Quantitative phase-field model for the isothermal solidification of a stoichiometric compound in a ternary liquid

Abstract

The phase-field (PF) model is one of the most powerful mathematical models to simulate the solidification of multicomponent alloys. A major challenge faced by the PF model is the treatment of stoichiometric compounds (SCs). In the PF model, compositional derivatives of the free energies of phases need to be treated; however, those of SCs are thermodynamically defined only at a certain composition with respect to the stoichiometric components. Therefore, conventional studies used parabolic functions to provide a pseudo-compositional dependence to free energies. In this paper, we propose a methodology to treat SCs without using the parabolic free energy function. Time-evolution equations were rederived assuming that the free energy of the SC is independent of the composition of its stoichiometric component. We performed numerical calculations for a ternary system comprising two phases, olivine (stoichiometric solid phase) in a basaltic melt (liquid phase), whose free energies were gathered from a thermodynamic database, and we confirmed that the model represents the stoichiometry of the solid phase with high accuracy. This model provides a simple and straightforward methodology to handle SCs in the quantitative PF model.