Kauzmann paradox and the crystallization of glass-forming melts

Abstract

© 2017 Elsevier B.V. General relations for the dependence of the thermodynamic driving force of crystallization and the specific interfacial energy melt-crystal of critical crystal clusters on temperature and pressure are derived. Its application to the analysis of experimental data on crystal nucleation seems to support at a first glance a proposal by Kauzmann on the existence of a pseudo-spinodal curve in melt-crystallization. Provided this assumption is true, Kauzmann temperature (and for pressure-induced nucleation, the Kauzmann pressure) cannot be reached by a metastable liquid due to intensive crystallization processes occurring in its vicinity. However, such suggestion cannot be retained taking into account the kinetic terms (diffusion coefficients, viscosity) in the expression for the nucleation rate. The absence of a pseudo-spinodal in melt-crystallization can be verified also in an alternative way by considering the characteristic time scales of crystallization and relaxation. Finally, it is shown that the phenomenon denoted commonly as Kauzmann paradox is merely an untypical as compared to normal conditions type of behavior. Neither in its original formulation nor in its consequences it results in any contradictions with basic laws of nature. They are prevented either by normal (not associated with a pseudo-spinodal) crystallization or a conventional glass transition.