Deymier / Runge / Muralidharan Multiscale Paradigms in Integrated Computational Materials Science and Engineering

Materials Theory, Modeling, and Simulation for Predictive Design
1. Auflage 2016
ISBN: 978-3-319-24529-4
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 226, 305 Seiten

Reihe: Springer Series in Materials Science

This book presents cutting-edge concepts, paradigms, and research highlights in the field of computational materials science and engineering, and provides a fresh, up-to-date perspective on solving present and future materials challenges. The chapters are written by not only pioneers in the fields of computational materials chemistry and materials science, but also experts in multi-scale modeling and simulation as applied to materials engineering. Pedagogical introductions to the different topics and continuity between the chapters are provided to ensure the appeal to a broad audience and to address the applicability of integrated computational materials science and engineering for solving real-world problems.

Autoren/Hrsg.

Deymier, Pierre

Runge, Keith

Muralidharan, Krishna

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Contributors;9
4;1 Introduction;10
4.1;Abstract;10
4.2;1.1 Conceptual Framework in Theory, Modeling and Simulation;10
4.2.1;1.1.1 Theory;11
4.2.2;1.1.2 Model;13
4.2.3;1.1.3 Simulation;14
4.2.4;1.1.4 Additional Remarks;15
4.3;1.2 Multiscale Modeling and Simulation;16
4.3.1;1.2.1 Multiscale Approaches;16
4.3.2;1.2.2 Serial and Concurrent Multiscale Modeling and Simulation;17
4.3.3;1.2.3 Consistent Embedding;18
4.3.4;1.2.4 Multi-theory and Multi-model Approaches;18
4.4;Acknowledgments;19
4.5;References;19
5;2 Path Integral Molecular Dynamics Methods;21
5.1;Abstract;21
5.2;2.1 Introduction;22
5.3;2.2 Theoretical Framework and Model Development;24
5.3.1;2.2.1 Feynman Path Integral;24
5.3.1.1;2.2.1.1 Partition Function for a Single Particle;24
5.3.1.2;2.2.1.2 Systems of Interacting Particles Obeying Maxwell-Boltzmann Statistics;29
5.3.1.3;2.2.1.3 Two-Electron System;31
5.3.1.4;2.2.1.4 Many-Electron System;35
5.3.2;2.2.2 Path Integral with Non-local Exchange Using a Mean Field Approximation;39
5.3.3;2.2.3 Restricted Path Integral Method;41
5.3.4;2.2.4 Classical Isomorphism for Many-Body Fermion System;44
5.3.5;2.2.5 Path Integral with Non-local Pseudo-potential;46
5.3.5.1;2.2.5.1 Local and Nonlocal Pseudo-potential;46
5.3.5.2;2.2.5.2 One Electron System;47
5.3.5.3;2.2.5.3 Evaluation of the Non-local Density Matrix Elements;49
5.3.5.4;2.2.5.4 One Electron Partition Function;53
5.3.5.5;2.2.5.5 Model of a Valence Electron in a Sodium Atom;54
5.4;2.3 Path Integral Molecular Dynamics Simulation Method;56
5.4.1;2.3.1 Molecular Dynamics Method;56
5.4.2;2.3.2 Molecular Dynamics Classical Hamiltonian for N-Electron Plasma;58
5.4.3;2.3.3 Molecular Dynamics Hamiltonian for N-Alkali Atom Metal;60
5.4.4;2.3.4 Molecular Dynamics Hamiltonian for a Single Alkali Atom with Non-local Pseudo-potential;61
5.4.5;2.3.5 Periodic Boundary Conditions;62
5.4.5.1;2.3.5.1 Ewald Summation Method;62
5.4.5.2;2.3.5.2 Maintaining the Continuity of the Necklace Representation of Quantum Particles;65
5.4.5.3;2.3.5.3 Evaluation of { \det }\left( {E^{{\left( {p,q} \right)}} } \right) of the Effective Exchange Potential with PBC;67
5.4.6;2.3.6 Calculation of Forces;69
5.4.7;2.3.7 Isothermal Molecular Dynamics;70
5.4.8;2.3.8 Calculation of Properties;71
5.4.8.1;2.3.8.1 Time Averages;72
5.4.8.2;2.3.8.2 Energy Estimator;72
5.4.8.3;2.3.8.3 Pair Correlation Function;74
5.5;2.4 Applications of the Pimd Method;75
5.5.1;2.4.1 Electron Plasma;75
5.5.2;2.4.2 Alkali Metal;80
5.5.3;2.4.3 Expanded Body Centered Cubic (BCC) Hydrogenoid Crystal;90
5.5.4;2.4.4 Electron in Non-local Pseudo-potential;100
5.5.5;2.4.5 Conclusions;104
5.6;Appendix 1: Free Particle Propagator;106
5.7;Appendix 2: Exchange Force Calculation;107
5.8;Appendix 3: Derivation of the Force on an Electron in a Non-local Pseudo-potential;109
5.9;Appendix 4: Exchange Kinetic Energy Estimator for N-Electron System;110
5.10;Appendix 5: Energy Estimator for Electron in Non-local Pseudo-potential;111
5.11;References;112
6;3 Interatomic Potentials Including Chemistry;115
6.1;Abstract;115
6.2;3.1 Background;115
6.3;3.2 The Fragment View of Hamiltonians for Materials and Molecules;120
6.4;3.3 A Different Way to Decompose a System;123
6.5;3.4 Selected Many-Electron, Valence Basis States;129
6.5.1;3.4.1 The Fragment Hamiltonian Approach;134
6.5.2;3.4.2 New Variables for the Charge States of Each Fragment;136
6.5.3;3.4.3 Three-State Fragment Energies;139
6.5.4;3.4.4 Applications;142
6.5.4.1;3.4.4.1 Application I: H2 Molecule;143
6.5.4.2;3.4.4.2 Application II: Mulliken Electronegativity, Parr-Pearson Hardness, and Their FH Counterparts;144
6.5.4.3;3.4.4.3 Application III: Metallic Character in an Atomistic Model;148
6.5.4.4;3.4.4.4 Application IV: Charge-Flow Regulation in a Two-State, Two-Fragment Model;151
6.5.4.5;3.4.4.5 Application V: Chemical Potential Equalization;152
6.6;3.5 Informing the Embedded-Atom Method from FH: Two-Variable Embedding Energy;153
6.6.1;3.5.1 General Form of the Model Potential from FH;153
6.6.2;3.5.2 Many-Body Interactions;154
6.6.3;3.5.3 Structure of the FH Embedding Energy for Metals;157
6.6.4;3.5.4 Coordination Dependencies of Energy Scales;159
6.6.5;3.5.5 Background Densities;160
6.6.5.1;3.5.5.1 Generalized Energy Scales;161
6.6.6;3.5.6 FH Model for Elemental Ni;164
6.6.7;3.5.7 Metallic Character of Ni Structures;167
6.7;3.6 FH Model as a Variable Charge Model;169
6.7.1;3.6.1 Charge-Dependent Functional Forms as Embedding Energies;171
6.7.2;3.6.2 Embedded Atom (EAM), Modified Embedded Atom (MEAM), and N-Body Methods;175
6.8;3.7 FH View of Bonding;178
6.9;3.8 Environment-Dependent Dynamic Charge (EDD-Q) Model Potentials;178
6.9.1;3.8.1 EDD-Q Potential for Water;181
6.9.2;3.8.2 EDD-Q Potential for Silica;186
6.10;Appendix;193
6.11;References;199
7;4 Phase Field Methods;203
7.1;Abstract;203
7.2;4.1 Introduction;203
7.3;4.2 Methods;204
7.3.1;4.2.1 Conventional PF Methods;204
7.3.2;4.2.2 PFC and AE Method;206
7.4;4.3 Applications;208
7.4.1;4.3.1 Solid-State Phase Transformations;208
7.4.2;4.3.2 Ferroelectric Materials;213
7.4.3;4.3.3 Dislocation;214
7.4.4;4.3.4 Grain Growth;215
7.4.5;4.3.5 Dendrite Solidification;217
7.4.6;4.3.6 Fracture;221
7.4.7;4.3.7 Vesicle Morphology;221
7.5;4.4 Perspectives;222
7.6;References;223
8;5 Peridynamics;226
8.1;Abstract;226
8.2;5.1 Introduction;226
8.3;5.2 Integral Representation of Continuum Mechanics;227
8.4;5.3 Practical Implementation;230
8.5;5.4 Applications;231
8.5.1;5.4.1 Damage in a Ceramic Layer Due to Small Particle Impact;232
8.5.2;5.4.2 Fracture Patterns in Anodized Aluminum;239
8.5.3;5.4.3 Dynamic Fracture of Glass;250
8.6;References;254
9;6 Consistent Embedding Frameworks for Predictive Multi-theory Multiscale Simulations;255
9.1;Abstract;255
9.2;6.1 Introduction;255
9.3;6.2 Example 1: The Consistent Embedding Framework for Quantum-Classical Coupling;258
9.3.1;6.2.1 Transfer Hamiltonian;258
9.3.2;6.2.2 Classical Interatomic Potential;259
9.3.3;6.2.3 Pseudo Atoms;260
9.3.4;6.2.4 Quantum-Classical Multiscale Framework;261
9.4;6.3 The Compound Wavelet Matrix Method;265
9.4.1;6.3.1 Compounding Methodology for Coupling Scales: Forming the CWM;267
9.5;6.4 Example 2: Microstructural Evolution of Materials Using the Compound Wavelet Matrix Method;273
9.6;6.5 Example 3: The Dynamic-CWM (dCWM) Approach Applied to Reactive Flows;278
9.7;6.6 Example 4: A Cautionary Tale: Multiscale Models for Elastic Wave Propagation in Materials;291
9.8;References;302
10;Index;304