Diffuse-interface modeling of solute trapping in rapid solidification: Predictions of the hyperbolic phase-field model and parabolic model with finite interface dissipation

Two recently developed phase-field models, a hyperbolic model and a parabolic model with finite interface dissipation, are employed to study the solute trapping in a Si-0.25 at.% As alloy during rapid solidification. The hyperbolic model is applied at the nanometer scale of the interface width δ. The parabolic model is derived by a coarse-graining procedure and is intended to operate with mesoscopic resolution of the interface η. The coarse-graining numerical parameters, namely interface width η and the interface permeability P, are adjusted in the parabolic model to fit the segregation coefficient calculated by the microscopic model on the nanoscale. Based on the optimal sets of η and P selected at small interface velocity, a linear relation between their logarithm values is obtained. This logarithmic relation provides a theoretical basis for choosing the appropriate values of η and P in the numerical phase-field simulation in three spatial dimensions.