3D Growth Kinetics of Precipitates with Anisotropic Interfacial Free Energy: A Phase-Field Study

Abstract

In this study, we report on the 3D growth kinetics of an isolated β precipitate growing from a supersaturated α matrix. The α-β interfacial energy is assumed to be cubic anisotropic; specifically, either (100) or (111) interfaces are preferred. The diffusivity is maintained a constant in our model; this constant diffusivity is achieved through a combination of Cahn–Hilliard and Allen–Cahn equations (with appropriate choice of model free energy parameters). Our results indicate that depending on the matrix supersaturation, the growth modes can either be shape preserving or non-shape preserving. In the case of shape preserving growth, we are able to verify, that as indicated by the earlier theoretical studies, the classical Zener-Frank theories can be used to predict the growth rates of precipitates.