A multiple-component order parameter phase field model for anisotropic grain growth

A phase field model for anisotropic grain growth is presented. The model uses multiple-component order parameters to describe the grain orientations. These order parameters are the structural amplitudes related to the star of the shortest reciprocal lattice vectors of the crystalline phase. The free energy of the system is formulated as a Landau expansion of the order parameters, which incorporates the symmetry of the crystalline phase. The spatial and temporal evolution of these order parameters is governed by the time-dependent Ginburg-Landau (TDGL) equations. In this model, the anisotropy is introduced naturally, since the effect of the underlying symmetry is taken into account in both the gradient and bulk terms in the free energy expansion. We consider a simple binary two-phase solid-liquid mixture in two dimensions with the solid having a square lattice. As an example, we studied the growth and morphology of a single solid particle in a liquid. Potential applications of the model to simulating the anisotropic grain growth in single-phase polycrystalline materials as well as in the presence of a liquid phase are discussed.