The diffuse interface approach in materials science : thermodynamic concepts and applications of phase-field models

Description

"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."--COVER. Read more... 1. Introduction -- 1.1. Structure and Scope of This Work -- 2. What Is an Interface? -- 3. Equilibrium Thermodynamics of Multiphase Systems: Thermodynamic Potentials and Phase Diagrams -- 3.1. Calculating Phase Diagrams from Energy Functionals -- 3.2. Abstracted Phase Diagrams -- 4. Thermodynamic Concepts of Phase-Field Modeling -- 4.1. Derivation of Transport Equations -- 4.2. Introducing the Phase-Field Variable [phi] -- 4.3. Thermodynamic Consistency -- 4.4. Appendix -- 5. Asymptotic Analysis -- 5.1. A Formal Mathematical Approach Towards Matching -- 5.2. Asymptotic Matching for Thin Film Epitaxial Growth -- 5.3. A Generalized Approach Towards the Asymptotic Analysis of Diffuse Interface Models -- 5.4. Discussion