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.

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The connection between CALPHAD models and Phase-Field models is discussed against the background of minimization of the total Gibbs energy of a system. Both methods are based on separation of a multiphase system into individual contributions of the bulk phases, which are described by appropriate models in composition, temperature, and pressure. While the CALPHAD method uses a global minimization of the total Gibbs energy, the Phase-Field method introduces local interactions, interfaces, and diffusion and allows for non-equilibrium situations. Thus, the Phase-Field method is much more general by its concept, however, it can profit a lot if realistic thermodynamic descriptions, as provided by the CALPHAD method, are incorporated. The present paper discusses details of a direct coupling between the Multiphase-Field method and the CALPHAD method. Examples are presented from solidification of technical Mg and Ni base alloys and some problems arising from common practice concerning thermodynamic descriptions in order-disorder systems.

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