InhaltsangabeAbout the Author. Series Preface. Preface. Abbreviations. 1 Introduction. 1.1 Material Properties Based on Hierarchy of Material Structure. 1.2 Overview of Multiscale Analysis. 1.3 Framework of Multiscale Analysis Covering a Large Range of Spatial Scales. 1.4 Examples in Formulating Multiscale Models from Practice. 1.5 Concluding Remarks. References. 2 Basics of Atomistic Simulation. 2.1 The Role of Atomistic Simulation. 2.2 Interatomic Force and Potential Function. 2.3 Pair Potential. 2.4 Numerical Algorithms for Integration and Error Estimation. 2.5 Geometric Model Development of Atomistic System. 2.6 Boundary Conditions. 2.7 Statistical Ensembles. 2.8 Energy Minimization for Preprocessing and Statistical Mechanics Data Analyses. 2.9 Statistical Simulation Using Monte Carlo Methods. 2.10 Concluding Remarks. References. 3 Applications of Atomistic Simulation in Ceramics and Metals. Part 3.1 Applications in Ceramics and Materials with Ionic and Covalent Bonds. 3.1 Covalent and Ionic Potentials and Atomistic Simulation for Ceramics. 3.2 Born Solid Model for Ionic-bonding Materials. 3.3 Shell Model. 3.4 Determination of Parameters of Short-distance Potential for Oxides. 3.5 Applications in Ceramics: Defect Structure in Scandium Doped Ceria Using Static Lattice Calculation. 3.6 Applications in Ceramics: Combined Study of Atomistic Simulation with XRD for Nonstoichiometry Mechanisms in Y3Al5O12 (YAG) Garnets. 3.7 Applications in Ceramics: Conductivity of the YSZ Oxide Fuel Electrolyte and Domain Switching of Ferroelectric Ceramics Using MD. 3.8 Tersoff and Brenner Potentials for Covalent Materials. 3.9 The Atomistic Stress and Atomistic-based Stress Measure. Part 3.2 Applications in Metallic Materials and Alloys. 3.10 Metallic Potentials and Atomistic Simulation for Metals. 3.11 Embedded Atom Methods EAM and MEAM. 3.12 Constructing Binary and High Order Potentials from Monoatomic Potentials. 3.13 Application Examples of Metals: MD Simulation Reveals Yield Mechanism of Metallic Nanowires. 3.14 Collecting Data of Atomistic Potentials from the Internet Based on a Specific Technical Requirement. Appendix 3.A Potential Tables for Oxides and Thin-Film Coating Layers. References. 4 Quantum Mechanics and Its Energy Linkage with Atomistic Analysis. 4.1 Determination of Uranium Dioxide Atomistic Potential and the Significance of QM. 4.2 Some Basic Concepts of QM. 4.3 Postulates of QM. 4.4 The Steady State SchrEURodinger Equation of a Single Particle. 4.5 Example Solution: Square Potential Well with Infinite Depth. 4.6 SchrEURodinger Equation of Multi-body Systems and Characteristics of its Eigenvalues and Ground State Energy. 4.7 Three Basic Solution Methods for Multi-body Problems in QM. 4.8 Tight Binding Method. 4.9 HartreeFock (HF) Methods. 4.10 Electronic Density Functional Theory (DFT). 4.11 Brief Introduction on Developing Interatomic Potentials by DFT Calculations. 4.12 Concluding Remarks. Appendix 4.A Solution to Isolated Hydrogen Atom. References. 5 Concurrent Multiscale Analysis by Generalized Particle Dynamics Methods. 5.1 Introduction. 5.2 The Geometric Model of the GP Method. 5.3 Developing Natural Boundaries Between Domains of Different Scales. 5.4 Verification of Seamless Transition via 1D Model. 5.5 An Inverse Mapping Method for Dynamics Analysis of Generalized Particles. 5.6 Applications of GP Method. 5.7 Validation by Comparison of Dislocation Initiation and Evolution Predicted by MD and GP. 5.8 Validation by Comparison of Slip Patterns Predicted by MD and GP. 5.9 Summary and Discussions. 5.10 States of Art of Concurrent Multiscale Analysis. 5.11 Concluding Remarks. References. 6 Quasicontinuum Concurrent and Semi-analytical Hierarchical Multiscale Methods Across Atoms/Continuum. 6.1 Introduction. Part 6.1 Bas

About the Author. Series Preface. Preface. Abbreviations. 1 Introduction. 1.1 Material Properties Based on Hierarchy of Material Structure. 1.2 Overview of Multiscale Analysis. 1.3 Framework of Multiscale Analysis Covering a Large Range of Spatial Scales. 1.4 Examples in Formulating Multiscale Models from Practice. 1.5 Concluding Remarks. References. 2 Basics of Atomistic Simulation. 2.1 The Role of Atomistic Simulation. 2.2 Interatomic Force and Potential Function. 2.3 Pair Potential. 2.4 Numerical Algorithms for Integration and Error Estimation. 2.5 Geometric Model Development of Atomistic System. 2.6 Boundary Conditions. 2.7 Statistical Ensembles. 2.8 Energy Minimization for Preprocessing and Statistical Mechanics Data Analyses. 2.9 Statistical Simulation Using Monte Carlo Methods. 2.10 Concluding Remarks. References. 3 Applications of Atomistic Simulation in Ceramics and Metals. Part 3.1 Applications in Ceramics and Materials with Ionic and Covalent Bonds. 3.1 Covalent and Ionic Potentials and Atomistic Simulation for Ceramics. 3.2 Born Solid Model for Ionic-bonding Materials. 3.3 Shell Model. 3.4 Determination of Parameters of Short-distance Potential for Oxides. 3.5 Applications in Ceramics: Defect Structure in Scandium Doped Ceria Using Static Lattice Calculation. 3.6 Applications in Ceramics: Combined Study of Atomistic Simulation with XRD for Nonstoichiometry Mechanisms in Y3Al5O12 (YAG) Garnets. 3.7 Applications in Ceramics: Conductivity of the YSZ Oxide Fuel Electrolyte and Domain Switching of Ferroelectric Ceramics Using MD. 3.8 Tersoff and Brenner Potentials for Covalent Materials. 3.9 The Atomistic Stress and Atomistic-based Stress Measure. Part 3.2 Applications in Metallic Materials and Alloys. 3.10 Metallic Potentials and Atomistic Simulation for Metals. 3.11 Embedded Atom Methods EAM and MEAM. 3.12 Constructing Binary and High Order Potentials from Monoatomic Potentials. 3.13 Application Examples of Metals: MD Simulation Reveals Yield Mechanism of Metallic Nanowires. 3.14 Collecting Data of Atomistic Potentials from the Internet Based on a Specific Technical Requirement. Appendix 3.A Potential Tables for Oxides and Thin-Film Coating Layers. References. 4 Quantum Mechanics and Its Energy Linkage with Atomistic Analysis. 4.1 Determination of Uranium Dioxide Atomistic Potential and the Significance of QM. 4.2 Some Basic Concepts of QM. 4.3 Postulates of QM. 4.4 The Steady State SchrEURodinger Equation of a Single Particle. 4.5 Example Solution: Square Potential Well with Infinite Depth. 4.6 SchrEURodinger Equation of Multi-body Systems and Characteristics of its Eigenvalues and Ground State Energy. 4.7 Three Basic Solution Methods for Multi-body Problems in QM. 4.8 Tight Binding Method. 4.9 Hartree-Fock (HF) Methods. 4.10 Electronic Density Functional Theory (DFT). 4.11 Brief Introduction on Developing Interatomic Potentials by DFT Calculations. 4.12 Concluding Remarks. Appendix 4.A Solution to Isolated Hydrogen Atom. References. 5 Concurrent Multiscale Analysis by Generalized Particle Dynamics Methods. 5.1 Introduction. 5.2 The Geometric Model of the GP Method. 5.3 Developing Natural Boundaries Between Domains of Different Scales. 5.4 Verification of Seamless Transition via 1D Model. 5.5 An Inverse Mapping Method for Dynamics Analysis of Generalized Particles. 5.6 Applications of GP Method. 5.7 Validation by Comparison of Dislocation Initiation and Evolution Predicted by MD and GP. 5.8 Validation by Comparison of Slip Patterns Predicted by MD and G ...