Crystallization of glass-forming liquids: Specific surface energy

Abstract

A generalization of the Stefan-Skapski-Turnbull relation for the melt-crystal specific interfacial energy is developed in terms of the generalized Gibbs approach extending its standard formulation to thermodynamic non-equilibrium states. With respect to crystal nucleation, this relation is required in order to determine the parameters of the critical crystal clusters being a prerequisite for the computation of the work of critical cluster formation. As one of its consequences, a relation for the dependence of the specific surface energy of critical clusters on temperature and pressure is derived applicable for small and moderate deviations from liquid-crystal macroscopic equilibrium states. Employing the Stefan-Skapski-Turnbull relation, general expressions for the size and the work of formation of critical crystal clusters are formulated. The resulting expressions are much more complex as compared to the respective relations obtained via the classical Gibbs theory. Latter relations are retained as limiting cases of these more general expressions for moderate undercoolings. By this reason, the formulated, here, general relations for the specification of the critical cluster size and the work of critical cluster formation give a key for an appropriate interpretation of a variety of crystallization phenomena occurring at large undercoolings which cannot be understood in terms of the Gibbs’ classical treatment.