The fast cooling/heating rate effects in devitrification of glasses. I. Number of nucleated particles

We consider nucleation of crystalline phase in a glass-forming melt which is quenched at some arbitrary rate, S, and then reheated at some other (typically smaller) rate, H. In conventional (steady-state) approaches it is assumed that the nucleation rate is a function of temperature only, so that the number of nucleated crystallites is proportional to 1/S+ 1/7H. We demonstrate, however, that in general the nucleation rate depends on the quench/heating rate and that there exists an S- and H-dependent temperature region which effectively does not contribute to nucleation, so that the aforementioned scaling does not hold. An expression for the non-steady-state nucleation rate is derived analytically. In certain cases, the number of nucleated crystallites can be reduced by orders of magnitude compared to the steady-state predictions. The results are tested against numerically exact data obtained from the Turnbull-Fisher nucleation model.