Atomistic simulations of grain boundary migration in face-centred cubic metals [Elektronische Ressource] / vorgelegt von Bernd Schönfelder

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• Physik

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• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2003
• Nombre de lectures: 21
• Langue: English
• Poids de l'ouvrage: 6 Mo

Extrait

Atomistic Simulations of
Grain Boundary Migration in
Face-Centred Cubic Metals
Von der Fakultät für Georessourcen und Materialtechnik
der Rheinisch-Westfälischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines
Doktors der Naturwissenschaften
genehmigte Dissertation
vorgelegt von Diplom-Physiker
Bernd Schönfelder
aus Wilhelmshaven
Berichter: Univ.-Prof. Dr.rer.nat. Günter Gottstein
Prof. Dr.rer.nat. Lasar S. Shvindlerman
Tag der mündlichen Prüfung: 28.November 2003
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar.Note of thanks
I am grateful to my PhD thesis advisor Prof. Dr. Günter Gottstein, director of the Institut
für Metallkunde und Metallphysik (IMM) at the RWTH Aachen, for giving me the oppor-
tunity to carry out this work, his support over the years and for keeping his faith in this
work. As well I like to thank Prof. Dr. Lasar S. Shvindlerman for his encouragement and
stimulating discussions.
I like to express my gratitude to the German academic exchange service who awarded me a
stipend in their HSP II/AUFE program which was the financial backbone for carrying out
my research activities at Argonne National Laboratory, Argonne, USA, from January 1995
until the end of February 1996.
Lots of thanks to the group leader of the materials interface science group, Dr. Dieter
Wolf, and Dr. Simon R. Phillpot of the Materials Science Division at Argonne National
Laboratory (ANL) for welcoming me in their group, supporting our research activities and
fortheirstimulatingdiscussions. AswellIliketothankallpeopleatANLthatImetduring
my stay, especially MSD librarian Robert Noel, Loren Thompson, Dr. Jeffrey Eastman, Dr.
Pawel Keblinski, Dr. Karl Merkle, Dr. Jim Vetrone and Carl Youngdahl.
I was happy to be a member of the research group "Korngrenzenbewegung" at the IMM,
RWTH Aachen, and like to thank all people involved in this group for their assistance and
stimulating discussions over the years. The same applies to the whole staff of the IMM.
Especially I like to name Dr. Myriam Winning, Dr. Karl Johann Draheim, Dr. Martin
Furtkamp and Dr. Jörn Verhasselt as well as Ralf Goßmann and Dr. Weiping Hu. I was
glad to have shared my office at the IMM with Dr. Franz Roters. His fruitful discussions
are well remembered and appreciated. Finally many thanks to Dr. Dmitri A. Molodov for
this friendly concern and support of my work and the ample discussions we had on various
scientific and personal issues.
Concluding,manythankstomyparents,JohannesH.andKarinSchönfelder,forsupporting
meallthewayandforenablingthiswork. AswellIliketothankmywife,EuniceNyaguthii,
and my son, Jonas Warui, for allowing me to concentrate on finalizing this work and their
patience and understanding during these times.Contents
1 Introduction 1
2 Fundamentals 5
2.1 Structural Models of Grain Boundaries . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Read-Shockley Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Coincident-Site Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.3 Interface-Plane Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.4 Asymmetrical CSL Tilt GBs . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Grain Boundary Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Review of Atomistic GB Migration Simulations . . . . . . . . . . . . . . . . 22
3 Computational Procedures 29
3.1 Introduction to atomistic simulations . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Interatomic Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Pair Potentials for fcc materials . . . . . . . . . . . . . . . . . . . . . 31
3.2.1.1 3d Lennard-Jones Potential . . . . . . . . . . . . . . . . . . 31
3.2.2 Many Body Potentials for fcc materials . . . . . . . . . . . . . . . . . 35
3.2.2.1 Long-Range Finnis-Sinclair Potential . . . . . . . . . . . . . 36
3.2.2.2 Embedded-Atom-Method Potential . . . . . . . . . . . . . . 38
3.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Molecular-Dynamics Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 Classical Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Parrinello-Rahman Method . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.3 Time Integration Schemes . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.4 Boundary Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
III CONTENTS
3.3.5 Finite Temperature MD Simulations . . . . . . . . . . . . . . . . . . 49
3.3.6 Geometry of MD Simulation Box . . . . . . . . . . . . . . . . . . . . 50
3.4 Driving Force Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.2 Elastic Driving Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.3 Peach-Koehler Driving Force . . . . . . . . . . . . . . . . . . . . . . . 56
3.4.4 Orientation-correlated Driving Force . . . . . . . . . . . . . . . . . . 57
3.5 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.5.1 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.5.1.1 Slicing Procedure and Detection Scheme of Planar GBs . . . 61
3.5.1.2 Radial Pair Distribution Function . . . . . . . . . . . . . . . 63
3.5.1.3 Common Neighbour Analysis . . . . . . . . . . . . . . . . . 64
3.5.2 Analysis of Diffusive Processes . . . . . . . . . . . . . . . . . . . . . . 65
3.5.3 How to detect vacancies in fcc systems ? . . . . . . . . . . . . . . . . 69
4 Properties of Lattice Mono-Vacancies 71
4.1 Cu EAM Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Cu 3d LJ Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 Results of three-dimensional [001] Twist GBs 79
5.1 Relaxed GB Structure of the studied [001] Twist GBs . . . . . . . . . . . . . 79
5.1.1 General Remarks on the GB Relaxation Procedure . . . . . . . . . . 79
5.1.2 Atomistic Structure of the Relaxed [001] Twist GBs . . . . . . . . . . 81
5.2 Studies on Planar [001] Twist GBs . . . . . . . . . . . . . . . . . . . . . . . 86
5.2.1 Overview on performed GB Migration Simulations . . . . . . . . . . . 86
5.2.2 GB Migration due to an Elastic Driving Force . . . . . . . . . . . . . 87
5.2.2.1 DF Verification : Indirect Quantification Scheme . . . . . . 87
◦5.2.2.2 Σ 29 [001] 43.60 . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.2.3 DF Verification : Direct Quantification Scheme . . . . . . . 94
◦5.2.2.4 Σ 5 [001] 36.87 . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2.2.5 Σ 17, Σ 13 and Σ 25 [001] twist GBs . . . . . . . . . . . . . 99
◦5.2.2.6 Σ 41 [001] 12.68 . . . . . . . . . . . . . . . . . . . . . . . . 102CONTENTS III
◦5.2.2.7 Σ 85 [001] 8.80 . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2.2.8 Discussion of the GB migration results due to an elastic DF 108
5.2.3 GB Migration due to an orientation-correlated Driving Force . . . . . 112
5.2.3.1 General aspects of the orientation-correlated DF concept . . 112
◦5.2.3.2 Σ 5 [001] 36.87 . . . . . . . . . . . . . . . . . . . . . . . . 115
◦5.2.3.3 Σ 17 [001] 28.07 . . . . . . . . . . . . . . . . . . . . . . . . 120
◦5.2.3.4 Σ 13 [001] 22.62 . . . . . . . . . . . . . . . . . . . . . . . . 122
◦5.2.3.5 Σ 85 [001] 8.80 . . . . . . . . . . . . . . . . . . . . . . . . 124
◦5.2.3.6 Σ 181 [001] 6.03 . . . . . . . . . . . . . . . . . . . . . . . . 126
5.2.3.7 DiscussionoftheGBmigrationresultsduetoanorientation-
correlated DF . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.2.4 GB Self-Diffusion of Planar [001] Twist GBs . . . . . . . . . . . . . . 131
5.2.5 GB Migration Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 140
5.2.5.1 Collective shuffle mechanism . . . . . . . . . . . . . . . . . . 141
5.2.5.2 Dislocation based mechanism . . . . . . . . . . . . . . . . . 148
5.2.6 Discussion of the overall [001] Twist GB results . . . . . . . . . . . . 154
6 Results of three-dimensional Tilt GBs 157
6.1 Relaxed GB Structure of the studied symmetrical Tilt GBs . . . . . . . . . . 157
◦6.1.1 Σ 5 [001] 53.13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
◦¯6.1.2 Σ 73 [111] 11.64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.2 Relaxed GB Structure of the studied asymmetrical Tilt GBs . . . . . . . . . 162
◦ ◦6.2.1 Σ 5 [001] 53.13 Φ=14.04 . . . . . . . . . . . . . . . . . . . . . . . 165
◦ ◦6.2.2 Σ 5 [001] 53.13 Φ=33.69 . . . . . . . . . . . . . . . . . . . . . . . 167
6.3 GB Migration of Planar Symmetrical Tilt GBs . . . . . . . . . . . . . . . . . 169
6.3.1 Elastic Driving Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.3.1.1 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
◦6.3.1.2 Σ 5 [001] 53.13 . . . . . . . . . . . . . . . . . . . . . . . . 172
6.3.1.3 Remarks on GB Migration of tilt GBs due to Elastic DFs . 176
6.3.2 External Shear Stress States . . . . . . . . . . . . . . . . . . . . . . . 179
◦¯6.3.2.1 Σ 73 [111] 11.64 . . . . . . . . . . . . . . . . . . . . . . . .