Dissipation-Theory Treatment of the Transition from Diffusion-Controlled to Diffusionless Solidification

Abstract

The steady-state velocity of a planar liquid-solid interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. A solute drag term and an intrinsic interfacial mobility term are included in the dissipation calculations for a binary alloy. The solute drag calculation employs a solute trapping model, which has been extended to concentrated alloys. The result is presented in terms of a single unknown parameter, the interfacial diffusivity Di. A transition from diffusion controlled to diffusionless solidification occurs over approximately an order of magnitude in growth velocity, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal.