Multiphase-field approach for multicomponent alloys with extrapolation scheme for numerical application

A multiphase-field model previously proposed by the authors is reformulated in a thermodynamically consistent form and extended to multicomponent systems. The phase-field and diffusion equations, derived from a free energy functional, are compared to those postulated in the previous model in the limit of a binary alloy. The constraint of local quasiequilibrium, which is equivalent to the postulate of equal diffusion potentials for coexisting phases, is deduced from a variational principle. Solute partitioning and evaluation of the thermodynamic driving force for phase transformation are done by numerical minimization of the free energy of the multiphase system using the Calphad approach. A local extrapolation scheme which enhances the computational efficiency for complex numerical simulations of technical alloys is presented. It is shown that this extrapolation scheme, used in a "multibinary" approximation, reproduces the former model without restriction to dilute solutions.