Model for isothermal pattern formation of growing crystals in undercooled binary alloys

Abstract

Using the model of local non-equilibrium solidification, which takes into account deviations from local thermodynamical equilibrium at the interface and bulk phases, a model for pattern formation of crystals in isothermal undercooled binary alloys is presented. The model equations describe the kinetics of the liquid-solid interface motion and local non-equilibrium solute diffusion in the liquid phase. For the self-consistency of the model, we have also taken into account the solute trapping at the interface and deviation of the liquidus line from its equilibrium value using local non-equilibrium diffusion. A main feature of the model equations is the inclusion of crystal growth velocities which are of the order of the diffusion speed in the bulk liquid. This allows one to describe rapid solidification in deeply undercooled alloys. To solve numerically the problem of the growth of crystals and obtain their morphology, an approximation for the model differential equations is formulated using the finite-difference technique.