Abstract
When a dilute binary mixture is pulled at constant velocity V in an external thermal gradient G, the solid-liquid interface exhibits a morphological instability when V becomes larger than a threshold velocity Vc(G). For V < Vc the stationary interface is planar, for V > Vc it develops a (quasi)periodic cellular structure. This instability, first analyzed by Mullins and Sekerka(1), results from the competition between the destabilizing effect of solute diffusion and the stabilization due to the thermal gradient and to capillarity.
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References
W. W. Mullins, R. F. Sekerka: Stability of a planar interface during solidification of a dilute binary alloy, J.Appl.Phys., 35: 444 (1964)
B. Billia: Recherches sur la morphologie du front de solidification lors de la croissance unidirectionnelle d’alliages binaires, Thèse, Aix-Marseille (1982)
see for example: D. K. Shangguan, J. D. Hunt: Modelling of cellular growth of faceting crystals, in: Proceedings of the Conference on Solidification Processing (Sheffield, 1987)
J.S. Langer: Instabilities and pattern formation in crystal growth, Rev.Mod.Phys., 52: 1 (1980)
M.Ben Amar, Y. Pomeau: Growth of faceted needle crystals: Theory, Europhys.Lett. 6: 609 (1988)
R. Bowley, B. Caroli, C. Caroli, F. Graner, P. Nozières, B. Roulet: On directional solidification of a faceted crystal, J. de Physique 50: 1377 (1989)
B. Caroli, C. Caroli, B. Roulet: Directional solidification of a faceted crystal II — Phase dynamics of crenellated front patterns, J. de Physique, to be published
A. A. Chernov, T. Nishinaga: Growth shapes and their stability at anisotropic interface kinetics: Theoretical aspects for solution growth, in: “Morphology of Crystals”, Part I, I.Sunagawa ed. (Terra Scient. Publ. Corp.) 1987
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© 1990 Plenum Press, New York
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Caroli, B., Caroli, C., Roulet, B. (1990). Directional Solidification of a Faceted Crystal. In: Busse, F.H., Kramer, L. (eds) Nonlinear Evolution of Spatio-Temporal Structures in Dissipative Continuous Systems. NATO ASI Series, vol 225. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5793-3_45
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DOI: https://doi.org/10.1007/978-1-4684-5793-3_45
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