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Phase Field Lectures

Overview

Global Initiative of Academic Networks (GIAN) course on Phase Field Modelling by Peter Voorhees at IITB in March 2018.

Lecture 1

Regular solution model for phase separating and ordering systems; Failure of classical diffusion equation for systems that undergo spinodal decomposition.

Lecture 2

Mathematical preliminaries: Taylor expansion of free energy, Gauss' theorem, group theory, and variational calculus.

Lecture 3

Modification of classical diffusion equation for systems that undergo spinodal decomposition; Cahn-Hilliard equation and the linear stability analysis.

Lecture 4

Analytical solution of Cahn-Hilliard equation in 1-D; Interface width and interfacial energy and their scaling with simulation parameters.

Lecture 5

Order-disorder transformation and Allen-Cahn equation; Analytical solution of Allen-Cahn in 1-D; Characterization of the tanh solution for the Allen-Cahn equation.

Lecture 6

Coherent misfitting precipitates; Eshelby problem; Khachaturyan's generalization.

Lecture 7

Introduction to asymptotic analysis; Derivation of motion by mean curvature from phase-field models of grain growth.

Lecture 8

Finite difference and spectral implementation of Allen-Cahn equation (order-disorder transformation, grain growth).

Lecture 9

Incorporating elastic stress effects into phase-field models.