Modified evolution equations for the precipitation kinetics of complex phases in multi-component systems

Recently, a model has been developed for the evolution of spherical precipitates in multi-component, multi-phase systems based on the assumption of a maximum Gibbs energy dissipation rate. The mean-field type equations determine the rate of change of the radius and the chemical composition of each individual precipitate from a system of linear equations. For precipitates with complex stoichiometric composition, this first approach is not applicable. In this paper, modified evolution equations are presented that allow for consideration of arbitrary compositional constraints in precipitates and thus overcome the limitations of the initial model formulation.