Pattern Selection in Three Dimensional Dendritic Growth

Abatraet-We study the selection of the shape and growth velocity of three dimensionaf dendritic crystals in cubically anisotropic materials. We demonstrate that aside from minor additional complexities due to the lack of axisymmetry, the recently discovered mechanism of “microscopic solvability” can be extended to these systems and used to find a unique needle crystal solution of the equations of thermal diffusion-controlled solidification. We compare the predictions of this approach with measured growth rates in succinonitrile. Finally, we extend our analysis to determine the ratio of the sidebranch wavelength to the tip radius.