The effect of the anisotropy of surface tension and interface kinetics on morphological stability

Abstract

The theory of the morphological stability of a planar interface during solidification of a binary alloy has been modified to account for an anisotropic departure from local equilibrium (anisotropic interface kinetics) at the solid-liquid interface. The temperature for local equilibrium is calculated from the Gibbs-Thompson equation for anisotropic surface tension. Departure from local equilibrium is characterized by taking the interface velocity to be a function of thermal undercooling, concentration, orientation, and curvature. A perturbation analysis leads to the conclusion that an isotropic departure from local equilibrium causes a modification of the capillary terms and liquidus slope as they enter the expression for the time evolution of perturbations; in addition, perturbation growth rate is retarded. Allowance for anisotropy of surface tension causes the capillary terms to depend on direction. Anisotropic interface kinetics leads to the additional important effect that sinusoidal perturbations are translated parallel to the unperturbed interface as they change in amplitude. The peaks of such sinusoidal perturbations will therefore grow at an angle to the normal of the unperturbed interface. This effect is believed to be an underlying cause for the existence of preferred directions for cellular and dendritic growth.