Crystallization of glass-forming liquids: Thermodynamic driving force

• General expressions for the thermodynamic driving force of crystallization are derived.
• Limits of validity of the classical expression are specified.
• The thermodynamic driving force of crystallization has a maximum at the Kauzmann temperature.
• Extensions of the classical relations for the thermodynamic driving force are derived.
• A new tool for the description of crystal nucleation is proposed.

The most general and accurate expressions for the thermodynamic driving force of critical cluster formation are derived employing both the classical and the generalized Gibbs approaches for the description of thermodynamic aspects of crystal nucleation and growth. The thermodynamic driving force of critical cluster formation in the form as applied commonly in classical nucleation theory can be obtained as a limiting case in both approaches introducing certain first-order approximations (truncated at first-order terms Taylor expansion with respect to pressure and temperature, incompressibility of the crystal phase). It is shown that in such approximation the thermodynamic driving force of crystallization has a maximum at the Kauzmann temperature. Improvements of the accuracy of the approximations by extending the Taylor expansion to second-order terms lead to negligible corrections for the thermodynamic driving force provided Gibbs classical treatment is employed. However, significant variations compared to the classical predictions are possible once the generalized Gibbs approach is utilized appropriately accounting for changes of the bulk state parameters of the critical clusters in dependence on the degree of undercooling. Supplemented by a generalization of the Stefan-Skapski-Turnbull relation, sketched briefly here and described in detail in an accompanying paper, the results give a new tool for the description of crystal nucleation and growth processes going considerably beyond the classical theory.