Three-dimensional dendrite-tip morphology at low undercooling

We investigate the three-dimensional morphology of the dendrite tip using the phase-field method. We find that, for low undercoolings, this morphology is ostensibly independent of anisotropy strength except for a localized shape distortion near the tip that only affects the value of the tip radius [Formula Presented] [which is crudely approximated by [Formula Presented] where [Formula Presented] is the Ivantsov tip radius of an isothermal paraboloid with the same tip velocity and [Formula Presented] is the stiffness anisotropy]. The universal tip shape, which excludes this distortion, is well fitted by the form [Formula Presented] where [Formula Presented] is the distance from the tip and all lengths are scaled by [Formula Presented] This fit yields [Formula Presented] in the range [Formula Presented] in good quantitative agreement with the existing tip morphology measurements in succinonitrile [LaCombe et al., Phys. Rev. E 52, 2778 (1995)], which are reanalyzed here and found to be consistent with a single [Formula Presented] mode nonaxisymmetric deviation from a paraboloid. Moreover, the fin shape away from the tip is well fitted by the power law [Formula Presented] with [Formula Presented] Finally, the characterization of the operating state of the dendrite tip is revisited in the light of these results.