Solute trapping in rapid solidification of a binary dilute system: A phase-field study

The phase-field model of Echebarria, Folch, Karma, and Plapp [Phys. Rev. E 70, 061604 ( 2004)] is extended to the case of rapid solidification in which local nonequilibrium phenomena occur in the bulk phases and within the diffuse solid-liquid interface. Such an extension leads to the fully hyperbolic system of equations given by the atomic diffusion equation and the phase-field equation of motion. This model is applied to the problem of solute trapping, which is accompanied by the entrapment of solute atoms beyond chemical equilibrium by a rapidly moving interface. The model predicts the beginning of complete solute trapping and diffusionless solidification at a finite solidification velocity equal to the diffusion speed in bulk liquid.