Overview

This book introduces new theoretical techniques in materials research. With the computer power now available, it is possible to use numerical techniques to study various physical and chemical properties of complex materials from first principles. Some typical examples are presented and all the necessary equations and plots are included so that readers can fully understand the details. This book offers the materials scientist access to, and an understanding of the modern development of molecular dynamics and Monte Carlo simulation. It will also be of interest to physicists and chemists engaged in materials research.

Full Product Details

Author:   Kaoru Ohno ,  Keivan Esfarjani ,  Yoshiyuki Kawazoe
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1999 ed.
Volume:   129
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   0.678kg
ISBN:  

9783540639619

ISBN 10:   3540639616
Pages:   329
Publication Date:   18 August 1999
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Replaced By:   9783662565407
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

Table of Contents

1. Introduction.- 1.1 Computer Simulation as a Tool for Materials Science.- 1.2 Modeling of Natural Phenomena.- 2. Ab Initio Methods.- 2.1 Introduction.- 2.2 Electronic States of Many-Particle Systems.- 2.2.1 Quantum Mechanics of Identical Particles.- 2.2.2 The Hartree-Fock Approximation.- 2.2.3 Density Functional Theory.- 2.2.4 Periodic Systems.- 2.2.5 Group Theory.- 2.2.6 LCAO, OPW and Mixed-Basis Approaches.- 2.2.7 Pseudopotential Approach.- 2.2.8 APW Method.- 2.2.9 KKR, LMTO and ASW Methods.- 2.2.10 Some General Remarks.- 2.2.11 Ab Initio O(N) and Related Methods.- 2.3 Perturbation and Linear Response.- 2.3.1 Effective-Mass Tensor.- 2.3.2 Dielectric Response.- 2.3.3 Magnetic Susceptibility.- 2.3.4 Chemical Shift.- 2.3.5 Phonon Spectrum.- 2.3.6 Electrical Conductivity.- 2.4 Ab Initio Molecular Dynamics.- 2.4.1 Car-Parrinello Method.- 2.4.2 Steepest Descent and Conjugate Gradient Methods.- 2.4.3 Formulation with Plane Wave Basis.- 2.4.4 Formulation with Other Bases.- 2.5 Applications.- 2.5.1 Application to Fullerene Systems.- 2.5.2 Application to Point Defects in Crystals.- 2.5.3 Application to Other Systems.- 2.5.4 Coherent Potential Approximation.- 2.6 Beyond the Born-Oppenheimer Approximation.- 2.7 Electron Correlations Beyond the LDA.- 2.7.1 Generalized Gradient Approximation.- 2.7.2 Self-Interaction Correction.- 2.7.3 GW Approximation.- 2.7.4 Exchange and Coulomb Holes.- 2.7.5 Optimized Effective Potential Method.- 2.7.6 Time-Dependent Density Functional Theory.- 2.7.7 Inclusion of Ladder Diagrams.- 2.7.8 Further Remarks: Cusp Condition, etc.- References.- 3. Tight-Binding Methods.- 3.1 Introduction.- 3.2 Tight-Binding Formalism.- 3.2.1 Tight-Binding Parametrization.- 3.2.2 Calculation of the Matrix Elements.- 3.2.3 Total Energy.- 3.2.4 Forces.- 3.3 Methods to Solve the Schrödinger Equation for Large Systems.- 3.3.1 The Density Matrix O(N) Method.- 3.3.2 The Recursion Method.- 3.4 Self-Consistent Tight-Binding Formalism.- 3.4.1 Parametrization of the Coulomb Integral U.- 3.5 Applications to Fullerenes, Silicon and Transition-Metal Clusters.- 3.5.1 Fullerene Collisions.- 3.5.2 C240 Doughnuts and Their Vibrational Properties.- 3.5.3 IR Spectra of C60 and C60 Dimers.- 3.5.4 Simulated Annealing of Small Silicon Clusters.- 3.5.5 Titanium and Copper Clusters.- 3.6 Conclusions.- References.- 4. Empirical Methods and Coarse-Graining.- 4.1 Introduction.- 4.2 Reduction to Classical Potentials.- 4.2.1 Polar Systems.- 4.2.2 Van der Waals Potential.- 4.2.3 Potential for Covalent Bonds.- 4.2.4 Embedded-Atom Potential.- 4.3 The Connolly-Williams Approximation.- 4.3.1 Lattice Gas Model.- 4.3.2 The Connolly-Williams Approximation.- 4.4 Potential Renormalization.- 4.4.1 Basic Idea: Two-Step Renormalization Scheme.- 4.4.2 The First Step.- 4.4.3 The Second Step.- 4.4.4 Application to Si.- References.- 5. Monte Carlo Methods.- 5.1 Introduction.- 5.2 Basis of the Monte Carlo Method.- 5.2.1 Stochastic Processes.- 5.2.2 Markov Process.- 5.2.3 Ergodicity.- 5.3 Algorithms for Monte Carlo Simulation.- 5.3.1 Random Numbers.- 5.3.2 Simple Sampling Technique.- 5.3.3 Importance Sampling Technique.- 5.3.4 General Comments on Dynamic Models.- 5.4 Applications.- 5.4.1 Systems of Classical Particles.- 5.4.2 Modified Monte Carlo Techniques.- 5.4.3 Percolation.- 5.4.4 Polymer Systems.- 5.4.5 Classical Spin Systems.- 5.4.6 Nucleation.- 5.4.7 Crystal Growth.- 5.4.8 Fractal Systems.- References.- 6. Quantum Monte Carlo (QMC) Methods.- 6.1 Introduction.- 6.2 Variational Monte Carlo (VMC) Method.- 6.3 Diffusion Monte Carlo (DMC) Method.- 6.4 Path-Integral Monte Carlo (PIMC) Method.- 6.5 Quantum Spin Models.- 6.6 Other Quantum Monte Carlo Methods.- References.- A. Molecular Dynamics and Mechanical Properties.- A.l Time Evolution of Atomic Positions.- A.2 Acceleration of Force Calculations.- A.2.1 Particle-Mesh Method.- A.2.2 The Greengard-Rockhlin Method.- References.- B. Vibrational Properties.- References.- C. Calculation of the Ewald Sum.- References.- D. Optimization Methods Used in Materials Science.- D.l Conjugate-Gradient Minimization.- D.2 Broyden’s Method.- D.3 SA and GA as Global Optimization Methods.- D.3.1 Simulated Annealing (SA).- D.3.2 Genetic Algorithm (GA).- References.

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