The influence of temperature gradient zone melting on microsegregation
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I.
INTRODUCTION
IN the last decades, numerical techniques have been developed for calculating the type, the composition, and the amount of solid phases as a function of the cooling conditions. Recent reviews of analytical and numerical solutions are available.[1,2,3] In the most advanced models,[4–10] various effects such as solid-state diffusion, dendrite arm coarsening, and undercooling are considered. At low to medium cooling rates, solid-state diffusion and dendrite arm coarsening contribute to the homogenization of an alloy. At high cooling rates, undercooling effects additionally influence the concentration distribution of the alloying elements or the amount of nonequilibrium phases. While the coarsening of dendrite arms during solidification and its influence on microstructure and microsegregation was investigated in a large number of articles,[11–14] the effect of temperature gradient zone melting (TGZM) first described by Pfann[15] for the case of dendritic solidification has not been examined adequately. Weinberg and Teghtsoonian[16] were the first to observe that in the presence of large temperature gradients, the growth of dendrite arms occurred preferentially on one side of an arm. This leads to sawtoothlike concentration profiles, as measured in unidirectionally cast copper alloys.[16] Asymmetric distribution profiles were also found by Tu¨rkeli and Kirkwood[17] in ternary steels after unidirectional solidification. According to these authors, the effect of TGZM can be seen in many alloy systems (References 18 through 21 provide details), but has not been considered even in cases when it can be directly observed in the figures provided in References 18 through 21. From the available experimental findings, it is not clear how effective TGZM is in increasing T. KRAFT and O. POMPE, Senior Scientists, and H.E. EXNER, Professor and Head of Department, are with the Department of Materials Science, Technical University of Darmstadt, D-64287 Darmstadt, Germany. Manuscript submitted April 14, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
the minimum concentration and in reducing the amount of microsegregation. Using an organic system, Allen and Hunt[22,23] observed that secondary dendrite arms can migrate along the primary stem toward the dendrite tip. The motion is a result of the composition gradient arising from the temperature difference at either side of the melt between two dendrite arms (Figure 1). Migration distances of up to four dendrite arm spacings have been measured. This movement proceeds as follows. Due to the concentration gradient in the liquid, solute is carried by the melt between two arms parallel to the heat flow direction toward the heat source. This leads to a decrease of the solute concentration at the warmer side of a dendrite arm and an increase at the cooler side. To obtain equilibrium at the interface, some solid will dissolve at the cold side and some liquid will solidify at the warm side. Thus, the core of the dendrite arm with the minimum concentration is shifted toward the
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