Abstract
The phase-field model of Echebarria, Folch, Karma, and Plapp (Phys. Rev. E 70 (2004) 061604) is extended to the case of rapid solidification in which local non-equilibrium 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.
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