TY - JOUR
T1 - A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth
AU - Golovin, A. A.
AU - Davis, S. H.
AU - Nepomnyashchy, A. A.
N1 - Funding Information:
This work was supported by a grant from the National Aeronautics and Space Administration, Program on Microgravity Sciences and Applications. We are grateful to A. Bernoff, P.C. Fife, A. Novick-Cohen, P. Metzener and P.W. Voorhees for fruitful discussions. We also thank A. Bayliss and H. Riecke for useful advice on numerical computations.
PY - 1998
Y1 - 1998
N2 - We consider solidification into a hypercooled melt in which kinetic undercooling and anisotropic surface energy are present. We allow the anisotropy to be strong enough that missing orientations would be present in equilibrium configurations, and track the unstable evolution of an initially planar front to a facetted front. Regularization by curvature-dependent surface energy is posed, and in the nonlinear regime a convective Cahn-Hilliard equation is derived. The emergence of facets is thus related to spinodal decomposition and subsequent coarsening. The presence of convective terms generated by the effect of kinetics destroys the binodal construction and leads to a fast coarsening, that for large times t goes as t 1/2.
AB - We consider solidification into a hypercooled melt in which kinetic undercooling and anisotropic surface energy are present. We allow the anisotropy to be strong enough that missing orientations would be present in equilibrium configurations, and track the unstable evolution of an initially planar front to a facetted front. Regularization by curvature-dependent surface energy is posed, and in the nonlinear regime a convective Cahn-Hilliard equation is derived. The emergence of facets is thus related to spinodal decomposition and subsequent coarsening. The presence of convective terms generated by the effect of kinetics destroys the binodal construction and leads to a fast coarsening, that for large times t goes as t 1/2.
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U2 - 10.1016/S0167-2789(98)00181-X
DO - 10.1016/S0167-2789(98)00181-X
M3 - Article
AN - SCOPUS:0001087994
SN - 0167-2789
VL - 122
SP - 202
EP - 230
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-4
ER -