Phase-field modeling of solute trapping: comparative analysis of parabolic and hyperbolic models

The phase-field model of Wheeler, Boettinger and McFadden is extended to the case of fast 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 characteristic diffusion speeds of atoms (both within the diffuse interface and inside the bulk phases) and to the speed of the interface propagation. As a result, the model is described by a system of hyperbolic equations for the atomic diffusion transport as well as for the phase-field. 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.