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Phase-field model for growth and dissolution of a stoichiometric compound in a binary liquid.

We propose a simple formulation of the phase-field model for a stoichiometric compound growing in a binary liquid. In previous models, chemical free energies of stoichiometric compounds have been approximated by parabolic functions of composition; however, the curvature has been determined arbitrarily in spite of the fact that the stoichiometric composition was undesirably modified depending on the curvature. To avoid this uncertainty, we supposed that the chemical free energy of the stoichiometric compound is represented by a single value at a given temperature and derived the phase-field equations without the parabolic free-energy approximation. The phase mobility was derived both for diffusion- and interface-controlled solidification based on a thin interface limit analysis. We carried out numerical simulations of one-dimensional calculations both in diffusion-controlled and interface-controlled cases and found that the growth velocities agreed with the analytic predictions. We also examined two-dimensional solidification of a circular crystal and confirmed that the equilibrium state was shifted, as suggested by the Gibbs-Thomson effect. This study is an important step for phase-field modeling that includes stoichiometric compounds with their accurate thermodynamic properties.