Crystallization of glass-forming liquids: Maxima of nucleation, growth, and overall crystallization rates

• The location and magnitude of the maxima of nucleation and growth rates are determined.
• The magnitude of the maximum nucleation rate decreases with increasing temperature.
• The magnitude of the maximum growth rate decreases with increasing temperature.
• Several experimental results on crystallization are given an interpretation.

A set of equations for determining the temperatures and magnitudes of the maximum nucleation, growth, and overall crystallization rates of glass-forming liquids is derived and analyzed. The analysis is performed based on the classical theories of nucleation and growth, without introducing additional assumptions such as the Stokes–Einstein–Eyring (SEE) equation, models for specific kinetic mechanisms of aggregation, a specification of the type of temperature dependence of the diffusion coefficient, or specific models for the computation of the driving force of crystallization and the work of critical cluster formation. Such approximations are employed only for analytical estimates and to illustrate the general results. In particular, it is shown that the magnitude of the maximum of the steady-state nucleation rate Jmax decreases upon increasing the ratio Tmax(nucl)/Tm (Tmax(nucl): temperature of maximum of the steady-state nucleation rate, Tm: melting or liquidus temperature). Similarly, the maximum growth rate, umax, decreases with increasing values of the ratio Tmax(growth)/Tm (Tmax(growth): temperature of maximum of the growth rate). Several experimental results on the crystallization kinetics of glass-forming liquids are interpreted theoretically for the first time employing the concepts developed here.