The effect of heat transfer on linear crystallization kinetics in one dimension

Abstract

The problem of one-dimensional crystal growth kinetics in a finite system in which coupling occurs between heat flow and the phase boundary reaction (the Stefan problem) is studied by means of a modification of Ehrlich's numerical method. The dimensionless parameters that characterize the problem are deduced by converting to dimensionless variables. They are: the ratio of conductivity and heat capacity in crystal and liquid (assumed unity in the numerical solutions), the Nusselt number, a dimensionless latent heat, the temperature dependence of the dimensionless interface resistance and the initial temperature as a fraction of the melting temperature. The numerical method is applied to the same three systems chosen by Hopper and Uhlmann; an inorganic glass, an organic glass, and tin. Temperature distributions and growth velocities are calculated and discussed for each of these cases under the simplifying but unnecessary assumption that growth rate depends linearly on the supercooling of the interface. For each of these cases, a dimensionless parameter is deduced which provides an accurate estimate of the fractional reduction in velocity due to interface heating.