Crystallization of rapidly heated amorphous solids

Traditional theoretical approaches to the description of a non-isothermal phase transformation view its initial stage -nucleation - as a quasi-steady-state (QSS) process. These approaches are approximate, however, and may fail completely even for quite moderate heating (cooling) rates due to very large internal relaxation times of the amorphous state. A simple way to adjust the QSS approximation to account for strong time-dependent nucleation effects during rapid heating of amorphous solids with no quenched in nuclei is proposed. In combination with the approximate expression for the growth of nucleated particles, this leads to explicit closed formulas for the rate of phase transformation and the volume fraction transformed. Results are tested by comparison with numerical solutions of the time-dependent Becker-Döring nucleation equation, and it is demonstrated that the present method provides highly accurate corrections to the QSS approximation.