Extended higher-order multi-phase-field model for three-dimensional anisotropic-grain-growth simulations

Based on the multi-phase-field (MPF) model reported by Steinbach et al., we constructed a higher-order MPF model in a previous study that contains a higher-order term and an additional kinetic parameter to represent the properties of triple junctions (TJs); this model was observed to be suitable for the simulation of 2D grain growth with anisotropic grain-boundary (GB) energy and mobility, which are strongly dependent on the misorientation angle (Δθ). In the current study, we attempt to improve the accuracy of 3D MPF simulations of anisotropic grain growth by extending this higher-order MPF model such that it accounts for the properties of quadruple junctions as well as those of TJs. In addition, using the extended higher-order MPF model, a series of grain-growth simulations are performed for a 3D columnar structure while considering the anisotropic GB properties, through which the accuracy of the model is examined in detail. The results confirm that the extended higher-order MPF model enables the anisotropic GB properties to be handled accurately for wider-ranging Δθ than in previous models.