Gottstein G., Shvindlerman L.S. Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications
Подождите немного. Документ загружается.
Grain
Boundary
Migration
in
Metals
SECOND EDITION
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 Rening 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
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
Boca Raton London New York
Grain
Boundary
Migration
in
Metals
Günter Gottstein
Lasar S. Shvindlerman
SECOND EDITION
Thermodynamics,
Kinetics,
Applications
© 2010 by Taylor and Francis Group, LLC
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2010 by Taylor and Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed in the United States of America on acid-free paper
10 9 8 7 6 5 4 3 2 1
International Standard Book Number: 978-1-4200-5435-4 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC,
a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.
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
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
© 2010 by Taylor and Francis Group, LLC
“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 IntroductoryRemarks ...................... 1
1.2 ThermodynamicsofSurfaces .................. 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 Gibbs Thermodynamic Method Applied to Grain Bound-
aries............................ 14
1.2.5 Grain Boundary Solutions . . . . . . . . . . . . . . . . 24
1.2.6 Statistical Analysis of the Adsorption on Internal In-
terfacesinSolids ..................... 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 TerminologyandDefinitions ...................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
© 2010 by Taylor and Francis Group, LLC
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 OriginofDragEffects ..................144
3.3.2 Impurity Drag in Ideal Solute Solutions . . . . . . . . 144
3.3.3 Impurity Drag in Regular Solutions . . . . . . . . . . . 150
3.3.4 VacancyDrag.......................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 BicrystalMethods ....................181
3.4.3 Shape of a Moving Grain Boundary . . . . . . . . . . 197
3.5 ExperimentalResults .......................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 Misorientation Dependence of Grain Boundary Mobil-
ity .............................223
3.5.4 Correlation of Grain Boundary Migration and Diffu-
sion ............................231
3.5.5 Segregation Effects 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:
ActivationVolume ....................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 ThermodynamicsofTripleJunctions ..............331
4.2.1 Grain Boundary Triple Line Tension — Experimental
Approach .........................335
© 2010 by Taylor and Francis Group, LLC
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 Motion of a Grain Boundary System with Triple Junc-
tioninaMaterialwithImpurities............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 Topological Rearrangements . . . . . . . . 377
4.6.4 GrainGrowthKinetics..................378
4.6.5 Uniform Grain Boundary Model and the Von Neumann-
Mullins Relation . . . . . . . . . . . . . . . . . . . . . 380
4.6.6 Effect of Triple Junction Drag on the Von Neumann-
Mullins Relation . . . . . . . . . . . . . . . . . . . . . 383
4.7 GrainGrowthin3DSystems ..................412
4.7.1 AnalyticalApproaches..................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 TimeIntegrationSchemes................455
5.1.4 Boundary Concepts . . . . . . . . . . . . . . . . . . . 457
5.1.5 Finite Temperature MD Simulations . . . . . . . . . . 457
5.2 DrivingForceConcepts .....................460
5.2.1 Introduction........................460
5.2.2 ElasticDrivingForce...................460
5.2.3 Peach-Koehler Driving Force . . . . . . . . . . . . . . 462
5.2.4 Orientation-Correlated Driving 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 CompensationEffect .......................483
5.6 Comparison with Experiments . . . . . . . . . . . . . . . . . . 484
5.7 Grain Boundary Diffusion . . . . . . . . . . . . . . . . . . . . 485
5.7.1 Computational Procedure . . . . . . . . . . . . . . . . 485
© 2010 by Taylor and Francis Group, LLC
5.7.2 ActivationEnergies....................487
5.7.3 TemperatureEffects ...................490
5.8 AtomicMechanisms .......................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 TheoreticalBackground .................497
5.9.2 SimulationMethod....................499
5.9.3 SimulationResults ....................501
6 Applications 509
6.1 Characterization of Microstructure and Texture . . . . . . . . 509
6.1.1 IntroductoryRemarks ..................509
6.1.2 Microstructure ......................510
6.1.3 Crystallographic Texture . . . . . . . . . . . . . . . . . 513
6.2 Recrystallization annd Grain Growth . . . . . . . . . . . . . . 535
6.2.1 Phenomenology and Terminology of Recrystallization
andGrainGrowth ....................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 GrainGrowth.......................558
6.3 OnPrecipitation-ControlledGrainSize .............563
6.4 Mechanisms on Retardation of Grain Growth . . . . . . . . . 573
6.5 Grain Boundary Junction Engineering . . . . . . . . . . . . . 577
7 Appendices 585
7.1 AppendixA ............................585
7.1.1 Mass Transport in Solids in Terms of Osmotic Pres-
sure ............................585
7.2 AppendixB ............................588
7.2.1 Calculation of the Rotation Matrix . . . . . . . . . . . 588
7.3 AppendixC ............................592
7.3.1 Indexing of Pole Figures . . . . . . . . . . . . . . . . . 592
8 Solutions 597
9 References 645
© 2010 by Taylor and Francis Group, LLC