The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy III. Weakly nonlinear theory

Abstract

The effect of a constant electric current on the crystal-melt interface morphology during directional solidification at constant velocity of a binary alloy is considered. A linear temperature field is assumed, and thermoelectric effects and Joule heating are neglected; electromigration and differing electrical conductivities of crystal and melt are taken into account. A two-dimensional weakly nonlinear analysis is carried out to third order in the interface amplitude, resulting in a cubic amplitude equation that describes whether the bifurcation from the planar state is supercritical or subcritical. For wavelengths corresponding to the most dangerous mode of linear theory, we calculate the demarcation between supercritical behaviour as a function of processing conditions and material parameters. The bifurcation behaviour is a sensitive function of the magnitude and direction of the electric current and of the electrical conductivity ratio.