A -Vector Formulation of Anisotropic Phase-Field Models: 3-D Asymptotics

In this paper we present a new formulation of a large class of phase-eld models, which describe solidiication of a pure material and allow for both surface energy and interface kinetic anisotropy, in terms of the Hooman-Cahn-vector. The-vector has previously been used in the context of sharp interface models, where it provides an elegant tool for the representation and analysis of interfaces with anisotropic surface energy. We show that the usual gradient-energy formulations of anisotropic phase-eld models are expressed in a natural way in terms of the-vector when appropriately interpreted. We use this new formulation of the phase-eld equations to provide a concise derivation of the Gibbs-Thomson-Herring equation in the sharp-interface limit in three dimensions.