The effect of latent heat on weakly non-linear morphological stability

• Published in: Journal of crystal growth 1986-12, Vol.79 (1), p.849-865
• Main Authors: Alexander, J.Iwan D., Wollkind, David J., Sekerka, Robert F.
• Format: Article
• Language: English
• ISSN: 0022-0248; 1873-5002
• DOI: 10.1016/0022-0248(86)90565-8

During directional solidification of a dilute binary alloy, the release of latent heat plays an important role in the determination of the weakly non-linear morphological stability of the solid-liquid interface. The non-linear stability of an initial planar interface is examined by using a Stuart-Watson type of approach, according to which the planar interface is subject to a two-dimensional perturbation that is predicted to be marginally stable by linear theory but no longer has an infinitesimal amplitude. In previous work of this nature, the latent heat of fusion, which appears explicitly in the equation describing the local balance of energy across the solid-liquid interface, was neglected. Allowing for a finite latent heat results in positive values of the Landau coefficient, and hence two-dimensional bands of small stable amplitude, for a much enhanced range of growth conditions, especially at low solute concentrations. We also find that the magnitude of n, the ratio of the thermal conductivities of the solid and fluid, can either augment or diminish the latent heat effect. For values of n less than unity there are values of the distribution coefficient for which no regions of weakly non-linear instability exist, while n greater than unity always admits the possibility of weakly non-linear instability. In general, it appears that two-dimensional bands with small stable amplitudes are favoured by a steep thermal gradient in the solid relative to that in the liquid.