Simulations of Phase-field Models for Crystal Growth and Phase Separation

Abstract

Phase-field theory is a thermodynamically consistent approach for modeling and simulating phenomena that exhibit complex structures such as those encountered in fluid flows and materials science. In this work, the main features of the theory will be reviewed, i.e. mathematical models which arise from the minimization of a thermodynamic potential such as the Helmholtz free energy describing the phenomenology of bulk phases and their interactions. An order parameter is also introduced which plays the role of a phase index avoiding to track explicitly the interface between liquid/liquid and liquid/solid phases. Next, various examples will be given on the basis of phenomena observed in nuclear glasses. Simulations are divided into two classes: for a non-conserved order parameter, simulations will be presented on crystal growth of a pure substance with and without hydrodynamic effect. For a conserved order parameter, an example will be given on phase separation by spinodal decomposition. Finally, the discussion will focus on the parameters needed for the phase-field models and their relationships with the sharp interface approach.