Cellular and dendritic growth in a binary melt - A marginal stability approach

A simple model for the constrained growth of an array of cells or dendrites in a binary alloy in the presence of an imposed positive temperature gradient in the liquid is proposed, with the dendritic or cell tip radius calculated using the marginal stability criterion of Langer and Muller-Krumbhaar (1977). This approach, an approach adopting the ad hoc assumption of minimum undercooling at the cell or dendrite tip, and an approach based on the stability criterion of Trivedi (1980) all predict tip radii to within 30 percent of each other, and yield a simple relationship between the tip radius and the growth conditions. Good agreement is found between predictions and data obtained in a succinonitrile-acetone system, and under the present experimental conditions, the dendritic tip stability parameter value is found to be twice that obtained previously, possibly due to a transition in morphology from a cellular structure with just a few side branches, to a more fully developed dendritic structure.