Abstract
We propose that the maximum-velocity principle conventionally used in theories of dendritic crystal growth be replaced by a stability criterion of the form ʋρ 2 = constant, where ʋ is the growth velocity and ρ is the tip radius. Our argument is based on a linear stability analysis of the nearly-paraboloidal steady-state solution in the case of small but nonvanishing capillary. We find that dendrites which are too broad and slow suffer tip-splitting instabilities, whereas those which are too sharp and fast tend to broaden and slow down because of a side-branching instability. Our calculated operating point (with no free parameters) determines a curve of growth versus undercooling which is in substantial agreement with the data of Glicksman, Schaefer and Ayers.
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