Computational Materials Science: From Basic Principles to Material Properties (Lecture Notes in Physics, 642)

✍ Scribed by Wofram Hergert (editor), Arthur Ernst (editor), Markus Däne (editor)

• Publisher: Springer
• Year: 2004
• Tongue: English
• Leaves: 320
• Edition: 2004
• Category: Library

✦ Synopsis

Computational Physics is now a discipline in its own right, comparable with theoretical and experimental physics. Computational Materials Science concentrates on the calculation of materials properties starting from microscopic theories. It has become a powerful tool in industrial research for designing new materials, modifying materials properties and optimizing chemical processes. This book focusses on the application of computational methods in new fields of research, such as nanotechnology, spintronics and photonics, which will provide the foundation for important technological advances in the future. Methods such as electronic structure calculations, molecular dynamics simulations and beyond are presented, the discussion extending from the basics to the latest applications.

✦ Table of Contents

front-matter
Chapter 1
Chapter 2
2.1 Density Functional Theory in a Nutshell
2.2 Full-Potential Local-Orbital Band Structure Scheme (FPLO)
2.2.1 The Local Orbital Representation
2.2.2 Partitioning of Unity
2.2.3 Density and Potential Representation
2.2.4 Basis Optimization
2.2.5 Examples
2.2.6 Comparison of Results from FPLO and WIEN97
Chapter 3
3.1 The Green’s Function and the Many-Body Method
3.1.1 General Considerations
3.1.2 Quasi-Particles
3.1.3 Self-Energy
3.1.4 Kohn-Sham Approximation for the Self-Energy
3.2 Methods of Solving the Kohn-Sham Equation
3.3 GW Approximation
Chapter 4
4.1 Introduction
4.2 Photonic Bandstructure Computation
4.3 Defect Structures in Photonic Crystals
4.3.1 Maximally Localized Photonic Wannier Functions
4.3.2 Defect Structures via Wannier Functions
4.3.3 Localized Cavity Modes
4.3.4 Dispersion Relations of Waveguides
4.3.5 Photonic Crystal Circuits
4.4 Finite Photonic Crystals
4.5 Conclusions and Outlook
Chapter 5
5.1 Introduction
5.2 Finite-Di.erence in Time-Domain
5.3 Uniaxial Perfectly Matching Layers (UPML) Boundary Conditions
5.4 Time-Domain Full Vectorial Maxwell-Bloch Equations
5.5 Computational Costs
5.6 Test Runs
5.7 Microdisk Laser Dynamics
5.8 Conclusion
Appendix A: Relations
Chapter 6
6.1 Introduction
6.2 Group Theory Packages for Computer Algebra Systems
6.3 Basic Concepts in Group Theory
6.4 Representation Theory
6.4.1 Matrix Representations of Groups
6.4.2 Basis Functions of Irreducible Representations
6.5 Symmetry Properties of Schr¨odinger’s Equation and Maxwell’s Equations
6.6 Consequences of Lattice Periodicity
6.7 Electronic Band Structure
6.7.1 Compatibility Relations
6.7.2 Symmetry-Adapted Basis Functions
6.8 Discussion of Photonic Band Structures
6.8.1 Assignment of the IRs to the Photonic Band Structure
6.9 Conclusions
Chapter 7
7.1 Introduction
7.2 Theoretical Methods
7.2.1 First-Principles Molecular Dynamics
7.2.2 Details of Calculations
7.3 Selected Applications to Clusters and Disordered Systems
7.3.1 CuOn Clusters
7.3.2 Si-Doped Heterofullerenes C59Si and C58Si2
7.3.3 Disordered Network-Forming Materials: Liquid SiSe2
7.4 Concluding Remarks
Chapter 8
8.1 Introduction
8.2 Theoretical Methods
8.2.1 Calculation of Electronic Structure
8.2.2 Molecular Dynamics Simulations
8.3 Magnetic Properties of Nanostructures on Metallic Surfaces
8.3.1 Metamagnetic States of 3d Nanostructures on the Cu(001)Surface
8.3.2 Mixed Co-Cu Clusters on Cu(001)
8.4 Quantum Interference and Interatomic Interactions
8.5 Strain and Stress on the Mesoscale
8.5.1 The Concept of Mesoscopic Mis.t
8.5.2 Strain and Adatom Motion on Mesoscopic Islands
8.5.3 Mesoscopic Relaxation in Homoepitaxial Growth
Chapter 9
9.1 Molecular Dynamics as a Multidisciplinary Numerical Tool
9.2 Simulation of Biochemical Systems
9.2.1 Molecular Dynamics Simulation of Liquid Water
9.
9.2.3 Simulation of Bovine Rhodopsin
9.3 Simulation of Chemical Reactions in the Gas Phase
9.4 Simulation of Structural Transformations in Solids and Particles
9.4.1 Simulation of the Phase Diagram of Fe-Ni and Ni-Mn-Ga Alloys
9.4.2 Simulation of the Structural Transformation in Fe-Ni Particles
9.4.3 Simulation of the Melting of Al Clusters
Chapter 10
10.1 Introduction
10.2 Geometry Optimization in Delocalised Internal Coordinates
10.3 Transition State Searching
10.4 Transition State Con.rmation Algorithm
10.5 Chemical Bonding and Elastic Properties of Corundum-Type Oxides: The Rhodium Oxide Case
10.6 Summary
Chapter 11
11.1 Introduction
11.2 Structure-Activity and Structure-Property Approaches
11.3 Atomistic and Mesoscale Simulations and Their Parameterisation
11.3.1 Atomistic Simulation
11.3.2 Mesoscale Methods
11.3.3 Applications of Mesoscale Modeling
11.4 Multiscale Modeling
11.4.1 From the Molecular to the Mesoscale
11.4.2 From Mesoscale to Finite Element Simulation
11.5 Conclusion
Chapter 12
12.1 Introduction
12.2 Principles of Modelling
12.3 Phenomenological Models
12.4 Classical and Nonclassical Material Behavior Models
12.5 Analysis of Thin-Walled Structures
Chapter 13
13.1 Introduction
13.2 A Short Introduction to MPI
13.3 Modeling the Execution Time of MPI Operations
13.4 Example: Solving Systems of Linear Equations
13.4.1 Standard Iterative Methods
13.4.2 Sparse Iteration Matrices
13.4.3 Red-Black Ordering
13.5 Task and Data Parallel Execution
13.5.1 Overview of the Tlib Library
13.5.2 Example: Strassen Matrix Multiplication
Chapter 14
14.1 Introduction
14.1.1 Historical Overview and Introduction to Multi-Grid Methods
14.1.2 Additive Multigrid
14.2 Convergence Theory
14.2.1 General Setting
14.2.2 The Smoothing Property
14.2.3 Approximation Property
14.3 Robustness
14.3.1 Robustness for Anisotropic Problems
14.3.2 Robustness for Convection-Di.usion Problems
14.4 Treatment of Systems of PDE
14.5 Adaptive Multigrid
back-matter