Multi-grain evolution under slow, intermediate and fast regimes of solidification in multi-component alloying system

Development of the theory of rapid growth in terms of phase field model was provided for multi-grain case. The growth of polycrystalline multi-component alloying systems, which driving force regarded as the Gibbs free energy change on crystallization, was studied with the help of the model of fast phase transformations. The special attention was given to the specific rapid solidification features, affecting on the need of using both classical slow and fast variables. Finally, the evolution equations for diffusion flux and gradient flow were developed concerning multi-phase interpolation among growing poly-crystallites. In the limit of relaxation time of fast thermodynamic variables the model tends to restore the Moelan’s phase field model of anisotropic grain growth.