A. Karma et A. Sarkissian, INTERFACE DYNAMICS AND BANDING IN RAPID SOLIDIFICATION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(1), 1993, pp. 513-533
Rapid-solidification experiments on metallic alloys in the last decade
have provided widespread observations of a novel ''banded structure.'
' We report the results of numerical and analytical studies of the int
erface dynamics underlying the formation of this structure in a model
of directional solidification which includes both solute and heat diff
usion and nonequilibrium effects. The thrust of these studies is on th
e unsteady dynamics of the planar interface and thermal effects. The m
ain conclusion is that the origin of banding can be related to relaxat
ion oscillations of the solidification front, characterized by large v
ariations of the interface velocity, which are dramatically affected b
y latent-heat diffusion. Without the latter, the oscillations are foun
d to be reasonably well approximated by the phenomenological model of
Carrard et al. [Acta Metall. 40, 983 (1992)], and the band spacing is
inversely proportional to the temperature gradient. In contrast, with
latent-heat diffusion the band spacing is insensitive to the temperatu
re gradient, but is controlled instead by the interplay of solute and
heat diffusion. The smallness of the solutal diffusivity to thermal di
ffusivity ratio is exploited to explain analytically this effect and t
o derive considerably simpler equations of interface motion that provi
de an efficient numerical means to study the nonplanar interface dynam
ics expected to cause dark bands. A reasonable agreement with experime
nt is found for the spacing of banded structures dominated by light-ba
nd microsegregation-free regions in Al-Fe alloys.