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A phase-field model for isothermal solidification of a binary alloy is developed that includes gradient energy contributions for the phase field and for the composition field. When the gradient energy coefficient for the phase field is smaller than that for the solute field, planar steady-state solutions exhibit a reduction in the segregation predicted in the liquid phase ahead of an advancing front (solute trapping), and, in the limit of high solidification speeds, predict an alloy solidification with no redistribution of composition. Such situations are commonly observed experimentally.
Wheeler et al. (Mon,) studied this question.