Phase-field simulations of crystal growth

This course gives an elementary introduction to the phase-field method and to its applications for the modeling of crystal growth. Two different interpretations of the phase-field variable are given and discussed. It can be seen as a physical order parameter that characterizes a phase transition, or as a smoothed indicator function that tracks domain boundaries. Elementary phase-field models for solidification and epitaxial growth are presented and are applied to the dendritic growth of a pure substance and the step-flow growth on a vicinal surface.