KJMA-exponent for the cold crystallization in the stepwise crystallization approach

Abstract

The stepwise crystallization approach is an extension of the classical Tammann's two stage nuclei development method. In Tammann’s method, crystal nuclei are formed at a given nucleation temperature and are grown up to macroscopic sizes at a higher development temperature. The effects on the number and sizes of the clusters caused by heating from the nucleation to the growth temperature are widely neglected there. The number and sizes of the crystals are typically determined by microscopy. The stepwise crystallization approach employs calorimetry for similar purposes. Instead of the second (development) stage of Tammann's method, stepwise crystallization analyzes the thermal effects evolving during the heating stage. A comparison of the magnitudes of the cold crystallization enthalpy registered during heating of the samples after isothermal (annealing) stage allows estimating the amount of crystal nuclei. Dependence of the magnitude of cold crystallization enthalpy on the annealing time provides in this way information on the nucleation kinetics of the respective material. The parametrization of kinetics is typically performed by fitting experimental data with Kolmogorov-Johnson-Mehl-Avrami type equations. The interpretation of the resulting parameters is not straightforward because the magnitude of cold crystallization effects depends not only on the sample state but also on the heating conditions. Here, the dependence of cold crystallization enthalpy on isothermal (annealing) and heating conditions is treated theoretically to estimate the expected values of model parameters for homogeneous nucleation.