Phase-field model for multiphase systems with different thermodynamic factors

A modified phase-field model for quantitative simulations of low-speed phase transitions in multiphase systems is proposed, which takes into account the difference between thermodynamic factors in all the phases. The presented model is based on the quantitative phase-field concept developed by Steinbach et al. I. Steinbach, F. Pezolla, B. Nestler, M. Seeelberg, R. Prieler, G.J. Schmitz, J.L.L. Rezende, A phase field concept for multiphase systems, Physica D 94 (1996) 135] for multiphase systems allowing to consider the multiphase transition as a superposition of pairwise interactions between two phases. We complete this approach and develop a model, which uses parameters derived from chemical free energy functions of individual phases evaluated from experimental data by the CALPHAD method Lukas et al. (2007) 17]. Because the thermodynamic factors are different in various phases we need to evaluate a special form of total chemical free energy function of a multiphase mixture and use it in the phase-field model. It is shown, that for the developed model the thin-interface asymptotic and the anti-trapping term developed previously for the solidification of pure substances can be applied. The model is verified by an example of the Al-Ni system whose peritectic structural morphology during the directional solidification is investigated. The suggested model can be also extended to multicomponent systems.