Fast algorithm for computing non-isothermal crystallization kinetics

Abstract

A fast algorithm is presented for computing fractional crystallized volume of an amorphous solid under non-isothermal conditions, as a function of the number of discrete time intervals, temperature history and (temperature dependent) nucleation and growth rates. The algorithm is a modification of the discrete Yinnon–Uhlmann approach to compute the standard double integral formula under quasi-steady-state conditions. Rather than re-computing the kinetics over the entire thermal history of all previous time intervals for each new interval, the crystallized fraction for a given time interval is computed by a sum of terms involving only the current and previous intervals, such that orders of magnitude increase in computational speed is obtained.