Insight into scale selection of dimensionless phase-field model of alloy solidification

The available phase-field models are generally limited to certain specific concentrations and temperatures, weakening the universality of the method. A unified dimensionless framework is developed by adopting arbitrary concentration and temperature scales for nondimensionalization, thereby eliminating scale dependence in model comparisons. The dimensionless phase-field equations are validated by simulating the growth of two kinds of typical alloys including four-fold symmetry morphology (e.g., Fe, Al, and Cu) and six-fold symmetry morphology (e.g., Mg, Zn, and α-Ti) patterns in both 2D and 3D cases. The effect of the scales on characteristic parameters, including capillary length and relaxation time, is discussed, and a reasonable scale range is determined by evaluating both numerical accuracy and computing performance. Four typical phase-field equations are perfectly mapped by selecting specific concentration and temperature scales, which validates the applicability of the reformulated model and provides guidance for further application of the phase-field models. Furthermore, the relationship between the reformulated model and the grand-potential based model is simply analyzed, and the relation with the phase-field equations with decoupled dimensionless concentration is also discussed.