Dynamic scaling in dendritic growth: significance of the initial nucleus size

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, sigma(1) and sigma(2), the above quoted scaling analysis permits a consistent determination of the dendrite tip curvature radius and solidification velocity. In this work, the parameter sigma(1) is shown to account for the divergence of the conventional dendrite tip scaling parameter, sigma, at low supercooling. The parameter sigma(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 sigma(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.