Grand-potential formulation for multicomponent phase transformations combined with thin-interface asymptotics of the double-obstacle potential

Abstract

In this paper, we describe the derivation of a model for the simulation of phase transformations in multicomponent real alloys starting from a grand-potential functional. We first point out the limitations of a phase-field model when evolution equations for the concentration and the phase-field variables are derived from a free energy functional. These limitations are mainly attributed to the contribution of the grand-chemical-potential excess to the interface energy. For a range of applications, the magnitude of this excess becomes large and its influence on interface profiles and dynamics is not negligible. The related constraint regarding the choice of the interface thickness limits the size of the domain that can be simulated and, hence, the effect of larger scales on microstructure evolution can not be observed. We propose a modification to the model in order to decouple the bulk and interface contributions. Following this, we perform the thin-interface asymptotic analysis of the phase-field model. Through this, we determine the thin-interface kinetic coefficient and the antitrapping current to remove the chemical potential jump at the interface. We limit our analysis to the Stefan condition at lowest order in ε (parameter related to the interface width) and apply results from previous literature that the corrections to the Stefan condition (surface diffusion and interface stretching) at higher orders are removed when antisymmetric interpolation functions are used for interpolating the grand-potential densities and the diffusion mobilities.