Theory of thermal analysis of non-isothermal crystallization kinetics of amorphous solids

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Abstract
The theoretical basis of thermal analysis of crystallization kinetics occurring by nucleation and growth under non-isothermal conditions of constant heating rate β has been studied by integrating the fundamental equation describing the crystallized volume fraction, x. Assuming a thermally activated growth rate of the form u=u0 exp (–EG/kT) two specific cases have been considered: (i) growth from a constant number of nuclei or growth following the saturation of nucleation sites and (ii) a temperature-dependent nucleation rate whose functional form over a limited temperature range is approximated by Iv=I0 exp (–EN/kT). It is shown that the expression for the crystallized fractional volume x(T) contains a function φn of the initial temperature T0. Except for one-dimensional growth under case (i), the rate of transformation x is also a function of T0, which implies that a Johnson–Mehl–Avrami type of description of the kinetics is inappropriate. The limits of applicability of current thermoanalytical methods of the following groups: Kissinger, Borchardt–Piloyan, Ozawa, Chen and Coats–Redfern–Sestak, have been critically examined and modifications have been proposed to include the effect of the initial temperature. A method of thermal analysis has been developed to determine the nature of the crystallization kinetics.

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