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

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 |

164 | |

175 | |

### Other editions - View all

The Diffuse Interface Approach in Materials Science ..., Volume 73 Heike Emmerich Limited preview - 2003 |

The Diffuse Interface Approach in Materials Science ..., Volume 73 Heike Emmerich No preview available - 2003 |

The Diffuse Interface Approach in Materials Science: Thermodynamic Concepts ... Heike Emmerich No preview available - 2011 |

### Common terms and phrases

anisotropy assumed asymptotic analysis boundary conditions bulk Chap chemical potential coefficient computational concentration conservation context curvature curve cusp defined denotes density change flow depend derivation described diffuse interface approach diffuse interface modeling diffusion limited dendritic dimensionless discussion domain ðū dynamics element employed energy functional epitaxial growth evolution free energy density Gibbs free energy given Glicksman gradient grid growth problem hydrodynamic inner expansion interfacial growth interfacial region kinetic leading-order limited dendritic growth liquid phase matching method Moreover morphology non-conserved numerical obtained order parameter outer expansion phase diagram phase-field equations Phys physical quadtree respect Sect sharp interface equations sharp interface formulation sharp interface limit sharp interface model simulation solid phase solidification solidus surface tension temperature term thermodynamic consistency thermodynamic equilibrium thermodynamic potential thin interface limit transport equations underlying variational vector velocity yields yo(a