Convective and Morphological Instabilities During Crystal Growth
Sam R. Coriell, Geoffrey B. McFadden, B T. Murray
We have studied the effects of interface morphology on the dynamics of dendritic growth. The Ivantsov solution for an isothermal paraboloid of revolution growing into a pure, supercooled melt provides a relation between the bulk supercooling and a dimensionless product of the growth velocity and tip radius of a dendrite. In order to model dendritic growth in cubic materials, approximate solutions for paraboloids having perturbations with four-fold axial symmetry have been found. These solutions provide self-consistent corrections through second order in the shape parameter to the Peclet number-supercooling relation of the Ivantsov solution. The shape parameter is proportional to the amplitude of the four-fold correction to the dendrite shape, as measured from the Ivantsov paraboloid of revolution. We have calculated the shape parameter by comparing the dendrite tip shape to the portion of the equilibrium shape near the growth direction for anisotropic surface free energy with cubic symmetry. This comparison results in a shape parameter that is independent of the Peclet number. The calculated shape parameter is in good agreement with recent measurements for succinonitrile by LaCombe et al. This research has also provided analytic representations for the equilibrium shape of anisotropic crystals.
Proceedings of the NASA Microgravity Materials Science Conference
, McFadden, G.
and Murray, B.
Convective and Morphological Instabilities During Crystal Growth, Proceedings of the NASA Microgravity Materials Science Conference
(Accessed February 25, 2024)