Phase-field model of growth and dissolution of stoichiometric phase in binary solution

The phase-field approach for describing the growth and dissolution of a phase of constant composition in a binary solution is considered. The relaxation equations for the phase field and impurity concentration in the phase of variable composition, taking into account the thermodynamic properties of compounds, are derived from the condition of non-decreasing Gibbs energy. It is demonstrated that the equations derived from the principles of nonequilibrium thermodynamics and the law of conservation of matter in volume imply the existence of two mechanisms of growth and dissolution of stoichiometries. The model permits the use of an arbitrary binary system with stoichiometries. For purposes of verification, the Si-Ti binary system, described by the experimentally calculated Gibbs energies of the phases, has been employed. A one-dimensional numerical simulation of the phase transition process under different initial conditions has been conducted, exhibiting qualitative agreement with the anticipated behaviour of the melting-solidification processes.