The Role of Microscopic Anisotropy in the Macroscopic Behavior of a Phase Boundary

A LandauGinzburg approach is implemented to study the influence microscopic anisotropy on the interfacial boundary between two phases. The continuum limit for a lattice spin system with anisotropic interactions J, and spacing a, leads to the system of equations ~(a&&) = xf=, (f(a*&/dxf) + t(4 4’) + 224 au/at + (//2)(a#/ar) = KAu. Here, 4 is an order parameter, u is the temperature, r is a relaxation time, 5, are related to J, and a,, I is the latent heat of fusion, and K is the diffusivity. Both equilibrium and non-equilibrium conditions are considered. A modified Gibbs-Thompson relation As u(r, 8) = [u(O) + o”(O)] h’ ~a(@)/~~(@) + @(6*) is obtained, where s is entropy density, K is curvature, u is normal velocity of the interface, and t,(S) is a measure of the thickness of the interface. f? 1986 Academic Press.