关键词: phase-field simulations, dendritic structure, interface energy anisotropy, tip shape selection parameter

Abstract: The effect of undercooling $\Delta T$ and the interface energy anisotropy parameter $\varepsilon_{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 $\rho $ 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 $\sigma^{\ast }$ decreases and then stabilizes with the increase of the fitting range, and $\sigma^{\ast }$ increases with the increase of $\varepsilon_{4} $. The relationship between $\sigma^{\ast }$ and $\varepsilon_{4}$ follows a power-law function $\sigma^{\ast }\propto \varepsilon_{4}^{\alpha } $, and $\alpha $ is independent of $\Delta T$ but dependent on the fitting range. Numerical results demonstrate that the predicted $\sigma^{\ast }$ is consistent with the curve of microscopic solvability theory (MST) for $\varepsilon_{4} <0.02$, and $\sigma ^{\ast }$ obtained from our phase-field simulations is sensitive to the undercooling when $\varepsilon_{4} $ is fixed.

Key words: phase-field simulations, dendritic structure, interface energy anisotropy, tip shape selection parameter