Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Shape Parameter for a Non-Axisymmetric Isothermal Dendrite



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 growth direction [001], for anisotropic surface free energy of the form γ = γ0 [1 + 4 ε4(n4/x + n 4/y + n 4/z)], where the ni are components of the unit normal of the crystal surface. This comparison results in ε = -2ε4, independent of the Peclet number. From the experimental value of ε4, we find ε {nearly equal to} -0.011, in good agreement with the measured value ε {nearly equal to} -0.008 of LaCombe et al.
- 6347
Report Number


dendritic growth, Ivantsov relation, non-axisymmetric dendrites, supercooled liquids


McFadden, G. , Coriell, S. and Sekerka, R. (1999), Shape Parameter for a Non-Axisymmetric Isothermal Dendrite, - 6347, National Institute of Standards and Technology, Gaithersburg, MD (Accessed February 23, 2024)
Created June 1, 1999, Updated October 16, 2008