Phase field model derivation for rapid crystal growth in polycrystalline alloys

A phase field model of rapid multi–grain growth is developed. Using a multi–phase model for polycrystalline growth in multi–component alloying systems and the model of fast phase transformations, the Gibbs free energy change on crystallization is formulated as a driving force for polycrystalline growth. The model of fast phase transitions, which introduces not only classical slow variables (concentration, chemical potential and phase field), but also the fast ones (diffusion flux and gradient flow), was used to capture short periods of times usually occurring in the rapid solidification and in the fast solid-state transformations. The evolution equations for the fast crystallization are written using multi–phase interpolation functions among growing polycrystallites.