Notes

Outline

Slide 1

Slide 2

Slide 3

Slide 4

Stefan Problem

Surface Energy

Critical Nucleus and Coarsening

Grain Boundary Grooves

Wavelength of Instabilities

Morphological Instability

Phase-Field Model

Cahn-Allen Equation

Ordering in a BCC Binary Alloy

Parameter Identification

Phase-Field Models

Phase-Field Model

Free Energy Function

Phase-Field Equations

Planar Interface

Sharp Interface Asymptotics

Numerics

Provatas, Goldenfeld & Dantzig (1999) Dendrite Simulation

Anisotropic Equilibrium Shapes

Slide 24

Diffuse Interface Formulation

Corners and Edges

Cahn-Hilliard Equation

Phase Field Equations - Alloy

Slide 29

Slide 30

Inclusion of Surface Properties

Surface Adsorption

Solute Trapping

Wetting in Multiphase Systems

Early Phase-Field Calculations

Adaptive Meshing

A. Karma & W.-J. Rappel (1997)

W. George & J. Warren (2001)

J. Jeong, N. Goldenfeld, & J. Dantzig (2001)

Conclusions