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

The effect of undercooling Δ T and the interface energy anisotropy parameter ε 4 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 A 4 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 ε 4 . The relationship between σ * and ε 4 follows a power-law function σ ∗ ∝ ε 4 α , and α is independent of Δ T but dependent on the fitting range. Numerical results demonstrate that the predicted σ * is consistent with the curve of microscopic solvability theory (MST) for ε 4 < 0.02, and σ * obtained from our phase-field simulations is sensitive to the undercooling when ε 4 is fixed.