Rapid solidification under local nonequilibrium conditions

The effects of local nonequilibrium solute diffusion on a solute concentration field, solute partitioning, interface temperature, and absolute stability limit have been considered. The model incorporates two diffusive speeds, ${\mathrm{V}}_{\mathrm{Db}}$, the bulk-liquid diffusive speed, and ${\mathrm{V}}_{\mathrm{Di}}$, the interface diffusive speed, as the most important parameters governing the solute concentration in the liquid phase and solute partitioning. The analysis of the model predicts a transition from diffusion-controlled solidification to purely thermally controlled regimes, which occurs abruptly when the interface velocity V equals the bulk liquid diffusive speed ${\mathrm{V}}_{\mathrm{Db}}$. The abrupt change in the solidification mechanism is described by the velocity-dependent effective diffusion coefficient ${\mathrm{D}}^{\mathrm{*}}$=D(1-${\mathrm{V}}^2$/${\mathrm{V}}_{\mathrm{Db}}^2$) and the generalized partition coefficient ${\mathrm{K}}^{\mathrm{*}}$. If V>${\mathrm{V}}_{\mathrm{Db}}$, then ${\mathrm{D}}^{\mathrm{*}}$=0 and ${\mathrm{K}}^{\mathrm{*}}$=1. This implies an undistributed diffusion field in the liquid (diffusionless solidification) and complete solute trapping at V>${\mathrm{V}}_{\mathrm{Db}}$.