Phase field modelling of interfaces from first principles

Abstract

Phase field modelling is a technique in (computational) material science that utilises diffuse interface constructions to simulate the dynamics of microstructural evolution. To date, phase field modelling of crystalline interfaces has been guided mainly by phenomenology and symmetry considerations, rather than microscopic physics. The central equation of motion minimises a free energy with respect to the phase field, which is considered as a space and time dependent, coarse-grained, continuous degree of freedom of the system. However, it is neither clear how to interpret the phase field microscopically, nor how to derive the equation of motion from atomic interactions. Based on the (classical) density functional theory by Haymet and Oxtoby, we derive the phase field model by Allen and Cahn, which is commonly used for modelling crystalline interfaces. In the present article, we summarise the physical implications of the various observables and parameters as well as the underlying approximations. © 2008 IOP Publishing Ltd.