Local non-equilibrium diffusion model for solute trapping during rapid solidification

A local non-equilibrium diffusion model (LNDM) for rapid solidification of binary alloys has been briefly reviewed and used to modify a number of solute trapping models with different solid-liquid interface kinetics. The LNDM takes into account deviation from local equilibrium of a solute diffusion field in bulk liquid on the basis that the exact solutions to hyperbolic diffusion equations govern the solute concentration and solute flux in bulk liquid under local non-equilibrium conditions. The LNDM leads to a velocity-dependent effective diffusion coefficient in bulk liquid ahead of the solid-liquid interface DbLNDM(V), which goes to zero when the interface velocity V → VDb, where VDb is the bulk liquid diffusion speed. The results show an abrupt transition from diffusion-limited to purely thermally controlled solidification, with the diffusion coefficient in bulk liquid DbLNDM(V) = 0 and complete solute trapping KLNDM(V) = 1 at a finite interface velocity V = VDb for any type of solid-liquid interface kinetics. The bulk liquid diffusion speed VDb is a critical parameter for the transition. The velocity dependence of partition coefficients KLNDM(V) has been calculated for different types of solid-liquid interface kinetics, with allowance for local non-equilibrium diffusion effects. The calculation shows that the local non-equilibrium partition coefficients KLNDM(V) reduce to the standard K(V) at low interface velocity (V ≪ VDb) and differ substantially at high interface velocity (V ∼ VDb).