A set of equations is derived for determining the pressure at which nucleation, growth, and overall crystallization rates of glass-forming liquids have their maximum values. The location and magnitudes of these maxima are determined and analysed. The analysis is performed based on the classical theories of nucleation and growth, however, without introducing additional assumptions such as the Stokes-Einstein-Eyring equation, models for specific kinetic mechanisms of aggregation, the specification of the type of pressure dependence of the diffusion coefficient, or specific models for the computation of the thermodynamic driving force of crystallisation, the specific interfacial energy, and the work of critical cluster formation. Particular theoretical models are employed only for analytical estimates and for an illustration of the general results. For the description of the pressure dependence of the viscosity, a new model developed by the authors is utilised. Moreover, the concept of fragility has been advanced to variations of the viscosity of glass-forming melts in dependence on pressure variations. Pressure fragility, defined appropriately, is shown to be one of the basic parameters determining the location and the magnitude of the maxima of nucleation, growth and overall crystallization rates as a function of pressure.
