Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications, Second Edition

685 Pages·1999·14.156 MB·English

by  Gunter Gottstein, Lasar S. Shvindlerman

S E C O N D E D I T I O N
Grain
Boundary
Migration

in
Metals
Thermodynamics,
Kinetics,
Applications
© 2010 by Taylor and Francis Group, LLC
CRC Series in
Materials Science and Technology
Series Editor
Brian Ralph
Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications,
Second Edition
Günter Gottstein and Lasar S. Shvindlerman
Corrosion Science and Technology, Second Edition
David E. J. Talbot and James D. R. Talbot
Surface Engineering of Metals: Principles, Equipment, Technologies
Tadeusz Burakowski and Tadeusz Wierzchon’
Image Analysis Applications in Materials Engineering
Leszek Wojnar
The Quantitative Description of the Microstructure of Materials
K J. Kurzydlowski and Brian Ralph
The Extraction and Refining of Metals
Colin Bodsworth
Control of Microstructures and Properties in Steel Arc Welds
Lars-Erik Svensson
Grain Growth and Control of Microstructure and Texture in Polycrystalline Materials
Vladimir Novikov
© 2010 by Taylor and Francis Group, LLC
S E C O N D E D I T I O N
Grain
Boundary
Migration

in
Metals
Thermodynamics,
Kinetics,
Applications
Günter Gottstein
Lasar S. Shvindlerman
Boca Raton London New York
CRC Press is an imprint of the
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© 2010 by Taylor and Francis Group, LLC
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Library of Congress Cataloging‑in‑Publication Data
Gottstein, G., 1944-
Grain boundary migration in metals : thermodynamics, kinetics, applications, /
authors, Günter Gottstein, Lasar S. Shvindlerman. -- 2nd ed.
p. cm.
“A CRC title.”
Includes bibliographical references and index.
ISBN 978-1-4200-5435-4 (hardcover : alk. paper)
1. Kirkendall effect. 2. Metals--Thermomechanical properties. 3. Metal crystals. I.
Shvindlerman, L. S. (Lazar’ Simkhovich) II. Title.
QC176.8.D5G68 2010
620.1’699--dc22 2009038935
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“That we find out the cause of this effect
Or rather say the cause of this defect
For this effect defective comes with cause”
— W. Shakespeare, “Hamlet”
© 2010 by Taylor and Francis Group, LLC
Contents
The Authors
Preface to the Second Edition
Acknowledgments
Introduction
List of Symbols
1 Thermodynamics of Grain Boundaries 1
1.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Thermodynamics of Surfaces . . . . . . . . . . . . . . . . . . 2
1.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Is Equilibrium Thermodynamics Applicable to Grain
Boundaries? . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 Gibbs Thermodynamics of Surface Phenomena . . . . 7
1.2.4 GibbsThermodynamicMethodAppliedtoGrainBound-
aries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.5 Grain Boundary Solutions . . . . . . . . . . . . . . . . 24
1.2.6 Statistical Analysis of the Adsorption on Internal In-
terfaces in Solids . . . . . . . . . . . . . . . . . . . . . 34
1.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.3.1 Adsorption . . . . . . . . . . . . . . . . . . . . . . . . 44
1.3.2 Grain Boundary Surface Tension . . . . . . . . . . . . 52
1.3.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 59
1.3.4 Adsorption of Vacancies at Grain Boundaries . . . . . 66
1.4 Applications of Grain Boundary Thermodynamics . . . . . . 69
1.4.1 Grain Boundary Phase Transitions . . . . . . . . . . . 69
1.5 The Equilibrium Shape of Grain Boundaries . . . . . . . . . . 102
1.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
2 Structure of Grain Boundaries 111
2.1 Terminology and Definitions . . . . . . . . . . . . . . . . . . . 111
2.2 Atomic Structure of Grain Boundaries . . . . . . . . . . . . . 115
2.2.1 Low-Angle Grain Boundaries . . . . . . . . . . . . . . 115
2.2.2 High-Angle Grain Boundaries . . . . . . . . . . . . . . 118
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2.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3 Grain Boundary Motion 135
3.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
3.2 Driving Forces for Grain Boundary Migration . . . . . . . . . 140
3.3 Drag Effects During Grain Boundary Motion . . . . . . . . . 144
3.3.1 Origin of Drag Effects . . . . . . . . . . . . . . . . . . 144
3.3.2 Impurity Drag in Ideal Solute Solutions . . . . . . . . 144
3.3.3 Impurity Drag in Regular Solutions. . . . . . . . . . . 150
3.3.4 Vacancy Drag . . . . . . . . . . . . . . . . . . . . . . . 158
3.3.5 Drag Effects by Second-Phase Particles . . . . . . . . 163
3.3.6 Groove Dragging . . . . . . . . . . . . . . . . . . . . . 171
3.4 Measurement of Grain Boundary Mobility . . . . . . . . . . . 181
3.4.1 PolycrystalMethods . . . . . . . . . . . . . . . . . . . 181
3.4.2 Bicrystal Methods . . . . . . . . . . . . . . . . . . . . 181
3.4.3 Shape of a Moving Grain Boundary . . . . . . . . . . 197
3.5 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 217
3.5.1 Relation between Driving Force and Migration Rate . 217
3.5.2 Kinetic Parameters of Grain Boundary Mobility . . . 222
3.5.3 MisorientationDependenceofGrainBoundaryMobil-
ity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
3.5.4 Correlation of Grain Boundary Migration and Diffu-
sion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
3.5.5 SegregationEffects Other Than Misorientation . . . . 233
3.5.6 Impurity Drag and Breakaway . . . . . . . . . . . . . 236
3.5.7 Athermal Motion of Grain Boundaries . . . . . . . . . 248
3.5.8 Effect of Pressure on Grain Boundary Migration:
Activation Volume . . . . . . . . . . . . . . . . . . . . 259
3.5.9 Effect of Grain Boundary Orientation . . . . . . . . . 267
3.6 Effect of Wetting Phase Transitions on Grain Boundary Mi-
gration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
3.7 Compensation Effect in Grain Boundary Motion . . . . . . . 294
3.7.1 The Fundamental Rate Equation . . . . . . . . . . . . 294
3.7.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 295
3.7.3 Thermodynamics of the Activated State . . . . . . . . 295
3.7.4 Applications. . . . . . . . . . . . . . . . . . . . . . . . 305
3.8 Mechanisms of Grain Boundary Migration . . . . . . . . . . . 311
3.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
4 Thermodynamics and Kinetics of Connected Grain Bound-
aries 329
4.1 Microstructural Elements of Polycrystals . . . . . . . . . . . . 329
4.2 Thermodynamics of Triple Junctions . . . . . . . . . . . . . . 331
4.2.1 GrainBoundaryTripleLine Tension—Experimental
Approach . . . . . . . . . . . . . . . . . . . . . . . . . 335
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4.3 Motion of a Grain Boundary System with Triple Junctions . . 337
4.4 Triple Junctions Motion in the Presence of Impurities . . . . 341
4.5 Experimental Investigations of Triple Junction Motion . . . . 344
4.5.1 MotionofaGrainBoundarySystemwithTripleJunc-
tion in a Material with Impurities. . . . . . . . . . . . 366
4.6 Triple Junction Drag and Grain Growth in 2D Polycrystals . 374
4.6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . 374
4.6.2 Topology of Grain Structures . . . . . . . . . . . . . . 376
4.6.3 Elementary TopologicalRearrangements . . . . . . . . 377
4.6.4 Grain Growth Kinetics . . . . . . . . . . . . . . . . . . 378
4.6.5 UniformGrainBoundaryModelandtheVonNeumann-
Mullins Relation . . . . . . . . . . . . . . . . . . . . . 380
4.6.6 Effect of Triple Junction Drag on the Von Neumann-
Mullins Relation . . . . . . . . . . . . . . . . . . . . . 383
4.7 Grain Growth in 3D Systems . . . . . . . . . . . . . . . . . . 412
4.7.1 Analytical Approaches . . . . . . . . . . . . . . . . . . 412
4.7.2 Computer Simulations of 3D Grain Growth . . . . . . 416
4.8 Kinetics of Grain Growth Inhibited by Vacancy Generation . 429
4.8.1 Diffusion-Controlled Creep in Nanocrystalline Mate-
rials under Grain Growth . . . . . . . . . . . . . . . . 443
4.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
5 Computer Simulation of Grain Boundary Motion 451
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
5.1.1 Classical Molecular Dynamics . . . . . . . . . . . . . . 452
5.1.2 Parrinello-RahmanMethod . . . . . . . . . . . . . . . 453
5.1.3 Time Integration Schemes . . . . . . . . . . . . . . . . 455
5.1.4 Boundary Concepts . . . . . . . . . . . . . . . . . . . 457
5.1.5 Finite Temperature MD Simulations . . . . . . . . . . 457
5.2 Driving Force Concepts . . . . . . . . . . . . . . . . . . . . . 460
5.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . 460
5.2.2 Elastic Driving Force . . . . . . . . . . . . . . . . . . . 460
5.2.3 Peach-KoehlerDriving Force . . . . . . . . . . . . . . 462
5.2.4 Orientation-CorrelatedDriving Force . . . . . . . . . . 464
5.3 Migration of [001] Twist Grain Boundaries . . . . . . . . . . . 466
5.3.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 466
5.3.2 Atomistic Structure of the Relaxed [001] Twist GBs . 466
5.3.3 GB Migration Due to an Elastic Driving Force . . . . 470
5.3.4 Data Analysis with Respect to GB Migration . . . . . 471
5.3.5 Mobility of [001] Twist GBs . . . . . . . . . . . . . . . 472
5.4 Motion of Tilt Boundaries . . . . . . . . . . . . . . . . . . . . 476
5.5 Compensation Effect . . . . . . . . . . . . . . . . . . . . . . . 483
5.6 Comparison with Experiments . . . . . . . . . . . . . . . . . . 484
5.7 Grain Boundary Diffusion . . . . . . . . . . . . . . . . . . . . 485
5.7.1 Computational Procedure . . . . . . . . . . . . . . . . 485
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5.7.2 Activation Energies. . . . . . . . . . . . . . . . . . . . 487
5.7.3 Temperature Effects . . . . . . . . . . . . . . . . . . . 490
5.8 Atomic Mechanisms . . . . . . . . . . . . . . . . . . . . . . . 495
5.8.1 GB Migration of [001] Twist Boundaries . . . . . . . . 495
5.8.2 Grain Boundary Diffusion of [001] Twist Boundaries . 496
5.9 Simulation of Triple Junction Motion . . . . . . . . . . . . . . 497
5.9.1 Theoretical Background . . . . . . . . . . . . . . . . . 497
5.9.2 Simulation Method . . . . . . . . . . . . . . . . . . . . 499
5.9.3 Simulation Results . . . . . . . . . . . . . . . . . . . . 501
6 Applications 509
6.1 Characterizationof Microstructure and Texture . . . . . . . . 509
6.1.1 Introductory Remarks . . . . . . . . . . . . . . . . . . 509
6.1.2 Microstructure . . . . . . . . . . . . . . . . . . . . . . 510
6.1.3 CrystallographicTexture. . . . . . . . . . . . . . . . . 513
6.2 Recrystallization annd Grain Growth . . . . . . . . . . . . . . 535
6.2.1 Phenomenologyand Terminology of Recrystallization
and Grain Growth . . . . . . . . . . . . . . . . . . . . 535
6.2.2 Nucleation of Recrystallization . . . . . . . . . . . . . 539
6.2.3 Kinetics of Primary Recrystallization . . . . . . . . . . 543
6.2.4 Recrystallization Texture . . . . . . . . . . . . . . . . 544
6.2.5 Grain Growth . . . . . . . . . . . . . . . . . . . . . . . 558
6.3 On Precipitation-ControlledGrain Size . . . . . . . . . . . . . 563
6.4 Mechanisms on Retardation of Grain Growth . . . . . . . . . 573
6.5 Grain Boundary Junction Engineering . . . . . . . . . . . . . 577
7 Appendices 585
7.1 Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585
7.1.1 Mass Transport in Solids in Terms of Osmotic Pres-
sure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585
7.2 Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588
7.2.1 Calculation of the Rotation Matrix . . . . . . . . . . . 588
7.3 Appendix C . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592
7.3.1 Indexing of Pole Figures . . . . . . . . . . . . . . . . . 592
8 Solutions 597
9 References 645
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The Authors
Since 1989,Prof. Dr. Gu¨nter Gottstein,hasbeendirectorofthe Institute
of Physical Metallurgy and Metal Physics of the RWTH Aachen University,
Germany.He obtainedhis doctoraldegree in metalphysics fromRWTH and,
following his habilitation at the faculty of mining and metallurgy of RWTH,
he spent about 10 years in the U.S. at Argonne National Laboratory, MIT,
and Michigan State University. He was promoted to the rank of full profes-
sor at Michigan State University in 1985. Prof. Gottstein has published over
400 scientific papers, primarily in refereed journals, on topics such as inter-
faces, recrystallization, textures, and high-temperature crystal plasticity. He
is theauthor,coauthor,orcoeditorof12booksonmaterialscience,including
a textbook which has been translated into several languages. Since 1991 he
has workedclosely with his co-author,Prof.Shvindlerman, on topics of grain
boundary migration.
Prof. Dr. Lasar S. Shvindlerman, is a leading scientific researcher at
the Institute of Solid State Physics (ISSP), Russian Academy of Sciences
(Cherno-golovka,Russia)andprofessorofmetalphysics atthe MoscowInsti-
tute ofSteelandAlloys.He studiedmaterialsscienceatthe KievPolytechnic
Institute, and obtained his doctoral degree in 1968 and his Dr. Sci. degree in
metal physics in 1980. Since 1967, he has been associated with the Institute
of Solid State Physics in Chernogolovka. Prof. Shvindlerman has published
over250scientificpapersand3books,primarilyontopicsofsurfacephenom-
ena in solids, diffusion in metals, and phase transitions of grain boundaries
in metals. Grain Boundary Migration in Metals: Thermodynamics, Kinetics,
Applications, Second Edition is the result of his 1991 research collaboration
with Prof. Gottstein.
© 2010 by Taylor and Francis Group, LLC