Chapter 12. Simulation Techniques

  1. Prof. Wolfgang Pfeiler
  1. Ferdinand Haider1,
  2. Rafal Kozubski2 and
  3. T.A. Abinandanan3

Published Online: 20 SEP 2007

DOI: 10.1002/9783527614196.ch12

Alloy Physics: A Comprehensive Reference

Alloy Physics: A Comprehensive Reference

How to Cite

Haider, F., Kozubski, R. and Abinandanan, T.A. (2007) Simulation Techniques, in Alloy Physics: A Comprehensive Reference (ed W. Pfeiler), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527614196.ch12

Editor Information

  1. University of Vienna, Faculty of Physics, Dynamics of Condensed Systems, Strudlhofgasse 4, 1090 Vienna, Austria

Author Information

  1. 1

    Universität Augsburg, Institut für Physik, Universitätsstr. 1, 86135 Augsburg, Germany

  2. 2

    Jagellonian University, M. Smoluchowski Institute of Physics, ul. Reymonta 4, 30-059 Cracow, Poland

  3. 3

    Indian Institute of Science, Department of Materials Engineering, Bangalore 560 012, India

Publication History

  1. Published Online: 20 SEP 2007
  2. Published Print: 11 JUL 2007

ISBN Information

Print ISBN: 9783527313211

Online ISBN: 9783527614196

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Keywords:

  • alloy physics;
  • simulation techniques;
  • molecular dynamics simulations;
  • Monte Carlo simulations;
  • phase field models

Summary

This chapter contains sections titled:

  • Introduction

  • Molecular Dynamics Simulations

    • Basic Ideas

    • Atomic Interaction, Potential Models

      • Pairwise Interaction

      • Many-Body Potentials, the EAM Method

    • Practical Considerations

    • Different Thermodynamic Ensembles: Thermostats, Barostats

    • Implementation of MD Algorithms

    • Practical Aspects: Time Steps

    • Evaluation of Data: Use of Correlation Functions

    • Applications to Alloys, Alloy Dynamics, and Alloy Kinetics

  • Monte Carlo Simulations

    • Foundations of Stochastic Processes – Markov Chains and the Master Equation

    • The Idea of Sampling

    • Markov Chains as a Tool for Importance Sampling

    • General Applicability

      • Simulation and Characterization of System Properties in Thermodynamic Equilibrium

      • Simulation of Relaxation Processes Toward Equilibrium

      • Simulation of Nonequilibrium Processes and Transport Phenomena

    • Limitations: Finite-Size Effects and Boundary Conditions

    • Numerical Implementation of MC

      • Classical Realization of Markov Chains

      • “Residence Time” Algorithm

      • The Problem of Time Scales

    • Applications to Alloys

      • General Assumptions

      • Physical Model of an Alloy

    • Practical Aspects

    • Review of Current Applications in Studies of Alloys

      • Computation of Phase Diagrams using Grandcanonical Ensemble

      • Reverse and Inverse Monte Carlo Methods: from Experimental SRO Parameters to Atomic Interaction Energies

    • Going beyond the Ising Model and Rigid-Lattice Simulations

    • Monte Carlo Simulations in View of other Techniques of Alloy Modeling

  • Phase Field Models

    • Introduction

    • Cahn–Hilliard Model

      • Energetics

      • Interfacial Energy and Width

      • Dynamics

    • Numerical Implementation

    • Application: Spinodal Decomposition

    • Cahn–Allen Model

      • Kinetics

    • Generalized Phase Field Models

      • Key Features of Phase Field Models

      • Precipitation of an Ordered Phase

      • Grain Growth in Polycrystals

      • Solidification

    • Other Topics

      • Anisotropy in Interfacial Energy

      • Elastic Strain Energy

  • Outlook

  • Appendix

  • References