Diffuse-interface modelling of solute trapping in rapid solidification: predictions of the hyperbolic phase-field model and parabolic model with finite interface dissipation
L. Zhang, E. V. Danilova, I. Steinbach, D. Medvedev, P. Galenko.
Acta Materialia, Elsevier Ltd., 61, 4155–4168, (2013)
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 Ρ, 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 Ρ 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 Ρ in the numerical phase-field simulation in three spatial dimensions.
Keyword(s): rapid solidification; phase-field models; non-equilibrium; segregation; solute trapping