Curvature dependence of the surface tension and crystal nucleation in liquids

To achieve a quantitative agreement of experimental data with theoretical predictions, in classical nucleation theory a curvature- or size-dependence of the surface tension of critical clusters has to be accounted for. For its description, frequently the Tolman equation is chosen. Tolman derived his relation originally in application to droplets or bubbles in one-component fluids assuming that nucleation is caused by variations of pressure. As shown here his approach and the resulting basic relations are applicable also to the description of crystal nucleation in multi-component fluids if either pressure or temperature is changed. Estimates of the Tolman parameter in application to crystallization are advanced for both the mentioned cases. The Tolman parameter is shown to depend on the surface tension for a planar interface, the number of components in the liquid, the bulk properties of both the liquid and crystal phases, and the way the metastable state is generated. In addition, we develop a method of improving the precision in the specification of the curvature dependence of the surface tension in melt crystallization going beyond the Tolman equation in its original form. The results are applied successfully to the description of crystal nucleation in silicate glass-forming melts.