1st Edition

Quantitative Phase Field Modelling of Solidification

    186 Pages 11 B/W Illustrations
    by CRC Press

    186 Pages 11 B/W Illustrations
    by CRC Press

    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 1. A Brief History of Phase Field Modelling

    Chapter 2. Overview of the Book

    Chapter 3. Recap of Grand Potential Thermodynamics

    Chapter 4. Grand Potential Phase Field Functional

    Chapter 5. Phase Field Dynamics

    Chapter 6. Re-Casting the Phase Field Equations for Quantitative Simulations

    Chapter 7. Equilibrium Properties of Grand Potential Funcional

    Chapter 8. Thermal Fluctuations in the Phase Field Equations

    Chapter 9. Special Cases of the Grand Potential Phase Field Model

    Chapter 10. Application: Phase Field Modelling of Ternary Alloys

    Chapter 11. Interpreting Asymptotic Analyses of Phase Field Models

    Chapter 12. The Regime of Rapid Solidification

    Chapter 13. Modelling Continuous Growth Kinetics in the Diffuse Interface Limit of the Grand Potential Phase Field Equations

    Chapter 14. Applications: Phase Field Simulations of Rapid Solidificaation of a Binary Alloy


    Nikolas Provatas is a professor of physics at McGill University and holds a Canada Research Chair (Tier 1) in Computational Materials Science. He is also the Scientific Director of the McGill High Performance Computing Centre. From 2001-2012, he was a professor of Materials Science and Engineering at McMaster University. His research uses high-performance computing, dynamic adaptive mesh refinement techniques, condensed matter physics and experimentation to understand the fundamental origins of nano-microstructure pattern formation in non-equilibrium phase transformations, and the role of microstructure in materials processes. He has made numerous scientific contributions to the understanding of length scale selection in dendritic solidification and meta-stable phase formation in solid-state transformations in metal alloys.

    Nana Ofori-Opoku is a Research Scientist at Canadian Nuclear Laboratories Ltd. He received his doctorate in materials science from McMaster University, where he explored computational models for microstructure evolution in materials. He did his postdoctoral work at McGill University, followed by a NIST-CHiMaD fellowship at Northwestern University and the National Institute of Standards and Technology. His research continues to develop theoretical and computational tools to study microstructure evolution in nuclear materials and the dynamics of phase transformations.

    Tatu Pinomaa is a Senior Scientist at VTT Technical Research Centre of Finland Ltd. He received his doctor of science (tech) degree from Aalto University (Finland), where he developed phase field modeling techniques to investigate rapid solidification microstructures in metal additive manufacturing conditions. In his current research, he combines various computational approaches to predict the formation, evolution, and micromechanical response of metallic microstructures for industrial applications.