusion mechanisms or in cases of exaggerated grain growth, it can indicate the presence of these factors. Second, the master sintering curve is a single valued function of density where the mean grain diameter and scaling parameters are only a function of the density of the material and not the time– temperature profile. Therefore, for a given powder system, green microstructure and green density the developed mastering sintering curve would be considered unique. The constructed master sintering curve would be ultimately modified if any changes were made to the green microstructure by variations in the particle size distribution, average particle size, initial pore-size distribution and particle packing properties. Under these assumptions and after some mathematical manipulation of the combined stage sintering equation the master sintering curve is developed through the underlying relation, Φ(ρ) ≡ θ(t, T(t)). The ability to predict and control sintering and densification from master sintering curve theory and ultimately link this to the ceramic processing, microstructure development and electronic properties provides the practical value from the concept and its use. This allows for the integration of fundamental scientific understanding into science-based processing technology to gain a better understanding and control over ceramic powder processing and sintering. Master sintering curve theory has been successfully applied to the sintering of numerous ceramic systems. The findings presented here demonstrate that a systematic approach to design, predict and control sintering of electroceramic systems is possible through the implementation of the master sintering curve.


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6.7

Acknowledgements

The authors sincerely thank I. Nettleship and T. Chen, University of Pittsburgh, Pittsburgh, PA, for contributions and discussions on the microstructure analysis for the ZnO varistor material, Markus reiterer, Medtronic, Minneapolis, Minnesota, for experimental contributions and discussions, and Alex Roesler, Sandia National Laboratories, Albuquerque, NM, for a critical review of the chapter contents. DOE/NNSA Funding Statement: Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

6.8

References

1. W. D. Kingery, H. K. Bowen and D. R. Uhlmann, Introduction to Ceramics, 2nd Edition, (1976), Wiley, New York. 2. A. J. Moulson and J. M. Herbert, Electroceramics: Materials, Properties, Applications, 2nd Edition, (2003), John Wiley and Sons Ltd. 3. R. L. Coble and J. E. Burke, ‘Sintering in Ceramics,’ in Progress in Ceramic Science, Volume 3, Edited by J. E. Burke, The Macmillan Company, New York, 1963, 197–251. 4. F. Thümmler and W. Thomma, ‘The Sintering Process,’ J. Inst. Metals 12, 69–108, 1967. 5. J. E. Burke and J. H. Rosolowski, ‘Sintering,’ in Treatise on Solid State Chemistry, Volume 4, Reactivity of Solids, Edited by N. B. Hannay, Plenum Press, New York, 1976, 621–59. 6. R. L. Coble, ‘Sintering of Crystalline Solids I: Intermediate and Final Stage Diffusion Models,’ J. Appl. Phys., 32 [5] 787–92 (1961). 7. R. M. German, Liquid Phase Sintering, Plenum Press, New York, 1985. 8. C. J. Brinker and G. W. Scherer, Sol-Gel Science, The Physics and Chemistry of Sol-Gel Processing, Academic Press, Inc., New York, 675–742, 1990. 9. K. G. Ewsuk, ‘Consolidation of Bulk Ceramics’ in Characterization of Ceramics, edited by R. E. Loehman, Butterworth-Heinemann, Greenwich, CT, 77–101, 1993. 10. J. S. Reed, Introduction to the Principles of Ceramic Processing, second edition, John Wiley & Sons, Inc., New York, 583–619, 1995. 11. K. G. Ewsuk, ‘Ceramics (Processing),’ in the Kirk-Othmer Encyclopedia of Chemical Technology, Fourth Ed., Vol. 5, John Wiley & Sons, Inc., New York, NY, 620–7, 1993. 12. D. W. Richerson, Modern Ceramic Engineering: Properties, Processing, and Use in Design, second edition, Marcel Dekker, Inc., New York, 519–64, 1992. 13. C. Herring, ‘Surface Tension as a Motivation for Sintering,’ pp. 143–179 in The Physics of Powder Metallurgy, edited by W. E. Kingston, McGraw-Hill Book Company, Inc., New York, 1949. 14. W. D. Kingery and B. Francois, ‘The Sintering of Crystalline Oxides, I. Interactions Between Grains Boundaries and Pores,’ in Sintering and Related Phenomena, edited by G. C. Kuczynski, N. A. Hooton, and C. F. Gibbon, Gordon and Breach Science Publishers, New York, 471–98, 1965.



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32. F. B. Swinkels and M.F. Ashby, ‘A Second Report on Sintering Diagrams,’ Acta. Metall., 29, 259–81, 1981. 33. M. P. Harmer, ‘Use of Solid-Solution Additives in Ceramic Processing’; pp. 679–96 in Structure and Properties of MgO and Al2O3 Ceramics, Advances in Ceramics, Vol. 10, edited by W. D. Kingery, The American Ceramic Society, Columbus, OH, 1984. 34. K. G. Ewsuk, ‘Sintering Maps for Ceramic-Filled-Glass Composites,’; pp. 125–35 in Ceramic Transactions, Vol. 19, Advanced Composite Materials: Processing, Microstructure, Bulk and Interfacial Characterization, Characterization Methods and Applications, edited by M. D. Sacks, The American Ceramic Society, Westerville, OH, 1991. 35. H. Su and D. L. Johnson, ‘Master Sintering Curve, A Practical Approach to Sintering,’ J. Am. Ceram. Soc., 79 [12] 3211–7, 1996. 36. C. B. DiAntonio and K. G. Ewsuk, ‘Controlled and Predicted Ceramic Sintering Through Master Sintering Curve Theory,’; pp. 15–23 in Ceramic Transactions, Vol. 157, edited by C. B. DiAntonio, The American Ceramic Society, Westerville, OH, 2004. 37. C. B. DiAntonio, D. N. Bencoe, and K. G. Ewsuk, ‘Characterization and Control of Low Temperature Co-Fire Ceramic (LTCC) Sintering,’ Proc. Soc Photo-Optical Instr. Eng. (SPIE), 5231, 160–4, 2003. 38. K. G. Ewsuk, C. B. DiAntonio, F. Uribe and S. Monroe, ‘Materials and Process Control Technology for LTCC Microelectronics Packaging,’; pp. 1–6 in Proceedings of the Ceramic Interconnect Technology. The Next Generation II, International Microelectronics and Packaging Society, Washington, DC, 2004. 39. D. Li, S.O. Chen, X. Q. Sun, W. Q. Shao, Y. C. Zhang and S. S. Zhang, ‘Construction and validation of master sintering curve for TiO2 for pressureless sintering,’ Advances in Applied Ceramics, vol. 107, no. 1, 52–6, 2008. 40. D. L. Johnson, ‘Finding and Utilizing the Master Sintering Curve’; pp. 15–7, Sintering 2003, International Conference on the Science, Technology, Application of Sintering, September 2003. 41. C. B. DiAntonio, K. G. Ewsuk and D. N. Bencoe, ‘Control of Low Temperature Co-Fire Ceramic Sintering’; pp. 15–7, Sintering 2003, International Conference on the Science, Technology, and Application of Sintering, September 2003. 42. D. C. Blaine, S. Park and R. M. German, ‘Master Sintering Curve for a Two-Phase Material’; pp. 264–7, Sintering 05, 4th International Conference on Science, Technology, and Application of Sintering, August–September 2005. 43. K. An and M. K. Han, ‘Microstructural Evolution Based on the Pressure-Assisted Master Sintering Surface,’ Mater. Sci. Eng. A, 391, 66–70, 2005. 44. T. R. G. Kutty, K. B. Khan, P. V. Hegde, J. Banerjee, A. K. Sengupta, S. Majumdar and H. S. Kamath, ‘Development of a Master Sintering Curve for ThO2,’ J. Nucl. Mater., 327, 211–9, 2004. 45. M. H. Teng, Y. Lai, and Y. Chen, ‘A Computer Program of Master Sintering Curve Model to Accurately Predict Sintering Results,’ West. Pacific Earth Sci., 2, 2171–80, 2002. 46. S. Kiani, J. Pan, J. A. Yeomans, ‘A New Scheme of Finding the Master Sintering Curve,’ J. Am. Ceram. Soc., 89 [11] 3393–6, 2006. 47. K. G. Ewsuk, D. T. Ellerby and C. B. DiAntonio, ‘Analysis of Nanocrystalline and Microcrystalline ZnO Sintering Using Master Sintering Curves,’ J. Am. Ceram. Soc., 89 [6] 2003–2006. 48. R. T. DeHoff, ‘A Cell Model for Microstructural Evolution during Sintering,’ in Materials Science Research, Vol. 16, Sintering and Heterogeneous Catalysis, edited by G. C. Kuczynski, A. E. Miller, and G. A. Sargent, Plenum Press, New York, 23–4, 1984.



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49. W. S. Young and I. B. Cutler, ‘Initial Sintering with Constant Rates of Heating,’ J. Am. Ceram. Soc., 53 [12] 659–63, 1970. 50. J. Wang and R. Raj, ‘Estimate of the Activation Energies for Boundary Diffusion from Rate-Controlled Sintering of Pure Alumina, and Alumina Doped with Zirconia or Titania,’ J. Am. Ceram. Soc., 73 [5] 1172–5, 1990. 51. K. An and D. L. Johnson, ‘The pressure-assisted master sintering surface,’ J. Materials Science, 37, 4555–9, 2002. 52. L. M. Levinson and H. R. Philipp, ‘The Physics of Metal Oxide Varistors,’ J. App. Phys., 46 [3], 1332–41, 1975. 53. D. R. Clarke, ‘Varistor Ceramics,’ J. Am. Ceram. Soc., 82 [3] 485–502.


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Part II Advanced sintering processes


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7 Atmosphere sintering C. B lais, Université Laval, Canada Abstract: This chapter discusses the different roles played by synthetic atmospheres during the various stages of the sintering process. It begins with a brief description of the most common industrial sintering atmospheres, followed by a generic thermochemical treatment of gas-solid interactions prevailing during sintering. The latter theoretical aspects are then used to discuss the roles of atmosphere sintering in terms of delubrication, sintering per se as well as cooling/sinter-hardening. Key words: synthetic sintering atmospheres, delubrication, oxide reduction, roles of atmospheres during sintering, sinter-hardening.

7.1

Introduction

Intuitively, sintering atmospheres are perceived as a precaution to prevent hightemperature interactions of the material to be sintered with its environment. In the case of metals and alloys, atmosphere selection is generally performed to prevent oxidation and promote oxide reduction to obtain clean surfaces. Nevertheless, the role of sintering atmospheres encompasses a much wider breadth. Indeed, the choice of sintering atmosphere significantly influences delubrication, heat transfer, oxide reduction, control of interstitial chemical elements, etc. All these aspects influence microstructure and therefore the final mechanical properties of sintered components. The following sections present and discuss the role of sintering atmospheres in more detail. Description of the types of atmosphere typically used in an industrial context will be presented. Thermodynamic aspects of sintering will be discussed to give the basic tools to understand the mechanisms involved during atmosphere sintering and select the appropriate atmosphere conditions for a given sintering project. Finally, examples will be presented throughout the chapter to put the rather theoretical information into perspective.

7.2

Types and sources of sintering atmospheres

As stated above, sintering atmospheres are selected for their propensity to prevent undesired interactions between the material to be sintered and its surrounding environment at high temperatures while providing an optimum surface condition for neck formation between particles. Several possibilities are available in terms of atmosphere selection for sintering of high-performance materials. Indeed, nowadays, bulk supply of high-purity gases such as nitrogen (N2), hydrogen (H2) and argon (Ar) is relatively affordable and ’synthetic atmospheres’ are steadily 165 © Woodhead Publishing Limited, 2010

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Table 7.1 Main characteristics of typical industrial sintering atmospheres

Composition (vol-%) Typical dew point (°C)

N2

H2

CO

CH 4

N2+H2 Exothermic gas Exothermic gas Dissociated ammonia

90–95 40–85 40–50 25

5–10 1–40 30–40 75

– 2–20 20–25 –

600°C m H (gas) CnHm(gas) nC(soot) + ––– [7.33] 2 2 In the case of metallic stearates, the vaporization products also contain metallic oxides such as ZnO for ZnSt and Li2O for LiSt (Auborn & Choo, 1994). The latter solid particles may deposit on the inside walls of the sintering furnace creating a potential contamination source. Indeed, as oxide particles and soot build up on the


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colder walls of the sintering furnace, bits of it may detach and fall on parts, leading to a discoloration problem. This situation does not cause a decrease in parts performance but will most certainly lead to suspicious interrogations from end users. Furthermore, it has been stated that zinc from zinc stearate may act as a catalyst for soot formation (Nayar, 1994). In this case, hydrocarbons degradation takes place at lower temperatures and sooting becomes more critical. A similar catalytic behavior is observed when admixed nickel is added to a metal powder blend (Pease & West, 2002). In some severe cases, soot formation and/or improper removal of gaseous species resulting from the thermal degradation of lubricants may cause blistering on parts surfaces. Blisters are formed by local increases in volume created by the presence of soot or by entrapped gaseous species that cannot escape the green compacts and see their pressure increase with the increasing temperature. Based on the description presented above, it can be seen that there is an optimum thermal profile that allows complete delubrication of PM components (Nayar, 1994). Indeed, part temperature should increase to 300 °C as quickly as possible to initiate thermal degradation of the lubricant. Part temperature should then increase at a rather slow rate that will ensure complete delubrication prior to reaching 550 °C, preventing soot formation. Several other factors influence delubrication. Among these we find: forward flow of furnace atmosphere, belt loading, furnace productivity, size and shape of part, green density, quantity of lubricant, etc. Table 7.3 summarizes these factors and their relative influence on delubrication performances. Fortunately, strategies can be employed to facilitate delubrication and minimize the manifestations of improper lubricant removal. These strategies all rely on using oxidizing gaseous species that react with lubricant molecules to reduce their concentration and prevent their breakdown into soot. Among the oxidizing gases used we find water vapor (H2O), carbon dioxide (CO 2) and oxygen (O2). As highlighted in Eq. 7.34, when an oxidizing gas is added to the delubrication process, all the reaction products are gaseous and sooting is prevented. O2(gas) or T>600°C CnHm(gas) + H2O(gas) → CO(gas) + CO2(gas) + H2(gas) + H2O(gas) or CO2(gas)

[7.34]

One of the easiest methods to incorporate an oxidizing gas in the furnace atmosphere, which is typically made of a combination of nitrogen (N2) and hydrogen (H2), is to make nitrogen bubble through a container filled with water. As nitrogen bubbles toward the outlet of the container, it picks up water vapor (H2O) which acts as the oxidizing gaseous species. This approach is often referred to as a ‘wet atmosphere’ for obvious reasons. Another approach is to burn hydrocarbons (natural gas (CH 4) or propane (C3H8)) with air to form an exothermic atmosphere that contains from 1 to 5vol-% of H2O and CO 2. It is extremely © Woodhead Publishing Limited, 2010


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Table 7.3 Selected parameters that influence delubrication Parameter critical to the delubrication operation

Comment

Proposed action

Lubricant type

Avoid metallic stearates when possible.

Use Ethylene bis (stearamide).

Size and shape of component

Bigger and/or intricate parts take more time to delube.

Adjust the thermal profile in the delube zone accordingly.

Component density

The denser the part, the more difficult it is for vapor species to reach the surface of parts.

Adjust the thermal profile in the delube zone accordingly.

Forward flow of atmosphere

Forward flow carries away the degradation products toward the front of the furnace.

Increase forward flow velocity.

Oxidation potential

Oxidants are required for lubricant degradation.

Make sure that the atmosphere in the delube section is oxidizing using a wet atmosphere or an exothermic gas.

Temperature profile for delubrication

The objective is to increase the parts temperature slowly and evenly.

Should be as gradual as possible between 150°C and 550°C.

Production rate

Related to the thermal profile seen by the parts.

Belt speed should be optimized to follow the ideal delubrication thermal profile identified above (also function of furnace dimensions).

Belt loading

Also related to the thermal profile seen by the parts.

Belt loading should be optimized to follow the ideal delubrication thermal profile identified above (also function of furnace dimensions).

important to note that the presence of oxidizing species is sought only for the delubrication stage of the sintering process. Indeed, if this type of atmosphere was to be used throughout the sintering process, it would lead to severe oxidation of the metallic species found in the green parts. The oxide layer that would form at the surface of the particles would act as a diffusion barrier that would prevent neck formation in between neighboring particles, thus yielding poor mechanical properties. Therefore, the presence of a partially oxidizing atmosphere for


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7.7 Schematic representation of a sintering furnace designed according to the zoned atmosphere approach.

delubrication purposes has to be constrained within the pre-heat/burn-off section of the furnace. Figure 7.7 shows a schematic representation of a sintering furnace designed according to the zoned atmosphere approach. After reading the previous praragraph, one could question the rationale behind the approach of using an oxidizing atmosphere for lubricant removal while at the same time trying to prevent oxidation of the metallic species. Is there not a risk of oxidizing the metallic particles surfaces while oxidizing (burning) the lubricant? The answer is yes, but it is rarely detrimental to the overall sintering process since it takes place at lower temperatures (< 550 °C). At such temperatures, the oxidation kinetics of most metallic species is slow and significant oxidation products do not form. This situation certainly demonstrates the need to adequately control the temperature and atmosphere profile of the sintering furnace to ensure that as little oxidizing gas as possible can trickle toward the high-temperature section of the furnace.

7.4.2 Role of furnace atmosphere during the high-temperature stage of sintering First, it is important to note that the expression ‘high temperature’ refers to the highest temperature seen by the compacts during their sintering cycle and is therefore material dependent. The role of furnace atmosphere during this portion of sintering is mainly to prevent undesired interactions between the material to be sintered and its surrounding environment while providing an optimum surface



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condition of neck formation between particles in intimate contact. These aspects have been treated in previous sections. This segment is rather aimed at presenting less suspected roles played by sintering atmospheres. Indeed, several authors have worked on studying the effect of sintering atmospheres chemistry on mass transport during sintering. As an example, McIntire (1964), in his paper ‘Effect of HCl-H2 sintering atmospheres on the properties of compacted iron powders’, showed that by adding hydrogen chloride (HCl) to the hydrogen-based sintering atmosphere, the contamination at the surface of iron particles was lower, leaving more active surfaces for surface diffusion and eventually pore rounding. Similarly, mass transport through the vapor phase is apparently increased by the presence of chlorides. The latter mechanisms would explain the improved mechanical properties observed for the specimens sintering in the H2-HCl gas mixture. Similar observations of the effect of an HCl atmosphere on significantly increasing vapor-phase mass transport have been reported for the sintering of ZrO2 and TiO2 (Ready and Ready, 1986, 1987). Nevertheless, the latter examples are more theoretical than practical because obviously the use of HCl in an industrial environment would lead to severe problems in terms of accelerated degradation of the stainless steel wire-mesh belts, steel muffles, etc.

7.4.3 Role of furnace atmosphere during cooling The cooling segment of the sintering cycle is particularly important because, besides its effect on furnace design and productivity, it can be used to significantly modify the final microstructure of PM components. One key example of this is certainly given by the development of sinter-hardening of steel components. Sinter-hardening has become one of the major growth areas for PM. One of its main advantages is that hardening can be performed during the cooling stage of the sintering without requiring a secondary heat-treating operation. Historically, sinter-hardenable powders were formulated based on the typical cooling rates available in the industry at the time. Thus, the concentrations of alloying elements needed to develop satisfactory microstructures were relatively high. Even though the properties were improved somewhat, the disadvantages of using higher concentrations of alloying elements were lower compressibility and higher powder cost. The lower compressibility aspect would ultimately be self-limiting due to the fact that there would be a lower maximum density achievable. Fortunately, furnace manufacturers developed fast cooling systems based on forced convection that significantly increased the cooling rates achievable during the last stage of sintering (Jesberger, 1999; Groak, 1999). In return, this led to the development of leaner and more compressible powders that helped make sinterhardening the popular process it is today. As for the effect of atmosphere on sinter-hardening, pure hydrogen has the highest thermal conductivity amongst all gases (BOC Gases, 1994). Figure 7.8 presents the evolution of thermal conductivity for selected gases as a function


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7.8 Evolution of thermal conductivity for selected gases as a function of temperature.

of temperature. From Fig. 7.8, it is seen that the thermal conductivity of pure nitrogen (N2) and argon (Ar) at 1400 K is 0.06 and 0.05 (W/m*K) while that of pure hydrogen at the same temperature is 0.56 (W/m*K). In the case of gas mixture, its thermal conductivity can be estimated with the following equation: Σi ki Xi Mi1/3 kmix = ––––––––––– Σ ki Mi1/3

[7.35]

i

Figure 7.8 also shows the theoretical thermal conductivity of an N2-H2 gas mixture as a function of the increasing volume fraction of H2. Figure 7.9 shows empirical measurements of the effect of hydrogen volume fraction in the cooling atmosphere on the local cooling rate measured in the middle of cylindrical parts made from a sinter-hardenable steel powder (Serafini and Blais, 2001). Increasing the proportion of hydrogen from its original value of 5 v/o to 22 v/o, 70 v/o and 92 v/o led to an increase of the cooling rate of 32%, 95% and 157% respectively. The latter results prove that, the higher the proportion of hydrogen in the cooling section of a sintering furnace, the higher will be the heat extraction rate (Poirier and Geiger, 1994). Indeed, previous laboratory scale studies have shown that the cooling rate could be significantly increased by using more hydrogen during the cooling stage of sintering (Serafini et al., 2002). Measurements performed with thermocouples embedded in test pieces showed that the local cooling rates were © Woodhead Publishing Limited, 2010


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7.9 Empirical measurements of the effect of hydrogen volume fraction in the cooling atmosphere on the local cooling rate measured in the middle of cylindrical parts made from a sinter-hardenable steel powder.

92% and 52% faster when 90v/o H2/10v/o N2 was used instead of 100v/o N2 and 5v/o H2/95v/o N2, respectively. Therefore, for the metallurgical systems studied, increases in the proportion of martensite of up to 31% were recorded leading to an increase of 17% of the apparent hardness. Figure 7.10 presents the gains in hardness obtained by increasing the hydrogen content of the cooling atmosphere from 5 vol-% to 92 vol-% as a function of the alloying elements content of the sinter-hardenable powder and the concentration of copper. The effect of hydrogen is somewhat uneven for the leaner alloys. This behavior is probably due to the lower hardenability of those two powders. Indeed, since the concentration in alloying element is small, the time available to prevent transformation of austenite into stable phases such as pearlite and ferrite is considerably shorter. Thus, for the latter alloys, small variations of the local cooling rate may prevent or promote the transformation of the austenite, leading to a more irregular behavior, especially during sinter-hardening operations. On the other hand, the more heavily alloyed powders show a regular behavior where the increase in hardness is proportional to the copper concentration in each premix. This is due to the longer time available to avoid transformation of austenite into stable phases upon cooling. Figure 7.11 compares standard deviations values, calculated from the dimensional change measurements from die size, for samples cooled with 5vol-% hydrogen and others cooled with 92vol-% hydrogen (copper fixed at 2.0 wt-%). © Woodhead Publishing Limited, 2010

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7.10 Gains in hardness obtained by increasing the hydrogen content of the cooling atmosphere from 5vol-% to 92vol-% as a function of the alloying elements content of the sinter-hardenable powders and the concentration of copper. (a)FC-0208, (b) FL-4205, (c) FL-4905, (d) FL-4905+0,5wt-% prealloyed Ni.

With the exception of one series of samples, smaller deviations were obtained when the hydrogen was at its highest. Figure 7.11 also shows that the standard deviation values decrease as the percentage of alloying elements in the base material increases. These results indicate that higher proportions of hydrogen in the atmosphere yield a more uniform heat extraction, leading to smaller dimensional variations from part to part. Finally, although the numbers presented above look interesting, some disadvantages of using higher hydrogen concentrations in the cooling section of a sintering furnace need to be addressed. First of all, cost is certainly one disadvantage and a cost analysis needs to be carried out to determine if the utilization of higher than typical hydrogen concentrations is worth it. Secondly, another problem with using high concentrations of hydrogen for cooling purposes is that it is mainly injected into a section of the furnace where the temperature might be below 760 °C, which is below the flammability limit of hydrogen. This problem is amplified by the fact that forced convection cooling units generate a turbulent flow of gas. Therefore, it is possible that air might get inside the furnace through the exit end, leading to an explosion. © Woodhead Publishing Limited, 2010


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7.11 Standard deviation values, calculated from the dimensional change measurements from die size, for samples cooled with 5vol-% hydrogen and others cooled with 92vol-% hydrogen (copper fixed at 2.0 wt-%).

7.5

References

ASM, 1984, ‘Production Sintering Practices’, in ASM Handbook vol. 7 – Powder Metallurgy, ASM International, Materials Park, OH, p. 368. Auborn, J.N., Choo, J. S., 1994, ‘Effect of Chemistry and Compact Density on the Decomposition of PM Lubricants’, in Advances in Powder Metallurgy and Particulate Materials – 1994, vol. 3, pp. 103–16. Ball, W. et al., 1994, ‘Replacing Internal with External Lubricants’, in Advances in Powder Metallurgy and Particulate Materials – 1994, vol. 3, pp. 71–82. Birks, N., Meier, G.H., 1983, Introduction to High Temperature Oxidation of Metals, Edward Arnold, London, UK, p. 168. Blais, C., 2004, ‘Sinter-Hardening: Process, Microstructures and Properties’, in PM Sintering Seminar, Erlanger, KY, September, 21–2. BOC Gases Inc., 1994, Industrial Gases Data Book, Murray Hill, NJ. Bockel-Macal, S., et al., 2004, ‘Industrial Performance of Low Reactive Atmospheres on Sintering Furnaces’, Proceedings of the 2004 International Conference on Powder Metallurgy and Particulate Materials, Chicago, IL, pp. 5-39–5-45. Dwivedi, R.K., 2008, ‘Effect of Powder Characteristics and Sintering Conditions on Density and Corrosion Resistance of MIM 316L Stainless Steel’, Proceedings of the 2008 MPIF/APMI International Conference on Powder Metallurgy and Particulate Materials, Washington, D.C., pp. 4-58–4.71. Gaskell, D.R., 1981, Introduction to Metallurgical Thermodynamics, Hemisphere Publishing Corp., New York, pp. 585–9. German, R.M., 2005, Powder Metallurgy & Particulate Materials Processing, Metal Powders Industries Federation, Princeton, NJ, p. 197.


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Groak, J.R., 1999, ‘Benefits of Convective Cooling’, in MPIF – Sinter Hardening Seminar, Cleveland, OH, 1999. Jesberger, T.J., 1999, ‘Furnace Design Issues Related to Sinter Hardening’, in MPIF – Sinter Hardening Seminar, Cleveland, OH, 1999. Lemieux, P. et al., 2005, ‘Pressing Challenging Parts on a Production Scale Using Die Wall Technology’, Proceedings of the 2005 International Conference on Powder Metallurgy and Particulate Materials, Montreal, IL, pp. 3-71–83. McIntire, R. D., 1965, ‘The effect of HCl-H2 Sintering Atmospheres on the Properties of Compacted Iron Powder’, Transactions of the ASM – Technical Notes, vol.57, pp. 351–4. Nayar, H.S., 1994, ‘Delubrication Problems and Solutions in the PM Industry’, in Advances in Powder Metallurgy and Particulate Materials – 1994, vol. 3, pp. 117–23. Nayar, H., Shaeffer, D., 1981, ‘How Furnace Zoning Can Optimize Atmosphere Efficiency’, in Heat Treating, March. Nowatki, J., 2008, Anhydrous Ammonia: Managing The Risks, North Dakota State University, online at http:#dRwww.ag.ndsu.edu/pubs/ageng/safety/ae1149-1.htm (viewed March 12, 2009) Pease, L.F., West, W.G., 2002, Fundamentals of Powder Metallurgy, Metal Powders Industries Federation, Princeton, NJ, p. 146. Poirier, D.R., Geiger, G.H., 1994, Transport Phenomena in Materials Processing, TMS, Warrendale, PA. Ready, J.R., Ready, D., 1986, ‘Sintering of ZrO2 in HCl’, J. Am. Ceram. Soc, 69, (7), 580–82. Ready, J.R., Ready, D., 1987, ‘Sintering of NiO2 in HCl Atmospheres’, J. Am. Ceram. Soc, 70, C358–C61. Robert-Perron, E. et al., 2005, ‘An Integrated Approach to the Characterization of Powder Metallurgy Components Performances during Green Machining’, Mater. Sci. Eng. A-Struct., 334, 402. Saha, D. et al., 2008, ‘Mechanisim of Delubrication During Sintering: Reaction Kinetics and Decomposition Stages’, in Proceedings of the 2008 MPIF/APMI International Conference on Powder Metallurgy and Particulate Materials, Washington, D.C. pp. 5-82–5.94. Samal, P.K., 2004, ‘Effect of Processing Parameters on the Room and Elevated Temperature Mechanical Properties of PM 409L and 434L Stainless Steels’, Proceedings of the 2004 International Conference on Powder Metallurgy and Particulate Materials, Chicago, IL, pp. 10-122–10-133. Sauer, H. et al., 1988, Härterei-Technische Mitteilungen, vol. 43, pp. 45–53. Schade, C., 2007, ‘Stainless Steel AISI Grades for PM Applications’, Proceedings of the 2007 MPIF/APMI International Conference on Powder Metallurgy and Particulate Materials, Denver, CO, pp. 7-24–7-39. Serafini, R.E., Blais, C., 2001, ‘Furnace Atmosphere Optimization for Sinter Hardening’, in Advances in Powder Metallurgy and Particulate Materials, Metal Powders Industries Federation, Princeton, NJ, part 5, pp. 5-57–5-72. Serafini, R.E. et al., 2002, ‘Sinter Hardening Optimization Through Atmosphere Modifications’, presented at PM2TEC-2002 World Congress, Special Interest Program – 9: Sinter Hardening: Materials, Processes and Properties, Orlando, FL, 16–21 June. Serafini, R., 2009, Personal communication, May 6, 2009. Thompson, C.B., 2005, in ‘ASM Handbook vol. 7 – Powder Metallurgy’, ASM International, Materials Park, OH, p. 190.


8 Vacuum sintering D. F. Heaney, The Pennsylvania State University and Advanced Powder Products, Inc., USA Abstract: Vacuum sintering is an effective method for obtaining dense sintered metals and ceramics. The chapter first discusses key issues with evaporation, purification and densification. It then describes equipment configurations and finally practical processing conditions for some metals and ceramics. Key words: vacuum sintering, metal, ceramic, evaporation, purification, densification, equipment.

8.1

Introduction

Vacuum sintering became a relevant technology when first used for the sintering of the Group VA elements – V, W, Ta, Mo, Nb, etc.1 The method was actually a reactive sintering approach where carbon was added to reduce the oxygen from the metal via carbon monoxide evolution under vacuum. This method produced a ductile metal and a modern sintering technology was born. Currently, vacuum sintering is often used for metals and less often for sintering ceramics. The reasons for the use of vacuum are to provide a clean atmosphere and in many cases to evaporate impurities from the high surface area powder starting material. The concern with using a vacuum is the potential to evaporate the material being sintered at elevated temperatures when the vacuum pressure approaches the vapor pressure of the material. In this chapter the effect that vacuum has on the purification of powders, reduction of oxides on powders, evaporation of metals and compounds, and the densification of powder from the sintering perspective are addressed. Also, equipment configurations are reviewed considering vacuum level requirements, binder removal and partial pressure sintering. These configuration topics are important since modern vacuum sinter processing often occurs in multiple steps, for example the use of high vacuum during initial processing to remove impurities followed by a partial pressure sintering at elevated temperatures to prevent metal evaporation. Other advanced processing techniques such as the use of reducing atmospheres at partial pressures at low temperatures followed by high vacuum at elevated temperatures are utilized when the metal is difficult to reduce and not susceptible to evaporation at elevated temperatures. Finally, example applications and starting point process conditions are provided for many common materials that are processed using a vacuum equipment configuration. 189 © Woodhead Publishing Limited, 2010

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8.2

Evaporation under vacuum

Evaporation leads to a change in the material stoichiometry, furnace contamination, and sintering behavior changes. Evaporation is typically not desirable; however, it needs to be addressed to select the maximum temperature, vacuum level and dynamic gas flow combination to process a particular material. Also, evaporating species will condense onto the cooler part of the furnace. Furnace configurations to cope with this situation are discussed in the furnace configuration section of this chapter. Unlike pure gas evolution, these evaporating species will typically condense in cool regions prior to affecting the pumping capacity; thus their presence is not easily empirically determined by watching the vacuum level of the furnace.

8.2.1 Metal evaporation The rate of evaporation of metals can be estimated if one assumes the evaporating metal behaves ideally. The rate of ideal evaporation, J, in a vacuum, as a function of temperature, is best described using the Langmuir equation:2 J=

Pv 2πMRT

[8.1]

where M is the molar mass of the evaporating species, R is the ideal gas constant, T the absolute temperature, and pv is the vapor pressure of the evaporating species. Vapor pressure is the gas pressure exerted when a material is in equilibrium with its own vapor – atoms escape at the same rate as the atoms re-condense on the material surface. The vapor pressure of a pure species, p– v, is typically estimated using the Clausius-Clapeyron equation: log p– v = – A + B + C log T + 10–3 DT T

[8.2]

where the pressure is given in Torr. The values for A, B, C, and D are available in Table 8.1 for some metal species.2 Others can be obtained elsewhere.3 Using Eq. 8.2, the vapor pressure can be calculated, and the subsequent evaporation rate can be calculated using Eq. 8.1. Evaporation can be retarded slightly when the vacuum furnace pressure is significantly greater than the vapor pressure of the evaporating species. The reason for this behavior is the collision of the vaporizing species with gas molecules within the furnace. Evaporation can also be retarded when the vaporizing species collide with other evaporating species either of the same material or another. Thus a low dynamic flow of gas can reduce evaporation since the evaporating elements will be colliding at a higher rate with other evaporating species. Conversely, a high dynamic flow rate will accelerate evaporation.


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Table 8.1 Clausius-Clapeyron equation constants for various elements2 Metal Ag Al Au B Co Cr Cu Fe Mn Mo Nb Ni Pd Pt Si Sn Ta Ti Ti (β) V W Zn

Temp range (K) 298–1234 1234–2400 1200–2800 298–1336 1336–3240 1000-m.p. 1000–1772 298-m.p. 298–1356 1356–2870 900–1812 1812–3000 993–1373 m.p.-b.p. 298-m.p. 298-m.p. 298-m.p. m.p.-b.p. 298-m.p. m.p.-b.p. 298-m.p. m.p.-b.p. m.p.-b.p. 505-b.p. 298-m.p. m.p.-b.p. 1155-m.p. 298-m.p. 298-m.p. 473–692.5 692–1000

A

B

C

D

14710 14260 16450 19820 19280 29900 22210 20680 17870 17650 21080 19710 14850 13900 34700 37650 22500 22400 19800 17500 29200 28500 20900 15500 40800 23200 24400 26900 44000 6883 6670

11.66 12.23 12.36 10.81 12.38 13.88 10.817 14.56 10.63 13.39 16.89 13.27 17.88 17.27 11.66 8.94 13.60 16.95 11.82 4.81 13.24 14.30 10.84 8.23 10.29 11.74 13.18 10.12 8.76 9.418 12.00

–0.755 –1.055 –1.023 –0.306 –1.01 –1.0 – –1.31 –0.236 –1.273 –2.14 –1.27 –2.52 –2.52 –0.236 +0.715 –0.96 –2.01 –0.755 +1.0 –0.855 –1.26 –0.565 – – –0.66 –0.91 +0.33 +0.50 –0.0503 –1.126

– – – –0.16 – – –0.223 – –0.16 – – – – – –0.145 –0.166 – – – – – – – – – – – –0.265 – –0.33 –

The following equation predicts the vapor pressure of species i above a multicomponent alloy: pvi = γi p– vi Xi [8.3] where pvi is the vapor pressure of species i, γi is the activity coefficient of species i, p– vi is the vapor pressure of pure species i, and Xi is the mole fraction of species i. This equation can be used for determining ‘ball park’ values for partial pressures and subsequent evaporation rate using Eq. 8.1; however, more accurate concentrations of gases can be determined using commercially available thermodynamic software packages such as Thermo-Calc.4 If an alloy is being sintered, metals with different vapor pressures exist and the metal with the highest vapor pressure will vaporize preferentially. Consider the case of a two-element composition: the composition of the vapor depends upon


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both the vapor pressure of the element as well as the bulk composition, as defined by Eq. 8.4, where C2 is the vapor concentration of element 2.5 C2 =

X2pv2 X1pv1 + X2 pv2

[8.4]

where X1 and X2 are the respective mole fractions in solution, and pv1 and pv2 are the vapor pressures of the two metals. Based on Eq. 8.4, one can see that the metals with the lower vapor pressures will have less effect on the composition of the vapor; thus, these elements are not being removed from the alloy being sintered. In fact, according to Smith et al., if the vapor pressure of an alloy component is less than 10–2 torr (10–5 atm) or that of the base metal, the evaporation of this alloy component is not likely.6 Studies on the evaporation from molten metal surfaces show that the evaporation rate is appreciably lower at total gas pressures above 1 torr.7,8

8.2.2 Compound evaporation The vapor pressures of compounds are often very different from the pure parent elements. In fact, the oxide or halide may have a vapor pressure that is higher than the metal itself. Thus, oxide or halide can evaporate during the vacuum sintering operation. This may be desirable if these oxides or halides are impurities as the result of previous processing, or it may be undesirable if the oxide or halide is the material of sintering interest. Metal oxides of molybdenum, niobium, rhenium, tantalum and tungsten are highly volatile as compared to the base metal. A comparative analysis of the temperatures required for a vapor pressure of 1 Pa (10−5 atm) for a few metals and their oxides implies that certain metal oxides will evaporate preferentially as compared to the base metal. For example, Mo has a temperature of 2530 °C and MoO3 has a temperature of 620 °C; thus the MoO3 will evaporate.9 This means these metals can be purified to a certain extent by using vacuum alone during the sintering operation. In contrast, Al has a temperature of 1000 °C and Al2O3 has a temperature of 2000 °C; therefore, the Al will evaporate and the Al2O3 will be unchanged. Experimental oxygen content change measurements for the Nb-O and Ta-O systems at different temperatures have been performed.10 During degassing, mass spectroscopy has shown that NbO and NbO2 evaporate from niobium and TaO and TaO2 evaporate from tantalum. The lowest oxygen content is reached when a steady state of evaporation of oxides and the subsequent condensation of oxygen from the vacuum atmosphere is reached. At very high temperatures, near the melting point of the metal, evaporation of the metal may be considerable. In this case, the gas content of the sample is a function of the complexity of the ratio of the rates of oxide evaporation, metal evaporation and pick-up from the residual atmosphere. Vapor pressures of various oxides can be calculated using Eq. 8.2 and the data for the Clausius-Clapeyron constants data, which is found in Table 8.2. © Woodhead Publishing Limited, 2010

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Table 8.2 Clausius-Clapeyron equation constants for various oxides2 Metal

Temp range (K)

A

B

C

D

B2O3 MoO3 P4O10‡ PbO Re2O7 TeO2 ThO2 UO 2 V2O5* WO 3

1300–1650 298-m.p. m.p.-b.p. 298-s.p. 298-m.p. m.p.-b.p. 273-m.p. m.p.-b.p. 298-m.p. 2500–2900 1500–2800 m.p.-1500 1000-m.p.

–16960 –15230 –12480 –4350 –13480 –13310 –7300 –3950 –13940 –34890 –33120 –7100 –24600

6.64 27.16 24.60 9.81 14.36 19.47 15.000 9.10 23.51 10.87 25.69 5.05 15.63

– –4.02 –4.02 – –0.92 –2.77 – – –3.52 – –4.03 – –

– – – – –0.35 – – – – – – – –

* Apparent vapor pressures. V2O5 loses oxygen with increasing temperature. ‡ hexagonal

8.3

Material purification

Material purification is often associated with vacuum use since the vacuum aids in pulling impurities from the material, thus promoting a clean surface to enhance sintering and a clean microstructure that provides better physical properties. The electrical conductivity, thermal conductivity, magnetic properties, hardness, yield strength, ultimate tensile strength, elongation, etc. are improved. For example, oxygen in titanium increases both the yield strength and the ultimate strength, but decreases the percentage elongation. This is due to solid solution strengthening. Hydrogen in titanium and zirconium decreases the notch impact strength of these metals.11 Thus, controlling the gas content of sintered material is extremely important and the need for a vacuum to remove the gas is a quick method of removing these gases. Degassing is a function of the temperature and the pressure and is typically performed before the powders are sintered and densified. Densification can inhibit the escape of gas from the metal. Degassing is often performed during the sintering step prior to densification; however, some metals are degassed prior to shape forming and sintering, such as tantalum and niobium. After the high-vacuum degassing treatment of these powders, they are more ductile and easier to shape by compaction.

8.3.1 Absorbed gases Particulate materials have a high surface area, and therefore they have a high propensity to absorb or adsorb gas impurities. These impurities can be water,


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hydrocarbons, nitrogen, oxygen, hydrogen, etc. Gas is adsorbed by the surface, physically due to Van der Waals’ forces or by chemical reaction. In the case of absorption, the gas molecules dissociate and dissolve in the lattice of the metal as atoms or ions. These atoms are often interstitial in nature due to their small size. Accumulation can occur at grain interfaces and dislocations. High gas content in the powders interferes with sintering if not properly removed. These impurities can be the result of the powder production method or storage, or from subsequent processing prior to sintering. Desorption of most impurities from the material being sintered can be obtained physically by increasing the temperature or decreasing the pressure. These changes displace the equilibria towards pure material (in most cases) and also improve the diffusion of these gases through the pores of the powder compact. For example, physical desorption occurs with water or hydrocarbons. This should be done at as low a temperature as possible to prevent chemical reactions of the impurities with the particulate material. Also, the temperature should be increased very slowly to allow the pumping system to keep up with gas desorption. In the case where the gas and metal form a compound (such as oxides, hydrides, nitrides, etc.) the secondary phase forms at the surface where the gas and the metal meet. This typically occurs at the outside surface of the powder or sintered structure; however, a supersaturated solution may precipitate the compound upon cooling. If the gas does not form a compound with the metal, the gas is given off upon cooling. This may result in defects such as pores or microcracks. In general, a decrease in pressure will lead to degassing, and an increase in pressure will lead to gas absorption. With regards to temperature, one would intuitively think that an increase in temperature will lead to degassing; however, thermodynamics shows that certain metals actually absorb gas upon heating, depending on the pressure and the metal/gas system. The phase diagram of a metal/gas combination can be used to predict the absorption of gas and the temperature at which the gas begins to evolve. Consider the reactive metals of niobium, tantalum, titanium and zirconium. These metals all react with hydrogen to absorb hydrogen as the temperature increases; however, at approximately 500–600 °C the hydrogen will be removed. For these types of materials, the furnace should be ramped at a high rate through the lower temperature regime to avoid component contamination and held under a high pumping rate vacuum until it is removed prior to high-temperature sintering. The thermodynamics of gas removal is discussed elsewhere.12

8.3.2 Oxygen removal Oxygen can be removed by one of three methods: oxide dissociation, chemical reaction, or, as previously discussed, evaporation of metal oxide species.


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Dissociation Oxygen removal by pure dissociation from most metals is difficult. Dissociation is the removal of oxygen considering the following generalized reaction, where M is a metal. 2MO → 2M + O2

[8.5]

Consider the relatively noble element copper. The dissociation pressure for CuO is only 10–4 Torr at 1000 °C. At this temperature and vacuum level, the copper would evaporate. Degassing of oxygen is only possible if the sintering temperature of the material can be very high without the evaporation of the metal. The dissociation pressure of different metals can be readily determined from thermodynamic calculations and easily seen by looking at an Ellingham or a Richardson Diagram. Figure 8.1 shows the approximate temperatures, at different vacuum levels, where metal oxide will dissociate provided the kinetics are high enough. Chemical reaction The use of chemical reaction is the only practical method of reducing oxide in a vacuum. Hydrogen is often used to remove oxygen at atmospheric pressure; however, hydrogen is converted to water vapor during this reduction sequence; thus the vacuum level is not critical for reduction. The water vapor partial pressure is the only way to adjust the efficiency of reduction in a hydrogen atmosphere. The most frequently applied method of chemical reduction in vacuum is by the use of carbon deoxidation. In this method, carbon is mixed with the starting material in an appropriate stoichiometric ratio to effectively remove the oxygen from the base particulate material. Consider the following reaction: Mx O(s) + C(s) → xM(s) + CO(g) ↑

[8.6]

The vacuum or flowing gas under partial vacuum affects the equilibrium of this reaction by continuously removing the carbon monoxide and subsequently produces reduced metal. This technique was first used for the sintering of the Group VA elements – V, W, Ta, Mo, Nb, etc. This reaction occurs for ferrous powders such as carbonyl iron. In this case, the unreduced carbonyl powder typically has a carbon level of 0.7% and an oxygen level of 0.2%. The resulting carbon level is 0.5% due to carbon monoxide evolution. This carbon deoxidation reaction is initiated at elevated temperatures and high vacuum levels. Temperature for this impurity removal should be slightly above where the reaction begins to occur. Empirically, this temperature can easily be determined by matching the stoichiometry of the oxygen in the material with carbon, and using thermal gravimetric analysis to determine the temperature of gas evolution due to the change of weight. Vacuum level is determined by evaluating the partial pressure of the base material at the determined temperature and subsequently calculating


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8.1 Dissociation pressures of various oxides at different temperatures (Smithells Metals Reference Book, 6th ed., E. Brandes, ed., Butterworth & Co., Boston, 1983, p. 29–2).

the evaporation rate using Eq. 8.1 to determine if this evaporation rate is sufficiently low to maintain the proper stoichiometry of your material.

8.4

Densification under vacuum

Evaporation of material is typically undesirable for most sintering stoichiometry; however, a unique opportunity for densification exists due to the use of vacuum and the evaporation. The evaporation/condensation mechanism for sintering can become a dominant player in sintering kinetics after pore closure. Although evaporation condensation does not show densification behavior during the early stages of sintering, its presence during the final stage of sintering is paramount for © Woodhead Publishing Limited, 2010

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obtaining high density in many materials that will not typically densify under atmospheric pressure. The reason for this is that the predominate mechanism in maintaining pores on grain boundaries during final stage sintering is evaporation/ condensation. Often a material will seem to quit sintering at approximately 92–95% density. This is because the grains have rapidly grown past the pores and must rely on the slow kinetics of bulk diffusion of vacancies to be eliminated, whereas if the pores remain on the grain boundaries the vacancies can diffuse via grain boundary diffusion to be eliminated. The primary mechanism for keeping pores on grain boundaries is evaporation/condensation. Envision the pores being closed off during densification: if they are closed under a vacuum or partial vacuum, the ability for the material being sintered to evaporate and transport is much greater since the number of gas molecules in the pores is minimal; thus, as the grains grow and try to grow past the pores, the material more easily evaporates and moves from the convex surface of the pore to the concave surface of the pore with the aid of the ease of evaporation. A schematic of this is shown in Fig. 8.2.

8.2 Pore movement during grain coarsening allows greater densification. Vacuum enhances the vapor phase movement of atoms across the pore during final stage sintering.

8.5

Equipment configurations

The configuration of a furnace is greatly dependent upon the final application. Sintering application requirements such as temperature, temperature uniformity, vacuum level, partial pressure gas, materials of construction to prevent contamination, and the need for debinding should be considered in specifying a furnace for a particular application. Initially this section provides a general description of various types of processes. This is followed by a review of different furnaces for many applications.

8.5.1 General process configurations Standard vacuum sintering process A standard vacuum process is one where a vacuum is pulled to a particular level and the temperature is then ramped to the sintering level followed by ramping © Woodhead Publishing Limited, 2010

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back to room temperature. The initial vacuum can go through multiple purges of inert gas prior to pulling a hard vacuum level. Materials that can be sintered in this fashion do not have any binder or atmospheric partial pressure requirements. A schematic of this configuration is shown in Fig. 8.3.

8.3 Standard vacuum process configuration.

Dynamic partial pressure process In this process, a vacuum furnace operates in partial pressure rather than full vacuum to prevent excessive removal of evaporating work. This can be done by injecting a gas such as N2, Ar or H2 into the furnace hot zone via a needle valve and at the same time pumping with the mechanical pump. Another variation is to have mass flow controllers on the gas inlet to control the flow rate of the gas into the furnace and a throttle valve between the furnace and the vacuum pump to control the partial pressure. A schematic of this configuration is shown in Fig. 8.4.

8.4 Dynamic partial pressure vacuum process configuration.


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Multistage processes A modern trend in vacuum furnace processing is a furnace that can be utilized for many different conditions. The furnace could have both a debinding and a vacuum sintering capability, a debinding and partial pressure sintering capability, or a combination of both debinding, high vacuum, and partial pressure. In these configurations, the debinding occurs at the low temperatures with a high gas flow that is controlled by mass flow regulators and the pumping is through a binder trap. Upon completion of debinding, valves are used to isolate the binder trap and to pump directly on the chamber. The furnace then goes into sintering mode where either hard vacuum or partial pressure sintering is used for the rest of the process. A schematic of this configuration is shown in Fig. 8.5.

8.5 Dynamic partial pressure vacuum process with binder trap configuration.

8.5.2 Vacuum level Vacuum level is typically defined in units of Torr, atmospheres, mm Hg or microns. A Torr (properly identified with a capital ‘T’) is a measure of vacuum equal to 1/760th of atmospheric pressure. The micron is used to indicate levels of vacuum equal to 1/1000th of a Torr, or 1 × 10 –3 Torr, which is equal to approximately one millionth of an atmosphere. The layman terms often used for vacuum are ‘rough’ or ‘hard’. These descriptive terms give qualitative meaning to vacuum levels; however, they lack specific quantitative values because each term covers a broad spectrum of vacuum level. Typically, they refer to the equipment configuration required for a vacuum level. Rough vacuum is typically obtained with just a mechanical pump or rough pump. A hard vacuum or high vacuum can be achieved in different configurations. If the particular application requires only a 10−3 Torr vacuum level, a mechanical pump equipped with a blower is sufficient. This configuration is pictured in Fig. 8.6. If a vacuum level of 10–4 to 10–7 Torr is


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8.6 Blower and rough pump arrangement used to obtain 10–3 Torr.

required, a configuration that has a mechanical pump with either a diffusion pump or a turbomolecular pump is needed. A configuration of the mechanical and diffusion pump is shown in Fig. 8.7.

8.5.3 Heating configuration The majority of modern vacuum furnaces use indirect resistance heating. In this design, the furnaces are configured where the heating elements and the work to be sintered are separated, and the work is heated by radiation either directly from the heating elements or through a refractory box within the heating elements. In this configuration, complex shapes can be sintered to net shape; thus it is often used for net shape sintering. Some higher temperature vacuum furnaces may use induction heating or direct resistive heating (The Coolidge Process). In the Coolidge process, the bars of material are clamped in electrical connectors and current as a result of the resistance in the powder compact is used to heat the bars. Although high-temperature materials such as Mo, W, Ta and Nb can be processed in this way to sufficiently high density (93–95%), the geometry is limited to billets that will subsequently be shaped using conventional metalworking practices and the areas that are connected to the heat source must be removed as scrap. Thus the Coolidge process has poor yield. Vacuum retort furnaces can be used for temperatures that do not exceed 1100 °C. These furnaces are typically constructed of heat resistant stainless steel or Inconel with heating elements that can be Nichrome (Ni-20Cr), Fecralco (Fe-23Cr-5Al-1Co) or silicon carbide (SiC).


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8.7 Diffusion pump with mechanical pump roughing pumps to pull the initial rough vacuum. This system is capable of obtaining a 10–6 Torr vacuum level. Notice the cooling lines spun around the diffusion pump and the cryogenic trap bolted on the top.

These furnaces are used for dewaxing and presintering of the work prior to high-temperature sintering or for materials that can be sintered at temperatures below 1100 °C.

8.5.4 General furnace configuration Typically an indirect resistant heating vacuum furnace has the following components: water-cooled furnace vessel, refractory material hot zone, refractory


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8.8 Modern vacuum furnace showing the power supply to the left, the control panel to the right, the furnace chamber in the center and the pumps, binder traps, and exhaust plumbing to the right of the chamber. (Photo courtesy of Centorr Vacuum Industries.)

material heating elements, vacuum pumping unit, power supply and control cabinet. Additional features could include: forced gas cooling device, mass flow gas controls to control gas flow rate during partial pressure sintering, a throttle valve to control partial pressure, binder trap to catch binders, properly sized pressure relief port for sintering in hydrogen, and finally a burn-off stack if flammable gases or organic binders are being burnt off. Figure 8.8 shows a furnace with many of these features – to the left in the picture is the power supply, the pressure vessel where the sintering is taking place is the round chamber in the center, the control cabinet is to the right and the pumping and exhaust features are shown to the right of the furnace chamber. These will be shown in more detail later in this section. Another configuration for vacuum furnaces is the ‘bell jar’ configuration, where the chamber is actually lifted up and down or the work is raised up or down. This configuration is shown in Fig. 8.9. Water-cooled furnace vessel The furnace vessel is typically constructed of a welded steel double wall where cooling fluid flows between the two walls to promote cooling. Both carbon steel and stainless steel are used. The stainless steel is more expensive; however, the stainless steel is more resistant to corrosion, provides better vacuum levels due to its less porous oxide layer (scale), and does not require painting. The carbon steel is less expensive and requires both internal and external painting. The internal


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8.9 Bell jar sintering furnace where the chamber is in the center and the cooling vessel is moved up and down between runs to access the area where sintering is occurring. The control panel is to the left and the power supply is to the right. (Photo courtesy of Thermal Technology, LLC.)

painting is typically a refractory type of coating. Some configurations have an outside wall constructed of carbon steel and an inside wall constructed of stainless steel. The chamber is constructed using ASME Section 8 code as a guideline for wall thickness; even though most vacuum furnaces seldom operate above 1 atm pressure the reason for this is the 35–40 psig (2.5–2.8 kg/cm2) pressure exerted on the outer chamber exterior by the water jacket. Typically, the wall thickness runs from 0.25 inch thick to 1 inch thick. If the furnace will be used as an over pressure furnace, the wall thickness will of course be thicker. Cooling of the chamber is extremely important. Typically the furnace has internal baffles to ensure that no cold spots exist on the chamber itself. The water


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typically enters through the bottom of the furnace and exits through the top. The entrance holes are smaller in size than the exit holes. This is to allow for the volumetric expansion of the water upon heating. The quality of the water is extremely important since poor water quality can promote localized corrosion, which results in pinhole leaks and is difficult to repair effectively. The chamber temperature can be surveyed during use using a noncontact thermocouple. This will give the operator knowledge of how the chamber is cooling and provides the opportunity to adjust the flow to different regions to promote better cooling. Other considerations for a vacuum chamber are to ensure that the furnace chamber is free to expand during heating. If the chamber is constrained it will experience additional stress during heating and cooling and have limited life. The feedthroughs on the furnace are where the heating elements’ electrical connections are fed through the furnace. These are typically designed with Nylon or Teflon bushings and are also water cooled. Note that the greater the number of feedthroughs on the furnace, the greater the difficulty to pull a high vacuum and the more easily the work can be contaminated. Figure 8.10 shows a photo of a set of heating element feedthrough. Hot zone The hot zone of a vacuum furnace consists of a set of radiation shielding, the heating elements, and a retort box or fixturing to hold components. Radiation shielding is typically constructed of molybdenum, tungsten or tantalum. In many cases, a lower temperature material such as stainless steel is used for the sheets furthest from the heating elements. One issue with stainless steel is that as the material ages, the surface generates a greater oxide layer, resulting in a greater emissivity and a subsequent greater heat loss. Another issue with stainless steel is that it will evaporate nickel or chromium if the sheets become too hot (the temperature of each sheet is approximately 100 °C less for each layer back from the controlled hot zone). The substitution of iron or nickel sheet can be used to minimize the change in emissivity if their lower temperature susceptibility can be tolerated.13 For ultra high vacuum systems, all refractory metal hot zones should be used. Figure 8.11 shows a photo of a typical all metal hot zone furnace. Sintering in graphite-containing furnaces must be for materials that do not require extremely high vacuum levels and are not too susceptible to the presence of carbon. The graphite insulation picks up gas due to its porous nature and subsequent high surface area. Thus, during heating, a large quantity of gas is driven off. The advantage of graphite and carbon is their relatively low cost to purchase, ease of shaping, and their shape stability even after many thermal cycles. Figure 8.12 shows the hot zone of a graphite furnace. Coatings are often used to treat the surface of graphite furnaces to control carbon. They are also used as barrier coatings for the substrate or fixture used to support components during sintering. Table 8.3 shows different coatings, their service temperature and their usages.


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8.10 Heating element feedthrough. (Photo courtesy of Centorr Vacuum Industries.)

Issues of concern are the fixturing that will be used to hold the samples and the potential for radiant shielding of the work to be sintered, resulting in gradients in density and subsequent dimensional variability. Heating elements Heating elements for vacuum and partial pressure furnaces are typically constructed of tungsten, molybdenum, graphite, and less commonly tantalum. Table 8.4 shows these materials and their general use temperatures. The refractory


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8.11 All metal hot zone of furnace. Notice the plenum retort with holes for the entrance of gas, and the large port at the bottom of the retort to allow the removal of binder. (Photo courtesy of Centorr Vacuum Industries.)

8.12 Graphite hot zone furnace. Notice that the heating elements, the insulation box and the retort box are all made of graphite. (Photo courtesy of Centorr Vacuum Industries.)


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Table 8.3 High temperature sintering substrates and coatings used for furnace components and component fixturing Material

Max use temp (ºC)

Y2O3 ZrO2 BN Al2O3

2000 vacuum/inert Most metals – Ti 2000 vacuum/inert/air Most metals – Ti 1100 air Ta, AlN, nitrides 1400 vac 1800 inert 1800 sapphire Most metals and oxides except WC and Ti 1650–1700 1500 on graphite 1900 vacuum/inert 1000 air 1850 inert/reducing Most metals 1100 vacuum 2000 vacuum/inert 350 air 1900 inert 1600 vacuum 350 air 2200 inert 1800 vacuum 600 air 2000 vacuum Carbides, Cu, SiC, TaC 2500 inert 2100 vacuum, inert 2800 vacuum, inert Mo, W, MoSi2

MoSi2 Si3N4 TiC TiN ZrB2 Graphite Mo W

Usages

Table 8.4 Temperature limit of common heating element materials used in vacuum furnacesi,ii

Heating element material

Upper limit (C) Carburizing

Decarburizing

Inert

Reducing

Vacuum

Molybdenum Tantalum Tungsten Graphite

– – – 2500

– – – 1700

1700 2500 2000 2000*

1700 – 2800 1700=

1700 2500 2800 2500

* will have some contamination due to carbon evaporation = work must be able to withstand methane, the heating elements will last months to year. i O. Winkler and R. Bakish (eds), Vacuum Metallurgy, Elsevier Publishing Company, Amsterdam (1971), p. 700. ii R. M. German, Sintering Theory and Practice, John Wiley & Sons, Inc. New York (1996), p. 475.


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metals are excellent for high temperature use, as their name implies; however, these metals are susceptible to oxidizing and carburizing environments. Molybdenum oxides evolve at temperatures of 600–700 °C; thus Mo cannot be used in an oxidizing environment. Tantalum will form oxides, nitrides and carbides, so it can only be used in pure vacuum sintering. Evaporation of the heating elements is also a concern at very high temperatures and can contaminate the sintering work. For example, graphite begins to evaporate under vacuum at temperatures above 2200 °C, thus it can only be used for materials that can handle a carburizing environment at these temperatures. Maximum temperature for graphite heating element furnaces used in pure vacuum is 2200– 2300 °C; if degradation of the heating elements is permissible for the work being processed or the furnace is run in inert gas, a temperature of 2500–2800 °C is possible. Evaporation from the work and condensation on the heating elements may destroy the heating elements. For example, tantalum heating elements are susceptible to carbide formation in an environment containing carbon monoxide at temperatures as low as 1000 °C. Tantalum in a hydrogen environment will form hydrides; therefore tantalum cannot be used for furnaces that run hydrogen. Tungsten heating elements can deteriorate in a carbon monoxide environment at temperatures of 1400 °C. Molybdenum may also deteriorate at low temperature (1350 °C) if the furnace is used to do thermal debinding, since the residual carbon from the binder system may form carbides with the molybdenum at high temperatures if it is not properly removed. In general, metal hot zone debind and sinter furnaces are not recommended for temperatures above 1600 °C because any residual carbon will react with the refractory metal to produce carbides and the hot zone will become embrittled. Provided no chemical reactions with the processing environment occur, the working temperatures of most high-temperature resistance materials are restricted by the tendency for the materials to recrystallize and embrittle, which eventually leads to failure. Two materials that are not prone to this behavior are graphite and tantalum. The heating element material can be doped to prevent recrystallization; for example, lanthanum is commonly used as a dopant for electrodes that are used in the lighting industry, and provides enhanced creep resistance in vacuum elements and shielding. Another doped alloy is TZM (Mo-0.5Ti-0.08Zr-0.03C), which gives greater high-temperature stability because it possesses oxide dispersion strengthening, for applications where the material is under compressive load. TZM is typically utilized for support rails and posts. Primary furnace shielding is typically made with lanthanated molybdenum. Furnaces that have horizontally arranged heating elements have intricately configured and supported heating elements to allow the thermal expansion upon heating and to permit uniform heating around the work. Figure 8.13 shows a tungsten rod heating element arrangement. Notice the ceramic insulating washers and the refractory metal support wires that are used to keep the heating elements uniformly spaced. With high sintering temperatures, a gradual distortion and


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8.13 Refractory metal hot zone with refractory metal heating elements. Notice the white ceramic insulators which prevent the heating elements from grounding to the retort during the application of current. (Photo courtesy of Centorr Vacuum Industries.)

warping of heating elements and the radiation shields occur over time. This results in heat loss from the box to the outer wall, making the furnace less efficient, the temperature uniformity poor and creating the potential for the shorting of heating elements on the shielding. The heating elements can also ground to the insulation shield pack when they become coated with evaporated metal after many sintering runs. In this case, these need to be replaced or removed and the evaporated metal needs to be removed either chemically or through sandblasting. Temperature control Temperature is typically controlled using sheathed thermocouples – Type C (1650–2315 °C), Type K (95–1260 °C), or Type S (980–1450 °C). Thermocouples typically have an accuracy of 0.75%. Optical pyrometers are also used for temperature control in the 800 to 3200 °C range. Optical pyrometers have an accuracy of +/– 1% with a 0.5% repeatability, thus at 2100 °C a variability of +/– 21 °C. Thus there is a need for multi-zone control. Gas flow consideration Gas flow is typically configured for entrance into the retort and the heating zone box. Higher gas flow in the heating zone box as compared to the retort gives the best binder removal properties. Volumes of gas flow at various pressure levels will make the difference between ‘molecular flow’ (where the gas travels like a pinball


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in a straight line) and ‘viscous or laminar flow’ (where gas travels or flows like a liquid), which offers improved debinding efficiencies.

8.5.5 Special furnace considerations Cooling The time required for cooling down a furnace charge or load is of particular importance for the economic consideration of furnace use. Thus a cooling method is required. Two methods exist for cooling. One is to remove the work from the furnace hot zone to a cooler chamber. This is often employed for semicontinuous vacuum systems. The other, which is the more common method, is to back fill the furnace with gas to give a better thermally conductive atmosphere. A gas selection of hydrogen or helium is preferred since these gases have the highest conductivity, as compared to nitrogen and particularly argon gas. If a greater cooling rate is required, a blower configuration is used to circulate the gas through the work zone and through a water-cooled heat exchanger. A picture of a water-cooled heat exchanger is shown in Fig. 8.14. Evaporant traps Evaporation and transport of metal and oxide occurs in many applications. Transportation of evaporated substances occurs only if there is a partial pressure gradient. The evaporant will condense onto the cooler part of the furnace, thus the design of the furnace should be considered to enhance the condensation of these evaporants in a known location. A typical example is the evaporation of metal from the work and condensation on the water-cooled feedthroughs on the furnace. This can often result in shorting of the heating elements and a loss of heating of the work. This will result in undersintered materials until the short is removed. Any location that is cooler will result in condensation of the material. Typically metals condense prior to leaving the retort and organics will condense on the outside wall of the furnace. Both these conditions require periodic maintenance to remove if the process cannot be modified to eliminate the evaporation and migration of evaporated material. To prevent shorting out of the heating elements or damage to other parts of the furnace over time, a ‘cold finger’ can be used. This device is a cooled rod or loop that is strategically situated to permit the condensation of the evaporant. The use of a cold trap near the entrance of the diffusion pump can also be used, as shown in Fig. 8.7. To reduce evaporation, the best way is to increase the pressure of the furnace by bleeding in a process gas. Hydrogen partial pressure When a furnace is designed for the use of hydrogen gas with a greater partial pressure than 15 Torr, certain safety requirements such as automatic inert gas purge, a burn-off stack and a properly sized pressure relief port are required. The © Woodhead Publishing Limited, 2010

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8.14 Heat exchanger for rapid cooling of the furnace load. (Photo courtesy of Centorr Vacuum Industries.)

15 Torr level is defined by NFP 86, which defines the flammability level as half of 4% of 760 Torr or 2% of 760 Torr, which is 15 Torr. Figure 8.15 shows a typical pressure relief port used on a vacuum furnace that is also equipped for hydrogen partial pressure sintering. Figure 8.16 shows the burn-off stack required for hydrogen use and for binder incineration. Binder collection Most powder-based processing that requires sintering has some form of binder to be removed. The organic binder can be paraffin wax, polypropylene, polyacetal, © Woodhead Publishing Limited, 2010

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8.15 Vacuum furnace designed for the use of partial pressure hydrogen. Notice the eight spring-loaded pressure relief ports. Also notice the red and blue lines which are used to cool the feedthroughs and the chamber. A cooling fan is also centered in the middle of this furnace. (Photo courtesy of Centorr Vacuum Industries.)

PEG, etc. Many modern vacuum systems incorporate a multi-stage process that allows the binder to be removed in the same device. In this case the process is held near atmospheric pressure during the binder removal step to prevent defect formation, and the binder is subsequently collected in a trap prior to hightemperature sintering. The trap is located between the furnace chamber and the pump. Valves and pipes are used to ensure that pumping through the trap only occurs at low temperatures and at near atmospheric pressure. Upon going into a sintering mode, the valves are used to isolate the binder trap during the sintering operation. The trap collects the organic binder and needs to be cleaned periodically and as much as once after each run. Figure 8.17 shows a typical trap. Notice the high surface area metal which has high thermal conductivity and surface area to enhance the condensation rate of the binder. Different trap styles can be used depending on whether the residual binder can be ‘condensed’ by creating a temperature change, or ‘mechanically trapped’ using filtration media.

8.5.6 Pressure sintering furnaces Pressure sintering furnaces are used to process carbides, nitrides and borides. In this process the material is filled into a graphite die, subjected to a pressure of 70–150 kgf/mm2 at temperatures up to 2500 °C in a vacuum. The heating can be direct, using the punches or the die to conduct the electricity, or indirect, using resistant heating or induction heating. High densities in excess of 95% theoretical are often obtained.


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8.16 Burn-off stack for binders and hydrogen gas usage. The burn-off is at the top of the long tube and a small binder trap is situated at the bottom of the tube to catch any low molecular weight binder residue. A thermal oxidizer or incinerator can replace the burn-off tower for the destruction of more aggressive binder systems (phenolic resin, etc.). (Photo courtesy of Centorr Vacuum Industries.)

8.6

Practical processing

In this section a review of vacuum processing of various materials is presented.

8.6.1 Cemented carbides Initially, cemented carbides were sintered in hydrogen gas.14 Specialty carbides, i.e. those containing titanium, niobium, tantalum and hafnium carbides were © Woodhead Publishing Limited, 2010

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8.17 Binder trap used to collect binder during a debinding and sintering process. The trap vessel is cooled and also isolated during the higher temperature sintering to prevent further contamination of the downstream pump due to the high temperature of the sintering process. (Photo courtesy of Centorr Vacuum Industries.)

processed under vacuum.15 Currently, carbide sintering is performed in partial pressure above 1000 °C to prevent the evaporation of cobalt and to peak temperatures of between 1400 and 1550 °C. A temperature uniformity of +/– 10 °C is required and this can be +/– 5 °C for some critical applications.16 To obtain this, the hot zone must be properly designed to center the workload symmetrically inside with proper clearances at the ends to minimize end-losses. Furnace vacuum level has an influence on cemented carbide carbon content. At high vacuum and


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temperature, the oxide on carbide surfaces depletes the carbon from the carbides. If the vacuum level is low, the carbon monoxide gas partial pressure becomes high and effectively increases the carbon content of the carbides by transporting carbon from the graphite sintering furniture. Thus a continuous flushing of inert gas in the sintering chamber is required to prevent the excessive build-up of carbon monoxide and subsequent carbon enrichment. Cemented carbides are produced using a Roots-type vacuum blower with an oil rotary as a backing pump pumping configuration. At temperatures above 1000 °C, a partial pressure sintering mode (from 10–3 Torr to 1 Torr) is employed to prevent any evaporation of the matrix phase, which is typically cobalt. TaC- and TiCbearing grades may show superior properties in higher vacuum configuration.17

8.6.2 Tantalum and niobium Tantalum and niobium are processed in vacuum to remove oxygen; hydrogen reduction is not an option since they are hydride formers. Tantalum and niobium are sintered in several temperature stages to evaporate impurities before closing the porosity at high temperatures. In the temperature range of 400–800 °C hydrogen and alkali metals are evaporated. These impurities are present from the metal reduction process (i.e. sodium reduction), or from the powder being produced by a hydride/ dehydride process. At temperatures between 800 and 1200 °C, further removal of the alkali metals occur. Also, in the case of tantalum, difluoride residuals from the reduction of K2TaF6 are evaporated. The oxide-carbon reaction begins at 1500 °C and continues to about 2200 °C. Carbon removal is only possible if sufficient oxygen is present to form carbon monoxide, thus a slight underestimate of carbon additions is recommended to give the best purity since oxygen can be removed simply by volatilization at peak sintering temperature, and carbon is only removed in combination with oxygen. At 2200 °C, the lower oxides evaporate followed by nitride decomposition and nitrogen gas evolution. Tantalum peak sintering temperature is 2400–2600 °C for high-density material. Porous tantalum electrical capacitors are usually sintered between 1850 and 2150 °C. At 2600 °C; the tantalum can evaporate up to 1–3%. To continue processing, the tantalum must be sintered to 92% density, preferably 95%. If this density level is not met, or a highly ductile process is sought, a mechanical working of 10–20% followed by sintering at 2400– 2600 °C for 4–6 hours in vacuum is recommended.18 Niobium sintering temperatures are 300–500 °C lower than tantalum. Niobium sintering times are typically 2–4 times as long as tantalum since self-purification is more difficult due to the smaller temperature window prior to pore closure sinter densification as compared to tantalum. Reactive metals such as tantalum and niobium that are very reactive should be removed from the furnace only after being completely cooled. Sintering is performed either indirectly or using the direct current application of the Coolidge process. Vacuum is typically in the 10–6 Torr range and produced using a diffusion pump configuration.


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8.6.3 Tungsten and molybdenum Limited sintering of molybdenum and tungsten occurs in vacuum since these alloys are essentially inert to hydrogen gas (i.e. do not form hydrides), so the reducing power of hydrogen can be used and the furnace design for this type of sintering is simpler. If vacuum is chosen, the material is pre-reduced in hydrogen prior to high-temperature vacuum sintering. Tungsten can be sintered at 2500– 2800 °C; however, finer particles may sinter at temperatures of 1900–2000 °C. Molybdenum sinters at temperatures between 1700 and 2200 °C. Since molybdenum oxides evaporate before molybdenum does, it is possible to obtain molybdenum material with less than 10 ppm oxygen while using a vacuum sintering configuration.

8.6.4 Beryllium Beryllium is densified by using vacuum hot pressing. A vacuum level of 10–3 torr at 1050–1100 °C at a pressure of 9–18 kgf/cm2 is a typical process.19 Beryllium is produced by magnesium reduction of beryllium fluoride or by electrolysis from beryllium chloride melts containing alkali metal halides. These reduction processes produce impurities in the powder that must be removed prior to densification. Beryllium in small quantities can be fatal.

8.6.5 Stainless steels There are many sintering processes for the sintering of stainless steels since there are multiple grades and there are multiple alloying additions that behave differently under different vacuum conditions. The main concern is the evaporation of high vapor pressure elements. 17-4PH stainless steel and 300 series stainless steels are sintered in both flowing hydrogen atmosphere and a partial pressure of hydrogen. 17-4PH stainless steel is typically sintered at 1325–1360 °C in 400–500 Torr pressure for high density. The vacuum level for the sintering of 300 series can be lower since it does not contain copper; however, the nickel and chromium may evaporate if the vacuum level is too high. For particles in the 20 micron and less range, 300 series stainless steels are sintered at 1350–1380 °C in 300–400 Torr pressure for high density. Coarser 300 series particles, designated for press and sinter application, are reported to be sintering in vacuum at 0.1 Torr at about 1150 °C. After cooling, the parts are coined to the final dimensions. During sintering of stainless steels at 1200–1250 °C and 10–1 to 10–2 Torr, oxygen and carbon are easily removed as carbon monoxide; thus carbon additions may be used to remove oxygen, if argon gas instead of hydrogen is used for sintering. 400 series stainless steels can be sintered in dynamic partial pressure conditions. Interestingly, these alloys typically experience runaway grain growth and pore


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separation from grain boundaries when sintering in typical atmospheric conditions and only densify to a closed pore condition of 92–95% density. Higher density is achieved by the use of niobium additions, which form carbides to pin grain boundaries. When sintered at 5–10 Torr these alloys can be sintered to higher density. Final stage sintering densification is controlled by keeping the pores on the grain boundaries; the predominant mechanism for this is evaporation/condensation across the pore face so that the pore can move as the grains coarsen. When a vacuum is applied, the ability for metals to evaporate and transport across the pore is greater, thus the higher sintered density. Typical sintering temperatures for these alloys are 1250–1300 °C. A non-hydrogen atmosphere such as argon or nitrogen is preferred to prevent decarburization. The nitrogen may form nitrides and compromise the corrosion resistance; however, densification and strength are not compromised.

8.6.6 Titanium Titanium is either sintered in argon or vacuum conditions. Titanium is a highly reactive metal and special care must be taken to ensure minimal carbon pickup during processing. The sintering temperature is in the 1250–1350 °C range for both pure titanium and titanium alloys such as Ti-6Al-4V. Best results are found with the highest possible vacuum level: 10–6 to 10–7 Torr are preferred. These vacuum levels are produced using a diffusion pump configuration or even oil-less turbomolecular or cryogenic pumping systems. The furnace is typically of all metal hot zone and heating element design. The titanium is normally sintered on a substrate of zirconium or yttria. Care must be taken to remove impurities such as salts or hydrides from the material at temperatures in the 300–800 °C range. These impurities are not a concern if high purity gas atomized powders are used.

8.6.7 Tool steels Tool steels such as T15, M2, M4, M42, etc. are sintering in vacuum conditions. These can be sintered in both an all metal hot zone furnace and a graphite furnace. Sintering setters are typically alumina. The vacuum level is in the 10–3 Torr range, and the sintering temperature ranges from 1230 to 1300 °C. These alloys sinter by super solidus liquid phase sintering and exhibit a very small sintering window; therefore extreme control on temperature uniformity is required. A uniformity of +/– 3 to 5 °C is preferred.

8.6.8 Steels Many steels can be sintered in a vacuum or partial pressure condition. Alloys such as Fe-0.5C, Fe-2Ni, 4605, 4340, 4140, and 52100 are processed under dynamic partial pressure conditions. The typical sintering temperature is 1240–1300 °C, depending on the alloy and desired properties. The vacuum level can be as high as


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10–3 Torr or a dynamic partial pressure of nitrogen or argon in the 10–400 Torr range can be used. Typical sintering fixtures are constructed of alumina.

8.6.9 Ceramic sintering Sintering of ceramics in vacuum is not typical; however, it is often performed for various applications that require certain unique features of the cold wall system furnaces. Optically transparent alumina can be processed in both reducing atmosphere and also in vacuum.20 Other materials such as silicon carbide, silicon nitride, aluminum nitride and boron nitride are processed in cold wall batch furnaces that are equipped with both vacuum and a slight over-pressure capability. The cold wall furnaces are the only furnace capable of the high temperatures that these materials require for sintering. Silicon carbide The most popular grades of silicon carbide are alpha silicon carbide, reaction bonded silicon carbide or recrystallized silicon carbide. Lesser known forms include beta-SiC and liquid phase sintered SiC. Typically a first stage debinding is employed in a separate furnace at temperatures between 250 and 400 °C to remove either a methyl-cellulose binder or a phenolic resin binder. These can also be removed in a high-temperature furnace that has the capabilities for debinding at low temperatures in its configuration. In the case of alpha SiC, special sintering aids such as alumina, boron, or boron carbide are added. At 1500 °C, carbon monoxide evolves. Sintering occurs at about 2150 °C in a 1–3 psi atmosphere of flowing argon gas, although some processes utilize relatively high partial pressures of argon or even vacuum up to the sintering temperature. The vacuum furnace is typically constructed of graphite and the components are set on graphite trays or placed in powdered graphite. Reaction bonded silicon carbide starts as a mixture of pure silicon and SiC with a free carbon source. The silicon melts at about 1450 °C and reacts with residual carbon. The final sintering is performed at about 1600 °C in a partial pressure of 10 Torr Ar. At this vacuum level, some silicon evaporates and coats the heating elements and insulation material. These furnaces are constructed from graphite with the components placed on graphite setters. Recrystallized SiC, which is commonly used for diesel particulate filters, is processed at about 2350 to 2400 °C in 1–3 psi flowing Ar. The components are set on graphite and the furnace is constructed of graphite. Some processes will utilize a vacuum or a partial pressure and low flow rate of argon gas at temperatures up to 1800 to 2150 °C to minimize argon usage. The issues associated with holding a partial pressure or vacuum at these temperatures is the evaporation of the SiC or SiO2 byproduct. Special controls and calculations are required for vacuum and partial pressure sintering of SiC.


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Table 8.5 Typical materials processed by vacuum Material

Peak Vacuum temperature (º C) level (Torr)

Support

Notes

Nb Superalloy 2250 Nb Ni Superalloy 1250–1350 Alumina Tool Steels: M2, 1200–1300 10–3 Torr Alumina M4, M42, T15 Steels:Fe-0.5C, 1240–1300 10–3 Torr to 400 Alumina Fe-2Ni, 4605, Torr N2, Ar 4340, 4140, 52100 300 series 1325–1380 10–400 Torr H2 Alumina stainless steels 400 series 1250–1300 10–20 Torr Ar Alumina stainless steels 17-4PH SS 1325–1360 300–400 Torr H2 Alumina Tantalum 2400–2600 10–6 Torr Tantalum Capacitor 1850–2150 10–6 Torr Tantalum tantalum Niobium 1900–2200 10–6 Torr Niobium Tungsten 2500–2800 10–6 Torr Tungsten Fine particle 1900–2000 10–6 Torr Tungsten tungsten Molybdenum 1700–2200 10–6 Torr Molybdenum Beryllium 1050–1100 10–3 Torr pressure of 9–18 kgf/cm2 Cemented 1400–1550 100 Torr Ar Graphite carbides 50%Fe-50%Ni 1325–1380 5–400 Torr H2 Alumina Titanium 1250–1350 10–6 Torr or Ar Zirconia or yttria AlN 1800 N2 partial BN, AlN, No pressure graphite 2300–2350 1–3 psi B4C flowing argon BN 1900–2000 1–3 psi flowing N2 Graphite SiN 1750–1850 1–3 psi flowing N2 SiN, BN, or AlN Alpha SiC 2150 1–3 psi of flowing Graphite Reaction 1600 Ar 10 Torr Ar Graphite bonded SiC Recrystallized 2350–2380 1–3 psi Graphite Sic flowing Ar Transparent 1700–1950 Vacuum and alumina hydrogen partial pressure

Silicon nitride Silicon nitride is typically sintered at temperatures between 1750 and 1850 °C, with a standard temperature of 1830 °C. Atmosphere is typically 1–3 psi flowing


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nitrogen. Furnaces are constructed of graphite. Components are packed in Si3N4, BN, or AlN powder. These are placed in BN crucibles. There is a potential for SiO outgassing. A lower nitrogen flow rate is used to prevent excessive material evaporation. Some processes start with silicon powder and run large quantities of nitrogen gas to produce the silicon nitride. This process is very difficult to control and the flow rate and control of temperature is critical. Aluminum nitride Aluminum nitride is sometimes co-sintered with Mo magnesium. Typical sintering temperature is 1800C in a nitrogen partial pressure. This is performed in a metal hot zone furnace. Sintering is performed in a separate furnace. Components are packed in BN or AlN coarse powder to protect from carbon used in the graphite furnaces. Boron nitride Boron nitride is typically sintered at 1900–2000 °C in 1–3 psi over pressure in flowing nitrogen. Typically sintered in a graphite furnace. B4C B4C is typically sintered at 2300–2350 °C in flowing argon at 1–3 psi in a graphite furnace.

8.7

References

1. W.

v. Bolton, Z. Elektrochem., 11/3 (1905) p. 45, 13/15 (1907), p. 145. Powell, J. Van Den Avyle, B. Damkroger, J. Szekely, and U. Pal, Metallurgical and Materials Transactions B, Volume 28B, December 1997, p. 1227. 3. Smithells Metals Reference Book, 6th ed., E. Brandes (ed.), Butterworth & Co., Boston, 1983, pp. 8–54. 4. http://www.thermocalc.com (accessed April 7, 2010). 5. J. A. Belk (ed), Vacuum Techniques in Metallurgy, Pergamon Press, Oxford, 1963, p. 14. 6. H.R. Smith, C. D. Hunt, and C. W. Hanks, Reactive Metals, Interscience, New York, 1959, p. 131. 7. L. Schumann-Horn, A. Mager and W. Deisinger, Z. Metallk, 47 (1956), p. 145. 8. B. Ilschner and J. Humbert, Z. Metallk., 51 (1960), p. 626. 9. R. M. German, Sintering Theory and Practice, John Wiley & Sons, Inc. New York, (1996), p. 470. 10. O. Winkler and R. Bakish (eds), Vacuum Metallurgy, Elsevier Publishing Company, Amsterdam, (1971), p. 502. 11. P. Cotterill, Hydrogen embrittlement of metals, In Progress in Materials Science, B. Chalmers (ed.), Vol. 9, Pergamon, Oxford, 1962. 12. O. Winkler and R. Bakish (eds), Vacuum Metallurgy, Elsevier Publishing Company, Amsterdam, (1971), p. 466. 2. A.


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13. O. Winkler and R. Bakish (eds), Vacuum Metallurgy, Elsevier Publishing Company, Amsterdam, (1971), p. 704. 14. J.T. Norton, J. Metals, 8 (1956), p. 49. 15. M. Donovan, Powder Met., 1/2 (1958) 104. 16. O. Winkler and R. Bakish (eds), Vacuum Metallurgy, Elsevier Publishing Company, Amsterdam, (1971), p. 705. 17. O. Winkler and R. Bakish (eds), Vacuum Metallurgy, Elsevier Publishing Company, Amsterdam, (1971), p. 718. 18. C.A. Hampel, Rare Metals handbook, 2nd ed, Reinhold, New York, 1961. 19. H. W. Dodds, U.S. Patent 2,818,339, 1957. 20. R. L. Coble, U.S. Patent 3,026,210, 1961.


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9 Microwave sintering of ceramics, composites and metal powders D. Agrawal , The Pennsylvania State University, USA Abstract: This chapter provides an overview of microwave sintering of ceramics, metals and composites including some of the latest developments in the field. The chapter first introduces microwave heating and how it is different from conventional sintering. The chapter then discusses the results of microwave sintering of some important ceramics, composites and metals such as alumina, zirconia, electroceramics, transparent ceramics, high-temperature ceramic eutectics, metal–ceramic composites, and finally metal powders and carbon nano tubes. The chapter also discusses some proposed mechanisms of explaining the microwave–matter interactions. Key words: microwave sintering, ceramics, ceramics–metal composites, metal powder sintering, energy savings.

9.1

Introduction

The fabrication technology of ceramics and composites involves various steps, namely powder synthesis, drying, calcination, consolidation, binder-burnout and finally sintering of green compact bodies into useful products. In this process the sintering step of raw precursor powders is the most important step to produce a product with the desired properties. The main objective of the sintering step is to produce a product with nearly full density, and fine and uniform microstructures leading to optimum properties. Innovations in material processing have always resulted in a better product and often cost-effective processing. There are many heating methods used for synthesis and sintering steps in materials processing. These methods can be broadly divided into two categories: contact and non-contact methods. Most traditional heating methods based on thermal conduction/radiation/ convection (such as electric/resistant and fuel heating methods) are categorized as contact heating methods in which the thermal energy is in direct contact with the work-piece. Heating methods such as induction, RF (radio frequency) or microwave heating heat the work-piece directly due to coupling of electromagnetic radiation with the matter, and are thus called non-contact methods. Microwave energy has emerged as the most versatile form of energy applicable to numerous diverse fields. Since its first use for radar in World War II, it has been applied in communication, chemistry, rubber vulcanization, drying, food processing, medical treatment and diagnosis, and a variety of materials processing fields. Microwave materials processing is well recognized for its many advantages over the conventional methods; these include substantial enhancements in the 222 © Woodhead Publishing Limited, 2010

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reaction and diffusion kinetics, relatively much shorter cycle time, finer microstructures leading to better quality products, substantial energy savings and eco-friendliness, etc. In the area of sintering and synthesis using microwave energy, extraordinary enhancements in the materials diffusion and reaction kinetics have been reported.1–5 It has been generally observed that microwave sintered products possess finer microstructures and other unique features leading to considerable improvement in the mechanical properties, and most importantly overall improvement in the quality and performance of the processed materials. Until 2000, microwave processing of materials was mostly confined to ceramics, semimetals, inorganic and polymeric materials. Now, it has been shown that all metals in powder form also absorb microwaves at room temperature and can be sintered very efficiently and effectively, often providing a better quality product.6–10 Perhaps the first reporting of microwave energy applied to ceramics processing appeared in 1968.1 Further reporting took place in 1975,2 but it was not until the 1980s that many groups all over the world began to report that a new unconventional field of ceramic processing was beginning to develop. Now the field is maturing and increasingly finding its application in a variety of materials processing, especially synthesis and sintering of ceramics, composites and metallic materials. This chapter will confine itself to the sintering aspect of microwave application to some selected important materials. Microwave sintering of materials is fundamentally different from conventional sintering. Conventional sintering involves radiant/resistance and/or convection heating followed by transfer of thermal energy via conduction to the inside of the work-piece through the thermal conductivity mechanism. It is rather a slow process and takes considerable time to achieve thermal equilibrium and material consolidation. It is independent of the nature of the material. On the other hand, in the case of microwave sintering, the heating takes place via absorption/coupling of the microwave field followed by the heating of the material as a whole (known as volumetric heating) by the conversion of the electromagnetic energy into thermal energy. In this process there is no thermal conductivity mechanism involved; the heating is instantaneous and rapid, and is a function of the material properties. The heat is generated internally within the material instead of originating from the external sources, and transmits towards the outside. Hence, there is an inverse heating profile, inside-out unlike in conventional heating outside-in. In general, microwave heating is very rapid, as energy conversion rather than energy transfer heats the material. Figure 9.1 illustrates some distinguishing features between conventional and microwave heating. Microwaves are a small part of the electromagnetic spectrum with wavelengths ranging from 1mm to 1m in free space and frequency between 300 GHz and 300 MHz, respectively. However, for research and industrial applications only very few energy bands are allowed. The most common worldwide microwave frequency is 2.45 GHz, used for almost all research in materials processing. Based on the microwave matter interaction, most materials can be divided into three categories:


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9.1 Comparison of heating procedure between conventional and microwave methods.

opaque (bulk metals), transparent (very low dielectrically lossy materials) and absorbers (moderate to high dielectrically lossy materials). It is well recognized that bulk metals are opaque to microwaves and are good reflectors at room temperature; this property is used in radar detection. However, as we will see in the subsequent sections, metals in powder form are very good absorbers of microwaves and get heated very effectively. Further, bulk metals, if pre-heated to moderate temperatures (~500oC), also become good microwave absorbers. Most other materials are either transparent or absorb microwaves to varying degrees at ambient temperature depending upon their inherent electrical and magnetic properties. The degree of the microwave absorption and consequent heating profile changes dramatically with the rise in temperature. Microwave heating is material dependent; therefore only those materials that couple in the microwave field will get heated and the rate of heating will depend upon their degree of absorption, which is a function of various factors including the dielectric loss (insulators), magnetic properties (metals), grain size, porosity, frequency, electrical conductivity, etc.

9.2

Microwave sintering of important materials

9.2.1 Ceramics Many traditional and advanced ceramics have been processed by microwave with reported enhancements in reaction, and diffusion kinetics exhibiting better properties than the conventionally processed material. Here only a few selected ceramic


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materials are reported. All these materials have been processed using 2.45 GHz microwave systems. Al2O3 Alumina is the most common ceramic and has been widely used in microwave sintering research by many scientists working in the field. Because of its highly refractory nature, pure alumina is difficult to sinter to full densification unless suitable sintering aids or some special processing techniques are adopted. Many people have successfully sintered alumina to high densification in microwaves.4 Nearly full sintering of the alumina using the microwave process has been achieved much faster and at lower temperature than the conventional process. Small disc alumina samples microwave sintered at 1400 °C, with no hold time, were 98% dense.11,12 In conventional heating it requires at least 1600 °C and two hours of soaking time to achieve the same degree of densification accompanied by substantial grain growth. In general, in the microwaves nearly full density has been achieved at about 200 °C less than the conventional temperature as shown in Fig. 9.2. Microwave sintering of alumina has now been successfully applied to fabricate some commercial alumina products with substantial improvement in their quality and performance. For example, sol-gel prepared alumina grit was sintered to full density using a continuous microwave process.13 The alumina grit precursor powder (Carborundum Universal Madras, India) with an average particle size of 0.8–1.0 mm (agglomerated grains) when microwave sintered at 1500 °C for 15 minutes provided density of 3.96 g/cc, which is very close to theoretical density. Table 9.1 compares the property data with conventionally prepared alumina grit. It is obvious that

9.2 Sintered density vs. temperature plots for microwave and conventionally sintered alumina.


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Table 9.1 Comparative properties of microwave and conventionally sintered alumina grit

Sintering conditions

Microwave

Conventional

Density g/cc

1450ºC/15 min 1400ºC/45 min 1500ºC/15 min

3.70 3.94 3.96

3.92 3.96 3.89

Abrasion Index


95 100 94

68 65 94

Micro Vicker’s Hardness (kg/mm2)


2205 2388 2317

732 1026 1885

microwave sintered alumina grit possesses much higher abrasion index and hardness values. In another study,14 large objects of alumina with diameter of 1cm to 10 cm and length up to 1 to 2 meters were also prepared using a continuous microwave system. These parts processed at 1400 °C had 98% of theoretical density with very uniform and homogeneous microstructure. In Japan, Sato et al.15 have reported successful sintering of large commercial alumina products for substrate, high-temperature optics and structural applications. In one example an alumina ring of 15 inch diameter was sintered to full density in the microwave in only 20% of total cycle time and only one tenth of the energy consumed when compared with the conventional process. Further, the properties such as bending strength were improved by almost 30% over the conventionally produced product; the shrinkage distortion was about 60% smaller than in the conventional process. ZrO2 Zirconia, being a refractory oxide ceramic, often requires high sintering temperatures and a long soaking time to obtain a high degree of densification. Fine-grained zirconia ceramics were sintered at 1360 °C with two minutes of soaking time in a multimode 2.45 GHz microwave system. The sintered density was about 97.8% and average grain size was 0.25 µm. Binner et al. in the UK 16 reported the fabrication of transparent zirconia ceramics using nanopowder and microwave hybrid heating at 1600 °C. Figure 9.3 shows the SEM photograph of a typical transparent zirconia sample prepared by microwave hybrid heating. PbZr0.52Ti0.48O3 (PZT) PZT is a very common ferroelectric material belonging to the perovskite family of important materials. It is generally fabricated at temperatures over 1200 °C for


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9.3 Microstructure of nano YSZ sintered using hybrid microwave sintering (Ref. 16).

several hours of soaking time in a conventional process. One common problem associated with PZT fabrication is the high loss of PbO due to lengthy sintering time. This is a serious environmental issue. In the microwave process, single phase PZT was obtained at as low as 600 °C17 by using TiO2-x. The use of nonstoichiometric TiO2-x enhances the microwave absorption and increases the reaction kinetics many times. It also leads to different reaction pathways for the formation of PZT. In another study, PZT samples were microwave sintered at temperatures 150 °C lower than the conventional process,18 resulting in finer grain size and minimal PbO loss. Table 9.2 shows a comparison of PbO loss in conventional and microwave process for different types of PZT sources. BaTiO3 (BT) It is recognized that virtually all solid state reactions for the synthesis of materials in a conventional process occur under isothermal conditions, i.e. two or more phases involved are at the same temperature. However, microwave processing for materials synthesis involving two or more phases may experience a situation known as an ‘anisothermal’ state if the reacting phases have different microwave absorption characteristics. The anisothermal situation is associated with huge temperature differences between the phases at micro-level. This is also one of the key factors behind dramatic enhancements in reaction and material diffusion rates. In the synthesis of PZT (as shown above) and BaTiO3 the anisothermal situation enhanced reactivity between the starting phases and produced the desired phase in a few minutes. For the synthesis of BT, BaCO 3 (a poor microwave absorber) and TiO2-x (an excellent microwave absorber) were used as the precursors. The reaction


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Table 9.2 PbO loss data during the sintering of PZT by various processes Open crucible method/PZT type →

MEGAC

TRS 200

TRS 200B

Conventional firing (10º/min) Fast conventional firing (25º/min) MW process, 2.45 GHz (25º/min) MW process, 30 GHz (30–50º/min)

3% 1.35% 0 0

– 5.7% 3000 °C), and therefore very high temperatures (>1600 °C) and long soaking periods are required to sinter them in a conventional furnace.


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Often, to obtain BMT/BZT ceramics with high density, sintering aids such as Mn and Sn are used. But the sintering aids also degrade their dielectric properties. However, in the microwave process single-phase materials using reduced oxide precursors were synthesized and sintered20,21 without adding any sintering aids. Just as in the cases of PZT and BT, an anisothermal situation was created by using reduced Ta2O5-x and other precursor oxides that remarkably enhanced the reaction kinetics and produced single-phase material at a much lower temperature (1300 °C/20 min) with higher densification than normally obtained by conventional processes. Microwave processed BMT samples exhibited density as high as 97% of theoretical when heated at 1600 °C for 30 minutes. The average grain size in microwave-sintered BMT was about 1 µm in contrast to 3 µm in conventional sintered material. BZT samples sintered at 1400 °C for five minutes to full density in the microwave process had average grain size < 5 µm. Transparent ceramics To achieve transparency in a ceramic, one must control the grain growth, eliminate porosity and achieve complete densification. The conventional methods to fabricate fully dense and reasonably transparent ceramics involve high temperatures, lengthy sintering conditions and various complex processing steps, which make the processing of transparent ceramics very difficult and uneconomical. However, the microwave method has been successfully used to fabricate transparent ceramics due to its ability to minimize the grain growth and produce a fully dense ceramic in a very short period of time without utilizing high-pressure conditions.22 Hydroxyapatite was fully sintered into a transparent ceramic at 1100 °C in 10 minutes by microwave processing.23 The densification was shown to be critically dependent on the starting materials. Transparent ceramics of spinel and alumina were also fabricated.24,25 Fully dense alumina26 and spinel ceramics using high purity and submicron size powders were developed with a reasonable degree of transparencies on laboratory size small samples at 1700 °C sintered for 15 minutes in the microwave system. Fully transparent AlON ceramics were also made using a multimode microwave system at 1800 °C.27 Translucent ceramics of AlN, which is a well-known high thermal conductivity material, were also developed in the microwave at 1900 °C in 60 minutes.28 Recently, MgO ceramic has been fabricated into a translucent form using nano starting powder and LiF as a sintering aid.29 Figure 9.4 shows some of the microwave-processed transparent and translucent ceramics of hydroxyapatite, alumina, AlN and ALON. Yttrium aluminum garnet (YAG), Y3Al5O12 is a host material for lasers and phosphors; however, its synthesis and subsequent sintering into a transparent product is very complex and requires high temperatures and a long sintering cycle. Panneerselvam et al.30 reported the successful application of microwave processing to produce translucent YAG ceramics at 1350 °C in 20 minutes. However, problems in making large samples of commercial products of transparent ceramics with microwaves still persist.


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(a)

(b)

(c)

9.4 Various kinds of transparent and translucent ceramics fabricated in microwave: (a) pure alumina, (b) doped alumina, (c) AlN, (d) ALON and (e) hydroxyapatite.


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(d)

(e)

9.4 Continued.

ZnO based ceramic varistors and micro-tubes Zinc oxide is an important material used for a variety of applications such as varistors in the form of bulk ceramics and for UV and blue light emitting devices in the form of single-crystal micro-tubes. Varistors are electronic ceramic devices possessing highly non-linear current–voltage characteristics, which enable them to be used as voltage surge suppressors. Their typical electrical behavior is controlled by their microstructure (grain size and grain boundary chemistry) and composition. The sintering procedure plays an important role in developing the microstructure necessary to obtain desired nominal voltage (Vnom), energy handling capability and clamping performance of the zinc oxide varistors. Various


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Sintering of advanced materials Table 9.4 Typical density and grain size data for ZnO radials of type V275LA4 Sinter condition

Density g/cc (%th.)

Grain size

Conv.1250ºC-2h MW1100ºC-15min MW1200ºC-15min MW1300ºC-15min

5.58 (98.4) 5.58 (98.4) 5.59 (98.6) 5.60 (98.8)

10 µm 6.0 µm 7.5 µm 9.5 µm

types of zinc oxide varistors under different processing conditions were sintered using microwave heating.31 Microwave sintering of ZnO varistor samples indicates significant reduction in the cycle time and substantial improvements in the electrical properties. Microwave sintered samples exhibited better densities, finer grain size and more uniform microstructure relative to the conventional process (Table 9.4 and Fig. 9.5). Electrical characterization of the microwave-sintered samples showed higher volts and better clamping properties as compared to the conventional sintering. A typical V-I curve obtained for V275LA4 type radials is shown in Fig. 9.6. Higher volts/mm response in the microwave samples signifies that (i) smaller devices with similar electrical properties can be used, and (ii) it enables using less material to develop similar devices obtained through a conventional process. ZnO is a promising material for UV and blue light emitting devices because of several advantages it has over its chief competitor, GaN. The single crystal microtube of ZnO has a band gap of 3.37 eV, with a 60-meV binding energy of the free exciton, and permits excitonic emission at room temperature. To date, most ZnO single crystals have been fabricated in the forms of bulk crystals or thin films or nanowires/nanorods. The ZnO single crystal micro-tubes exhibit strong near band-edge emission, highly selective UV light response, excellent electron field emission and interesting piezoelectric properties. Recently, ZnO micro-tubes have been grown by microwave heating and were found to be colorless, fully transparent, contamination-free and of near-perfect crystallinity.32 The morphology of the ZnO micro-tubes observed by optical microscope and SEM is shown in Fig. 9.7. The ZnO crystals are grown in a hexagonal hollow tube with well-faceted end and side surfaces. The wall thickness of the ZnO micro-tubes is less than 2 µm, typically between 0.5 and 1 µm. By adjusting microwave growth conditions such as the temperature and time, the ZnO tubes have been fabricated into different cross-sectional dimensions ranging from 100 to 250 µm, and different lengths up to 5 mm. ZnO has a high melting point of 1975 °C, and sublimes or thermally decomposes rapidly at temperatures above 1400 °C, which makes it very difficult to achieve high-temperature crystal growth. In a carefully designed microwave cavity and insulation package, ZnO sublimation and selective


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9.5 Typical microstructures of (a) conventional and (b) microwavesintered ZnO-based varistor samples showing more uniform and finer microstructure of the microwave-sintered part than the conventional product.


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9.6 A comparison of V-I curves between microwave and conventionally sintered ZnO varistor samples.

9.7 Single crystal ZnO micro-tubes synthesized by microwave process.

nucleation and growth into micro-tubes was achieved. The self-contained vapor phase growth is a unique feature of the encapsulated microwave heating process critical for the growth of high quality ZnO single crystals, which is not achieved by conventional heating methods. High temperature ceramic eutectics Directionally solidified eutectics (DSE) of oxide and non-oxide ceramic compositions are attractive composite materials due to their unique thermodynamic, mechanical and electrical properties. In general these materials have excellent thermal stability, high-temperature strength and fracture toughness, which make them attractive candidates for ultra-high-temperature structural materials. In addition to their outstanding mechanical properties, some of the DSE compositions of rare-earth,


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alkali-earth and d-transition metal borides possess other exceptional properties such as high-electron emission, high neutron absorption ability and specific magnetic and electrical characteristics. The two most promising eutectic systems are Al2O3-Y3Al5O12 (YAG) and B4C-TiB2, which show outstanding potential for high hardness and high toughness. Currently, the conventional methods for making these materials include resistive furnace, inductive heating with an external susceptor, infrared heating by halogen or xenon lamps, laser beam heating, and heating by electric arc or by electron beam bombardment. The main drawback of all of these methods is the presence of a thermal gradient within the rod, which may lead to an inhomogeneity of microstructure and restrict the sample diameter. The microwave heating method has been utilized for the first time to make these materials successfully.33 In this method the material is first melted and then recrystallized to obtain unique microstructures in the resultant composite. Microwave melting was conducted on presintered pellets of Al2O3-Y3Al5O12 (YAG) (Tm = 1827 °C) and B4C-TiB2 (Tm = 2310 °C) by using a 6 kW, 2.45 GHz multimode microwave system and they were successfully melted using a specially designed thermal insulation package. The cross-sectional view of processed samples and corresponding microstructures of both oxide and non-oxide eutectics are presented in Fig. 9.8 and 9.9. The Al2O3-YAG composition shows a typical eutectic microstructure (Fig. 9.8b), in which the dark phase is Al2O3 and the white phase is YAG. In the case of B4C-TiB2 composition (Fig. 9.9b), the microstructure

9.8 The cross-section view (a) and corresponding microstructure (b) of Al2O3-YAG eutectic composition.

9.9 The cross-section view (a) and corresponding microstructure (b) of TiB2-B4C eutectic composition.


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consists of the dark B4C matrix phase with white elongated TiB2 inclusions. In the directionally solidified form, the B4C-TiB2 consists of TiB2 fibers in a B4C matrix. The formation of eutectic microstructures and the complete distortion of the initial cylindrical-sample shape confirm that the microwave heating is able to reach ultra-high temperatures (higher than 2350 °C).

9.2.2 Metal–ceramic composites Composites of metals and ceramics offer tailorable physical, thermal and mechanical properties for a variety of applications. Microwave heating has been utilized for making various kinds of composite materials. Here, two of these representative materials are described. WC-Co based cemented carbides WC-Co composites (also known as cemented carbides), due to their unique combination of hardness, toughness and strength are universally used for cutting tools, machining of wear resistant metals, grinding, mining, and geothermal oil and gas drilling operations. Conventional methods for sintering WC with Co as a binder phase involve high temperatures (up to 1500 °C) and lengthy thermal cycles (~24 hours) in order to achieve high densification. Such conditions favor undesirable WC grain growth in the presence of Co melts. Consequently, the mechanical strength and hardness of the tools are diminished. The finer microstructures provide superior mechanical properties and enable longer life of the product. Often, additives such as titanium carbide (TiC), vanadium carbide (VC) and tantalum carbide (TaC) are used to suppress the grain growth, but unfortunately such additives deleteriously affect the mechanical properties of the tools, and add substantially to the overall cost of the product. Since microwave heating requires very little time to obtain nearly full densification, the grain growth is relatively suppressed and finer microstructure is generally obtained without using any grain growth inhibitors. In 1991, J. P. Cheng in a Ph.D. thesis34 first showed that WC/Co composites could be sintered in a microwave field. Gerdes and Willert-Porada35 also reported the sintering of similar WC objects from normal-size powders, but they followed a reactive sintering route using a mixture of pure W, C and Co instead of normal sintering. At Pennsylvania State University, using a newly designed microwave apparatus, fully sintered WC commercial green bodies containing 12% and 6% Co were achieved,36 and it was observed that microwave-processed WC/Co bodies exhibited better mechanical properties than the conventional parts, fine and uniform microstructure with little grain growth and nearly full density without adding any grain-growth inhibitors when sintered at 1250 °–1320 °C for only 10–30 minutes.37–39 The microstructural examination of the microwave-sintered WC/Co samples, in general, exhibited smaller average grain size than the


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conventionally sintered sample. Microwave sintered parts also showed significant property improvements without varying the component materials, and without the addition of grain-growth inhibitors. The WC/Co part produced by the microwave sintering process exhibited an unprecedented improvement in abrasion resistance (15–30% better), erosion resistance (22% better) and corrosion resistance in 15% HNO 3 (20% better) without any noticeable loss in hardness or fracture toughness. These improvements in the properties are believed to be due to the fine microstructure, uniform cobalt phase distribution and pure Co phase at the grain boundaries in microwave-sintered samples.40 Figure 9.10 illustrates some commercial WC/Co parts which have been fabricated very successfully using microwave technology. Now several companies are commercially exploiting this technology for specialty carbide products. Multi-layer ceramic capacitors (MLCCs) MLCCs are in fact ceramic metal composites consisting of ceramic and metal in layer formulations. They are used in almost all areas of electronics as important ceramic components. Their manufacturing is quite a large industry, producing

9.10 Microwave-sintered cemented carbide based cutting and drilling tools.


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over 1012 components per year. Over 80% of modern multilayer capacitors involve the co-firing of the BaTiO3 dielectric formulations with nickel inner electrodes. In order to co-fire a dielectric with nickel, processing has to be conducted at a low pO2; typical firings involve temperatures ~1260 °C to 1300 °C and atmospheres with pO2 ≈ 10–10 to 10–12 atm. However, the problems related to oxidation of metallic electrodes and reduction of ceramic layers may persist. Microwave sintering of Ni-electrode X7R MLCCs at pO2 × 10-6 atm. and at the temperature of 1250 °C produced fully dense and uniform parts without any delaminations or cracks or oxidation.41 Representative SEM micrographs of the fracture surface and free surface of the microwave-sintered Ni-electrode MLCC chips (cross-section) are shown in Fig. 9.11.42 The internal electrodes were found to be continuous and without any oxidation. Since the total processing time in the microwave sintering was only about 10% of that in the conventional sintering, the dense microstructures suggest that the densification kinetics of the MLCCs was substantially enhanced in the microwave sintering. The average grain size of the microwave-sintered X7R matrix was 0.5–0.6 µm, similar to that of the conventionally sintered sample. The dielectric properties were comparable to the standard products sintered by the conventional process. A selected batch of microwave-sintered MLCCs also passed HALT. Compared to the conventional process, the microwave sintering – conducted in a dry and static atmosphere, with heating rate one order of magnitude higher, heating time one order of magnitude shorter, and sintering temperature 100 °C lower than the conventional process – produced MLCC parts of similar quality and saved about 90% in processing time. MLCCs with Cu and noble metal electrodes have also been successfully produced in the microwave using the same process as that described above.

9.11 A typical microstructure of microwave-sintered MLCC showing continuity in Ni electrodes and very uniform and homogeneous sintering of BaTiO3 ceramic layers.


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9.2.3 Metal powders Until recently, microwave processing of materials has mostly been confined to ceramics, semi-metals, and inorganic and polymeric materials. There has been hardly any detailed report on microwave processing of metallic materials. The main reason for this small amount of work in microwave heating/sintering of metals was due to the misconception that all metals reflect microwaves and/or cause plasma formation, and hence cannot be heated in a microwave field. This observation is evident from the conventional view shown in Fig. 9.12, depicting a plot of microwave absorption in the solid materials of varying electrical conductivity.43 It is evident from this that only semiconductors should be good microwave absorbers, ceramics/insulators should be transparent in microwaves, and metals should reflect microwaves. However, this relation is valid only for sintered or bulk materials at room temperature, and not valid for powdered materials and/or for bulk metals at elevated temperatures. Now it has been proved that all metallic materials in powder form do absorb microwaves at room temperature, and if even bulk metals are pre-heated to a temperature to at least 400oC, they also start coupling in a microwave field and get heated rapidly, so much so that they can be melted. The earliest work of microwave interaction with metallic powders is reported by Nishitani,44 who found that by adding a few percent of electrically conducting powders such as aluminum, the heating rates of the refractory ceramics is considerably enhanced. Walkiewicz et al.45 likewise simply exposed a range of materials, including six metals to a 2.4 GHz field, and reported modest heating (but not sintering) in the range from 120 °C (Mg) to 768 °C (Fe). Whittaker and Mingos46 used the high exothermic reaction rates of metal powders with sulfur for the microwave-induced synthesis of metal sulphides. Sheinberg et al.47 heated Cu powders coated with CuO to 650 °C but did not report any sintering of them. Narsimhan et al.48 succeeded in heating Fe alloys in a microwave oven only up to 370 °C in 30 minutes. But in all these studies no sintering of pure metal or alloy powders was reported. It was only in 1998 that the first attempt of microwave sintering of the powder metals6 was reported and since then many other researchers have reported successful sintering of many metallic materials.8,9,49, 50

9.12 Microwave energy absorption is a function of electrical conductivity.


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9.13 Various metal/steel parts sintered by the microwave process.

It has been observed that microwave sintering of metal powders produces a superior product. The steel commercial parts of FC208 and FN208 have been sintered to near net shape. Figure 9.13 shows some commercial products sintered in the microwave. Many commercial powder-metal components of various alloy compositions including iron and steel, Cu, Al, Ni, Mo, Co, Ti, W, WC, Sn, etc. and their alloys have also been sintered in microwaves producing essentially nearly fully dense bodies. The microwave sintering of PM green bodies comprising various metals, steels and metal alloys produced highly sintered bodies in a very short period of time.7 Typically, the total cycle time was about 90 minutes, sintering temperature ranged between 1100 °C and 1300 °C and soaking time was from 5 to 60 minutes. The mechanical properties such as the modulus of rupture (MOR) and hardness of microwave-processed samples were much higher than in the conventional samples. As an example, copper steel (MPIF FC-0208 composition) was successfully sintered by the microwave technique to produce good sintered density, hardness, flexural strength and near net dimensions, thus yielding equivalent or even sometimes superior mechanical properties to conventional sintering. In this material a Rockwell B hardness (HRB) as high as 82±2 was obtained for microwave-processed samples sintered at 1260 °C for five minutes soaking in a flowing forming gas atmosphere. The maximum flexural strength of 1077±10 MPa was obtained for microwavesintered samples at 1140 °C for 20 minutes. Takayama et al.9 used green sample compacts of C, V, Ti and Mg metal powders surrounded by BN powder and sintered in the microwave successfully. They reported that higher tensile strength was obtained in the microwave sintered products than in the conventional sintering. A comparative study of the sintering behavior of Cu-12Sn bronze system8 reported that bronze was microwave sintered in significantly less time, resulting in higher density and more uniform microstructure. Also the hardness of the microwave-sintered samples compacted


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at 300 MPa was 50% higher than the conventionally sintered samples. Gupta and Wong compared the properties of pure aluminum sintered using conventional and microwave heating51 and found that microwave-sintered material exhibited improved properties including higher hardness and ultimate tensile strength, etc.

9.2.4 Carbon nanotubes Carbon nanotubes (CNTs) are hollow cylindrical molecular species that can be conceptually constructed by rolling up a grapheme sheet. Due to CNTs’ unique one-dimensional structure and outstanding electronic and mechanical properties, they are considered as excellent materials for nanoelectronic devices, nanoelectromechanical (NEMS) and microelectromechanical (MEMS) systems and for the next-generation composite materials that can offer high strength and stiffness. Since the first observation of carbon nanotubes in arc-discharge soot materials,52 numerous methods have been developed for synthesis of wellgraphitized nanotubes, such as arc-discharge and laser vaporization of a graphite electrode in the presence of metal catalysts, plasma-enhanced hot-filament chemical deposition, thermal catalytic decomposition, and microwave-enhanced chemical vapor deposition. Recently, at Penn State, using a TE 103 single-mode cavity at 2.45 GHz and E and H field separation approach, multi-wall carbon nanotubes were synthesized on Fe-coated Si wafers in the H field using acetylene or ethylene as the gaseous carbon source at a temperature of 700 °C in 10 minutes (Fig. 9.14). The diameter of microwave-synthesized CNTs could be tailored from 30 nm to 150 nm by adjusting the acetylene/hydrogen ratio. By using thermal oxide on B-doped Si wafer as the substrates, well-aligned CNTs were fabricated with average diameter of ~30 nm and the length of ~10 microns. The morphology and diameters of the

9.14 Multi-wall carbon nanotubes synthesized in a single-mode microwave cavity using Si substrate with Fe catalyst in C2H2.


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CNTs synthesized in microwave H field on Fe-coated Si wafer vary with the concentration of the gaseous carbon source and the temperatures.

9.3

Mechanisms to explain microwave–matter interactions

In the case of microwave sintering, there are two main issues: rapid heating, and rapid material diffusion and/or enhancement in reaction kinetics. The rapid heating part has been widely studied and explained to a certain degree of satisfaction, but the rapid material diffusion and enhancements in the reaction kinetics have not yet been fully understood and explained as there are reportedly some ‘non-thermal’ (microwave) effects responsible for material diffusion. Many different physical phenomena are involved in the microwave processing of materials. Classically, there are various absorption mechanisms identified in microwave-matter interaction, almost always connected to the E field. Some of them are dipole reorientation, space and ionic charge, etc., that are primarily found in insulators or dielectric materials. When microwaves penetrate and propagate through a dielectric material, the internal electric field generated within the affected volume induces translational motions of the free or bound charges (e.g. electrons or ions) and rotates charge complexes such as dipoles. The resistance of these induced motions due to inertial, elastic and frictional forces causes energy losses and attenuates the electric field. As a consequence of these losses, volumetric heating inside the solid material occurs. Due to this volumetric heating, the thermal gradients and the flow of heat in microwave-processed materials are the reverse of those in conventional heating. Other losses depending upon the material under interaction include electric conduction and/or magnetic coupling and eddy currents. In the case of metal powders the interaction will be mainly based on the electric conduction, scattering and/or probably magnetic field coupling through magnetic domains, hysteresis losses (ferrites), magnetic flux, etc. Rapid heating of the materials in a microwave field can be explained to a certain extent by taking the aforementioned factors into account, but the rapid material diffusion aspect has not yet been very well explained. The classical sintering equations based on thermal contribution cannot fully explain the material diffusion in a microwave field. The microwave power absorbed per unit volume (P in W/m3) is expressed by the equation P = 2πfo(ε0ε″E2 + µ0µ″H2)

[9.1]

where E and H are the electric and magnetic fields, f0 is the frequency, and ε″ and µ″ dielectric and magnetic loss factors respectively. So it can easily be explained that the microwave power absorbed (the resultant heat) is directly proportional to the dielectric and magnetic losses, and of course field intensity and frequency. There is another factor responsible for providing uniform and volumetric heating: penetration depth, D, which is the distance in the direction of penetration at which


Microwave sintering

243

the incident power is reduced to half of its initial value, and is a strong function of the loss and frequency of the field D = 3λ0 / 8.686πtanδ(ε′)1/2

[9.2]

where λ0 is the wavelength of the microwaves. The equation suggests that there is a slight advantage in working at lower frequencies when large samples are involved, but is associated with a payoff in terms of power absorbed per unit volume. In bulk metallic materials, the microwave penetration is rather low at room temperature, and it is commonly described by a quantity known as skin depth δ, given by δ = 1/(πνµσ)1/2

[9.3]

where ν is microwave frequency, µ is the permeability and σ is the electrical conductivity. From this equation it is noted that a bulk metallic material at room temperature would have only a few microns of skin depth and would reflect most of the incident power due to the development of negative magnetic flux on the surface. However, the situation in the case of powdered metallic materials is entirely different. They would easily get heated more effectively; smaller metallic particles, especially the nano size powders, would be most effective in 2.45 GHz frequency: due to the complete penetration of the microwave field inside the particle and hence absorption and conversion into heat associated with the thermal conductivity, the entire powdered compact will get heated simultaneously and rapidly. As it turned out, results from experimental investigations of microwave processing of materials have periodically suggested the existence of a controversial unexplained nonthermal interaction between high-strength microwave fields and ceramic materials. This nonthermal interaction lacked a credible or verifiable explanation, and was broadly termed as a ‘microwave effect’. For high-temperature reaction experiments, involving thermally-activated chemical diffusion, the common manifestation of the microwave effect was (is) to enhance the process kinetics either by reducing the temperature or the time necessary to complete the reaction.53 As far as the mechanisms for enhanced kinetics and sinterability are concerned, there are several hypotheses proposed by researchers. These are associated with the so-called ‘microwave effect’ or non-thermal factors responsible for such enhancements in reaction and sintering kinetics. The most common theories are: 1. Ponderomotive force interaction: Booske and Rybakov proposed that microwave-excited ionic currents become locally rectified (near the interface), giving rise to an additional driving force for mass transport.54–56 Their model and experiments with ionic crystals such as NaCl do show some validity of enhanced material diffusion. But whether the model can be applied to nonionic solids, or even to metals, is doubtful.


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2. Electric field and porosity interaction: In the case of materials with substantial amount of porosity (green samples of ceramics), there is an enhancement in the electric field at convex surfaces of the pores. This enhancement in the electrical fields would provide a non-ohmic and a localized plasma contribution to the driving force for pore removal and thereby accelerating material diffusion as proposed by Willert-Porada.57 However, no experimental verification for such a hypothesis has yet been demonstrated. 3. Anisothermal condition in multi-phasic systems: Anisothermal heating caused in two different phases of widely varying microwave absorption characteristics can provide a strong driving force to allow enhancement in the reaction kinetics followed by sintering as has been observed by Roy et al.58,59 Several systems have been shown to prove this theory experimentally. But this is applicable only to multi-phase systems with selective heating. Single-phase materials cannot be explained by this theory.

9.4

Future trends

In the last two decades, many significant developments and advances have taken place in the field of high-temperature microwave processing of materials. Many traditional and advanced ceramics, composites and metals have been fabricated using microwave technology with the potential of huge savings in time and energy and overall quality improvement. It is expected that in the next few years the microwave technology could be developed for new products and new fields, and the commercialization will be successfully accomplished for many niche applications. Considering all aspects of microwave technology for high-temperature materials processing, including its inherent limitations and the reluctance of the industry to adopt new technology for fear of losing capital investment in the existing conventional technology, it is believed that the future of microwave technology is quite bright. New microwave high-temperature system manufacturers in China, Japan and India are expected to dominate and change the scene in the next five years. In fact, all the successes so far achieved have been with the continuous microwave processing systems for specialty materials such as cemented carbides, ferrites, varistors, metal products, etc. The coming decade will witness more such systems to be built for many other materials and products. Over several decades, microwave energy has been applied in ceramic processes such as process control, drying of ceramic sanitary wares, calcination, and decomposition of gaseous species by microwave plasma. Some of these areas have been commercially developed successfully. However, these applications involve the use of microwaves at low temperatures (>1000s A/cm2). The macroscopic current density within a fully conductive sample is of the order of 100–200 A/cm2 (assuming ~1000A and 2–3 cm specimen diameter). An amplification of the current density is expected to occur due to geometric constriction offered by the interparticle contacts. The amplification factor is of the order of (d/α)2 where d is the powder particle diameter and α is the contact size. It is therefore conceptually possible that under low pressures at the early stages of the process, significant current density may be present to trigger current effects on diffusion at the vicinity of the interparticle contacts. Note that even if the powder particles are conductive, the overall specimen resistance is high at low relative densities in the early stages of sintering due to the geometric constriction of the contacts. Experimental observations of sparking (Yanagisawa et al., 2003) in lightly pressed 550 micron diameter copper particles occurred at a local current density of the order of 22 000 A/cm2, aided by localized melting of the metal. Such effects are transient as the sintering progresses. An important issue in FAST is the uniformity of the electrical current. In the early stages, when the relative density of the powder is small, the size of interparticle contacts varies significantly and concentration of the current along discrete favorable paths is possible. If the resulting localized heat cannot be effectively transferred away, then a further reduction of the local resistance occurs with catastrophic effect (localized melting) (Raichenko, 1987). This unfavorable localization of the electric current in the compact is alleviated effectively with the application of pressure. The utilization of a pulsed current promotes the uniformity of thermal conduction. Although it has not been proven yet, it is possible that the optimization of processing conditions may require a careful balance of the characteristic time due to heat transfer (t~λ/d2, λ is the thermal conductivity, and d is the size of the powder), and the time between pulses. In intermediate and final stages of sintering, a gradient is developed in the vicinity of pores with different sizes. Similar to initial particle contacts, the electrical field increases as the concentration of equipotential lines increases. In comparison, electrical current density is larger next to large pores than small pores. This creates a temperature gradient, i.e., the temperature is higher next to large pores than next to small pores. Raichenko (1987) calculated the temperature gradient, ∇T, which develops in the vicinity of these pores under pulsed field application 1 σ0 T0E02∆τ ∇T ≈ –– ––––– · –––––––– R 2CM n



[10.1]

where R is the pore radius, σo electrical conductivity, CM specific heat, To initial temperature, Eo intensity of electric field, ∆τ time of electric field effect, and n number of electrical impulses. In turn, this temperature gradient generates a


Fundamentals of field/current assisted sintering

253

vacancy gradient, ∇CV, or more vacancies are created in the vicinity of large pores. The vacancy flow, J, is given by Raichenko (1987): J = DV (kT /T ∇T–∇CV)

[10.2]

where DV– is the diffusion coefficient of vacancies and kT is the thermal diffusivity. Therefore, vacancy diffusion occurs from large pores towards the small pores (Fig. 10.2), resulting finally in the shrinkage of large pores. This is opposite to conventional sintering in which large pores may grow at the expense of small pores.

10.2.2 Sintering mechanisms under an external field/current The effects of electrical current or electric field have been the subject of a few recent reviews, which emphasize the major phenomena leading to enhanced processing (Munir et al., 2006, and Orru et al., 2009). The effects of pulsing Although pulsed current is routinely applied either at the beginning or during the entire sintering process in FAST, the role of the pulsing remains controversial. As shown in the Introduction, pulsing is suggested to influence the sintering kinetics, especially during the initial stage of sintering (by impurity removal and surface activation) and results in clean particle surfaces with increased rate of neck formation (Tokita, 1993, and Groza and Zavaliangos, 2000). TEM observations showed clean grain boundaries down to atomic scale level. The initial thin surface layer (several nm) of Al2O3 is completely removed from the AlN powder particles and redistributed at triple junctions in the dense AlN (Risbud et al., 1994, Groza et al, 2001). This redistribution may be due to phenomena such as localized overheating at particle contacts and removal of impurities by electrical discharges.

10.2 Agglomerated powder (a), bimodal pore distribution as a result of inefficient packing of agglomerates (b), and electric field amplification at the root of the pores resulting in temperature gradients (c), which in turn produce vacancy gradient (arrows) and mass transport in the opposite sense.


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Visual observation of spark (electric arc) formation was recorded by Yanagisawa et al. (2003), who studied the effect of pulsed current on neck formation during the sintering of Cu powder in a custom-designed FAST apparatus. Local melting was also observed at locations where strong sparks occurred. There seems to be a minimum current density above which spark can occur, and the threshold level increases with applied pressure. Yanagisawa et al. (2003) reported a macroscopic current density of 10 kA cm−2 as the threshold current density at an applied pressure of 6.9 MPa; the local current density at particle contact can be higher. This macroscopic current density is, however, about two orders of magnitude greater than what is usually applied in a typical FAST experiment. Even when the condition for spark formation is satisfied, the probability for such an event to occur at each particle contact is extremely low (less than 2% in the above work). Pulsing current effects, to reach higher densities or the same densities at lower temperatures, have been reported in ceramics (Mishra et al. 1998, and Stanciu et al., 2007) and metals (Sastry et al., 2005, and Wang et al., 2000). Wang et al. (2000) found that the pulsed current promoted an earlier onset of sintering compared to direct current. When the magnitude of the applied current was high, however, no difference was found. Specific pulsing effects on late sintering stages have not been studied. Xie et al. (2003) found no effect of pulsing on final density, electrical resistivity and mechanical properties of fully sintered Al. It is possible that the magnitude of the pulsed current overshadows any influence of the pulse pattern. Effects of pulsing have been studied in reactive diffusion and intermetallics growth. For instance, Chen et al. (2005) investigated the pulse sequence in the FAST apparatus and its influence on the reactivity between Mo and Si. Different pulse sequences ranging from 2:8 on:off to 12:2 did not affect the layer thickness of the intermediate phases (mostly MoSi2) that formed. Certainly, more fundamental investigations of pulsing effects in various sintering stages, from necking and bonding to pore elimination and grain growth, are highly desirable. The effects of electrical current on the sintering of conductive powders The effects of electrical current or electric field have been the subject of a few recent reviews, which emphasize the major phenomena leading to enhanced processing (Conrad 2000, and Munir et al., 2006). Direct current has been shown to have a pronounced impact on the kinetics of various processes such as nucleation and growth of intermetallic compounds in diffusion couple studies in metals (e. g., Ni-Ti in Garay et al., 2003 or Zn-Ni in Chen and Chen, 2000). In some cases, a dependence of current direction is observed, and electromigration is believed to play a major role in these diffusion processes with a flux, J, given by:

(

)

DN RT∂(ln N) J = ––– ––––––––– + Fz * E RT ∂x


[10.3]


255

where D is the diffusion coefficient, N is the concentration of the diffusing species, z* is the effective charge of a metal, E is the electric field, F is Faraday constant, and other parameters have their usual meaning. In other studies, an enhanced kinetic is shown independent of the current direction. Electromigration may still influence the kinetics of these latter cases but may affect both metals equally. As mentioned in Section 10.2, another explanation for the faster diffusion under an electrical current/field is based on the effect of current on vacancy concentration and vacancy mobility (Conrad 2000, Garay et al., 2003, and Asoka-Kumar et al., 1996). It is shown that high current density can facilitate the formation of vacancies and enhance their mobility. Recent work by Yanagisawa et al. (2003), Song and Zhang (2006) and especially Frei et al. (2007) on sintering showed that current enhances neck formation. The fitting of experimental data to a simplified model for the initial stage of sintering (Frei et al., 2007) results in some values of n (as high as 20) that do not have any physical meaning: n x = Ct –– –– [10.4] r rm

()

where x is the neck radius, r is particle radius, t is time, C is a constant related to diffusivity, and n and m are constants and mechanism dependent. Neck microstructures and fracture surfaces near the necks (Song et al., 2006) show interesting features that are attributed to the melting or evaporation of Cu. While Frei et al. (2007) suggested a current-induced evaporation which was also found in other metals (Shingubara et al., 2002, and Ramanath et al., 2002), simple theoretical calculations from Yanagisawa et al. (2003) and Song et al. (2006) indicated local melting/boiling of Cu near the neck region due to excessive Joule heating from a very high current density in this region. These calculations, however, should be taken with caution because their analysis is based upon the assumption that no heat flow from the neck region to the surrounding occurs during the duration of a pulse. That assumption is hardly true for a good thermal conductor like Cu. Based on the influence of electromigration on the flux equation (Eq. 10.3), the interaction between the electron wind and metal atoms can be considered as an additional driving force for matter transport. In a phenomenological sense the sintering of conductive powders in FAST can be driven by three factors: intrinsic surface curvature, applied pressure and electromigration. The sintering equations for FAST of conductive powders can be obtained from a general densification rate, dρ/dt, equation for hot pressing (Rahaman, 1995, p. 430):

(

)

γSV 1 dρ –––– ––– = B ––– r + ΦKPa 1– ρ dt

[10.5]

where ρ is the fractional solid density, B represents a collection of kinetics parameters including temperature, diffusivity and grain size, r is a parameter


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representing a microstructure scale (related to particle size), γSV is surface energy of the sintering particle, Φ is stress intensity factor, K is a factor depending on γ sintering stage, and Pa is applied pressure. The term rSV is called sintering stress and inherently causes densification. B, the kinetic term, is strongly related to temperature; therefore, at high temperature, densification happens faster. The rate of densification slows down as ρ approaches 1 in the final stage of sintering. In FAST, the terms inside the parentheses in Eq. 10.5 can be replaced by γ ( rSV + ΦKPa + A), where A is a parameter accounting for electromigration which is related to electric field and the effective charge of the adatom. In a model that will be further adjusted, Olevsky and Froyen (2006) incorporated electromigration into the sintering model where grain boundary diffusion was dominant and applied the framework to FAST sintering of Al powder. The modeling results agreed fairly well with experimental data, especially at later stages of sintering where Olevsky and Froyen (2006) believe that effects from electromigration become predominant compared to those of surface tension and applied pressure. Although it is agreed that the driving forces for densification due to surface curvature and applied pressure are significantly reduced during later stages of sintering, it is also important to point out that local current density at these later stages becomes much smaller due to an increase in contact area. The question remains whether this reduced current density is high enough to cause any significant electromigration. In order to resolve this ambiguity, experimental works that separate electricalfield effects from those of surface tension and external pressure at these late sintering stages are needed. The sintering of nonconductive powders in FAST As a low-voltage, high-current processing technique, it is demonstrated that no current can pass through insulators such as Al2O3 during FAST (Carney and Mah, 2008). The powder compact is heated up through heat transfer from the die. The advantages of field-assisted sintering over other conventional sintering techniques are explained based on the high heating rate and large thermal gradient due to intense cyclic heating of the pulsed current. These effects are applicable not only to nonconductive powders but to metallic systems as well. Besides affecting the duration of the sintering cycle, fast heating rates have a considerable influence on the sintering mechanism. Generally, fast heating rates are known to bypass the non-densifying and grain-coarsening mechanisms at lower temperatures (Johnson, 1990). At high heating rates the powder condition that is more favorable for densification (i.e., finer grain structure) is preserved to the point where densification mechanisms become active. An example is the sintering of Al2O3 at 50 and 300 °C/min in FAST (Zhou et al., 2004). The densification starts at a lower temperature when a heating rate of 300 °C/min is used. As the powder compact enters the final stage of sintering, however, slower heating seems to give a better final density. This trend is confirmed in another study on alumina by Shen



257

et al. (2002a) and is seen very often in the processing of transparent ceramics (Morita et al., 2009). The above paradox can be explained by the effect of thermal diffusion on densification as proposed by Olevsky and Froyen (2009). Thermal gradient within the sintering sample not only creates a gradient in vacancy concentration but also promotes the separation of atoms (ions) and vacancies under the Ludwig-Soret effect: Q ∇T [10.6] J = –D ∇CV + CV ––– ––– kT T where CV is vacancy concentration and other parameters have their usual meaning. Olevsky and Froyen (2009) showed that at the initial stage of sintering the separation of vacancy and atoms (ions) can lead to neck formation. During the final stage of sintering, however, pores can act as sinks of vacancies, and the separation of vacancies and atoms under the Ludwig-Soret effect can lead to an increase in pore size mentioned by Raichenko (1987).

(

)

The effects of mechanical pressure The application of pressure during sintering has both mechanical and intrinsic roles. Mechanical pressure can help rearrange particles and break powder agglomerates. On the intrinsic side, the effect of applied pressure on densification is described by Eq. 10.5. As already seen, the densification rate depends on both temperature (via B) and applied pressure (via Pa). In other words one can trade temperature for pressure and still achieve the same density. This concept is especially important in the processing of nanostructured materials as grain growth is more sensitive to sintering temperature than pressure (Anselmi-Tamburini et al., 2006). At not very high temperatures (i.e., B is not very large) effects from mechanical pressure can be observed easily. In FAST it is found that the effects from applied pressure are similar to what is observed in conventional pressureassisted sintering. At low to moderate temperatures, higher applied pressure yields better final density. An example is the effect of applied pressure on the density of 8 mol% yttria-stabilized zirconia prepared in FAST (Anselmi-Tamburini et al., 2004) and hot pressing (Jayaratna et al., 1986). Samples sintered in FAST at 1200 °C for five minutes and in a hot press at 1300 °C for 30 minutes show a similar density–pressure relationship: higher density for higher pressure. Since pressure assists densification and changes pore configuration, it also indirectly affects grain growth. A higher density results in a higher packing coordination number, which leads to an early onset of grain growth. Shen et al. (2002a) sintered Al2O3 powder under field application and found that a higher pressure up to 200 MPa gave a larger average grain size for sintering temperature above 1250 °C where grain growth became more significant. A similar behavior was also found during HIP of Al2O3 at 1300 °C (Besson and Abouaf, 1991). No


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effect of pressure application on final grain size was seen in FAST for sintering temperature below 1250 °C though. Anselmi-Tamburini et al. (2004), on the other hand, found no effect of pressure on the average grain size of cubic zirconia sintered at 1200 °C for five minutes in FAST. The authors argued that the increased driving force for densification due to the application of pressure leads to a reduction in sintering temperature and limited grain growth. At the same applied pressure (100 MPa), the grain size-relative density sintering trajectories of 3 mol% yttria-stabilized zirconia obtained by FAST and hot pressing are very similar up to 98% theoretical density (Bernard-Granger et al., 2008). This again indicates that the effects of applied pressure in FAST and hot pressing are very similar.

10.2.3 Modeling/simulations of external field effects in sintering (thermal-electric-sintering models) While numerical analysis of the conduction through a porous medium had been conducted on the micro scale (Raichenko et al., 1973, and Geguzin et al., 1975) in the 1970s, it was not until much more recently that models specific to FAST type processes began to appear. For instance, Matsugi et al. (2003 and 2004) used the finite difference method to perform a steady-state thermal-electric analysis of the punch and die along with the sintering compact (Ti and Al2O3). Their work showed temperature and electrical distribution were dependent on conductivity of the compact. Zavaliangos et al. (2004) were the first to develop a transient thermalelectric finite element model (FEM) of the entire system. It was shown that understanding the local conditions in the specimen necessitates a model of the entire system so that heat transfer patterns and current conduction within and around the specimen are established. An additional feature of this simulation is the incorporation of thermal and electrical contact resistances. The various heat losses routes are shown in Fig. 10.3. At low temperatures the majority of heat losses occur along the loading train, while at high temperature radiation dominates and establishes a radial temperature gradient in the specimen die. The model and validating experiments (Zavaliangos et al., 2004) showed that a sizable gradient exists between die surface and sample center. By confirming that the temperature at the center of the compact is usually higher than the die surface, these results clearly challenged the assertions of several experimental papers which claimed that it was possible to sinter materials at lower temperatures than by conventional techniques. The conductivity of the sample was shown to play a large role in the thermal and electrical distributions in the system by comparing results between graphite and alumina (Al2O3). Vanmeensel et al. (2005) and Anselmi-Tamburini et al. (2005) used a similar thermal-electric FEM approach to further demonstrate the effect of sample conductivity by showing the difference between conductors (Cu or TiN), and insulators (ZrO2 or Al2O3). Vanmeensel et al. (2005) also proposed a



259

10.3 Experimental data show the temperature excess of interior temperatures θcenter over the die surface temperature θsurface. The incorporation of thermal contact resistance (thermal gap conductances, hg, are 2.4 × 103 and 1.32 × 103 W/m2-K at horizontal and vertical direction, respectively) makes the simulated results to match experimental data.

novel process control scheme in which they focused a pyrometer through a borehole in the punch to measure temperature closer to the specimen. While the models of electric field assisted sintering predict reasonably well the general trends in thermal and electrical distributions within the system, they fail to consider the salient feature of the process: densification of the material and its effect on thermal-electrical gradients as the effective material properties change during sintering. Most FAST models to date consider thermal-electric phenomena but neglect the sintering/densification part of the problem. Wang et al. (2007) recently published results of a coupled thermal-electric-stress finite element analysis which was the first to predict temperature, current and stress fields in copper and alumina samples. This model again assumes constant material properties and does not account for densification. In reality, thermal, electrical and sintering phenomena are fully coupled. At the particle level or microscale the coupling of these phenomena is mainly related to mass, thermal and electrical transport between atoms. The electrical properties depend on temperature and affect Joule heating. Temperature is required for the activation of diffusion which is the driving force for sintering. As discussed above, electrical current can also contribute to mass transport. Furthermore, both thermal and electrical properties have a strong dependence on density. This coupling on the micro scale manifests as thermal-electrical-sintering coupling on the macro scale. Densification will lead to shrinkage of the sample, which in turn will alter the thermal and electrical fields.


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The thermal part of the fully coupled thermal-electrical model of the entire FAST system considers conduction, convection and radiation heat transfer mechanisms through the well-known energy balance equation: ρC ––– ∂θ dV = ∇(k∇θ)dV + q. dV + (q. ; q. ; q. ; q. )dS ∫ ∫ e s∫ c conv r ec ∫ ∂t

V

V

[10.7]

V

where V (m3) is any control volume enclosed by a surface S (m2); ρ (kg/m3), Cp (J/kg K), θ (K), k (W/mK) and t (s) are density, specific heat, temperature, thermal conductivity, and time respectively. The rate of heat generated throughout . the volume V by Joule heating is represented by qe(W/m3). The surface heat fluxes (W/m2) correspond to heat conduction from neighboring volumes, heat transfer by convection, heat transfer by radiation and interfacial heating effects. The rate of internal heat generation per unit volume due to Joule heating is given by: . qe = (–∇ϕ)σ(–∇ϕ) = (∇ϕ)σ(∇ϕ) [10.8] where σ(Ω–1m–1) is the electrical conductivity and ϕ is the electric potential. Convection at the surface can be considered if the process does not take place in vacuum. Radiation to the environment and between surfaces of system components needs to be included as boundary heat fluxes at the relevant surfaces, as well as heat generated at interfaces due to contact resistance is given by: . qec = J(ϕ1 – ϕ2) = σg (ϕ1 – ϕ2)2 [10.9] where J is the electric current flowing between interfaces, ϕ1 is the electric potential of one surface, ϕ2 is the electric potential of the other surface and σg is the electrical gap conductance. Details of the implementation as well as an extensive discussion of the presence and the estimation of contact resistances are given in Zhang (2004). Recently a two-part finite element approach was utilized to create a fully coupled model that incorporates thermal, electrical and sintering phenomena (McWilliams and Zavaliangos, 2008). The two modules consist of a fully coupled thermal-electric simulation and a sintering (thermal-displacement) simulation. The temperature history resulting from an external current applied over a short time period ∆t is calculated by a coupled thermal-electric simulation which considers a fixed specimen geometry. This is used as an input to the sintering simulation, which tracks the local relative density of the material and produces an estimate of the shape and volume evolution of the specimen during the same time period ∆t. The updated mesh is fed to the thermal-electric simulation and the process is iterated. In addition, stresses at the end of each sintering iteration are stored to maintain continuity over time. This also ensures that internal energy is conserved from simulation to simulation as density and the volume of the compact changes since the work from the previous time step is accounted for.



261

For sintering we chose to implement a phenomenological model of the type proposed by Kim and Gillia (2002) for free (pressureless) sintering and later developed for use for sintering under the application of external load (Kim et al. 2003). Details of the model are omitted for brevity. Starting with a basic sintering behavior of a two-layer model, Plate I (see between pages 256 and 257) shows the sintering (density) results in parallel and series configurations for two levels of thermal diffusivity (McWilliams and Zavaliangos, 2008). For the series arrangement the electric current density is uniform with most of the Joule heating occurring in the low-density layer due to higher resistivity. For the parallel arrangement most of the Joule heating occurs in the high-density layer because the bulk of the current goes through this layer. Minimal intermediate distortion is predicted when the thermal diffusivity is high enough to homogenize the temperature. For low thermal diffusivity, a strong intermediate distortion is predicted. The sense of the distortion is opposite in series and parallel arrangements as a different layer densifies faster under the higher temperature. This case study is instructive because it demonstrates the coupling between sintering and heat transfer in the case of density gradients and low thermal conductivities.

10.3 Applications of field/current activated sintering A sizeable body of literature (over 50 papers/mo in the last year) reports FAST densification of the largest variety of materials, from conductors to insulators, nanocrystalline to coarse grained, metastable to stable, monolithic to graded and composites, precursors or final chemistries, common or exotic, laboratory or industrial materials. An extended review of FAST applications to specific material systems has been recently published (Orru et al., 2009). Some other reviews cover specific materials (e.g., nanocrystalline by Chaim et al. (2008) and Ragulya (2008)) or provide examples of FAST utilization for certain applications (Munir et al., 2006, and Omori, 2000). Therefore, this review covers only selective recent relevant references. The combination of powerful densification tools provided by FAST sintering – effective heating, electrical current effects, applied pressure and high heating rates – results in specific advantages towards very short times, high densities and microstructural benefits. While the latter two are occasionally contentious, the short time/rapid densification is a widely recognized FAST feature. Table 10.1 summarizes some benefits of FAST sintering as applied to different material categories.

10.3.1 FAST sintering benefits As already mentioned, the effects of processing parameters (temperature, time, pressure, heating rate) and of initial powders (particle chemistry and size, surface activation, agglomeration, binders) on overall densification and grain growth


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Table 10.1 Synopsis of FAST benefits (selected examples) FAST results Material FAST processing Comparison feature to other techniques

Reference

Earlier densification onset

Al2O3 (0.4 µm)

Densification starts at 1223K

NA

Shen et al., 2002a

Y2O3 20 nm (undoped)

Densification starts at 873 K

CS: starts at ~ 1473 K

Yoshida et al., 2008

Enhanced densification rate

ZnO, ZrO2, Al2O3

Maximum shrinkage rates at 973 K for ZnO, 1373 K for ZrO2 and 1423 k for Al2O3

1–2 orders of magnitude faster shrinkage rate than in CS

Nygren and Shen, 2003

Higher densities

ZrW2O8

98.6% at 873 K/10 min/50 MPa 92.4% at 1163K/10 min/40 MPa Fully dense at 1873–1973 K/5min/100MPa

HP: 63.1% at 873 K/1h

Kanamori et al., 2008

CS: 61.3% at 1273 K/3h

Scarlat et al., 2003

CS: 90% dense at 2043 K/6h

Ricote et al., 2008

Ultrafine Ni

773K/1/min/150 MPa

Gubicza et al., 2009

Undoped Y2O3 20 nm

1123 K at 10 K/ min/ 83 MPa

HIP: 973 K/150 min/140 MPa CS: 1873 K at 5C/min, air/180 min

Additive free composites Enhanced reaction rate

ZrB2 – 15 vol% MoSi2 FeCr2S4 from FeS and Cr2S3

2023 K/7 min/ 30 MPa 1273 K/10 min/45 MPa

HP: > 2373K

Guo, 2009

Conventional reaction:>5 days

Zestrea et al., 2008

Transparent ceramics

Al2O3

1423K/8 min/ K/20 min/80 MPa

CS: Slow heating rate

Kim et al., 2007

Densification of metastable phases

Co65Ti20W15

Final amorphous structure

99.6% dense, ~ 300K/min

ElEskandarany et al., 2005

Controlled porosity

Al – high strength foam

773K/5min/ 20 MPa

CS: 923 K/3h

Oh et al., 2000

Good bonding

Cubic BN on Cu

1273/3min/57 MPa

NA

Yoo et al., 1996

Superplasticity

Al2O3 (50%)-Al2MgO4 (50%)

1253 K, 75% dense. Strain rate of 10-2s-1 at 1273 K

NA

Zhan et al., 2005

SnO2 BaZr0.9Y0.1 O3−δ Lower sintering temperatures

CS – Conventional sintering, HP – Hot pressing, HIP – Hot isostatic pressing


Yoshida et al., 2008


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are similar to other sintering avenues, but with considerably faster kinetics (Table 10.1). Notable enhancements are reported to occur in early sintering stages, with densification onsets at low temperatures and most of the densification taking place within a few minutes (e.g., Shen et al, 2002a). Electrical current application enhances neck formation and growth in metals (pure copper (Frei et al., 2007)) and ceramics (Shen et al., 2002a, and Stanciu et al., 2007). Densification onsets were observed at very low temperatures (e. g., 0.38 Tm in ZnO, Nygren and Shen, 2003), with shrinkage rates 1-2 orders of magnitude higher than in conventional sintering (e. g., Shen et al., 2002a). Generally, a maximum shrinkage rate occurs at a certain FAST temperature, depending on heating rate, pressure and type of powder. These early sintering benefits translate into final full densities and desirable microstructures (e.g., small grain sizes or retention of metastable phases), if late sintering stages are controlled. Often, densification results are superior to those in conventional sintering (CS) or hot pressing (HP), as reflected in higher densities or advantageous sintering conditions (shorter times, lower temperatures and narrow temperature ranges, no binders or additives required, processing difficult-to-sinter materials) (e.g., Bordeneuve et al., 2009, Guo, 2009, Cao and Zhao, 2009, and Yoshida et al., 2008). Lower final sintering temperatures or shorter durations benefit the densification of non-equilibrium systems (e.g., retaining amorphous metal structure (Graeve et al. 2008), or cubic BN (Hotta and Goto 2008)). Full densification of metastable phases was reported by FAST without phase decomposition (e.g., pure hydroxyapatite below 950 C, Tran 2009) or formation of undesirable phases (e.g., no β-phase in α-Si3N4 (Suganuma et al., 2003)). Early sintering advantages in FAST appear to be insufficiently studied and exploited and quite often these advantages are masked by the collective contribution of FAST features in the final densification stages, which may coarsen microstructures or alter the desirable structures. Pressure effect to enhance sintering and reduce temperatures in FAST sintering was shown to be at least qualitatively the same as for other pressure assisted techniques (e.g., Sastry et al., 2005). For instance, pure W was densified to 87% density at 1800 °C under 90 MPa, but to 94% at 1300 °C using 200 MPa pressure (Quach et al., 2009). Commonly, pressure is applied throughout the sintering cycle, but more effective plastic deformation effects are reported when pressure (or increased level) is applied at higher temperatures or at levels exceeding material’s yield strength (Shen et al., 2002a; Chaim et al., 2008). Late pressure application is also efficient for gas elimination, which is important in transparent ceramics (Dahl et al., 2007; Meir et al., 2009). Recently, very high pressure FAST densification has been applied to minimize sintering temperatures, and suppress grain growth, particularly in nanomaterials (e.g., Anselmi-Tamburini et al., 2006) (see Table 10.2). Heating rate effects are apparently controversial in FAST with both reduced or enhanced grain growth reported when heating rate increases. As already mentioned in Section 10.2.2, high heating rates overcome coarsening by suppressing low


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Table 10.2 Selected FAST results for sintering dense* nanomaterials Material

Initial particle size, nm

FAST parameters Final (temp, ºC/ time, grain min/pressure, MPa) size, nm

References

CeO2

7

625/5/600

12–14

MgO 3 and 8% Y2O3-ZrO2 BaTiO3

11 17–21

800/5/150 1000/5/280

52 50

20–30

50**

ZrO2(2.4% Y2O3) SrTiO3 Hydroxyapatite

13 50 45

850/2/70 (heating rate:400K/min) 1150/5/70 875/5/200 900/15/45

Anselmi-Tamburini et al., 2006 Chaim et al., 2004 Anselmi-Tamburini et al., 2007 Deng et al., 2008

70 80 90

Muroi et al., 2008 Maca et al., 2008 Tran, 2009

* Density at least >98% ** 97% dense, 10 h annealing at 600 °C in air

temperature non-densifying mechanisms (e.g., surface diffusion) in materials characterized by higher activation energy for densification than grain growth (e.g., Stanciu et al., 2001, Zhou et al., 2003, and Zhao et al., 2009). In the other materials, the effect of heating rate on grain coarsening is negligible. However, significant coarsening may occur during holding at high temperatures, particularly if densities are high, and closed pores will provide no pinning effects. Therefore, enhanced, sometimes abnormal grain growth in late sintering stages has been reported despite high heating rates (e.g., Shen et al., 2004, and Kim et al., 2007). Most reports show a negligible effect of heating rates on densification (e.g., Shen et al., 2002a, and Anselmi-Tamburini et al., 2004). However, some studies showed high heating rates (or at least in certain ranges) to be effective in densification due to macroscopic thermal gradients and retention of small grain size until high temperatures (Guo et al., 2008, Wang et al., 2000, and Olevsky et al., 2007). In some systems, fast heating rates are useful to avoid transient, undesirable phases such as oxides and oxynitrides in sialon ceramics (Nygren and Shen, 2003). Conversely, slower heating rates reached higher densities in transparent alumina (e.g., Kim et al., 2007). In some cases, the high-temperature gradients may create problems related to differential shrinkages, pore structures and internal stresses, depending on material, sample size, etc. (e.g., Jayaseelan et al., 2004, and Kim et al, 2009). Grain growth behavior follows the classical principles, with similar sintering trajectories as by other densification pathways (CS or HP) (Fig. 10.4). Noteworthy is grain coarsening during very short dwelling time in FAST, as compared to conventional sintering. For instance, Li and Gao (2000) noted a similar final grain size in 3 min by FAST as in 2h by conventional sintering of nanocrystalline zirconia at the same temperature (1300 °C). Faster grain growth kinetics in late sintering stages is due to enhanced diffusion (including grain boundary migration)



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10.4 Sintering trajectories for powders sintered by FAST technique – 150 nm alumina (Langer et al., 2009), 50–80 nm zirconia (BernardGranger et al., 2008) and 11 nm magnesia (Chaim et al., 2004). Note: the sintering trajectory for hot pressing the 150 nm alumina powders directly overlaps the FAST curve.

by current application (Eq. 10.3). As expected, the most significant coarsening is reported in liquid-phase sintering (LPS), when the liquid phase quickly develops under highly non-equilibrium conditions (e.g., anisotropic growth of elongated Si3N4 grains in 1 min at 1600 C (Shen et al., 2002b). Although enhanced diffusion in FAST is responsible for grain coarsening, temperature uncertainties may also play a role, with samples actually densifying at higher temperatures than what is measured or reported (see Section 10.2.3). The effects of particle size, powder agglomerations and materials properties on grain growth are similar to other densification techniques. Enhanced FAST densification creates processing opportunities for retaining small grain sizes in the final dense parts (Table 10.2). Pressure and high heating rates are commonly applied to create a temperature window between full


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densification and the coarsening start, of most significance for nanocrystalline and transparent materials (e.g., Shen et al., 2004). Changes in sintering mechanisms (e.g., sintering only in solid state for cemented carbides or predominance of viscous flow for Si3N4) may suppress abnormal grain growth specific to LPS (Groza et al., 2000, Huang et al., 2007, and Herrmann et al., 2009). Reactive sintering has been used to shorten the reaction time in processing compounds and composites or in controlled doping of functional materials (e.g., Locci et al., 2009, Umeda et al., 2009, and Luo et al., 2009). For instance, synthesis of FeCr2S4 spintronic from a powder mixture of Cr2S3 and FeS shows complete reaction and gives a fully dense final product in 10–15 min at 1000 °C as compared to days in conventional processing (Zestrea et al., 2008). High-rate self-propagating reactions in FAST have also been applied to prepare various compounds (e.g., Korchagin et al., 2000). General features of reactively FAST sintered materials are homogeneous microstructures, no need for additives, good chemistry control and improved properties (Wu et al., 2007, Guo, 2009, and Rocha-Rangel et al., 2005).

10.3.2 Unique properties Although properties comparable to conventionally densified materials are generally described, FAST sintering was shown to induce a number of enhanced or novel properties. For instance, ionic conductivity and permittivity twice higher than by CS were measured in BaZr0.9Y0.1O3-#lx (Ricote et al., 2008) and BaTiO3 (Tomonari et al., 1999) ceramics, respectively, and maximal photoluminescence intensity was observed in ZnO (Wang and Gao, 2005). Controlled and improved mechanical and biological properties were reported in porous Al2O3 and composites and hydroxyapatite (Dibyendu et al., 2009, Yang et al., 2009, and Tran, 2009). Magnetic properties show more distinct departures from conventionally sintered materials. FAST processed MnFePGe compound displayed one of the highest values of magnetic entropy value, while hard (NdFeB)-soft (CoFeSiB) magnetic composites yielded higher remanent magnetization and magnetic energy than in conventional materials (Yue et al., 2009, and Lupu et al, 2009). The FAST synthesized FeCr2S4 spintronic displayed a diffuse ferromagnetic transition, with no magnetic anomaly at 10 K, as in the CS sample (Zestrea et al., 2008). Further clarification is required to separate the intrinsic current effects on properties from those due to higher densities or smaller grain size in FAST processing.

10.3.3 FAST processing issues Temperature reporting must be carefully considered. As mentioned in Section 10.2.3, the reported lower sintering temperatures may not always be real. The usual measured surface temperature is lower than the center (Fig. 10.3). Measurement type (pyrometer vs. thermocouple) and location, and machine configuration (e.g., die insulation) must be accounted for. Lately, temperature



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measurements closer to sintering powder beds seem to provide more accurate values, and the existing temperature differences are often reported (e.g., BernardGranger et al., 2008). Temperature overshoots in FAST machines are common and occasionally reported (Langer et al., 2009), particularly at high heating rates. Microstructural inhomogeneities in fully dense samples have been occasionally observed and mainly attributed to temperature gradients due to high heating rates and short holding times (Jayaseelan et al., 2004, and Sun et al., 2002). Generally, the sample inhomogeneity increases with the sample size (i.e., larger in larger samples) (Wang et al., 2000). However, a few papers indicated more uniform densification and microstructures by FAST as compared to HP (e.g., Li and Gao, 2000). Stoichiometry changes occur in oxide ceramics or in materials with high vapor pressure components (e.g., iodine losses, Campayo et al., 2009). Darkening of light-colored oxide ceramics has often been observed and attributed to reducing atmosphere inside graphite tools or direct carbon contamination (e.g., Ricote et al. 2008, Dahl et al., 2007, and Quach et al., 2008). A post-sintering annealing in air restores the oxide chemistry. More work is needed to identify the source of these changes, quantify them and establish their material or processing dependence. Carbon contamination from the graphite die and punches inevitably occurs. For most materials, it is only on the surface and it is mechanically eliminated by grinding/polishing. Problems with residual surface carbon have been reported in carbon sensitive materials (e.g., Fe-based alloys such as Fe-Nd-B magnets (Lee et al., 2009) or in processing of transparent materials (Meir et al., 2009)). The manufacturing potential of FAST is promising due to process simplicity, fewer processing steps with no need for cold pressing/compaction and binders, simultaneous reaction and densification, high throughput (whole cycle ~ 30 min, vs HP with few samples/day), capability for process control (monitoring the relative displacement) and process flexibility (simple changes in sintering temperature, time, pressure and sintering environment, but also on heating rates, timing, levels and rate of pressure application) in one/multiple sintering steps. New manufacturing capabilities have been developed such as net shape manufacturing, superplastic forming, graded/hierarchical/cellular structures, bonding or combining FAST with other processing such as isostatic pressure application, extrusion, forging or using current assisted sintering for localized densification (CATS) (Akhtar et al., 2009, Groza and Kodash, 2008, Jiang et al., 2007, Lin et al., 2009, Morsi et al., 2009a, 2009b, and Yoo et al., 1996).

10.4 Conclusions Distinct FAST advantages have been shown in sintering refractory, additive free, hard to sinter nano- or transparent materials and in reaction sintering. However, careful control of FAST processing parameters and tailoring them according to the material type is required, implying that a better foundation of FAST sintering is desirable. Further theoretical and experimental efforts are required to understand


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current/field effects in early sintering, including possible discharges or other surface effects, pulse effects in late sintering, control of specific material-electrical current/field interactions (e.g., current effects in nonconductive materials) and machine handling to optimize sintering to make FAST processing a manufacturing avenue applicable to novel, engineered materials for large and net shape parts while saving energy.

10.5 Acknowledgement The authors acknowledge the continuous NSF support of their FAST research.

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Hotta M and Goto T (2008) ‘Densification and microstructure of Al2O3–cBN composites prepared by spark plasma sintering’, J. Ceram. Soc. Japan, 116, 744–8. Huang S G, Li L, Vanmeensel K, Van der Biest O and Vleugels J (2007), ‘VC, Cr3C2 and NbC doped WC–Co cemented carbides prepared by pulsed electric current sintering’, International J. Refractory Met. Hard Mater., 25, 417–22. Hulbert D M, Anders A, Dudina D V, Andersson J, Jiang D, Unuvar C, Anselmi-Tamburini U, Lavernia E J and Mukherjee A K (2008), ‘The absence of plasma in “spark plasma sintering” ’, J. Appl. Phys., 104, 033305/1–7. Jayaratna M, Yoshimura M and Somiya S (1986), ‘Hot pressing of Y2O3-stabilized ZrO2 with Cr2O3 additions’, J. Mater. Sci., 21, 591–6. Jayaseelan D D, Ueno S, Ohji T and Kanzaki S (2004), ‘Differential sintering by improper selection of sintering parameters during pulse electric current sintering’, J. Am. Ceram. Soc., 87, 159–61. Jiang D, Hulbert D M, Kuntz J D, Anselmi-Tamburini U and Mukherjee A K (2007), ‘Spark plasma sintering: A high strain rate low temperature forming tool for ceramics’, Mat Sci Eng A, 463, 89–93. Johnson D L (1990), ‘Comment on “Temperature-Gradient-Driven Diffusion in RapidRate Sintering” ’, J. Am. Ceram. Soc., 73, 2576–8. Kaiser K (2005), Electrostatic Discharge, CRC Press, Taylor and Francis Group. Kanamori K, Kineri T, Fukuda R, Nishio K, Hashimoto M and Mae H (2008), ‘Spark plasma sintering of sol-gel derived amorphous ZrW2O8 nanopowder’, J Am Ceram Soc, Volume Date 2009, 92(1), 32–5. Kim H and Gillia O (2002), ‘Near net shape processing of a sintered alumina component: Adjustment of pressing parameters through finite element simulation’, Int. J. Mech. Sci., 44, 2523–39. Kim H Gillia O and Bouvard D (2003), ‘A phenomenological constitutive model for the sintering of alumina powder’, J. Eur. Ceram. Soc., 23, 1675–85. Kim H C, Shon I J, Garay J E and Munir Z A (2004), ‘Consolidation and properties of binderless sub-micron tungsten carbide by field-activated sintering’. International J. Refractory Met. & Hard Mater., 22, 257–64. Kim T S, Lee J K, Kim H J, and Bae J C (2005), ‘Consolidation of Cu54Ni6Zr22Ti18 bulk amorphous alloy powders’, Mat Sci Eng A, 402, 228–33. Kim B-N, Hiraga K, Morita K and Yoshida H (2007), ‘SPS of transparent alumina’, Scr Mater., 57, 607–10. Kim B-N, Hiraga K, Morita K, Yoshida H, Miyazaki T and Kagawa Y (2009), ‘Microstructure and optical properties of transparent alumina’, Acta Met Mater., 57, 1319–26. Korchagin M A, Grigor’eva T F, Barinova A P and Lyakhov N Z (2000), ‘Solid-state regime in self-propagating high-temperature synthesis (SPS )’, Doklady Akademii Nauk, 372, 40–2. Langer J, Hoffmann M J and Guillon O (2009) ‘Direct comparison between hot pressing and electric field-assisted sintering of submicron alumina’, Acta Mater. 57, 5454–65. Lee S, Kato H, Kubota T, Makino A and Inoue A (2009) ‘Fabrication and soft-magnetic properties of Fe-B-Nb-Y glassy powder compacts by spark plasma sintering technique’, Intermetallics, 17, 218–21. Li W and Gao L (2000), ‘Rapid sintering of nanocrystalline ZrO2(3Y) by spark plasma sintering’, J. Eur. Ceram. Soc., 20, 2441–5. Lin Y-H, Lan J, Shen Z, Liu Y and Nan C-W, Li J-F (2009) ‘ High-temperature electrical transport behaviors in textured Ca3Co4O9-based polycrystalline ceramics’, Appl. Phys. Lett., 94, 072107/1–3.



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Orru R, Licheri R, Locci A M, Cincotti A and Cao G (2009), ‘Consolidation/synthesis of materials by electric current activated/assisted sintering’, Mat Sci Eng R, 63, 127–287. Quach D V, Levchenko A A, Navrotsky A and Groza J R (2008), ‘Constraint of oxygen fugacity during field-assisted sintering: TiO2 as a test case’, J Am Ceram Soc, 91, 970–4. Quach D V, Stach E and Groza J R (2009), Sintering of pure W powders by SPS, private communication, University of California, Davis, summer 2009. Ragulya A (2008), ‘Consolidation of ceramic nanopowders’, Adv. Appl. Ceram, 107, 18–134. Rahaman M N (1995), Ceramic Processing and Sintering, New York, Marcel Dekker. Raichenko A I, Burenkov G L and Leshchinsky V I, (1973), ‘Theoretical analysis of the elementary act of electric discharge sintering’, Physics Sinter., 5, 215–25. Raichenko A I (1987), Fundamental Processes in Powder Sintering, Metalurgiya, Moscow Ramanath G, Kim H, Goindi H S, Frederick M J, Shin C S, Goswami R, Petrov I and Greene J E (2002), ‘Electromigration in epitaxial Cu(001) lines’ Proceedings of the Sixth International Workshop on Stress Induced Phenomena in Metallization, ed. S. P. Baker, M. A. Korhonen, E. Arzt, and P. S. Ho, AIP Conference Proceedings, 612, 10. Ricote S, Caboche G, Estournes C and Bonanos N (2008), ‘Synthesis, sintering, and electrical properties of BaCe0.9-xZrxY0.1O3-lx’, J. Nanomaterials, Article ID 354258, 5p. Risbud S H, Groza J R and Kim M (1994), ‘Clean grain boundaries in aluminum nitride ceramics densified without additives by a plasma activated sintering process’ Phil. Mag.B, 69, 525–33. Rocha-Rangel E, Diaz-de-la-Torre S, Umemoto M, Miyamoto H and Balmori-Ramirez H (2005), ‘Zirconia-mullite composites consolidated by spark plasma reaction sintering from zircon and alumina’, J. Am. Ceram. Soc., 88, 1150–7. Sastry K Y, Froyen L, Vleugels J, Van der Biest O, Schattevoy R and Hummert K (2005), ‘Effect of process parameters on density, structure and properties of Field assisted sintered Al-Si-Fe-X alloy’, Sintering ‘05 Conference Proceedings, Grenoble, 80–3. Scarlat O, Mihaiu S, Aldica Gh, Zaharescu M and Groza J R (2003), ‘Enhanced properties of Ti(IV) oxide based materials by field-activated sintering’, J Am Ceram Soc 86, 893–7. Shen Z, Johnsson M, Zhao Z and Nygren M (2002a), ‘Spark plasma sintering of alumina’ J. Am. Ceram. Soc., 85, 1921–27. Shen Z, Zhao Z, Peng H, Nygren M (2002b), ‘Formation of tough interlocking microstructures in silicon nitride ceramics by dynamic ripening’, Nature, 417, 266–9. Shen Z, Peng H, Liu J and Nygren M (2004), ‘Conversion from nano- to micron-sized structures: experimental observations’, J. Eur. Ceram. Soc., 24, 3447–52. Shingubara S, Miyazaki S, Sakaue H and Takahagi T (2002), in Proceedings of the Sixth International Workshop on Stress induced Phenomena in Metallization, ed. S. P. Baker, M. A. Korhonen, E. Arzt and P. S. Ho, AIP Conference Proceedings, 612, 94. Song X, Liu X and Zhang J (2006), ‘Neck formation and self-adjusting mechanism of neck growth of conducting powders in spark plasma sintering’, J. Am. Ceram. Soc., 89, 494–500. Stanciu L A, Kodash V Y and Groza J R (2001), ‘Effects of heating rate on densification and grain growth during field-assisted sintering of α-Al2O3 and MoSi2 powders’, Met. Mater. Trans. A, 32, 2633–8. Stanciu L, Quach D, Faconti C, Groza J R and Raether F (2007) ‘Initial stages of sintering of alumina by thermo-optical measurements’, J. Am. Ceram. Soc., 90, 2716–22. Suganuma M, Kitagawa Y, Wada S and Murayama N (2003), ‘Pulsed Electric Current Sintering of Silicon Nitride,’ J. Am. Ceram. Soc. 86, 387–94.



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Current

Density contours

High density Low density

RD (Ave. Crit.: 75%) +1.000e+00 +9.658e–01 +9.317e–01 +8.975e–01 +8.633e–01 +8.292e–01 +7.950e–01 +7.608e–01 +7.267e–01 +6.925e–01 +6.583e–01 +6.242e–01 +5.900e–01

Time

(a)

Temperature contours Current

Density contours

Temp (Ave. Crit.: 75%) +1.420e+03 +1.402e+03 +1.383e+03 +1.365e+03 +1.347e+03 +1.328e+03 +1.310e+03 +1.292e+03 +1.273e+03 +1.255e+03 +1.237e+03 +1.218e+03 +1.200e+03


Time

(b)

Temperature contours High initial density

Density contours

Current

Low initial density

Temperature contours Density contours

Current

Low initial density


Time

(c)

High initial density




Time

(d)

Temperature contours


Plate I Predictions of density, temperature and distortion evolution in sintering under electric current of a layered two-density configuration. (a) and (b) represent a flow of current with the layers in series while in (c) and (d) the layers are in parallel configuration. (a) and (c) represent a high thermal diffusivity behavior while in (b) and (d) the thermal diffusivity is low.


11 Photonic sintering – an example: photonic curing of silver nanoparticles J. West, J. W. Sears, S. Smith and M. Carter, South Dakota School of Mines and Technology, Usa Abstract: Silver nanoparticles are currently used to obtain highly conductive printed circuits. Sintering these nanoparticles involves a lengthy heat treatment process or laser curing on high-temperature substrates. Photonic curing is a new technology that allows the sintering of nanoparticles upon low temperature substrates in less than 2 ms. Studies of the sintered density and resistivity of silver nanoparticle films sintered using photonic curing have been conducted and compared with traditional sintering methods. To improve the process of photonic curing, numerical simulations of the optical absorption and the temperature profile of silver nanoparticle films during sintering were made and related to experimental results. Key words: photonic sintering, direct write, Aerosol Jet® printing, Mie theory, Bruggeman model, fluent.

11.1 Introduction Photonic curing is a low thermal exposure sintering method developed to functionalize deposited nanoparticle thin films. Photonic curing was developed by Nanotechnologies (now NovaCentrix) of Austin, Texas, and first made public in 2006.1 This process involves exposing deposited nanoparticles to a high-intensity, short duration, broad-wavelength pulse of light from a xenon flash lamp. Conductive thin films of gold and silver nanoparticle depositions, when exposed to this short pulse (< 1 ms) of high-intensity light, are transformed into functional printed circuits. One of the primary advantages of this method is that the highintensity pulse of light produces minimal damage on low-temperature substrates, much less than oven and laser sintering do. This allows the nanoparticles to be deposited and cured on a high variety of low-temperature substrates such as cloth, paper and Mylar. Another advantage of using photonic curing is the speed at which nanoparticle depositions can be sintered. Rather than spending hours in an oven or programming a laser to follow the deposition path, the photonic curing process can sinter large areas (~ 200 cm2 per 10 cm long lamp) in < 2 ms. The sintered depositions can be tailored for use as flexible circuit boards, RFID tags and flat panel displays.2 The nanoparticle films discussed here were prepared using Aerosol Jet® printing, a new and flexible method for printed electronics using nanoparticle based inks. In this chapter, the systematic studies of photonic curing/sintering of 275 © Woodhead Publishing Limited, 2010

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silver nanoparticle films and their properties, including sintered density and resistivity measurements, are described. To further improve the method and develop a predictive model of the photonic curing process, numerical simulations of the optical absorption and melting processes in these films were performed, and compared to experimental results. The experimental results showed that photonic curing of aerosol ink jet-deposited silver nanoparticles can produce a surface resistivity approaching those found using traditional sintering methods, and that the optical absorption of these films is strong over a broad spectrum of wavelengths. The absorption model described herein closely matches the experimentally determined absorption. The heat-equation-based simulations indicate that the films reach their melting temperature very quickly, followed by rapid solidification and cooling to room temperature.

11.2 Background Aerosol Jet® printing is a direct write technology that was developed through the Defense Agency Research Program Agency (DARPA) Meso Integrated Conformal Electronics (MICE) program.3 The goal of this program was to create new technologies for the formation of micron-sized electrical circuits while not using the lithographic process.3 The Aerosol Jet® printing process involves three steps: First an ink is transformed into an aerosol by an ultrasonic or pneumatic atomizer. Second the aerosol is entrained in a carrier gas, in this case nitrogen, and finally at the head the aerosol is concentrated into a narrow stream of particles by a shaping gas onto the substrate, which is typically 2–5 mm below the tip of the deposition head. The main ink used for the photonic curing measurements discussed here was the V2 silver ink. The V2 ink is a suspension of Novacentrix 25 nm ST2 silver nanoparticles in a DMA solution. In the last step of the Aerosol Jet® printing process the deposition is heat treated in order to sinter the nanoparticles and reduce the resistivity of the printed circuit. The Aerosol Jet® printing head is shown in Fig. 11.1. There are many advantages to using Aerosol Jet® printing. Aerosol Jet® printing technology deposits the nanoparticles onto the substrate in lines as small as 10 microns wide.2 This allows nanoparticle depositions printed using Aerosol Jet® printing to be used in circuits, transistor displays, semiconductors, sensors, speakers, RFID tags and grids that can be used in tissue engineering.2,4 Aerosol Jet® printing can deposit almost any type of nanoparticulate material as long as it can be suspended in a liquid with a viscosity of less than 1000 cP.2 This includes biological materials and nanomaterials suspended in solution.2 Aerosol Jet® printing can deposit these materials on a wide variety of substrates and can deposit in 3-D.2 The Aerosol Jet® printing system can also read CAD files directly (a trait of all direct write technologies), which allows a quick and easy way to transfer the design to the deposition.2 Aerosol Jet® printing has a deposition speed similar to other direct write technologies with a speed of greater than 100 mm per second.5


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11.1 Photograph of the M3D aerosol deposition used in the Direct Printing Laboratory to print micron scale lines of nanoparticle inks.

11.2.1 Photonic curing Photonic curing was first introduced at the 2006 NSTI Nanotechnology Conference and Trade Show.1 It was developed by NovaCentrix for the purpose of rapidly sintering metal nanoparticle based films.1 The technology sinters the nanoparticles without significantly raising the temperature of the substrate. This is accomplished through use of a xenon flash lamp. There are two main parameters that control the amount of sintering from the flash lamp: the duration of the light pulse and the intensity of the lamp. The flash lamp is suspended anywhere from 0.5 cm to 20 cm above the deposition and a high-intensity current is run through the flash lamp.6 The high-intensity current causes the xenon flash lamp to issue a high-intensity, broad spectrum pulse of light. This pulse of light is absorbed by the nanoparticles, which heats them to such a degree that they fuse into a single component. Figure 11.2 shows a diagram of the photonic curing lamp sintering depositions on a conveyor. Because photonic curing results in minimal effect on the substrate, it enables nanoparticle films to be cured on lower temperature substrates such as paper, Mylar and PET. Besides allowing low-temperature substrates to be used, the speed at which the films are sintered allows the use of inks that would oxidize if sintered for long periods of time (yielding nonconductive results), such as copper.1,7 Both of these advantages allow printed electronics manufacturers to


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11.2 Diagram of the photonic curing lamp sintering depositions on a conveyor.

vastly reduce the cost of production by using lower cost substrates and more inexpensive inks. The Novacentrix PCS-1100 Photonic Curing System is a research and development model in use at South Dakota School of Mines & Technology (SDSM&T). The PCS-1100 has a pulse duration that can be set from 35 µs to 1000 µs.6 The voltage of the flash lamp (which controls the intensity and spectral distribution of the lamp) can also be adjusted in the PCS-1100 with a maximum operational voltage of 4000V.6 The PulseForge 3100 is a production model (now in operation at Oak Ridge National Laboratory) that can be incorporated with a roll-to-roll production system or a conveyor belt to sinter continuous or discrete items.7 Three basic assumptions were considered during the development of Photonic Curing for sintering nanoparticles: (i) nanoparticles are predominantly black, so they should absorb light very well;1 (ii) once light is absorbed by the nanoparticles, due to their high surface area to mass ratio, the nanoparticles would heat easily and sinter quickly; and (iii) as nanoparticle films are very thin, they should not retain heat very well and would cool rapidly, minimizing damage to the substrate. Photonic curing has been shown to sinter conductive nanoparticle metals (e.g., silver, gold and copper) as well as dielectric nanoparticles made of alumina, zirconia, barium titanate and mica, as well as the soft magnetic materials cobalt ferrite and iron-nickel permalloy.2

11.3 Experimental results Test specimens consisting of printed lines of nanoparticle silver were deposited by Aerosol Jet® printing onto low-temperature substrates and photonically cured.


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The resistivity, densification and optical absorption of these films were measured for varied photonic curing conditions in order to optimize the process. Surface resistivity was measured using a four-point probe, densification was determined by measuring the film thickness before and after curing, and the optical absorption was measured using a UV-VIS spectrometer on unsintered depositions of similar thickness to the deposited lines.

11.3.1 Surface resistivity To characterize the photonic curing process the resistivity of sintered silver depositions was measured and compared to depositions sintered using oven and laser sintering. The silver was deposited in 1 cm2 squares and then cured. The furnace sintering was done at a temperature of 500 °C for two hours. The laser sintering was done using a laser fluence of 2800 J/cm2. The photonic curing was done using a lamp voltage of 1200 volts with a pulse length of 900 µs. The surface resistivity of the samples were measured using a Lucas/Signatone 4-point, 38 micron pitch probe. Besides the V2 silver ink, similar tests were conducted using the UT Dot (Champaign, IL) 7 nm silver particles as part of the investigation of the particle size dependence on the photonic curing system (see Table 11.1). From these measurements it was observed that the surface resistivity of the photonically cured silver was comparable to the surface resistivity of the oven and laser sintered silver.

11.3.2 Densification To observe the volume shrinkage that occurs during photonic curing, a Zeiss Imager M1M microscope was used to determine the focal length at the surface of the deposition prior to and after curing, using the microscope’s 3-D imaging software. The silver nanoparticles were deposited in lines 3 mm × 10 mm and with an average thickness of 4.7 µm. The sample was weighed and compared with the mass of the empty slide to obtain the mass of the deposition. This gave a silver density in the deposition of 3.8 g/cm3. Knowing the mass of the total deposition, size of the silver nanoparticles, density of bulk silver, and volume of the deposition allowed the calculation of the volume density of the silver nanoparticles. The volume fraction of silver nanoparticles in these depositions was found to be 36%. The thickness of these depositions after photonic curing at various lamp voltages and pulse durations was measured. The densification of the deposition was then calculated and the results are shown in Fig. 11.3. Significant volume shrinkage occurred at higher intensities and longer pulse lengths. The volume shrinkage was dependent on how much voltage was running into the flash lamp and the duration of the pulse. However, the depositions were damaged if the flash lamp intensity was set greater than 1600 volts.


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11.3 plot showing the density of the sintered silver vs. the flash lamp voltage. This was done for three different pulse lengths. The density of bulk silver is 10.6 g/cm3.

11.4 Graph showing the absorption percentage vs. the wavelength for two thicknesses of deposited silver nanoparticles.

11.3.3 Absorption of the nanoparticle films To characterize the absorption of the silver nano-ink depositions, a UV-Vis spectrometer was used to measure the absorption of the uncured depositions. The silver nanoparticles were deposited in 1 cm × 1 cm squares at operational deposition thickness, verified using the Zeiss optical microscope. The UV-Vis spectrometer measures the absorbance every 2 nm in wavelength, from 190 nm to 820 nm. The absorption percentage for two thicknesses is shown in Fig. 11.4. These measurements show significant absorption over a broad spectrum, indicating that Mie resonance is not the dominant absorption mechanism in photonic curing.


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The absorption and scattering of metallic nanoparticle-based inks is the result of multiple physical mechanisms that contribute to the total absorption. We calculated the contribution due to the metallic nanoparticles themselves, first in the dilute limit, using the Mie theory, and second, by the effective medium theory of Bruggeman, and compared these to absorption measurements. Two things were learned by these simulations: (i) that the plasmon resonance associated with the nano size of the particles does not dominate the absorption and (ii) that the effective medium theory of Bruggeman, using published optical constants, reproduces the spectral dependence of the absorption of these films, and may be a useful guide when planning deposition processes. The heat equation was solved for a slab of metal-nanoparticle composite, in contact with air on the irradiated face and conductively cooled by the substrate on the opposite face, in order to simulate the heating and melting processes that occur during photonic curing. These simulations place constraints on the photonic curing process, based on heat transfer and thermodynamics. These simulations reproduce the very fast sintering of metallic nanoparticle-based inks observed in the laboratory, confirm that traditional sintering models do not apply to photonic curing, and may act as a guide in designing deposition and photonic curing processes.

11.3.4 Optical absorption We calculated the absorption due to a dilute suspension of nanoparticles based on the Mie theory,8 by a simple method using code developed by Bohren and Huffman.9 The light absorption and scattering cross-sections of single Ag nanoparticles were added together in accordance with the nanoparticle density to obtain an estimate of the absorption from the nanoparticle film. To obtain good agreement with the experiment, however, the effective medium theory of Bruggeman10 was applied. The two main methods of calculating the absorption and scattering cross sections of small particles are Rayleigh scattering and the Mie theory.8,9 Rayleigh scattering was discarded as a theory of finding the absorption and scattering crosssections as Rayleigh scattering deals with the regime where the wavelength of the light is much greater than the size of the particles.9 As the wavelength of the light produced by the lamp goes from 200 nm to 1000 nm, and the silver nanoparticles being used are 25 nm in diameter, concern over the wavelength being one order of magnitude larger than the diameter ruled out use of Rayleigh scattering. Mie theory meanwhile is valid for all ratios of the nanoparticle diameter to the wavelength of the light.8,9 Mie theory is primarily designed for spherical nanoparticles but has been modified for other shapes.11 According to Mie theory, the absorption cross-section Ca is the difference between the extinction cross-section Cext and the scattering cross section Cs, Ca = Cext – Cs.8,9 The cross-sections are calculated for every desired wavelength. The extinction cross section is defined as


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2p ∞ (2n + 1)Re{a + b } Cext = ––– [11.1] n n k2 n = 1 and the scattering cross section is defined as 2p ∞ (2n + 1) a 2 + b 2 Csca = ––– [11.2]9 (| n| | n| ) 2 k n = 1 In these equations k is the wave number, and defined as k = 2pN / λ, λ is the light wavelength, N is the refractive index of the medium the nanoparticles are suspended in, and an and bn are the scattering coefficients. The scattering coefficients an and bn are defined as mψn(mx)ψ′n(x) – ψn(x)ψ′n(mx) ψn(mx)ψ′n(x) – mψn(x)ψ′n(mx) and bn = –––––––––––––––––––––––––– [11.3]9 an = –––––––––––––––––––––––––– mψn(mx)ξ n′ (x) – ξn(x)ψ′n(mx) ψn(mx)ξ n′ (x) – mξn(x)ψ n′ (mx)

Σ

Σ

Here x = kr and is the size parameter, r is the radius of the nanoparticles, m = n / N is the relative refractive index, n is the refractive index of the particle, and ψn and ξ n are Riccati-Bessel functions. As the mean free path for bulk silver is larger than the size of the silver nanoparticles, the refractive index is modified by surface scattering of the electrons.12,13 We take this into account by introducing the extended Drude model to modify the refractive indices prior to use in the Mie theory. The extended Drude model states that the complex dielectric constant e consists of contributions from the conduction electrons A1 and A2 and the bound electrons B1 and B2, as in the following expression: ε(ω, r) = ε1 + iε2 = (n2 – k2) + i(2nk) = (A1 + B1) + i(A2 + B2)

[11.4]

In this equation n is the refractive index, k is the absorption coefficient, ωP2 ω P2 ω 0 A1 = 1 – –––––––– and A = ––––––––––– 2 ω2 + ω02 ω(ω2 + ω02)

[11.5]

where ω is the frequency, ωP = 4pNe2 / m* is the plasma frequency, ω0 = 1/τs is the collision frequency, N is the density of electrons, e is the electron charge, m* is the effective mass of an electron, and τs is the collision time.12,13 To modify the dielectric constant for nanoparticles using the extended Drude model A1 and A2 are first calculated for bulk silver and then subtracted from ε1 and ε2 to find B1 and B2. ω0 is then modified to depend on the radius r and the Fermi velocity vF, as follows: ω0(r) = ω0 + vF / r.12,13 A new A1 and A2 are then found using the new collision frequency and used to calculate the modified dielectric constant. These calculations utilized a prewritten FORTRAN code that was modified using the Drude model to make the program more accurate.9,12–13 After using this program to calculate the absorption cross-section for an individual silver nanoparticle, Beer’s law was used to calculate the absorption of a deposition.14 In


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the UV region the simulated absorption compared well with the absorption measurements. However, in the visible and IR regions of the spectrum, due to the fact that the theory ignores all other contributions to optical absorption, the simulation did not match with the measurement. Thus, Mie theory is useful around the resonance frequency, but the broad spectrum of the lamp needs to be considered in an accurate model of the absorption.

11.3.5 Bruggeman model An effective medium theory, due to Bruggeman,10 was found to accurately predict the absorption of Ag nanoparticle films. In such a theory, the average dielectric function of an inhomogeneous medium is found by averaging the dielectric function of the medium’s constituents, taking into account their respective volume fractions in the medium. The most popular effective medium theories are the Maxwell Garnett theory and the Bruggeman theory. Research has shown that the Maxwell Garnett theory breaks down with high-volume fractions of material suspended within the medium.9,15–16 The calculations using the Maxwell Garnett theory do not compare well to measured absorption, confirming the well-known fact that Maxwell Garnett theory cannot describe inhomogeneous media at high-volume fractions. The Bruggeman dielectric function has been shown to work well with higher volume fractions.9,10 The Bruggeman dielectric function is defined by the expression: ε – εAV εm – εAV f –––––––– + (1 – f ) –––––––––– = 0, ε + 2εAV εm + 2εAV

[11.6]

where ε is the dielectric function of the particles in the medium, εm is the dielectric function of the medium, εAV is the average dielectric function, and f is the volume fraction of the particles contained in the medium.9 Once the average dielectric function is found, the imaginary portion of the refractive index and the absorption coefficient for the effective medium can be calculated by the expression: α′ = ––––, 4pk λ

[11.7]

where k is the imaginary part of the refractive index and λ is the wavelength of light.14 From this, using the Beer-Lambert law,14 the absorption spectra can be calculated. A graph comparing the absorption results using Bruggeman’s theory with the measured absorption is shown in Fig. 11.5.

11.4 Heat equation simulations of the photonic curing process To model the sintering of the silver nanoparticle film, we solved the heat equation under the conditions of radiative heating from the top surface, convective cooling


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11.5 Graph displaying the absorption vs. wavelength for silver nanoparticles comparing a measured absorption that has a thickness of 1.3 µm with the absorption calculated applying Bruggeman’s theory using a thickness of 150 nm.

of the top surface, and conductive cooling from the bottom surface using the relevant solvers built into the fluid dynamics and heat transfer modeling package Fluent. The results give the simulated temperature that the nanoparticles reached as a result of the photonic curing process as a function of time. These two properties are fundamental in understanding the solid state sintering process.17,18 Using this software allowed us to model the temperature profile of a silver nanoparticle film during the photonic curing process, the amount of time the film took to cool following heating, the progression of the melting of the film, and the effect of different deposition substrates upon the film temperature. These simulations can help explain how the silver nanoparticle films are sintered so rapidly and completely and may be used as a guide to predict the optimum settings for the photonic curing system. The physical modeling of the nanosilver film was done using Gambit version 2.4.0. Gambit is a geometric modeling and grid generation tool that creates the geometries that are used in Fluent. In Gambit a 10 × 100 × 100 slab was created as Gambit is a unitless program. A mesh was then applied to the slab with a grid surrounding the edges of every 1 × 1 × 1 volume. The slab was then transported into the Fluent 6.3 program for thermodynamic modeling. Fluent is a computational fluid dynamics program that uses the finite volume method on a grid to calculate fluid flow, acoustics and combustion. Fluent also has heat transfer, phase change, and radiation models, which are the models that were used for this work. Once the slab was imported into Fluent the units for the slab were set so that the slab was a 10 µm × 100 µm × 100 µm volume. After setting the units for the slab the boundary conditions for the simulation were set. The top surface of the slab was set to undergo convective cooling by air along with radiative heating by the


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light from the flash lamp. The sides of the slab were convectively cooled by the air and the bottom of the slab was set to be conductively cooled by a glass substrate. In order to simulate the radiative heating, Fluent asks for the external radiation temperature and the external emissivity to be input. The external emissivity was taken from the earlier experimental measurements and set to 0.99 for the 10 µm thick slab, meaning that virtually all of the radiation would be absorbed by the slab. The external radiation temperature was found using Stefan’s 4 ––––––– law. Stefan’s law states T = √RT / σ , where T is the radiation temperature of a black body, RT is the energy flux on the surface, and σ is the Stefan-Boltzman constant.19 After inputting the data to simulate the heating, the next input is for the convective cooling of the slab by the air. To simulate convective cooling Fluent needs the temperature of the air far from the slab and the heat transfer coefficient for the air. The temperature of the air far from the slab was set to 294 K. Calculating the heat transfer coefficient was done using the Nusselt number. However, the Nusselt number first had to be calculated from the Rayleigh number and the Prandtl number. The Prandtl number is defined as: c µ Prx = ––p––, k

[11.8]

where cp is the specific heat, µ is the dynamic viscosity, and k is the thermal conductivity.20 The Prandtl number is evaluated at the film temperature, which is defined as: (Tw – T∞) Tf = ––––––––, 2

[11.9]

where Tw is the temperature of the wall and T∞ is the temperature far from the wall.20 After finding the Prandtl number the Rayleigh number can be found by multiplying the Prandtl number by the Grashof number, Rax = Grx*Pr.20 The Grashof number for a heated vertical flat plate is gβ (Tw – T∞)x3 Grx = –––––––––––––, v2

[11.10]

where g is the gravitational constant, β is the coefficient of volumetric expansion, x is the characteristic length, and v is the kinematic viscosity.20 For an ideal gas the coefficient of volumetric expansion is β = 1/Tf .20 The Grashof number is also evaluated at the film temperature. Once the Rayleigh and Prandtl numbers have been found, the Nusselt number for free convection at a vertical wall is calculated as: 0.67 Rax1/4 Nux = 0.68 + –––––––––––––––––––– 4/9 , 9/16 1 + (0.492/Pr ) x

[

]


[11.11]

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11.6 Graph showing the simulated temperature vs. time at the center of the slab, using 900 µs of heating with a flash lamp voltage of 1200 V, followed by 900 µs of cooling.

for Rayleigh numbers less than 109,20 After calculating the Nusselt number the heat transfer coefficient can be found from Nuxk h = –––––– x ,

[11.12]

using the thermal conductivity at the film temperature9,20 In Fluent the heat transfer coefficient can only be input as a single value, so to find a heat transfer coefficient that would affect the simulation for the longest period of time, a heat transfer coefficient of 3500 was used which corresponds to a slab temperature of 834 °C. The convective cooling model in Fluent needs the thermal conductivity, specific heat and density of the glass, Mylar, and Kapton substrates. The interior of the slab was specified to be a porous medium containing 33% silver and 67% air to correspond to the volume densities previously measured. The properties of the silver that Fluent required were the density, thermal conductivity, specific heat, melting heat, viscosity, solidus temperature and liquidus temperature. The thermal Table 11.1 Comparison of resistivities obtained using different sintering methods for two silver nanoparticle based inks Material

Curing method

Resistivity (µΩ-cm)

UT Dot (7 nm silver) AgSt2(Novacentrix 25 nm silver)

Furnace Photonic Furnace Laser Photonic

2.1 ± 0.9 2.8 ± 0.8 3.8 ± 0.3 5.3 ± 0.3 7.9 ± 0.5


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conductivity was set to change with the temperature. The solidus and liquidus temperatures were set to 600 °C, which is the temperature the V2 ink has been observed to melt at. A graph of the temperature vs. time is shown in Fig. 11.6. The simulations indicated that the deposition rapidly heated to the melting point and melted during the curing process. Following the end of the pulsed irradiation, the deposition quickly solidified and cooled to room temperature. These results indicate that traditional solid-state sintering models do not apply to photonic curing, as in solid-state sintering the temperatures applied do not melt the materials, and the heat is applied over a long period of time, allowing diffusive mass transport.17,18

11.5 Conclusions In examining the photonic curing process a number of interesting results were found. It was observed that the surface resistivity of a photonically cured silver nanoparticle based Aerosol Jet® printing deposition approached the resistivity of traditional oven and laser-sintered silver. It was shown that there is significant densification of the photonically cured silver, with the photonically cured silver reaching 84% of the density of bulk silver. In measuring light absorption in uncured silver nanoparticle films it was observed that the absorption is broadband, and that the plasmon resonance is not the dominating feature of this absorption. The Bruggeman effective medium model was shown to approximate the absorption for the silver nanoparticle ink. The Fluent thermodynamic modeling program indicated that the silver depositions melted during the photonic curing process, which would mean that solid-state sintering models do not apply to photonic curing.

11.6 References 1. Schroder, K.A., McCool, S. C. and Furlan, W. R. (2006). Broadcast Photonic Curing of Metallic Nanoparticle Films. Technical Proceedings of the 2006 NSTI Nanotechnology Conference and Trade Show, Volume 3, 198–201. 2. Carter, M. and Sears, J. (2007). Photonic Curing for Sintering of Nano-Particulate Material. Advances in Powder Metallurgy & Particulate Materials – 2007: Proceedings of the 2007 International Conference on Powder Metallurgy & Particulate Materials, May 13–16, Denver, Colorado. 3. Colvin, J., Carter, M., Starovoytov, O., Puszynski, J. and Sears, J. (2005). Laser Sintering of Silver Nano-Particle Inks Deposited by Direct Write Technology. Proceedings of the International Conference on Applications of Lasers and Electro-Optics. 4. Khan, A., Rasmussen, N., Marinov, V. and Swenson, O., (2008). Laser sintering of direct write silver nano-ink conductors for microelectronic applications. Proceedings of SPIE. 6879, 687910–687910–11. 5. Colvin, J. (2005). Characterization of Maskless Mesoscale Material Depositions. Master’s thesis. SDSM&T, Rapid City, SD. 6. PCS-1100 Photonic Curing System Operations and Safety Manual. Austin: NovaCentrix Corp., 2007.


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7. PulseForge 3100: Manufacturing Development and Production. 2009. NovaCentrix. 10 Sept. 2009. . 8. Mie, G., (1908). Beiträge zur Optik trüber Medien speziell kolloidaler Metallösungen, Ann Phys., (Leipzig), 25, 377–445. 9. Bohren, C. F. and Huffman, D. R. (1983). Absorption and Scattering of Light by Small Particles. New York: John Wiley & Sons, Inc. 10. Bruggeman, D. A. G., (1935). Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen, Ann. Phys. (Leipzig), 24, 636–79. 11. Lechner, M.D., (2005). Influence of Mie scattering on nanoparticles with different particle sizes and shapes: photometry and analytical ultracentrifugation with absorption optics. J. Serb. Chem. Soc., 70, 3, 361–9. 12. Haiss, W., Thanh, N., Aveyard, J. and Fernig, D. (2007). Determination of Size and Concentration of Gold Nanoparticles from UV-Vis Spectra. Analytical Chemistry. 79, 4215–21. 13. Kreibig, U. and Vonfrags. C. (1969). The Limitation of Electron Mean Free Path in Small Silver Particles. Z. Physik. 224, 307–23. 14. Skoog, D., Holler, F. J. and Nieman, T. (1998) Principles of Instrumental Analysis; Thompson Learning. 15. Maxwell Garnett, J. C., (1904). Colors in metal glasses and in metallic films. Philos. Trans. R. Soc., A203, 385–420. 16. Garahan, A., Pilon, L., Yin, J. and Saxena, I., (2007). Effective optical properties of absorbing nanoporous and nanocomposite thin films. Journal of Applied Physics, 101, 014320. 17. German, R. M. (1996). Sintering Theory and Practice. New York: John Wiley & Sons, Inc. 18. Kang, S. L. (2005). Sintering Densification, Grain Growth, and Microstructure. Oxford: Elsevier Butterworth-Heinemann. 19. Eisberg, R. and Resnick, R. (1974). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. New York: John Wiley & Sons, Inc. 20. Schmidt, F. W., Henderson, R. E. and Wolgemuth, C. H. (1984). Introduction to Thermal Sciences. New York: John Wiley & Sons, Inc.


Part III Sintering of advanced materials


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12 Sintering of aluminium and its alloys M. Qian and G. B. Schaffer, The University of Queensland, Australia Abstract: The conventional press-and-sinter powder metallurgy (P/M) technique is a unique cost-effective method for net shape or near net shape fabrication of complex aluminium parts. The chapter begins by providing a historical account of aluminium P/M and its application in North America, where the industry originated. It then reviews key issues of the press-and-sinter aluminium P/M technique and the science of sintering aluminium and its alloys under nitrogen, including the distinctive roles of magnesium and tin. Key words: aluminium, powder metallurgy, sintering, nitrogen.

12.1 Introduction This chapter is about the sintering of aluminium and its alloys. The scope is restricted to the conventional press-and-sinter powder metallurgy (P/M) routes and to where aluminium differs from other sintering systems. Section 12.2 provides a historical account of aluminium P/M in North America, where the industry originated, and an overview of aluminium P/M applications. Section 12.3 discusses green shape formation from aluminium powder and the importance of the use of internal lubricants. The effect of the sintering atmosphere and dew point control is considered in Section 12.4. A critical review of the surface characteristics of airatomised aluminium powder and the oxidation behaviour of aluminium powder is presented in Section 12.5, which constitutes a basis for understanding the sintering complexity of aluminium. This is followed by Section 12.6, which is concerned with the disruption of the oxide film by powder compaction and the amorphous-tocrystalline transformation of the oxide. Section 12.7 discusses the unique sintering response of aluminium under nitrogen. The thermodynamics is analysed first, followed by the effects of Mg, AlN and Sn. A summary of the commercial grade aluminium P/M alloys and their mechanical properties is given in Section 12.8, and compared to those of ferrous and copper P/M alloys. The future directions for aluminium P/M are considered in Section 12.9.

12.2 Aluminium P/M and its application The first major attempt to manufacture P/M parts with aluminium powder as an important constituent dates back to the 1930s (Howe, 1942), following the invention of the Al-Ni-Fe permanent magnet alloys (ALNICO) by Dr Tokushichi 291 © Woodhead Publishing Limited, 2010

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Mishima of Tokyo Imperial University in 1931 (Cullity and Graham, 2008). The intention was to utilise P/M’s advantages to produce small Al-Ni-Fe magnet products of intricate design with a dense and fine-grained structure. However, the practice of sintering Al-Ni-Fe green bodies made from blended elemental powders encountered considerable difficulties due to the inherent Al2O3 film on each aluminium powder particle, which are not reducible by hydrogen (Schwarzkopf, 1947). The sintering method which finally proved successful was through the use of an Al-50%Fe master alloy, which can be readily disintegrated into fine powder (Howe, 1942; Schwarzkopf, 1947). The introduction of aluminium in this fashion practically eliminated the ruinous oxidation problem with aluminium powder. A detailed bibliography of the work on aluminium P/M prior to 1949 can be found from Bickerdike’s paper (Bickerdike, 1947) and Goetzel’s Treatise on Powder Metallurgy (Goetzel, 1952). The earliest was that by Sauerwald and Elsner in 1925, followed by Kikuchi in 1937 (Bickerdike, 1947). Systematic trials were made to sinter aluminium and its alloys in air, vacuum and ammonia in the 1940s (Kempf, 1940; Bickerdike, 1947; Goetzel, 1950), where ten different binary Al-X systems (X = Mg, Zn, Cu, Fe, Ni, Si, Pb, Sn, Tl and C) and a variety of their combinations were sintered. Table 12.1 provides a snapshot of some of these early efforts; useful properties were attained from pressing and sintering aluminium in air or vacuum. A variety of factors that affect the attendant mechanical properties of the sintered aluminium alloys were identified. These include: (i) the compaction pressure; (ii) alloy composition; (iii) heating rates and atmosphere; and (iv) sintering temperature in relation to the solidus of the alloy Table 12.1 Pressed-and-sintered aluminium alloys in the 1940s (Kempf, 1940; Bickerdike, 1947) Alloy chemistry (wt pct)

Compaction pressure (MPa)

Sintering Sintering temperature medium (°C) and time

Al-10Mg 275 427; 24 hr Al-10Mg 768 427; 24 hr Al-10Zn 552 510; 24 hr Al-5Cu 552 549; 4 hr Al-7Zn-3Mg 552 510; 24 hr Al-6Cu 207 590; 20 hr Al-6Cu 207 590; 20 hr Al-6Cu 689 500; 20 hr Al-6Cu 689 500; 20 hr Al-6Cu 689 590; 20 hr

Air furnace Air furnace Air furnace Air furnace Air furnace (quenched) Air furnace Vac. furnace Air furnace Vac. furnace Vac. furnace

Tensile strength (MPa)

Source

37 172 107 223 276

[1] [1] [1] [1] [1]

218 277 210 244 331

[2] [2] [2] [2] [2]

Note: [1]: Kempf, 1940; [2]: Schwarzkopf, 1947. Most data were converted from their English units.



293

(Kempf, 1940; Bickerdike, 1947; Goetzel, 1950). These technical factors are still largely characteristic of today’s aluminium P/M. The SAP material, which denotes ‘Sinter-Aluminium-Pulver’ (sintered aluminium powder), is a related development disclosed in 1949 (Irmann, 1949). The name is deceptive as SAP is in fact a dispersion-strengthened Al-Al2O3 composite fabricated from aluminium powder (Irmann, 1952; Grant et al., 1967; Blakeslee, 1971). Containing up to 21 vol.% of Al2O3, SAP was made by extruding or pressing superfine aluminium flakes (< 1 µm) at 500–600 °C (Irmann, 1952). The high oxide content stems from the fine particle size. For example, the oxide content of an aluminium particle with a diameter of 100 nm is about 20 vol.% (Irmann, 1952). Owing to the extraordinary oxide dispersion strengthening (ODS) effects, the compositionally simple (Al and O) SAP materials were superior to any other aluminium material at temperatures above 200 °C, including even those precipitation-hardened (Blakeslee, 1971). The ODS-SAP approach is still pursued today with micrometer-sized ( 0 at POeq2 = 2.91 × 10259 Pa, which means that Al2O3 is no longer thermodynamically stable and will decompose into Al and O2. Metallic Al is established. The chemical disruption of the Al2O3 oxide film by magnesium helps to initiate the sintering of aluminium while the virtually oxygen-free local sintering atmosphere created by magnesium enables sintering to fully develop. Both roles of magnesium are crucial for the effective sintering of aluminium.

12.7.3 The role of AlN Aluminium is generally sintered in the presence of a liquid phase. Liquid-phase sintering (LPS) offers advantages over solid-state sintering of fast densification, high sintered densities and mechanical properties, and good consistency in the performance of the sintered products. The sintering shrinkage or densification that occurs during LPS can originate from a variety of processes (German, 1996), including: (i) solidstate sintering either before the liquid forms or after the liquid has disappeared; (ii) particle rearrangement due to capillary forces which pull particles to a higher coordination number; (iii) solution-reprecipitation through the liquid due to the difference in the mean curvature between either different parts of a particle or particles; and (iv) pore filling by persistent liquid in the later stage of sintering. While all these mechanisms occur during the LPS of aluminium alloys in nitrogen, the process is further distinguished by the formation of AlN, which plays a central role in the densification of the aluminium compacts (Schaffer et al., 2006; 2008). The distinct features of LPS of aluminium alloys in nitrogen are underlined below through the LPS responses of four variants of 2xxx alloys in argon and nitrogen: (i) A1-3.8Cu1Mg; (ii) Al-3.8Cu-1Mg-0.7Si; (iii) Al-3.8Cu-1Mg-0.1Sn; and (iv) Al-3.8Cu-1Mg0.7Si-0.1Sn. Right cylinders (φ10mm×10mm) made from air-atomised A1 powder (d50 = 77µm) and elemental Cu, Mg, Si and Sn with a mean particle size of < 45 µm were investigated using dilatometry. The samples were pressed at 200 MPa and had a typical green density of 2.56 g cm-3 (Schaffer et al., 2008). © Woodhead Publishing Limited, 2010


311

12.14 Dilatometer curves of four alloys sintered under argon at 590 °C. There is a single expansion and shrinkage event in all cases. Sintering is essentially complete after 10 min at temperature (Schaffer et al., 2008).

The sintering responses for the four alloys under argon are shown in Fig. 12.14. There is a single expansion event that initiates at about 480 °C followed by a single shrinkage event, wherein the rate of shrinkage decays monotonically over time. Sintering is effectively complete for all four alloys after 10 min at temperature; additional shrinkage thereafter is slow. Silicon increases the liquid volume and therefore enhances sintering. However, adding Sn to either Al-3.8Cu1Mg or Al-3.8Cu-1Mg-0.7Si is detrimental. Similar dilatometer curves under nitrogen are shown in Fig. 12.15. Although the expansion event is similar to that in argon, shrinkage is markedly altered by nitrogen. Shrinkage occurs in three distinct stages. There is a first rapid contraction followed by an arrest; then a second contraction where the shrinkage rate is much less than that during the first; leading directly into a third, rapid contraction. The Al-3.8Cu1Mg base alloy sinters slowest and shrinks the least. In contrast to sintering under argon, adding Sn increases both the shrinkage rate and sintering densification for each of Al-3.8Cu-1Mg and Al-3.8Cu-1Mg-0.7Si under nitrogen, while Si remains beneficial. Adding Si and Sn together proves to be the most efficacious. The difference in the sintering response under nitrogen and argon is most obvious when the argon and nitrogen curves are superimposed, as shown in Fig. 12.16 for the Al-3.8Cu-1Mg-0.7Si(-0.1Sn) alloys. The dilatometer curves for the first shrinkage event under argon and nitrogen are identical. However, a distinct difference develops after that. The shrinkage curves under argon are also expected from classical sintering theory. The sintering rate is initially rapid as the particles re-arrange in response to the sintering stress, σs (Kingery, 1959; Kingery et al., 1961) as:


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12.15 Dilatometer curves of four alloys sintered under argon at 590 °C. There are three distinct events in all cases (Schaffer et al., 2008).

2γLV σs = –––– rp – ∆Pgas

[12.11]

where γLV is the surface tension of the liquid, rp is the pore radius and ∆Pgas is the difference in pressure between the gas trapped in closed pores and the sintering atmosphere. Essentially, the surface tension of a wetting liquid pulls the particles

12.16 Dilatometer curves of (a) Al-3.8Cu-1Mg-0.7Si and (b) Al-3.8Cu1Mg-0.7Si-0.1Sn under argon and nitrogen. The expansion and initial shrinkage are similar under both atmospheres, but the total shrinkage is substantially greater under nitrogen. There is a premature arrest in the shrinkage in the alloy without tin under nitrogen.



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12.16 Continued.

together. The sintering rate in this stage is high because the process is not dependent on atomic migration. The sintering rate then decays monotonically over time as primary re-arrangement is exhausted and diffusion induced secondary re-arrangement processes take over. This occurs in most sintering systems even though multiple densification mechanisms operate during sintering. However, the same sintering rate law over time is not observed for the sintering of aluminium under nitrogen, where the rate accelerates twice (see Fig. 12.15). This is correlated with the formation of AlN. The first shrinkage event under nitrogen, which is identical to that under argon, is similarly due to the change in wetting characteristics between the liquid and the surface of the Al particles, leading to primary re-arrangement, as it is in argon. The second shrinkage event is believed to originate from the formation of AlN, which reduces the pressure in the pores relative to the external atmosphere (Schaffer et al., 2006). Consequently, the sintering stress σs will increase, which will increase the flattening strain rate during solution-reprecipitation (Svoboda et al., 1996). The consumption of nitrogen within closed pores thus leads to an increase in the shrinkage rate and a second stage of densification. This will only occur in aluminium sintered under nitrogen and not under argon. The rapid development of the third shrinkage event suggests that this stage is not diffusion controlled, but due to the combined effect of pore filling and the closure of pores (Schaffer et al., 2006). Although pore filling happens over the whole sintering period (Lee et al., 1998), it is expected to dominate in the final stages as the pressure differential destabilises the meniscus forces. The formation of AlN thus plays an active role in the sintering of aluminium. The AlN forms as individual nanoscale AlN crystals. Figure 12.17 shows an image of the AlN formed in a nitrogen sintered Al-2Mg-2Si-0.25Cu alloy. The AlN crystals identified have a hexagonal structure with the lattice parameters of a = b = 3.1 Å and c = 5 Å, typical of the AlN phase.


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12.17 TEM images with an EDS (energy dispersive X-ray spectroscopy) spectrum showing the nanoscale AlN crystals formed in Al-2Mg-2Si0.25Cu sintered under nitrogen at 590 °C for 60 min. The AlN phase has an hcp structure with the lattice parameters being determined to be a = 3.1 Å and c = 5 Å. The Mg2Si was liquid during sintering.

12.7.4 The role of tin The role of tin is unique. As shown in Fig. 12.14 and 12.15, a trace amount of tin aids the LPS of aluminium under nitrogen but hinders LPS under argon. The surface tension of liquid tin is about 40% less than that of liquid aluminium (Brandes and Brook, 1992). In-situ XPS analyses revealed that tin will first



315

segregate to the aluminium powder surface, just beneath the oxide film, at temperatures above 505 K during sintering (Kondoh et al., 2001). It will then present as a liquid film on the aluminium powder surface once the original oxide film is destabilised by magnesium (Kondoh et al., 2001). Hence tin can effectively decrease the surface tension of the system. The change in surface tension will be beneficial to sintering if it transforms the liquid from non-wetting to wetting. However, it will be detrimental to sintering for a wetting liquid because a decrease in the surface tension will lessen the capillary pressure and therefore the sintering stress. This could be responsible for its detrimental effect demonstrated on the LPS of Al-Cu-Mg(-Si) alloys under argon. Tin is, however, known to retard the nitridation of solid aluminium under nitrogen (Kondoh et al., 1999, 2001; Sercombe and Schaffer, 2006). It is therefore also expected to retard the nitridation of liquid aluminium. The first shrinkage event in the tinned alloy is identical under both atmospheres (Fig. 12.16(a).) This indicates that neither system has nitrided so that the sintering response is the same. Without tin, the first shrinkage event terminates prematurely under nitrogen (Fig. 12.16(b).) This is consistent with a nitride layer forming on the surface of the liquid aluminium, which is expected to deteriorate wetting in the same way that an oxide layer does. Sintering only commences again when the nitrogen in the pore is consumed, establishing a pressure difference across the sample. It is thus beneficial to avoid the formation of AlN in the early stages of the LPS under nitrogen in order for the first shrinkage event to fully develop. As evident from Fig. 12.14, the difference is significant in the first shrinkage event between the Al-Cu-Mg(-Si) alloys with and without tin. On the other hand, the formation of AlN will be desired in the final stages of sintering from both a pore filling and pore closure perspective. Fortunately, tin will be gradually consumed as sintering proceeds. As a result, tin will not interfere with the formation of AlN in the final stages of sintering. A trace amount of tin is therefore an effective process control agent for the LPS of aluminium in nitrogen.

12.8 Mechanical properties of sintered aluminium alloys Although Alcoa® no longer offers a standard aluminium P/M premix, alloys similar to 601AB, 201AB, 602AB and 202AB, or their variants, are still among the most important commercial aluminium P/M alloys. Table 12.2 lists their mechanical properties with reported chemical compositions. The tensile strength typically ranges from 110 to 330 MPa, depending on the green density, alloy composition and post-sintering treatments. Current commercial grade aluminium P/M alloys and their mechanical properties are listed in Table 12.3. AMPAL’s 2905 is a tin-containing alloy developed for sintering under nitrogen. ECKA’s AlSiCuMg is a high silicon wear resistant P/M alloy. Both AMPAL’s 7775 and ECKA’s AlZnMgCu are equivalent to wrought alloy 7075.


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Table 12.2 Typical mechanical properties of nitrogen sintered (15 min at 620°C) Alcoa® aluminium P/M alloys Alloy

Compacting Green Sintered Temper Tensile Yield Elongation Hardness pressure density density strength strength (pct) (HRH) (MPa) (MPa) (MPa) (g cm23) (g cm23)

601AB 96 2.29 2.45 165 2.42 2.52 345 2.55 2.58 602AB 165 2.42 2.55 345 2.55 2.58 201AB 110 2.36 2.53 180 2.50 2.58 413 2.64 2.70 202AB 180 2.49 2.56

T1 T4 T6 T1 T4 T6 T1 T4 T6 T1 T4 T6 T1 T4 T6 T1 T4 T6 T1 T4 T6 T1 T4 T6 T1 T4 T6

110 141 183 139 172 232 145 176 238 121 121 179 131 134 186 169 210 248 201 245 323 209 262 332 160 194 227

48 96 176 88 114 224 94 117 230 59 62 169 62 65 172 145 179 248 170 205 322 181 214 327 75 119 147

6 5 1 5 5 2 6 6 2 9 7 2 9 10 3 2 3 0 3 3.5 0.5 3 5 2 10 8 7.3

55–60 80–85 70–75 60–65 80–85 75–80 65–70 85–90 80–85 55–60 65–70 55–60 55–60 70–75 65–70 60–65 70–75 80–85 70–75 75–80 85–90 70–75 80–85 90–95 55–60 70–75 45–50

Chemical compositions: 601AB: Al-0.25Cu-1.0Mg-0.6Si; 201AB: Al-4.4Cu-0.5Mg-0.8Si; 602AB: Al-0.6Mg-0.4Si; 202AB: Al-4.0Cu Source: Stevenson, 1984; ASM 1998

12.9 Future trends The conventional press-and-sinter P/M technique is a unique cost-effective method for net shape or near net shape fabrication of complex aluminium parts. Although aluminium powder is readily available, aluminium P/M unfortunately remains a minor participant in the overall aluminium powder market. Similar to the development of any other manufacturing industry, the future of aluminium P/M will largely depend on more value-added innovative designs and products and improved productivity. This will require relentless innovation in R and D. At present aluminium P/M parts are used primarily in low-stress applications where the combination of low-grade properties and net shape forming capability is required. On the one hand, this is because commercial grade aluminium P/M


© Woodhead Publishing Limited, 2010 240 120 400 (T76)

2.67 2.47 2.55

Source: EPMA-JPMA-MPIF, 2009; AMPAL, 2009; ECKA, 2009

55 HRB 55 HB

220 165 160

2.5–2.7 2.50

1–2 5 2

3.8 5

100 HB 40 HB 150 HB

63–80 HRH 93–97 HRH 53–57 HRH 78 HRH 42 HRB

1.9 2.4–3.3 4.4 3.5

2.73 2.62 158 87 2

175 171–186 232 145

bal bal bal bal bal bal bal bal bal

Hardness

2.5–2.6 185 2.5–2.6 231–261 2.5–2.6 2.65 210

Elongation pct

bal bal bal bal

Yield MPa

Al-0.6Mg-0.5Si-0.1Cu 0.1 0.6 0.5 Al-3.4Cu-0.6Mg-0.5Si 3.4 0.6 0.5 Al-2Mg-0.4Zn-0.5Cu 0.5 2 0.4 AMPAL 2712 3.6–4.0 0.8–1.2 0.6–0.9 0.45AMPAL 2905 2.8–3.2 1.0–1.4 0.15–0.35 0.75 AMPAL 6711 0.15–0.35 0.8–1.2 0.65–0.9 AMPAL 2712A 4.4 0.5 0.6 AMPAL 7775 0.7–1.3 2.2–2.8 6.0–8.0 ECKA 13 or AlCuMg 4.5 0.5 ECKA 123 or AlCuSiMg 4.5 0.5 0.7 ECKA 231 or AlSiCuMg 2.5 0.5 14 ECKA 321 or AlMgSiCu 0.2 1 0.5 ECKA 431 or AlZnMgCu 1.5 2.5 5.5

UTS MPa

Sintered properties Density g cm-3

Typical chemical composition (wt pct)

Cu Mg Si Zn Sn Al

Alloy

Table 12.3 Selected commercial grade aluminium P/M alloys

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alloys are still very limited; design engineers do not specify P/M parts for new applications because of limited options. On the other hand, existing aluminium P/M alloys do not meet the needs for an expanded range of applications because they do not possess the required modulus, wear resistance or elevated temperature property retention (Hunt, 2000). Although these limitations were well recognised a decade ago, progress has been slow. Innovation is needed from a research perspective for the development of a wide range of high performance aluminium P/M alloys that would be suited to medium- to high-stress applications, including those subject to dynamic stresses. In particular, post-sintering heat treatment should be fully exploited. Innovative alloy design for high-strength aluminium P/M alloys should be directed to using P/M as a means of net shape forming and post-sintering heat treatment as a means of strengthening by precipitation hardening. Heat treatment is a key factor to develop a significantly high level of mechanical property for aluminium P/M alloys (Martin and Castro, 2003). P/M has significant advantages over casting in composite design and fabrication. In addition to the usual tensile strength data, a significant improvement in the stiffness of aluminium P/M parts, e.g. > 100 GPa, at a cost-effective approach will open new markets for aluminium P/M. Aluminium P/M composites thus still represent an important research direction. They are likely to find applications in advanced transmissions such as dual-clutch designs and continuously variable transmissions. Fatigue is an important design consideration for P/M parts subject to dynamic stresses. In general, the fatigue strength of press-and-sinter aluminium P/M parts is about half that of wrought alloys of corresponding composition (ASM, 1998). While this is suitable for low-stress non-dynamic applications, much improved fatigue strengths are necessary in order for the aluminium P/M parts to penetrate into highly loaded applications in the drive train systems of automobiles. Because of the involvement of pores, the fatigue of a sintered aluminium alloy may differ appreciably from that of a cast or wrought alloy of similar composition. At present experimental data on the fatigue of sintered aluminium alloys are still very limited (Grayson et al., 2006). Net shape or near net shape forming is a key feature of the press-and-sinter approach. Zero-dimensional change is designed for virtually all sintered components assuming the attendant properties are satisfied. Aluminium powder materials have excellent compressibility. Process upgrades for improved green density uniformity in combination with compositional control and use of a low sintering temperature will facilitate precision dimensional control. Zero-dimensional change will make aluminium P/M a precise art of the quick and complex for cost-effective manufacturing.

12.10 Acknowledgements The authors are pleased to acknowledge the valuable help received from Dr Peng Yu (Section 12.7.1 and Fig. 12.11); Dr Martin Balog (Fig. 12.9 and 12.10); Dr Ming Yan



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(Fig. 12.17); Mr Stephen Bonner (Fig. 12.1 and 12.7); Mr Rizwan Abdul Rahman Rashid (Fig. 12.12); Prof Katsuyoshi Kondoh (Fig. 12.13); and Prof Edward L Dreizin (Fig. 12.8). US Metal Powders, Inc and AMPAL Inc. are acknowledged for providing the information used in Table 12.3 and Metal Powder Products (MPP) for Fig. 12.1 and 12.2. Useful discussions with Dr Shuhai Huo are appreciated. This work has been supported in part by the Australian Research Council (ARC), the ARC Centre of Excellence for Design in Light Metals, the CAST-CRC and AMPAL Inc. The document delivery team at the Dorothy Hill Physical Sciences and Engineering Library of The University of Queensland are gratefully acknowledged for the provision of a significant number of the references listed below.

12.11 References AMPAL (2009), Aluminium Powder Metallurgy. Available from: http://www.ampal-inc. com/aluminum-powder-metallurgy.htm [accessed 20 August 2009]. Anon. (1969), ‘High strength sintered aluminium parts arrive’, Metalworking Production, 113, No. 25, 7. Anon. (2003), ‘Big Three eye lightweight PM con rods: Aluminium in the spotlight as automakers look for weight loss …’ Metal Powder Report, 58, No.10, 26–7. Anon. (2006), ‘PM aluminium drives forward in new BMW breakthrough’, Metal Powder Report, 61, No. 2, 13–15. Anon. (2008), ‘Japan’s powder shipments up: prize winners are revealed’, Metal Powder Report, 63, No. 2, 20–6. Arbuzova L A, Danilkin V A and Kunin L L (1976), ‘Amount of H2O on the surface of an aluminum powder’, Powder Metallurgy and Metal Ceramics, 15, 663–5. ASM (1998), ‘Conventional aluminium powder metallurgy alloys’, in ASM Handbook, Vol. 7, Powder Metal Technologies and Applications, Materials Park, ASM, 835–839. Balog M, Simancik F, Bajana O and Requena G (2009), ‘ECAP vs. direct extrusiontechniques for consolidation of ultra-fine Al particles’ Mater. Sci. Eng. A, 504, 1–7. Beaumont F (2000), ‘Aluminium P/M: Past, present, and future’, Inter. J. Powder Metallurgy, 36, No. 6, 41–3. Bickerdike R L (1947), ‘An aluminium alloy made by powder metallurgy’, in Powder Metallurgy, Vol. 9, Selected Government Research Reports, London, Her Majesty’s Stationery Office (1951), 119–28. First published by the Iron and Steel Institute in Special Report No. 38, 1947. Blakeslee H W (1971), Powder Metallurgy in Aerospace Research – A Survey, Washington D. C., NASA Aeronautics and Space Administration, 73–9. Brandes E A and Brook G B (1992), Smithells Metals Reference Book, 7th ed., Oxford, Butterworth-Heinemann. Capus J M (2005), Metal powders: A global survey of production, applications and markets to 2010, 4th ed., Oxford, Elsevier, 98–101. Clauser H R (1946), ‘Aluminium alloy bearings for heavy duty applications’, Materials and Methods, 24, No. 3, 633–6. Cullity B D and Graham C D (2008), Introduction to Magnetic Materials, 2nd ed., Hoboken, NJ, Wiley-IEEE, 485–90. Daver E M and Trombino C J (2006), ‘State of the North American PM industry – 2006’, Inter. J. Powder Metallurgy, 42, No. 4, 35–40.


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13 Sintering of titanium and its alloys M. Qian and G. B. Schaffer, The University of Queensland, Australia and C. J. Bettles, Monash University, Australia Abstract: Powder metallurgy (P/M) is a particularly attractive manufacturing process for titanium (Ti) components as conventional shape casting routes are not practical due to the reactivity of molten Ti with most gas atmospheres and with most materials which might serve as crucibles. This chapter discusses the conventional press-and-sinter Ti P/M process. It begins by providing a historical overview of the methods of production for Ti powder and the characteristics of the powders produced. It then reviews key issues in the cold pressing and sintering processes of Ti and its alloys. Key words: titanium, powder metallurgy, sintering, cold pressing, powder compaction.

13.1 Introduction Currently aerospace parts makers often buy about eight times as much titanium as needed for the finished part (DuPont, 2006). The target set by Lockheed Martin for the F35 Program is to reduce the buy-to-fly ratio to 5:1 (Barnes et al., 2009). Clearly, there is an obvious economic advantage to producing near net shape titanium parts, but there are also sound processing advantages as titanium is difficult to machine and not easy to recycle through the conventional remelting process. However, unlike many metals, the conventional methods of shape casting are not practical with titanium because molten Ti reacts with most metallic and non-metallic materials which might serve as crucibles for melting prior to casting. For this reason, skull melting techniques have been developed for Ti but these processes require expensive equipment and careful control. In addition, a highpurity argon atmosphere needs to be sustained in the crucible and the mould during melting and casting. These processing difficulties of casting make Ti P/M attractive. In addition, there are mechanical property advantages of finer grain size and greater chemical homogeneity for titanium parts made from powders (Friedman, 1970). A titanium part can be made from powder through a range of techniques. These include press-and-sinter, press-sinter-and-hot-work, extrusion or direct roll compaction of loose powders, hot-press-and-machine, hot isostatic pressing and metal-injection-moulding-and-sinter. The press-and-sinter route is technically the simplest and economically the most attractive approach. The scope of this chapter is thus restricted to the conventional press-and-sinter P/M route and to where titanium differs from other sintering systems. Section 13.2 provides an overview of the 324 © Woodhead Publishing Limited, 2010


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methods of production for Ti powder and the characteristics of the various types of Ti powders produced. Section 13.3 discusses the cold pressing characteristics of Ti powder. Section 13.4 is divided into three subsections. The sintering of commercially pure (CP) Ti is discussed in Section 13.4.1. Section 13.4.2 focuses on the sintering of Ti-6Al-4V (all in wt.% unless stated otherwise). This is followed by a case study on enhanced sintering by alloy design (Section 13.4.3). A summary of the mechanical properties of press-and-sinter Ti materials is given in Section 13.5. The future directions for Ti P/M are considered in Section 13.6.

13.2 Titanium powder 13.2.1 Methods of production and powder characteristics The titanium powder market is small, even when simply measured against the total global titanium market. There is no reliable information about tonnages produced, but the total powder consumption (from all production processes) was thought to be less than 10,000 tpa in 2007 whereas the global sponge market was reported to be ~120,000 tpa in 2006, and this was expected to increase to 225,000 tpa by 2011 (Hogan et al., 2008). Clearly most of this is used as feedstock for ingot-based processing. Currently there are few powder producers worldwide. Table 13.1 lists those producing commercial quantities of titanium powder at present. The powder production routes can broadly be divided into those based on sponge production, those using ingot as the starting material and those using variants of gas atomisation and rotating electrode processes. Production of titanium powder

Table 13.1 Companies producing commercial quantities of titanium powder Company

Powder process

Country

Bongen Ti (China) Company Cristal Global (formerly ITP) Crucible Research Metalysis Phelley Material PyroGenesis Inc Reading Alloys Se-Jong Materials Ltd. Starmet Corporation Sumitomo Corporation TLS Technik GmbH ToHo Titanium Company Ltd. Zunyi Titanium Company

GA and HDH Armstrong GA FFC HDH Plasma Atom. HDH HDH PREP GA and HDH GA HDH Sponge

China USA USA UK USA Canada/Greece USA Korea USA Japan Germany Japan China

GA: gas atomised; HDH: hydrogenation-dehydrogenation; FFC: Chen-Fray-Farthing; PREP: plasma rotating electrode process


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did not begin in a serious manner until the late 1940s, although sponge had been available since the development of the Hunter process in 1910 (Hunter, 1910; Kroll, 1940a). A timeline for the various processes is shown in Fig. 13.1, and it is clear that most progress has been made since the 1960s (the patents shown in this figure are referenced in the text following). The largest barrier to greater take-up of Ti P/M is the cost of the powder feedstock, and this is directly related to the difficulties associated with handling the highly reactive material. The relative prices of powders produced via these routes are shown in Fig. 13.2, with the average price for aluminium, copper and iron powders included for comparison. Several projects are being conducted throughout the world attempting to reduce the cost through novel processing, most avoiding the highly reactive molten state. Similar to any P/M process, particle size, size distribution and morphology are important characteristics of a powder product. However, for Ti P/M there are added requirements of low bulk contaminant levels (oxygen, nitrogen, hydrogen and chlorine being the most problematic) and low contents of surface oxide layers. These characteristics all contribute to the quality of the final product. The salient properties of the powders produced by the various processes are discussed in the paragraphs below, and a summary of the powder properties is given in Table 13.2. Figure 13.3 presents the particle size distributions of various commercial powders, and Fig. 13.4 shows the three dominant morphologies found in titanium powder products. Titanium metal is most commonly extracted from the natural ore by firstly a chlorination step to form TiCl4 and secondly a reduction of the chloride using

13.1 Timeline for the development of processes to produce titanium powder.



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13.2 A schematic showing the prices for titanium powders produced by the various routes (prices from www.titaniuminfogroup.com, Data sheet 16). Prices for iron, aluminium and copper are included for comparison. Note that the price axis is logarithmic. Table 13.2 Average chemical and physical properties of powders produced by the various processes Description

Sponge (Kroll/Hunter)

Sponge HDH PREP™ (CaH2)

Gas atomised

Oxygen Nitrogen Hydrogen Chlorine Particle Size Median (µm) Spread Flow rate (s) Relative Tap Density (%)

0.13 0.03 0.07 0.13

0.19 0.06 0.34 0.004

0.15–0.3 0.01 0.03–0.05 0.06–0.15 0.002 0.06–0.08 –

0.1–0.3 0.01

75 20–150 20 20–26

40 10–150 15 20–30

90 25–150 75 30–37

80 20–200

175 100–300 25–35 65

–

60–70

either magnesium (Kroll process (Kroll, 1940a; Kroll, 1940b; Kroll, 1950; Evdokimov, 2001)) or sodium (Hunter process (Hunter, 1910)). In more recent times, in an effort to develop a continuous process, vapour phase reactions have been investigated for both the Hunter and Kroll routes (Leland, 1996; Hansen and


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13.3 Particle size distributions for commercial or near-commercial powder processes.

Gerdemann, 1998). Alexander developed a process for the direct reduction of TiO2 in the presence of CaH2 (Alexander, 1947). A similar process was later taken up in Russia (Froes, 1998). The product of the reduction stage from all of these processes is titanium sponge. In the case of the Hunter or Kroll routes, the majority of the sponge produced is vacuum distilled to remove residual chlorine and melted and resolidified to form ingot product. This sponge can, however, become the basis for titanium powder (again after vacuum distillation to reduce the chlorine content). After reduction using magnesium or sodium, the sponge is nodular in form and may be many centimetres in size. The preparation of powder for P/M applications requires a crushing step and this is not always easy as high-purity titanium is ductile (see Table 13.3). Under these circumstances, the sponge may be hydrogenated to embrittle it, and then crushed to a powder. Hydrogen removal is achieved through a vacuum heat treatment. This hydrogenation-dehydrogenation (HDH) approach is also applied to ingot, which is discussed in the next paragraph. The major disadvantage of sponge material is the high chlorine content which, even after some purification, may be up to 0.15wt.%. Chlorine causes problems with densification, and leads to reductions in the fracture toughness and fatigue properties of the final products (Kim et al., 1984; Gerdemann and Alman, 2000; Alman and Gerdemann, 2004). The powder produced by the CaH2 reduction process, which is considerably finer than that from the Kroll or Hunter process, but still irregular in shape, does not suffer from chlorine contamination. However,



(a)

(b)

(d)

(c)

(e)

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(f) 13.4 Titanium powders: (a) and (b): titanium sponge; (c) and (d): CP Ti HDH powder; and (e) and (f) gas atomised Ti-10V-2Fe-3Al alloy powder.


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it generally has a hydrogen content of ~0.34wt.% and this can cause serious embrittlement problems (Moll and Yolton, 1998; Gopienko and Neikov, 2009). Both processes can produce powder with acceptable oxygen levels (~0.13wt.% for the chlorine-based routes and ~0.19wt.% for the CaH2 route). The powders are irregular in shape, often being likened to coral in morphology. The median particle sizes are 75 µm and 40 µm respectively (see Fig. 13.4). The flow characteristics are acceptable with flow rates (ASTM B213) of 20 and 15 seconds respectively, but the relative tap densities are poor, being 20–26% and 20–30% respectively (Gopienko and Neikov, 2009). To overcome the impurity problems found with sponge, the HDH process was applied to high-purity ingot. The feedstock, with low levels of chlorine, oxygen and nitrogen, is treated in a hydrogen atmosphere to form brittle TiH2, which is then crushed in a comminution stage and reheated under vacuum to remove the hydrogen and form powdered titanium metal. The particles are angular in shape and the size is largely controlled by the choice of crushing parameters. This morphology can be disadvantageous with respect to flow and packing behaviour, but in general there are gains with lower compaction pressures. The major problems are residual hydrogen, which can be as high as 0.16wt.%, and increased oxygen levels which can be as much as 800 ppm greater than the initial feedstock (Froes and Eylon, 1990). The median particle size is generally ~90 µm, relative tap densities are 30–37%, but flow characteristics are poor (up to 75s). Since the 1980s there has been renewed interest in this route, especially in Japan (Toho Titanium Company, 1993; Toho Titanium Company, 1995; Nippon Steel Corporation and Toho Titanium Company, 1995; Nippon Steel Corporation, 1995; Sumitomo Titanium Corporation, 2003). There are two commercial processes for the preparation of spherical powders: rotating electrode process (REP) or plasma rotating electrode process (PREP™) (Nuclear Metals Inc., 1963, 1984; State Street Bank & Trust Co., 1974; Starmet Corp., 1993), and gas atomisation (GA) (Crucible Materials Corp., 1985, 1989; 1992). The PREP™ process is used for commercial purity titanium powder, but is most commonly associated with the preparation of titanium alloy powders. The feedstock for this process is a metal bar, either pure titanium or an alloy, which also acts as the consumable electrode for the process. The bar is spun at a high speed in an inert atmosphere while the end is melted by gas plasma arc. Small droplets fly off the end of the bar and are quenched in flight as spherical powder particles (Abkowitz et al., 1971). The powders are relatively coarse, with a median size of ~175 µm, although some refinement is possible with careful selection of the process parameters. Both Nachtrab and Schwanke report that PREP™ powders are pourable and that tap densities of up to 65% are possible (Nachtrab et al., 1992; Schwanke and Schaeffer, 1999). However, other authors have reported that the spherical powder is less amenable to cold consolidation than irregularly shaped powders of an equivalent size (Froes and Eylon, 1990; Moll and Yolton, 1998). The gas atomisation process was developed to use wire feedstock to



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produce spherical powder particles. Crucible Materials Corporation has commercialised the TGA process (Titanium Gas Atomisation) and can produce powders of commercially pure titanium, various titanium alloys and titanium aluminide compositions (Moll, 2000). The powders are reported to have a median particle size of ~100 µm, flow values in the range 25–35s, relative tap densities of 65–70% and oxygen levels under 800 ppm (although this is dependent on the particle size of the powders). An advantage of alloy powders prepared by either of these processes is that the microstructures are uniform, in terms of both composition and grain size. However, the cooling rate for GA is faster than that for the PREP™ process, and these powders generally have the finer microstructure.

13.2.2 Novel production methods under development Two processes are being developed. Armstrong and co-workers developed a lowcost alternative to the Hunter process, which was applied to powder production (Armstrong et al., 1998; Int. Titanium Powder LLC, 2008a, 2008b). The powder from this process is similar to sponge, being described as having a dendritic ‘corallike’ morphology where the dendrite arms are of the order of 1 µm in diameter (Crowley, 2003; Weil et al., 2009; Eylon et al., 2009). The powder tends to be agglomerated and in its ‘as processed’ form can have a median particle size in excess of 400 µm and a relative tap density of less than 8%. Ball milling and jet milling can improve the relative tap density to 12% or 21–34%, respectively. Despite this low density, the compaction behaviour of the powder is similar to that of the commercially available powders (Sathaye et al., 2005). The second process, known as the FFC process, came out of work at the University of Cambridge by Chen, Fray and Farthing and is currently being scaled up to full production by the UK company Metalysis (Chen et al., 2000; Anon., 2004; 2005; 2009). The powder is described as near-spherical in shape, with the size range 20–250 µm, but containing up to 50% porosity. Flow properties are somewhere between those of GA and HDH powders, and the oxygen content can be controlled within a broad range (350–4000 ppm). The quest for cost-effective powders is continuing because of its critical importance to the Ti P/M industry. Novel laboratory or pre-commercial processes are being developed for the production of micron and nanometer size titanium powders. The TiRO™ process, developed in Australia, uses Kroll chemistry but produces powder continuously in a fluidised bed facility. Very little is known about the chemistry or shape of the resulting powders, but it has been reported that the particles may have either a honeycomb or a shell-like morphology, and that the process is sufficiently flexible to tailor morphology to accommodate the packing requirements of various P/M processes (Hogan et al., 2008; Glenn et al., 2009). In Japan, a magnesiothermic reduction process has been developed in which a friable titanium metal powder is produced in a two-stage reaction (Suzuki et al., 1999; Fuwa and Takaya, 2005). Depending on the process conditions, the morphology can be either columnar (40–100 µm in length) or aggregated irregular particles 6–30 µm


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across. In the earlier of the two papers oxygen and nitrogen levels were reported to be as high as 3.4wt.% and 0.79wt.% respectively. In the more recent paper (some six years later) these had been reduced to 0.22wt.% and 0.34wt.%. The oxygen is within tolerable limits at this level, but the nitrogen is still an order of magnitude too high for commercial purposes. Process developments based on a calciothermic reduction reaction have resulted in two experimental processes: EMR, which uses an electronically mediated reaction, and PRP, which is a preform reduction process (Uda et al., 2000; Okabe et al., 2004; Park et al., 2005). EMR produces an agglomerated powder tens of microns in diameter, with the individual particles again displaying the irregular coral-like morphology. It is reported that these particles may be oxygen-free, although higher oxygen contents are possible. Chlorine levels appear to be below 0.06wt.%. PRP also produces homogeneous powder with the coral-like morphology, the size of the primary particles being controlled by processing conditions (but this was usually 1–5 µm). Oxygen levels were usually ~0.66wt.%, but under certain conditions this could be reduced to 0.28wt.%. The above processes result in micron-sized particles, but there is a group reportedly preparing nanosize particles by a route other than ball or cryo milling. General Motors (GM) are using a sonochemical route that is claimed to have significantly fewer processing steps than the Armstrong process (Halalay and Balough, 2008a). The advantage of the process is the fine particle size, generally of the order of 20nm (but with changes to the process parameters this may be increased to 5 µm). The metal formed is either amorphous or nanocrystalline in nature (Halalay and Balough, 2008b). The disadvantage of such fine powders is the high reactivity in air which would normally necessitate processing in a vacuum immediately following production of the powder. The GM powder can be handled in air after the penultimate processing step, which provides some scope for larger scale production, but nonetheless the powder is highly reactive after the final removal of halide salts.

13.3 Powder compaction 13.3.1 Compaction High-purity titanium in the most ductile state is similar to annealed copper in terms of the hardness, modulus, elongation and ultimate tensile strength. Table 13.3 lists the property data of pure titanium, annealed copper and iron. In the powder form, the microhardness of titanium powder varies in a broad range depending on its impurity content, which is determined by the manufacturing process, and particle size (Arensburger et al., 1968). Accordingly, the compression ratio of titanium powder varies but in general CP titanium powder presses well (Dean et al., 1946; Bunshah et al., 1956; Ivasishin et al., 2002). Compaction of titanium powder can be carried out at room temperature using standard presses in closed steel dies. The irregular shape of sponge fines (see



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Table 13.3 Property data of pure titanium, annealed copper and iron Property

Metal

Ti

Cu

Fe

Hardness, Brinell 70 146 Hardness, Vickers 60 50 150 Tensile Strength, Ultimate (MPa) 220 210 540 Tensile Strength, Yield (MPa) 140 33.3 50 Elongation at Break (%) 54 60 Modulus of Elasticity (GPa) 116 110 200 Source: Matweb, 2009.

13.5 Pressing characteristics of sponge titanium powder (- 30 mesh with no more than 15% – 200 mesh). (After Dean et al., 1946. Redrawn with permission from The Minerals, Metals & Materials Society (TMS).)

Fig. 13.4 (a, b)) facilitates powder compaction. Figure 13.5 shows the relationship between the compaction pressure, up to nearly 1400 MPa (100 tsi), and the attendant green density for CP titanium powder (Dean et al., 1946). The increase in green density with compaction pressure is rapid up to 690 MPa (50 tsi) and slows down significantly thereafter. At 690 MPa, the powder compression ratio is about 3.5 to 1 and the resulting green density is above 80% theoretical (Dean et al., 1946). Similar pressing characteristics have been observed for fine electrolytic titanium powder (250 µm), coarse electrolytic titanium powder (250–1000 µm), and fine titanium


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powder (< 30 µm) reduced by calcium hydride (CaH2) except that the 80% theoretical density occurred at a lower compaction pressure, 500 MPa (Arensburger et al., 1968). The pressing characteristics of a powder mixture (for the preparation of alloys via a blended elemental (BE) route) are, in general, determined by the base titanium powder, but may also be affected by the form of the alloying element powders. Figure 13.6 shows the pressing characteristics of seven different powder mixtures of Ti-6Al-4V with specified particle size, impurity content including the oxygen content, and methods of alloying addition. A detailed description of each mixture is given in Table 13.4, where mixtures 1, 2, 4 and 6 are based on CP titanium powder while mixtures 3, 5 and 7 are based on TiH2 (Ivasishin et al., 2002). BE powder mixtures 1, 2 and 4 attain obviously higher green densities than mixture 6 with master alloy additions. The highest density was attained in the mixture 2 based on the coarsest titanium powder, which is the most ductile due to its lowest oxygen content (0.21%) and lowest concentration of total impurities (0.7%). For the same base CP titanium powder (−100 mesh, 0.29%O and 1% impurity), the use of coarse elemental alloying additions (mixture 1, 700 MPa may have


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to be used when TiH2 or pre-alloyed powders are compacted. For example, BE powder mixtures of Ti-6Al-4V can achieve a green density of 84% theoretical at 413 MPa (30 tsi) while to achieve an equivalent green density using prealloyed powders, pressures of 965 MPa (70 tsi) are necessary, which is about the yield strength of Ti-6Al-4V (Abkowitz et al., 1971).

13.3.2 Lubrication Due to the reactive nature of titanium, titanium powder is usually pressed without an internal lubricant in order to avoid interfering with the subsequent sintering and possible contamination (Friedman, 1970; Eloff, 1984). This differs from the compaction of other metal powders such as aluminium and iron, where internal lubrication is an important aspect of powder pressing. On the other hand, despite the concerns over the use of internal lubricants, it has been found that excessive friction during titanium powder pressing leads to a non-homogeneous green density, increased ejection forces and reduced die life (Hong et al., 2008; Hovanski et al., 2009). A recent assessment of the effect of lubrication on the cold pressing of a CP titanium powder confirms that lubrication has a distinct effect on both the frictional properties of the powder as well as the ability to achieve desired green densities (Hovanski et al., 2009). The lubricants assessed include camphor-stearic acid mixtures at different ratios, pyrene, anthracene anthragallol and mixtures of camphor, octadecanol and oleyl alcohol. Green densities > 90% theoretical were attained at a pressure of 560 MPa with a 2% lubricant addition. However, no information was given about the resultant contamination in the sintered products. A thorough assessment is necessary of the effect of the use of internal lubricants on the static, dynamic and corrosion performances of a sintered titanium product before lubricated powder compaction is employed. In contrast to lubricating the powder, die-wall lubrication has proved to be acceptable and effective in reducing both die wear and ejection force and is therefore commonly used (Minabe and Endoh, 1989; Panigrahi et al., 2005; Chen and Zhou, 2007; Low et al., 2009). Die walls can be lightly lubricated with typical commercial grade P/M lubricants such as zinc and lithium stearates and Acrawax (Robinson and Paul, 2001).

13.4 Sintering 13.4.1 Sintering of CP titanium The first major sintering trials of titanium were made by Kroll, who sintered fourteen binary titanium alloys in argon at 50 mm mercury pressure (0.066 atm) using samples made from elemental powders and pressed at 207 MPa (Kroll, 1937). The subsequent investigation by Dean and co-workers on the sintering of titanium in vacuum (1024 torr or 1022 Pa) stands as an important milestone in the history of press-and-sinter Ti P/M (Dean et al., 1946).



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Cold-pressed titanium green parts are now usually sintered in vacuum at pressures of the order of the 1022 Pa used by Dean and co-workers because of the chemical affinity of titanium for oxygen, nitrogen, carbon and hydrogen (Friedman, 1970; Eloff, 1984; Donachie, 2000). For sponge fines from the Kroll process, vacuum sintering is further necessary in that it removes the hydrogen absorbed during the leaching and it distils off residual magnesium (Dean et al., 1946). Significant outgassing often occurs during heating in a sintering cycle of sponge fines. Figure 13.7 shows the effects of sintering temperature on hydrogen evolution, weight loss, porosity and hardness in vacuum sintering. The loss of hydrogen, magnesium and possibly other volatiles gives rise to a decrease in the total weight. Hydrogen can be effectively removed above 600 °C in vacuum. A thorough removal of the volatiles from the powder is important to the subsequent sintering. High-purity helium was assessed as a sintering atmosphere for titanium but it was found that the use of helium did not permit impurities such as hydrogen and magnesium to be removed (Dean et al., 1946). Argon sintering, which was first used by Kroll (1937), poses a similar problem with the removal of volatiles. However, it is still used largely because of ease of operation and economic considerations compared to the installation of a high-temperature high-vacuum furnace. To secure adequate protection against oxidation, commercially pure

13.7 Effect of sintering temperatures on weight loss, void space, hydrogen evolution and Rockwell hardness. Samples were made from sponge titanium powder having a maximum particle size of 30 mesh (595 µm) with not more than 15–20% minus 200 mesh (75 µm) particles by pressing at a pressure of 690 MPa (50 tsi). (After Dean et al., 1946. Redrawn with permission from The Minerals, Metals & Materials Society (TMS).)


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argon needs to be purified before entering the sintering zone. This can be done by allowing argon to pass over heated titanium chips (800–1000 °C) or pass through a separate tube with titanium sponge preheated to a similar temperature (Arensburger et al., 1968). Argon sintering is likely to be more economical and productive for the sintering of large titanium sheets and parts than vacuum sintering because large vacuum furnaces are usually difficult to operate at high temperatures from a production point of view due to leakage of oxygen and nitrogen from the surrounding atmosphere. Nonetheless, vacuum sintering is preferred for Ti P/M. Similar to other metal powders, titanium powder particles are enveloped with an oxide film, which is estimated to be ~10 nm in most cases. Persistent oxide films disable the sintering of metal powders. However, unlike most other metal powders, the oxide films on titanium powders can diffuse into the titanium metal at a low temperature (Bickerdike and Sutcliffe, 1951). Early work indicated that the oxide film on titanium powder disappears around 550 °C in the α phase (Bickerdike and Sutcliffe, 1951). Subsequent work by Watanabe and Horikoshi (1976) revealed that it takes ~ 60 min for the oxide film to disappear on the surfaces of loose titanium powders at 1000 °C (β phase). The diffusion coefficient of oxygen in titanium is a few orders of magnitude faster than in TiO2 in both the a and β regions (Watanabe and Horikoshi, 1976). Disappearance of the oxide film can thus occur in either region. The hardness profile shown in Fig. 13.7 suggests that sintering appears to start developing from about 700 °C. Dilatometric studies on the sintering of titanium samples made from powders in the size range 3–45 µm and pressed at 300 MPa confirmed that sintering starts to develop from about 700–800 °C in the a region after 60 min of holding (Panigrahi et al., 2005; Panigrahi, 2007). It is clear that the oxide films can be assumed to have little influence on the course of the sintering of titanium; they do not have to be reduced via the use of a reducing atmosphere or a disrupting element (Eloff, 1984). Sintering of titanium occurs in both the α and β regions, and the sintered density generally increases with sintering temperature over the broad range 700–1350 °C. The activation energy for titanium self-diffusion in the α region ranges from 169 to 192 kJ mol21 (Herzig et al., 1991) and in the β region from 131 to 328 kJ mol21, according to a number of studies (Panigrahi et al., 2005). The activation energy data obtained from dilatometric studies suggests that the development of the Ti-Ti sinter bonds in the α region is controlled by the lattice diffusion of titanium (Panigrahi et al., 2005; Panigrahi, 2007). The sintering of titanium in the β region may be via a different mechanism. The activation energy (Q) of titanium selfdiffusion in the bcc β titanium phase was found to exhibit a curved Arrhenius plot with Q increasing with temperature (Naik et al., 1969; Mishin and Herzig, 2000). It has been suggested that while the sintering of titanium in the β region may still be controlled by lattice diffusion there are also other mechanisms operative such as grain boundary rotation (Panigrahi et al., 2005). This conclusion was reached after



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the observation that the measured value of Q for sintering in the β region at high temperatures is actually very low compared to the reported values for the Q for self-diffusion, which increase sharply with temperature in the β region. In general, a high green density favours the attainment of a high sintered density for the sintering of titanium (Abkowitz et al., 1971; Robertson et al., 2007; Hovanski et al., 2009). In addition, it improves dimensional stability by avoiding excessive shrinkage. Apart from the use of a reasonably high compaction pressure, a reduction in particle size can effectively increase both the sintering rate and sintered density because of the higher driving force, shorter diffusion distances, smaller pores in the green state and more surface area/grain boundary area where diffusion can take place (Panigrahi and Godkhindi, 2006). Figure 13.8 summarises literature data on the sintered density of CP titanium with respect to compaction pressure (green density), particle size and sintering temperature and time (Robertson and Schaffer, 2010). The sintered density of CP titanium varies over a wide range. In general, sintered densities of about 95% are not difficult to achieve but densities of 98% or higher require use of fine powder ( 950 MPa, and sintered at temperatures in excess of 1300 °C (Abkowitz et al., 1971). The conventional press-and-sinter approach is thus not really practical with pre-alloyed Ti-6Al-4V powder. As a result, the principal methods of consolidating pre-alloyed Ti-6Al-4V powder appear to be hot isostatic pressing and metal injection moulding plus sintering (Donachie, 2000; Shibo et al., 2006; Wang et al., 2007; Ergul et al., 2009). The use of blended elemental powders to produce in-situ alloyed products has thus been adopted. It was originally thought that the most cost-effective source of powder was Ti sponge, and this was the starting material, combined with an Al-V master alloy, for the initial sintered Ti-6Al-4V products. These early efforts combined a simple blending step with cold isostatic pressing and sintering at a temperature above the beta transus (βt) for the desired final alloy composition (Smugeresky and Dawson, 1981). The final microstructures were finer than those expected from ingot metallurgy, but the compacts contained a significant amount of porosity and ductility values were lower than achievable from ingot routes. Hot isostatic pressing was included as a final processing step, and there was some improvement in properties. It was likely that the high chlorine levels in sponge powder contributed to the poor sintered density (Mahajan et al., 1980). Andersen and Eloff discussed a new method which resulted in increases in sintered densities to greater than 99% (Andersen and Eloff, 1980). The residual porosity was found to be made up of two discrete pore families, referred to as macro- and micropores. The macropores occurred at grain and lamellar boundaries and also in regions with higher chlorine levels. They were contained within the a grains, and were most likely a consequence of differing diffusion rates – a Kirkendall effect (Welsch et al., 1983). In 1984, a BE process for titanium alloys was patented in the USA (Imperial Clevite Inc. 1984). This patent recognised the importance of controlling the particle size of both the majority titanium powder and the minority master alloying compounds. The titanium powder was selected to be in the range 40 µm–177 µm, while the master alloy was 0.5 µm–20 µm in size. A homogeneous dispersion was achieved through mechanical blending and, after sintering at 1150 °C–1250 °C, a relative sintered density in excess of 99% was achieved. Eylon and Froes found that the final microstructure in the BE compacts could be refined by judicious heat treatment steps: a solution treatment close to the βt (5% below to 10% above) followed by a rapid quench, normally water or oil, and a further anneal at 10%–20% below βt and final air cooling (United States of America, 1985). This process was adopted and adapted by NKK Corporation (and named the TiARA process). The substitution of HDH powder was


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342 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X


13.9 Description of the stages of sintering in the TiARA prepared Ti-6Al-4V (after Fujita et al., 1996).

investigated in order to reduce the detrimental effects of high chlorine levels (Fujita et al., 1996). The various stages of sintering are shown in Fig. 13.9 (Fujita et al., 1996), which describes the microstructure development as sintering proceeds. It was also established that the use of HDH powder was not detrimental to the sintering of the compact, although the microstructure was somewhat coarser than that obtained from sponge fines. Nippon Steel has also investigated the sintering of Ti-6Al-4V, specifically concentrating on particle size effects and the suppression of grain growth following alloying (Fujii et al., 2002). One aspect of titanium metallurgy not mentioned to date is the effect of retained oxygen – there are strict upper limits for oxygen levels to ensure that excessive strengthening and ductility loss do not occur. In Ti P/M the oxygen contamination can be directly related to the powder size and the ratio of fine:coarse particles can be critical in controlling this effect. The optimum fines fraction was considered to be approximately 0.4. However, as the fines fraction increased, the problem of grain growth was exaggerated, resulting in an increase in grain size from 100 µm to 300 µm due to inadequate boundary pinning. The solution was to introduce stable particles in the boundaries, and two particle types were investigated: inert particles (in this case fine Y2O3) which were initially blended in with the Ti and master alloy powders, but subsequently mixed with molten master alloy and crushed, and



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active particles which transformed to produce the stabilising phase (B4C transforming to TiB and a small amount of C in solid solution). Direct introduction during blending of 2 µm Y2O3 particles caused a deterioration in the relative sintered density (98.5 rather than 99.5%), possibly interfering with diffusion of the alloying elements. The solution was to melt the master alloy and mix in the Y2O3 and blend the crushed composite powder with the HDH Ti powder. Sintered densities were back at 99.5% and the grain sizes were kept to 150 µm. The in-situ formation of the pinning phase (TiB from B4C) was considerably more successful, again achieving densities in excess of 99.5% but retaining grain sizes of 60 µm. In a further effort to reduce cost, the use of the intermediate TiH2 product from the HDH process has been investigated (Ivasishin et al., 2000; Moxson et al., 2006; Ivasishin et al., 2008). The authors compared compacts produced from titanium and elemental alloying additions with those produced from TiH2 powders and the same elemental additions. Figure 13.10 shows the dependence of the sintered density of Ti-6Al-4V made from various powder mixtures (see Table 13.4). The corresponding green densities are shown in Fig. 13.6. The sintered densities were increased from ~93% (mixture 4) to ~98% (mixture 5) when the hydride was used for similar particle sizes. It is believed that in the presence of the hydride, diffusion of the aluminium in the solid state is possible, whereas melting of the aluminium occurs

13.10 Sintered density vs. Compaction pressure for Ti-6Al-4V made from various powder mixtures (see Table 13.4 for detailed descriptions of the powder mixtures). Samples (10 mm diameter and 5 mm high) were sintered in vacuum at 1350°C. (With kind permission from Springer Science + Business Media: Powder Metallurgy and Metal Ceramics, 'Synthesis of Alloy Ti – 6Al – 4V with Low Residual Porosity by a Powder Metallurgy Method’, Vol. 41, 2002, 382–390, O. M. Ivasishin et al., Figure 2.)


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when Ti powder is used, and an exothermic reaction forming Ti3Al takes place. However, solid state diffusion does create problems (besides the Kirkendall effect) as the Al diffuses ahead of the V and forms areas which are highly a stabilised. These islands of a are themselves barriers to V diffusion, and densification is further delayed. Generally it is preferred to add the Al and V as a master alloy (60Al:40V), so that the concentration gradients are reduced and diffusion can be controlled to a greater extent. The combined use of TiH2 and Al-V and Ti-Al additions resulted in 99% theoretical density (mixture 7 in Fig. 13.10). However, the optimum master alloy composition has yet to be determined. There appears to be an additional benefit from using the master alloys, in that larger particle sizes can be tolerated. The use of the hydride feedstock is still under investigation, with the removal of the hydrogen being of prime importance. The volume of hydrogen produced is large, and the collection of the gas does not seem to have been addressed to date. In addition, residual hydrogen can cause embrittlement and the tolerance levels in Ti-6Al-4V are very small. The benefits gained from the TiH2 must be balanced against any additional processing required to ensure its complete removal from the final product.

13.4.3 Sintering of other titanium alloys Apart from CP Ti and Ti-6Al-4V many other compositions have been sintered. Early work examined the sintering response of a number of binary alloys made from BE powders. These include Ti-Fe, Ti-Ni, Ti-Co, Ti-Mn, Ti-W, Ti-Mo, Ti-V, Ti-Ta, Ti-Cr, Ti-Zr, Ti-In, Ti-Al, Ti-Be, Ti-Si, Ti-B and Ti-C in a range of compositions (Kroll, 1937; Larsen et al., 1949), where Ni, Fe and Co, followed by Cr and Mn, are of high diffusivity in both α- and β-titanium (Lutjering and Williams, 2007). These sintered binary alloys were then processed by cold-rolling or hot-rolling to assess their ductility and tensile strength. Binary systems are still investigated today in order to better understand their sintering behaviour, and provide a basis for alloy design (Wei et al., 2003; Liu et al., 2006; Panigrahi, 2007; Robertson and Schaffer, 2010). There is a large body of literature on the sintering of various ternary and multi-component titanium alloys. Other than Ti-6Al-4V, alloys that are of commercial importance and have been produced in powder form include Ti-6Al-6V-2Sn; Ti-5Al-5Mo-1.5Cr; Ti-5Al-2Sn-2Zr-4Cr-4Mo; Ti-6Al2Sn-4Zr-(2/6)Mo; Ti-10V-2Fe-3Al; Ti-11.5Mo-6Zr-4.5Sn (Donachie, 2000), and Ti-6Al-7Nb (Aust et al., 2006; Itoh et al., 2009). Of them, the Ti-6Al-7Nb alloy has been developed to replace Ti-6Al-4V as a more suitable bio-titanium material due to the toxicity of vanadium (Itoh et al., 2009). The alloy can be fabricated by metal injection moulding (MIM) and then sintered to densities of >97% with properties comparable to those of wrought materials (Aust et al., 2006; Itoh et al., 2009). MIM differs from cold pressing but the subsequent sintering of the so-called brown parts is essentially the same as that of cold-pressed parts. Currently Ti P/M chemistries are based on those of common wrought alloys; no alloys exist exclusively for Ti P/M (Donachie, 2000). Since wrought alloys were



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not designed to be sintered, it is not surprising that the sintered densities are not always satisfactory. Using the Ti-Ni binary system as an example, the paragraphs below present a case study of the enhanced sintering of titanium by alloy design. Kroll first sintered a Ti-4.77Ni alloy in argon, made from elemental powders and pressed at 207 MPa into 19 mm diameter cylinders (Kroll, 1937). The sintered samples showed excellent hot-rollability. The system was further investigated by Larsen et al. (1949), who sintered a Ti-10Ni alloy in vacuum (1 hr at 1200 °C) and then cold-rolled the alloy, which showed limited cold-rolling reduction (6%). Binary Ti-Ni alloys containing >10%Ni were thus not recommended. However, press-and-sinter Ti-Ni alloy preforms containing around 5%Ni could readily be processed by hot working. Low Ni content Ti-Ni alloys thus show good potential as press-sinter-and-hot-work Ti P/M alloys. In addition, nickel is known to be a fast diffuser in titanium (Lutjering and Williams, 2007) and this aids sintering. This has recently stimulated a detailed study on the sintering response of low Ni content Ti-Ni alloys (Panigrahi, 2007). Figure 13.11 shows the dilatometric curves of Ti, Ti-2 at.%Ni (2.4 wt.%) and Ti-5 at.%Ni (6 wt.%Ni) samples sintered at 1000 °C for 60 min in argon. Although there is no obvious difference in the onset temperature for shrinkage due to Ni addition, the amount of shrinkage increased significantly with an increase in Ni content from 2 at.% to 5 at.%. The expansion noticed during cooling at about

13.11 Dilatometric curves of Ti, Ti-2 at.%Ni (2.4 wt.%Ni) and Ti-5 at.%Ni (6 wt.%Ni) samples sintered at 1000°C for 60 min in argon. The dilatometer samples (diameter: 6.53; height: 4–5 mm) were made from titanium and nickel powders of < 45 µm (99.7% purity) and pressed at 300 MPa. The green density was about 70% theoretical. (Reprinted from Materials Letters, Vol. 61, B. B. Panigrahi, ‘Sintering behaviour of Ti–2Ni and Ti–5Ni elemental powders’, 152–155 (2007), with permission from Elsevier.)


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220–250 °C was due to the precipitation of Ti-Ni intermetallic compounds. The Arrhenius plots of the sintering shrinkage rate as a function of temperature are shown in Fig. 13.12. The experimental data obtained indicate that the activation energy (Q) for sintering was decreased noticeably by the Ni addition and that Q continued to decrease with increasing Ni addition. The observed Q value (161.9 kJ/mol) for the Ti-2 at.%Ni alloy in the low temperature region is close to that for lattice self-diffusion of a-Ti (169 kJ/mol) while the Q value of 139.0 kJ/mol observed for the Ti-5 at.%Ni alloy is close to that (142 kJ/mol) for the diffusion of Ni in α-Ti. These results suggest a change in the controlling diffusion process from self-diffusion to solute diffusion with higher additions of Ni. The sintered densities show a clear increase with Ni addition (see Fig. 13.13). Figure 13.14 shows the sintering response of a slightly higher Ni content alloy, Ti-7Ni alloy, made from HDH titanium powder (particle size Rc is reached, grain boundary migration will occur, leading to the second step of grain growth by the grain boundary migration. Figure 17.16 and 17.17 schematically illustrate the two-step process.



457

17.4.3 Initial grain growth mechanisms From the very porous structure at the start of sintering, several possible mechanisms for grain growth during sintering of nano particles exist, including: 1) coarsening as the result of inter-particle diffusion; 2) grain boundary migration; 3) solution and reprecipitation (two phases system); and 4) coalescence. Generally, the initial grain growth during sintering is attributed to the coarsening of nano particles due to inter-particle diffusions. Surface diffusion especially plays a major role for inter-particle mass transport. In a study of the sintering of BaTiO3, Shi et al. observed that the contacting particles become one particle via surface diffusion, as shown in Fig 17.18.58 Surface diffusion transported the atoms from the dissolving small particle to be re-deposited on the surface of the larger particle. This is a direct evidence of the role of surface diffusion in the coarsening of nano particles at the beginning of sintering. It is noted that surface diffusion causes coarsening of larger particles by consuming small particles, i.e.

17.18 Observations of the grain growth in BaTiO3 powder at different temperatures from 940 °C (a), 950 °C (b, c) to 960 °C (d to o). Grains grow through reduction of smaller grains and enlargement of larger ones. The distance between the particle centers decreases simultaneously. © Woodhead Publishing Limited, 2010

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458 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X


17.18 Continued

grain growth without requiring either grain boundary migration and rotation, or grain boundary diffusion. Considering that nano particles are usually not at equilibrium states and are likely to contain excess amounts of various defects that are created during the production of nano particles, there will be a relaxation period for migration, redistribution and annihilation of the defects.96,97 Owing to the non-equilibrium structure of nano particles, diffusivity is dramatically enhanced during the relaxation process,98–101 which may contribute to dynamic grain growth at the beginning of sintering. Dynamic grain growth usually dominates during the heat-up stage and for the first few minutes after reaching a preset isothermal holding temperature. Therefore, rapid dynamic grain growth accounts for the experimental observation that the first data point during isothermal holding is several times that of the initial grain size. The relaxation time depends on materials, nano particle production methods and temperature. The role of grain boundary migration should also be considered in discussing the initial grain growth during sintering of nano particles. As discussed earlier, for single-phase materials at late stages of sintering when relative density is



459

greater than 90%, grain boundary migration is the most logical mechanism of grain growth found in bulk single-phase materials. Grain boundary migration has also been observed during early stages of sintering nanosized Al2O3.59 Figure 17.19 shows that when the nanosized Al2O3 particles were subjected to high temperatures in a flash sintering set-up, instant grain growth was observed and grain boundary migration was believed to be part of the process. This confirms the analysis of the coarsening of nano particles that when r1/r2 is greater than Rc, grain boundary migration will take place. Coalescence is another grain growth mechanism that is often cited to qualitatively explain rapid grain growth. Coalescence is a term that is often loosely used to describe various phenomena. For example, coalescence is sometimes used interchangeably with the term ‘sintering’ to describe the growth of particles during particle synthesis and growth process.102–105 For clarity in this article, coalescence is used strictly to describe the increase of grain size due to the merging of two grains by eliminating the common grain boundaries between them. Differing from other grain growth processes, which may also be described as the merging of two grains, the two original grains should not demonstrate significant change from their morphology prior to coalescence. The term coalescence, as defined above, describes a unique method of grain growth, which can be accomplished only through various diffusion mechanisms. Possible mechanisms for coalescence include grain boundary diffusion, dislocation climb along grain boundaries, or even grain rotations. In liquid-phase sintering systems, it is believed that the solution-reprecipitation mechanism may also help facilitate the coalescence of grains. Direct evidence of coalescence is, however, very difficult to identify. Fang et al.79 studied the grain growth of nano WC during

17.19 Alumina particles cluster sintered at 1200°C. One particle’s ‘grain’ has grown, outlined, and has distinct grain boundary (left). The grain boundary migrated into small particles (right).


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460 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 20 1 2 3 4 5 6 7 8 9 30 1 2 3 4 5 6 7 8 9 40 1 2 43X


17.20 Coalescence of two platelet shaped grains of a nanocrystalline WC-Co compact heated up to 1200 °C at a heating rate of 10 °C/min. and held for 1 min.

sintering and found the growth of nanosized tungsten carbide grains within aggregates via coalescence, as shown in Fig. 17.20. Kumar and Fang’s analysis of the sintering of WC-Co composites suggests that the lattice shift along lowenergy CSL grain boundaries is a viable mechanism for materials with a high degree of crystallographic anisotropy.106 Effects of agglomerates on initial grain growth Another important factor in grain growth mechanisms during sintering of nano particles is the role of agglomerates in grain growth. Agglomerates are defined as loosely-packed particles forming fractals, while aggregates are particles packed together in a more defined equi-axial shape. Mayo3 pointed out that grain size is often related to the size of agglomerates at the beginning of sintering. As Mayo summarized, the larger the agglomerate size, the higher the sintering temperature required to eliminate large inter-agglomerate pores. By contrast, the crystallite size has little effect on the temperature required to reach full density. The same temperatures, however, promote grain growth to such an extent that the grain size can easily balloon to the agglomerate size. Fang et al.107 observed a similar phenomenon. Figure 17.21 shows an agglomerate of WC-10%Co when heated to 800 °C within a powder compact, while Fig. 17.22 shows the structure when the same compact is heated to 1200 °C. It can be seen that the original agglomerates, within which the WC grains are visible at 800 °C, no longer exist at 1200 °C. Instead, the individual grains with sizes similar to those of the agglomerates at lower temperatures constitute the microstructure. It is thus deduced that the densification and grain growth processes during sintering of nano



461

17.21 Densification and grain growth within individual aggregated particles prior to bulk densification.

17.22 Microstructure of same sample as Fig. 17.21 at 1200 °C. Agglomerates were transformed into individual grains.

particles progressed via consolidation and grain growth within individual agglomerates, and then proceeded to the consolidation and elimination of porosities between agglomerates. This mechanistic process of sintering was also observed and discussed by Petersson and Ågren.72 The process that first takes place within individual agglomerates was characterized as ‘nucleation’ sites.


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17.23 Schematic diagram of the hierarchical structure of agglomerates (large circle), domains (small circle) and primary particles (dots within small circles).

To explain the effect of agglomerates, Lange63 classified the structure of a powder compact as a hierarchical structure of agglomerates, domains and primary particles, as shown by Fig. 17.23. Defining the coordination number as the number of particles surrounding the pore, Lange explained that pores within domains have the lowest coordination number, pores between domains have higher, and pores between agglomerates have the highest coordination number. Figure 17.24 shows schematically the volume distribution of the three classes of pores as a function of coordination number. When N

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