Numerical Simulations of Metal-Oxides Numerische Simulationen von Metalloxiden Andreas ...

131 Pages·2014·3.01 MB·English

Numerical Simulations of Metal-Oxides
Numerische Simulationen von Metalloxiden
Von der Fakult¨at fu¨r Mathematik und Physik der
Universit¨at Stuttgart zur Erlangung der Wu¨rde eines Doktors der
Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung
Vorgelegt von
Andreas Chatzopoulos
aus Ludwigsburg
Hauptberichter: Prof. Dr. H.-R. Trebin
Mitberichter Prof. Dr. C. Holm
Tag der mu¨ndlichen Pru¨fung: 30.03.2015
Institut fu¨r Theoretische und Angewandte Physik
der Universit¨at Stuttgart
2015

Meinen Eltern.

Contents
Summary in English xiii
Zusammenfassung in deutscher Sprache xix
1 Introduction 1
2 Atomistic Computer Simulations 3
2.1 Ab-initio Methods . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Classical Molecular Dynamics . . . . . . . . . . . . . . . . . 5
2.3 Molecular Dynamics with Long-Range Interactions . . . . . 8
2.3.1 Ewald Summation Technique . . . . . . . . . . . . . 8
2.3.2 The Model of Streitz and Mintmire . . . . . . . . . . 16
2.3.3 Beyond Streitz and Mintmire . . . . . . . . . . . . . 21
2.3.4 The Model of Tangney and Scandolo . . . . . . . . . 29
3 Methodological Progresses 31
3.1 Iterative Solvers . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.1 Minimization of a Quadratic Form . . . . . . . . . . 32
3.1.2 Implementation . . . . . . . . . . . . . . . . . . . . . 41
3.2 Wolf Summation Method . . . . . . . . . . . . . . . . . . . 41
3.2.1 Charge Optimization with Wolf . . . . . . . . . . . . 49
3.2.2 Wolf Summation for Dipoles . . . . . . . . . . . . . 51
3.3 Potentials for Oxides . . . . . . . . . . . . . . . . . . . . . . 54
3.3.1 Simulations with ReaxFF . . . . . . . . . . . . . . . 59
3.3.2 CuSiO with COMB . . . . . . . . . . . . . . . . . . 60
2
3.3.3 Variable Charges for Dipoles . . . . . . . . . . . . . 61
4 Flexoelectricity 67
4.1 MD Simulations . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1.1 Displacement Modes . . . . . . . . . . . . . . . . . . 70
4.1.2 Primary Polarization . . . . . . . . . . . . . . . . . . 72
v
vi Contents
4.1.3 Induced Polarization . . . . . . . . . . . . . . . . . . 75
4.2 The Flexoelectric Constant µ . . . . . . . . . . . . . . . . 77
11
4.3 The Resulting Flexoelectric Constants . . . . . . . . . . . . 79
5 Conclusion and Outlook 85
A The Software Package IMD 87
B Interactions Integrals 89
C Transformation of the Flexoelectric Tensor 91
Literaturverzeichnis 93
Bibliography 93
List of Symbols
E Electrostatic energy, page 16
es
r real space cut-off, page 8
c
COMB Charge Optimized Many-Body, page 25
CTIP Charge Transfer Ionic Potential, page 21
DCT-BOP Dynamic Charge Transfer Bond Order Potential, page 24
EAM Embedded Atom Method, page 8
EIM Embedded Ion Method, page 23
HV Hong and Vanderbilt, page 68
IMD ITAP Molecular Dynamics, page 5
LCP Local Chemical Potential, page 24
MD Molecular Dynamics, page 3
MPI Message Passing Interface, page 85
ReaxFF Reactive Force Field, page 28
SM Streitz and Mintmire, page 16
TS Tangney and Scandolo, page 29
TTM Two-Temperature Model, page 85
vii
viii List of Symbols
List of Figures
2.1 Motion of a single particle during a MD step. . . . . . . . . 7
2.2 The main idea of the Ewald summation method.. . . . . . 11
3.1 Path to the minimum via the method of steepest descent. . 34
3.2 Error terms for A-orthogonalsearch directions. . . . . . . . 36
3.3 Using conjugate search directions for reaching the minimum. 38
3.4 Spherical truncation and charge neutralization. . . . . . . . 43
3.5 The Madelung energy in case of charge neutralization. . . 45
3.6 Energy oscillations are additionally damped.. . . . . . . . . 48
3.7 Charge optimization with the modified model of SM. . . . . 50
3.8 Charge distribution of an Al O /Al-interface structure. . . 51
2 3
3.9 The dipole structure scalar of liquid silica. . . . . . . . . . . 53
3.10 Equation of state for liquid silica at 3100 K. . . . . . . . . . 54
3.11 Tensile test of bulk AlO along the 1210 -direction. . . . . . 55
h i
3.12 Tensile test of bulk AlO along the 1010 -direction. . . . . . 56
h i
3.13 Tensile test of bulk AlO along the 0001 -direction. . . . . . 57
h i
3.14 Al/Al O relaxed by ab-initio and MD simulation. . . . . . 58
2 3
3.15 Charge difference across the Cu/α-quartz interafce . . . . . 61
3.16 Crack propagation with variable charges.. . . . . . . . . . . 63
3.17 Visualizing the crack propagation with MegaMol . . . . . . . 64
4.1 Visualization of the crack tip with MegaMol . . . . . . . . . 68
4.2 Different displacements modes for periclase. . . . . . . . . . 71
4.3 Convergence behavior of the polarization. . . . . . . . . . . 74
4.4 Orientation of the TS dipoles. . . . . . . . . . . . . . . . . . 76
4.5 The direction of the electric field. . . . . . . . . . . . . . . . 76
4.6 Convergence behavior of the polarization for mode (a) . . . 78
′
4.7 Both parts of polarization as a function of strain gradient. . 80
ix
x List of Figures