Dendritic growth in the carbon tetrabromide and hexachlorethane system
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Dendritic Growth in the Carbon Tetrabromide and Hexachlorethane System V. S E E T H A R A M A N , L.M. FABIETTI, and R. TRIVEDI Dendritic microstructures are the most frequently observed solidification microstructures in metallic alloys. In addition, the evolution of the steady-state dendritic structures with well-developed sidebranches is one of the complex and fascinating problems in our understanding of pattern formation in physical and biological systems.~l Consequently, a significant number of theoretical and experimental studies have been carried out to understand precisely how the microstructural scales of dendrites, viz., dendrite tip radius, primary spacing, and secondary arm spacing, are related to the driving force. Often it is rationalized that the microstructural scales of dendritic morphology become finer with the increasing driving forces, because a finer scale can efficiently dissipate the latent heat of fusion or can readily redistribute solute with the increase in the solidification rate. However, it has been recognized for a long time that for a given driving force, an infinite number of solutions are possible, which is consistent with the latent heat removal or with the solute redistribution. A mathematical solution of this problem was first obtained by Ivantsov. Izl In contrast, experimental studies show a unique selection of dendrite tip radii for a given driving force. Thus, one of the challenging problems in the theory of dendritic growth has been to understand the criterion that the system follows in selecting the unique dendrite tip radius from an infinite set of solutions of the thermal and mass transport equations. For a number of years, it was assumed that the dendrite in an undercooled melt selects the tip radius which corresponds to the maximum in the growth rate. The invalidity of such an assumption was documented by
V. SEETHARAMAN, formerly with Ames Laboratory, United States Department of Energy, is with Universal Energy Systems, Dayton, OH 45432. L.M. FABIETTI, Graduate Assistant, and R. TRIVEDI, Senior Scientist and Professor of Materials Science and Engineering, are with Ames Laboratory, United States Department of Energy, lowa State University, Ames, IA 50011. Manuscript submitted May 26, 1989. METALLURGICAL TRANSACTIONS A
Glicksman and co-workers p.4'sl by their very careful and thorough experimental studies in a well-characterized system of pure succinonitrile. In an analogous problem of directional solidification, the experimental studies by Trivedi and co-workers 16"7"81 and Esaka and K u r z t91 have shown the invalidity of the criterion based on the minimum undercooling at the interface. Langer and Miiller-Krumbhaar t~~ subsequently examined the selection criterion based on the stability of the dendrite tip. They carried out a linear stability analysis of the Ivantsov parabola and showed that of all possible solutions of the transport equations, only a finite number of solutions give rise to a stable tip radius. The largest stable radius was found to agree remarkably we
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