Quantitative Phase Field Modelling of Solidification

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 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 the 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.