Dendritic tip selection during solidification of alloys: Insights from phase-field simulations

The effect of undercooling ΔT and the interface energy anisotropy parameter ε₄ on the shape of the equiaxed dendritic tip has been investigated by using a quantitative phase-field model for solidification of binary alloys. It was found that the tip radius ρ increases and the tip shape amplitude coefficient A₄ decreases with the increase of the fitting range for all cases. The dendrite tip shape selection parameter σ* decreases and then stabilizes with the increase of the fitting range, and σ* increases with the increase of ε₄. The relationship between σ* and ε₄ follows a power-law function ${\sigma }^{\ast }\propto {\epsilon }_4^{\alpha }$, and α is independent of ΔT but dependent on the fitting range. Numerical results demonstrate that the predicted σ* is consistent with the curve of microscopic solvability theory (MST) for ε₄ < 0.02, and σ* obtained from our phase-field simulations is sensitive to the undercooling when ε₄ is fixed.