Insight into scale selection of dimensionless phase-field model of alloy solidification - Tang, Yuchen; Zhang, Ang; Liu, He; Zhang, Gengyun; Li, Chuangming; Li, Yongfeng; Dong, Zhihua; Huang, Guangsheng; Jiang, Bin (Materials & design, 2025)
[Display omitted] •The phase-field model for alloy solidification is reformulated based on arbitrary concentration and temperature scales.•The dimensionless phase-field equations with arbitrary scales are validated and applied by simulating typical alloys.•A reasonable range of arbitrary scales is determined by evaluating both numerical accuracy and computing performance.•The reformulated model establishes the connection between models with different scales. 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.