Three-dimensional dendrite-tip morphology at low undercooling

Journal Article · Sat Apr 01 04:00:00 EST 2000 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.61.3996· OSTI ID:20216092

Karma, Alain ^[1]; Lee, Youngyih H ^[1]; Plapp, Mathis ^[1]

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1. Physics Department and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115 (United States)

We investigate the three-dimensional morphology of the dendrite tip using the phase-field method. We find that, for low undercoolings, this morphology is ostensibly independent of anisotropy strength except for a localized shape distortion near the tip that only affects the value of the tip radius {rho} [which is crudely approximated by {rho}{approx_equal}(1-{alpha}){rho}{sub Iv} where {rho}{sub Iv} is the Ivantsov tip radius of an isothermal paraboloid with the same tip velocity and {alpha} is the stiffness anisotropy]. The universal tip shape, which excludes this distortion, is well fitted by the form z=-r{sup 2}/2+A{sub 4}r{sup 4} cos 4{phi} where |z| is the distance from the tip and all lengths are scaled by {rho}{sub Iv}. This fit yields A{sub 4} in the range 0.004-0.005 in good quantitative agreement with the existing tip morphology measurements in succinonitrile [LaCombe et al., Phys. Rev. E 52, 2778 (1995)], which are reanalyzed here and found to be consistent with a single cos 4{phi} mode nonaxisymmetric deviation from a paraboloid. Moreover, the fin shape away from the tip is well fitted by the power law z=-a|x|{sup 5/3} with a{approx_equal}0.68. Finally, the characterization of the operating state of the dendrite tip is revisited in the light of these results. (c) 2000 The American Physical Society.

• OSTI ID: 20216092
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 61; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

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