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Full Description
This book presents a study of phase field modelling of solidification in metal alloy systems. It is divided in two main themes. The first half discusses several classes of quantitative multi-order parameter phase field models for multi-component alloy solidification. These are derived in grand potential ensemble, thus tracking solidification in alloys through the evolution of the chemical potentials of solute species rather than the more commonly used solute concentrations. The use of matched asymptotic analysis for making phase field models quantitative is also discussed at length, and derived in detail in order to make this somewhat abstract topic accessible to students. The second half of the book studies the application of phase field modelling to rapid solidification where solute trapping and interface undercooling follow highly non-equilibrium conditions. In this limit, matched asymptotic analysis is used to map phase field evolution equations onto the continuous growth model, which is generally accepted as a sharp-interface description of solidification at rapid solidification rates.
This book will be of interest to graduate students and researchers in materials science and materials engineering.
Key Features
Presents a clear path to develop quantitative multi-phase and multi-component phase field models for solidification and other phase transformation kinetics
Derives and discusses the quantitative nature of the model formulations through matched interface asymptotic analysis
Explores a framework for quantitative treatment of rapid solidification to control solute trapping and solute drag dynamics
Contents
1. A Brief History of Phase Field Modelling. 2. Overview of the Book. 3. Recap of Grand Potential Thermodynamics. 4. Grand Potential Phase Field Functional. 5. Phase Field Dynamics. 6. Re-Casting the Phase Field Equations for Quantitative Simulations. 7. Equilibrium Properties of Grand Potential Funcional. 8. Thermal Fluctuations in the Phase Field Equations. 9. Special Cases of the Grand Potential Phase Field Model. 10. Application: Phase Field Modelling of Ternary Alloys. 11. Interpreting Asymptotic Analyses of Phase Field Models. 12. The Regime of Rapid Solidification. 13. Modelling Continuous Growth Kinetics in the Diffuse Interface Limit of the Grand Potential Phase Field Equations. 14. Applications: Phase Field Simulations of Rapid Solidificaation of a Binary Alloy
