A model was proposed which was based upon a phase-field approach to the study of the effect of solute drag on moving grain boundaries in a binary alloy system. By considering the grain boundary to be a distinguishable phase and by adopting a so-called segregation potential in the grain boundary region, the effect of solute drag was automatically incorporated into the model. It was shown that, at equilibrium, the model could reproduce the equilibrium solute segregation and Gibbs adsorption. It was also demonstrated that, at a 1-dimensional steady-state, the model included both the solute drag proposed by Cahn and the free energy dissipation of Hillert & Sundman. In the dilute-solution limit, simple expressions for the concentration distribution around the interfacial region and for solute drag were obtained as functions of the boundary velocity, diffusivity and segregation potential. They were found to be consistent with previous theories for solute-drag phenomenon. In a 2-dimensional quasi-steady state, the phase-field model reduced to the relationship between normal velocity and boundary curvature and the relationship between phase-field mobility and grain-boundary mobility was obtained.

A Phase Field Model for the Solute Drag on Moving Grain Boundaries. P.R.Cha, S.G.Kim, D.H.Yeon, J.K.Yoon: Acta Materialia, 2002, 50[15], 3817-29