Planar isothermal solidification from an undercooled melt: Unsteady solute segregation studied with the phase-field model

The planar isothermal solidification of a binary alloy is studied through the phase-field model. The model includes gradient energy terms for both the phase and concentration fields. The long time attractor of the process was identified in a previous study by Wheeler, Boettinger, and McFadden [Phys. Rev. E 47, 1893 (1993)] in the limit of vanishing small values of epsilon/delta, where epsilon and delta are the coefficients of the phase-field and concentration gradient energies, respectively. In that limit the main results of the continuous growth model (CGM) of Aziz and Kaplan [Acta Metall. 36, 2335 (1988)] were substantially recovered. The present study is focused on the first transient of the process, when the solute profile is not yet fully developed. We found that in this stage the solute segregation at the solid-liquid interface deviates from the predictions of the CGM, as the solute partitioning is contrasted by the energy cost required to substain large concentration gradients.