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

chapter Chapter 1|8 pages

A Brief History of Phase Field Modelling

chapter Chapter 2|4 pages

Overview of This Book

section |36 pages


chapter 14Chapter 3|4 pages

Recap of Grand Potential Thermodynamics

chapter Chapter 4|6 pages

The Grand Potential Phase Field Functional

chapter Chapter 8|6 pages

Thermal Fluctuations in Phase Field Equations

section |32 pages


chapter 50Chapter 9|30 pages

Special Cases of the Grand Potential Phase Field Model

chapter Chapter 10|12 pages

Application: Phase Field Modelling of Ternary Alloys

section |10 pages


chapter 94Chapter 11|8 pages

Interpreting Asymptotic Analyses of Phase Field Models