Numerical Simulation of Three-Dimensional Dendritic Growth

Dendritic crystal growth in a pure undercooled melt is simulated quantitatively in three dimensions using a phase-field approach. The classic parameter ${\sigma }^{*}$ that characterizes the dynamically selected operating state of the dendrite tip as well as the full nonaxisymmetric tip morphology are determined as a function of anisotropy for a crystal with a cubic symmetry. Results are compared to experiment and used to critically test solvability theory.