TY - JOUR
T1 - Modeling the formation of facets and corners using a convective Cahn-Hilliard model
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 P.C. Fife, P. Metzener, A. Novick-Cohen and P.W. Voorhees for fruitful discussions. We also thank A. Bayliss and H. Riecke for useful advice on numerical computations.
PY - 1999/3
Y1 - 1999/3
N2 - We consider solidification into a hypercooled melt in the presence of kinetic undercooling and anisotropic surface energy. We allow the anisotropy to be strong enough that equilibrium configurations would contain facets divided by corners, 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 the presence of kinetic undercooling and anisotropic surface energy. We allow the anisotropy to be strong enough that equilibrium configurations would contain facets divided by corners, 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/S0022-0248(98)01000-8
DO - 10.1016/S0022-0248(98)01000-8
M3 - Conference article
AN - SCOPUS:0033514532
SN - 0022-0248
VL - 198-199
SP - 1245
EP - 1250
JO - Journal of Crystal Growth
JF - Journal of Crystal Growth
IS - pt 2
T2 - Proceedings of the 1998 10th International Conference on Vapor Growth and Epitaxy and Specialist Workshops on Crystal Growth, ICVGE-10
Y2 - 26 July 1998 through 31 July 1998
ER -