Initial conditions implied by [formula omitted] solidification of a sphere with capillarity and interfacial kinetics

Abstract

We explore the initial conditions implied by t 1 2 growth ofa spherical crystal solidifying from a pure, undercooled melt, including the effects of both capillarity and interface kinetics, and relate our findings to initial conditions that would be expected on the basis of classical nucleation theory. For crystal sizes near the nucleation radius, the calculated temperature profiles show a cold region ahead of the advancing interface that is even more undercooled than the undercooled bath. This cold region acts as a local heat sink that compensates for the reduced growth speed that would otherwise result from capillarity and kinetics, leading to precisely the same t 1 2 growth law that would have been obtained had both capillarity and kinetics been neglected. We submit that this t 1 2 solution should not be taken seriously in the context of the classical theory of nucleation of a crystal from an isothermal melt.