Crystalline symmetry and the melt-growth kinetics of solid-liquid interface

One of the important factors governing the growth morphology of materials is the interface kinetic coefficient \mu, which is the proportionality constant between the velocity of solid-liquid interface and undercooling. We employ Ginzburg-Landau (GL) free energy functional to derive an analytical expression of kinetic coefficients. The anisotropy of kinetic coefficients naturally arise from the broken symmetry at the solid-liquid interface for various crystalline orientations. The analytical expression of kinetic coefficients is compared to Mikheev-Chernov theory [J. Cryst. Growth 112, 591 (1991)] derived from hydrodynamic equations. In addition, we use equilibrium density wave profiles to evaluate kinetic coefficients and compare them with that from MD simulations. Our results are in good agreement with Mikheev-Chernov theory and MD simulations and shed lights on a possible origin of anisotropy of interfacial kinetics.