Hurle, D.T.J., Jakeman, E. and Wheeler, A.A.
Effect of solutal convection on the morphological stability of a binary alloy.
Journal of Crystal Growth, 58, (1), . (doi:10.1016/0022-0248(82)90223-8).
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The effects of the coupling between the morphological stability of a planar, horizontal crystal-melt interface of a growing crystal and solutal convection in the melt are explored using linear perturbation theory. The results are compared with the Mullins-Sekerka criterion (J. Appl. Phys. 35 (1964) 444) for morphological stability which neglects the effects of convection and with the recent numerical study by Coriell et al. (J. Crystal Growth 49 (1980) 13). It is found that the deformation of the interface due to the onset of solutal convection occurs above a critical value of the solutal Rayleigh number but that, below this critical value, the Mullins-Sekerka criterion for interface breakdown is not significantly altered by the inclusion of the fluid dynamics. An exception to this is the case where the temperature gradient in the melt is extremely small, when some small stabilisation of the interface against breakdown is predicted. Overstable modes of breakdown have been investigated and the form of the bifurcation studied. It is concluded that, under commonly encountered conditions of growth, the stationary instability is the first to occur.
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