A critical review is presented of mathematical methods advanced over the last 20 years for the analysis of data obtained from non-isothermal thermoanalytical studies of crystallization of glass-forming liquids. Methods proposed by Ozawa, Piloyan and Borchardt, Coats, Redfern and Sestak, Ozawa and Chen, Takhor, Kissinger, and Augis and Bennett are examined in detail. All these methods are based on the Avrami treatment of transformation kinetics and define an effective crystallization rate coefficient having an Arrhenian temperature dependence. Several different ways of mathematically treating the data have been proposed. Most are shown to be based on an incorrect neglect of the temperature dependence of the rate coefficient. By taking proper account of the temperature dependence of the crystallization rate coefficient, all the methods are shown to lead to similar conclusions. In detail, it is shown that the effective activation energy of the overall crystallization process can be calculated from the slope of the line obtained by plotting 1n[ Q /( T P − T 0 )] versus 1/ T P is the temperature of maximum crystallization rate, T O is an initial temperature and Q is the heating rate employed in the experiment. It is further argued that in general the overall crystallization rate coefficient is not Arrhenian in character. Thus, in general, non-isothermal transformation cannot be treated analytically. A detailed description of nonisothermal transformation can, however, be obtained by numerical methods. Such a method is described and its uses in obtaining kinetic data from thermoanalytical studies are demonstrated.

Applications of thermoanalytical techniques to the study of crystallization kinetics in glass-forming liquids, part I: Theory☆

Homer Kissinger and the Kissinger equation

Augis and Bennett (J. Thermal Anal. 13 (1978) 283.) [6] recently proposed a modified Kissinger method for determining the activation energy of a transformation. It is shown that the proposed method was, in fact, based upon a modification to the equation for the rate of reaction under non-isothermal conditions. The apparent discrepancy between the proposed method and the original Kissinger method is therefore resolved. The modified rate equation appears to have, at best, only a limited application. However, if the equation should be appropriate for a particular transformation, it is demonstrated that Augis and Bennett's method would be the correct method for determining the activation energy.

On the calculation of activation energies using a modified Kissinger method

The crystal nucleation of Li2O-2SiO2 glass is studied by differential thermal analysis. A simple method, based on the shift of the differential thermal analysis (DTA) crystallization-peak temperature, for evaluating the influence of temperature and time of heat-treatments on bulk nucleation, is described. The experimental results are in good agreement with results obtained by other workers.

Nucleation in glass and differential thermal analysis

Differential scanning calorimetry (DSC) is a powerful tool to address some of the most challenging issues in glass science and technology, such as the nonequilibrium nature of the glassy state and ...

Understanding Glass through Differential Scanning Calorimetry

Several isothermal experiments are generally needed to determine the parameters of the Avrami equation which describe most of the heterogeneous solid state reactions. Differential scanning calorimeters are suitable for such experiments. While most differential thermal analysis (DTA) apparatus cover a wider temperature range than DSC apparatus they cannot be used to perform isothermal determinations. However, Kissinger has already shown how activation energy and frequency factor can be calculated from DTA experiments for the case of homogeneous reactions following first order kinetics. We derive in this paper an extension of the Kissinger method and show its applicability to heterogeneous reactions described by an Avrami expression. The new method will allow the study of the kinetics of metallic reactions at the higher temperature range obtainable with DTA. The transformation kinetics of the metastable equiatomic tin-nickel alloy are given as an example.

J. A. Augis

Papers

Calculation of the Avrami parameters for heterogeneous solid state reactions using a modification of the Kissinger method