Recent advances in the phase-field model for solidification

The recent development of the phase-field models for solidification and their application examples are briefly reviewed. The phase-field model is firstly proposed for pure material systems and then extended to binary alloy, multi-phase and multi-component systems theoretically. Though the calculation conditions are limited due to the sharp interface limit parameters in the early stage, it is widened in the thin interface limit model, The development of the phase-field model is summarized from a viewpoint of the formulation of phase-field equation and parameters. The important studies and the latest results such as application examples of free dendrite growth, directional solidification, Ostwald ripening, interface-particle interaction and multi-phase simulation are mentioned. Finally future works of the phase-field model are prospected.