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

Abstract

The theoretical basis of thermal analysis of crystallization kinetics occurring by nucleation and growth under non-isothermal conditions of constant heating rate / 3 has been studied by integrating the fundamental equation describing the crystallized volume fraction, x. Assuming a thermally activated growth rate of the form u = uo exp ( -E , / k T ) 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 I, = lo exp ( -E N / k T ) .It is shown that the expression for the crystallized fractional volume x ( T ) contains a function ( P, , of the initial temperature To. Except for one-dimensional growth under case (i), the rate of transformation x is also a function of To, 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.

An alternative method for analyzing the non-isothermal glass-crystal transformation kinetics

“…In general, the temperature dependence of the nucleation frequency is far from Arrhenian, and the temperature dependence of the crystal growth rate is also not Arrhenian when a broad range of temperature is considered [19]. Over a sufficiently limited range of temperature (such as the range of transformation peaks in DTA or DSC experiments), both I V and u may be described in zeroth-order approximation by [21] …”

A study on the non-isothermal transformation kinetics of glassy alloys when the nucleation frequency and crystal growth rate depend on time as a power law

“…In this sense, a great number of analytical methods, proposed in the literature to describe the above-mentioned reactions, assume that the reaction rate constant can be represented by means of an Arrhenius type temperature dependence [28,38]. This assumption involves that the maximum values of the kinetic exponent are 4 and 3 in continuous nucleation and in "site saturation" processes, respectively [29].…”

Crystallization kinetics of amorphous alumina–zirconia–silica ceramics

“…16,19,20 In the JMA model, the relationship for the fractional conversion in a system with a constant heating rate has the form…”