The Diffuse Interface Approach in Materials Science: Thermodynamic Concepts and Applications of Phase-Field Models / Edition 1

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More About This Textbook

Overview

The book is devoted to the application of phase-field (diffuse interface) models in materials science. In materials science phase-field modeling emerged only recently as a theoretical approach to tackle questions concerning the evolution of materials microstructure, the relation between microstructure and materials properties and the transformation and evolution of different phases. This volume brings together the essential thermodynamic ideas as well as the essential mathematical tools to drive phase-field model equations. Starting from an elementary level such that any graduate student familiar with the basic concepts of partial differential equations can follow, it shows how advances in the field of phase-field modeling will come from a combination of thermodynamic, mathematical and computational tools. Also included are two extensive examples of the application of phase-field models in materials science.
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Product Details

  • ISBN-13: 9783540004165
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 5/29/2003
  • Series: Lecture Notes in Physics Monographs Series , #73
  • Edition description: 2003
  • Edition number: 1
  • Pages: 188
  • Product dimensions: 6.20 (w) x 9.40 (h) x 0.50 (d)

Table of Contents

1 Introduction 1
1.1 Structure and Scope of This Work 1
2 What Is an Interface? 7
3 Equilibrium Thermodynamics of Multiphase Systems: Thermodynamic Potentials and Phase Diagrams 19
3.1 Calculating Phase Diagrams from Energy Functionals 21
3.2 Abstracted Phase Diagrams 23
4 Thermodynamic Concepts of Phase-Field Modeling 31
4.1 Derivation of Transport Equations 32
4.2 Introducing the Phase-Field Variable [phi] 38
4.3 Thermodynamic Consistency 46
4.4 Appendix 53
5 Asymptotic Analysis 59
5.1 A Formal Mathematical Approach Towards Matching 59
5.2 Asymptotic Matching for Thin Film Epitaxial Growth 68
5.3 A Generalized Approach Towards the Asymptotic Analysis of Diffuse Interface Models 78
5.4 Discussion 92
5.5 Appendix 93
6 Application of Diffuse Interface Modeling to Hydrodynamically Driven Growth 97
6.1 Diffuse Interface Modeling for Hydrodynamically Influenced Growth 99
6.2 The Selection Problem of Dendritic Growth Revisited 104
6.3 Comparison to Experimental Data 119
6.4 Summary 127
6.5 Appendix 129
7 Application to Epitaxial Growth Involving Elasticity 131
7.1 Elastic Driving Forces within the Diffuse Interface Approach 132
7.2 Comparing Simulations and Experiments 134
7.3 Discussion 140
8 Conclusions and Perspectives 141
Appendix 145
A Numerical Issues of Diffuse Interface Modeling 145
References 165
Index 175
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