A phase field model for the solute drag on moving grain boundaries

Abstract

We propose a model based on a phase-field approach to study the effect of the solute drag on moving grain boundaries in a binary alloy system. By considering the grain boundary as a distinguishable phase and adopting a “segregation potential” in the grain boundary region, the effect of solute drag is automatically incorporated into the model. It is shown at equilibrium that the model can reproduce the equilibrium solute segregation and Gibbs adsorption. It is also demonstrated at a one-dimensional steady state that the model includes both the solute drag proposed by Cahn and the free energy dissipation by Hillert and Sundman. In the dilute solution limit, the simple expressions for the concentration distribution around the interfacial region and the solute drag are obtained as functions of boundary velocity, diffusivity and segregation potential and they are found to be consistent with the previous theories for solute drag phenomenon. In two-dimensional quasi steady state, the phase field model reduces to the relationship between normal velocity and the curvature of the boundary and the relationship between phase field mobility and the grain boundary mobility is obtained.