Phase and solute fields across the solid-liquid interface of a binary alloy

Solidification of binary alloys is characterized by a sharp structural transition across the solid-liquid interface. It is a typical situation which suggests a nonlocal dependence of the appropriate thermodynamic potential on its associate fields. Phase-field models with a gradient contribution for the order parameter have proved to account for nonequilibrium effects, as solute trapping and kinetic undercooling of the solid-liquid interface. The inclusion of a gradient term for the concentration field has also been theoretically investigated, but in this case the correspondence between predicted phenomena and experimental results is still rather unexplored. In the present study we analyze numerical solutions of a phase-field model in both steady and transient conditions. We focus on effects which are critically dependent on the composition field across the solid-liquid interface; the extent of the concentration gradient correction is related to measurable quantities to suggest methods for a comparison between the model predictions and experimental data.