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Shape Parameter for a Non-Axisymmetric Isothermal DendriteIn previous work, we found approximate solutions for paraboloids having perturbations with four-fold axial symmetry in order to model dendritic growth in cubic materials. These solutions provide self-consistent corrections through second order in a shape parameter e to the Peclet number-supercooling relation of the Ivantsov solution. The parameter e is proportional to the amplitude of the four-fold correction to the dendrite shape, as measured from the Ivantsov paraboloid of revolution. We calculate e by comparing the dendrite tip shape to the portion of the equilibrium shape near the growth direction, (001), for anisotropic surface free energy, where the ni are components of the unit normal of the crystal surface. This comparison results in epsilon = -2(epsilon 4), independent of the Peclet number. From the experimental value of epsilon 4, we find epsilon approximately 0.011, in good agreement with the measured value epsilon approximately 0.008 of LaCombe et al.
Document ID
20000010591
Acquisition Source
Headquarters
Document Type
Other
Authors
McFadden, G. B.
Coriell, S. R.
Sekerka, R. F.
Date Acquired
September 7, 2013
Publication Date
June 1, 1999
Subject Category
Solid-State Physics
Report/Patent Number
PB99-150468
NISTIR-6347
Funding Number(s)
CONTRACT_GRANT: NSF DMR-96-34056
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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