Phase Field Lectures
Global Initiative of Academic Networks (GIAN) course on Phase Field Modelling by Peter Voorhees at IITB in March 2018.
Regular solution model for phase separating and ordering systems; Failure of classical diffusion equation for systems that undergo spinodal decomposition.
Mathematical preliminaries: Taylor expansion of free energy, Gauss' theorem, group theory, and variational calculus.
Modification of classical diffusion equation for systems that undergo spinodal decomposition; Cahn-Hilliard equation and the linear stability analysis.
Analytical solution of Cahn-Hilliard equation in 1-D; Interface width and interfacial energy and their scaling with simulation parameters.
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.
Coherent misfitting precipitates; Eshelby problem; Khachaturyan's generalization.
Introduction to asymptotic analysis; Derivation of motion by mean curvature from phase-field models of grain growth.
Finite difference and spectral implementation of Allen-Cahn equation (order-disorder transformation, grain growth).
Incorporating elastic stress effects into phase-field models.