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Effect of Surface Free Energy Anisotropy on Dendrite Tip Shape



Geoffrey B. McFadden, Sam R. Coriell, R F. Sekerka


In 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 ε to the Peclet number -- supercooling relation of the Ivantsov solution. The parameter ε is proportional to the amplitude of the four-fold correction to the dendrite shape, as measured from the Ivantsov paraboloid of revolution. We calculate ε by comparing the dendrite tip shape to the portion of the equilibrium shape near the [001] direction for a four-fold anisotropic surface free energy. This comparison results in good agreement with the measured value ε {nearly equal to} -0.008 of LaCombe et al.
Acta Materialia


dendritic growth, ivantsov relation, non-axisymmetric dentrites, supercooled liquids


McFadden, G. , Coriell, S. and Sekerka, R. (2000), Effect of Surface Free Energy Anisotropy on Dendrite Tip Shape, Acta Materialia, [online], (Accessed May 21, 2024)


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Created July 1, 2000, Updated February 17, 2017