Abstract
Abstract This paper is concerned with the physical origin of one of the recently introduced dendrite tip scaling parameters [V. Pines, A. Chait, M. Zlatkowski, J. Crystal Growth 167 (1996) 777]. Using at least two parameters, σ 1 and σ 2 , the above quoted scaling analysis permits a consistent determination of the dendrite tip curvature radius and solidification velocity. In this work, the parameter σ 1 is shown to account for the divergence of the conventional dendrite tip scaling parameter, σ, at low supercooling. The parameter σ 1 is traced to the linear stage of development of the morphological instability of a small spherical nucleus placed in a supercooled melt. We demonstrate that σ 1 is proportional to the characteristic initial mean curvature of an unstable nucleus. The initial curvature may take different values depending on the origin of the unstable nucleus, and could be specified in a careful experimental setup.
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