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This book deals with the use of the hodograph equation in phase transformations in condensed matter, especially, for crystallization and solidification processes. The main focus of the book is the interpretation of the phase-field equations for isotropic and anisotropic interfaces based on the advanced Gibbs-Thomson and Herring conditions, respectively. Beginning with the basic ideas behind the extended irreversible thermodynamics, the kinetic phase-field model for slow and arbitrarily fast phase transformations is derived where the unified hodograph equation follows from:
- the sharp interface limit of the diffuse interface or
- the traveling wave solution of the propagating phase field.
Under the example of solute trapping and disorder trapping effects, comparing theoretical results with molecular dynamics simulations, and with the analysis of experimental data, the concrete workability of the developed hodograph equation is demonstrated for widest range of driving force in phase transformations.
List of contents
Phase Interfaces.- Phase Field.- Gibbs Free Energy: Equilibrium and Dynamics.- Approach to Fast Transformations.- The Hodograph Equation.- Velocity-Dependent Herring Equation.
About the author
Peter K. Galenko earned his PhD (1991) and Habilitation (2005) at the Ural Branch of the Russian Academy of Sciences, Physics-Technical Institute, Izhevsk, Russia. Presently, he is working at the Faculty of Physics and Astronomy at Friedrich Schiller University Jena, Germany. In 2008, he became Scientific Prize Winner of the German Aerospace Center for his work on microstructure formation of metals and alloys on the ground and under microgravity conditions. Peter Galenko is an Alexander von Humboldt Fellow, author of 5 books, 15 book chapters, and over 200 peer-reviewed publications.
Summary
This book deals with the use of the hodograph equation in phase transformations in condensed matter, especially, for crystallization and solidification processes. The main focus of the book is the interpretation of the phase-field equations for isotropic and anisotropic interfaces based on the advanced Gibbs–Thomson and Herring conditions, respectively. Beginning with the basic ideas behind the extended irreversible thermodynamics, the kinetic phase-field model for slow and arbitrarily fast phase transformations is derived where the unified hodograph equation follows from:
• the sharp interface limit of the diffuse interface or
• the traveling wave solution of the propagating phase field.
Under the example of solute trapping and disorder trapping effects, comparing theoretical results with molecular dynamics simulations, and with the analysis of experimental data, the concrete workability of the developed hodograph equation is demonstrated for widest range of driving force in phase transformations.
