Recent advances in the phase-field model for solidification

The recent development of the phase-field models for solidification and the ir application examples are briefly reviewed. The phase-field model is firs tly proposed for pure material systems and then extended to binary alloy, m ulti-phase and multi-component systems theoretically. Though the calculatio n conditions are limited due to the sharp interface limit parameters in the early stage, it is widened in the thin interface limit model, The developm ent of the phase-field model is summarized from a viewpoint of the formulat ion of phase-field equation and parameters. The important studies and the l atest results such as application examples of free dendrite growth, directi onal solidification, Ostwald ripening, interface-particle interaction and m ulti-phase simulation are mentioned. Finally future works of the phase-fiel d model are prospected.