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

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Springer Science & Business Media, Jun 17, 2004 - Science - 180 pages
The book is devoted to the application of phase-field (diffuse interface) models 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 derive 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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Contents

1 Introduction
1
2 What Is an Interface? Interfaces in Materials Science and Beyond
6
Thermodynamic Potentials and Phase Diagrams
19
4 Thermodynamic Concepts of PhaseField Modeling
31
5 Asymptotic Analysis
59
6 Application of Diffuse Interface Modeling to Hydrodynamically Driven Growth
97
7 Application to Epitaxial Growth Involving Elasticity
131
8 Conclusions and Perspectives
141
A Numerical Issues of Diffuse Interface Modeling
145
References
164
Index
175
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