A method for determining crystallization kinetic parameters from one nonisothermal calorimetric experiment
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A new equation was developed for evaluating kinetic parameters in the isokinetic range of a phase transformation using nonisothermal calorimetric techniques. The Johnson–Mehl–Avrami equation was extended by considering that the transformation rate in an isothermal process can be translated into the nonisothermal transformation in an isokinetic range. The Avrami exponent, n, activation energy, E, and frequency factor, K0, were calculated from only one nonisothermal experiment by using the new kinetic equation for amorphous Se (a-Se), polysilane/polycarbosilane (PS/PCS), and lithium disilicate (LiO2 ⭈ 2SiO2 or LS2) samples with nucleation site saturation. The values of E and K0 calculated using the new kinetic equation agree well with those obtained by the Kissinger equation for the prenucleated a-Se, PS/PCS, and LS2 samples. The values of n indicate that volume crystallization is dominant in the bulk a-Se and LS2 samples, whereas surface crystallization is dominant in the powdered PS/PCS sample. These results for a-Se were confirmed by scanning and transmission electronic microscopy.
I. INTRODUCTION
The most widely used theory for interpreting the isothermal crystallization kinetics of amorphous materials is that of Johnson–Mehl–Avrami (JMA).1–4 Although isothermal transformations are theoretically simpler, it is difficult to obtain a truly isothermal experiment as phase changes can occur during the nonisothermal heating period prior to the isothermal segment. Unfortunately, difficulties exist in describing the kinetics of a nonisothermal process due to the temperature dependence of both nucleation and growth rates. Several well-known methods have been developed for determining crystallization parameters in nonisothermal crystallization processes, such as the Kissinger equation5–7 and the Ozawa equation,8 all of which require multiple nonisothermal experiments in order to obtain kinetic parameters. In this paper, a method is proposed for calculating the kinetic exponent, n, and activation energy, E, from a single, nonisothermal experiment, thus representing a substantial experimental improvement over existing methods. Using the principle of additivity, this kinetic equation is deduced by extending the JMA equation in an isokinetic system. The analytical method obtained in this work was used to interpret the kinetics of nonisothermal crystallization in amorphous selenium (a-Se), Li2 ⭈ 2SiO2
(LS2) glass and amorphous polysilane/polycarbosilane (PS/PCS) samples, in which nucleation sites were saturated in a prenucleation step. II. THEORETICAL BACKGROUND A. Isothermal transformations
For many isothermal transformations, the volume fraction transformed with time can be expressed in terms of the JMA equation1–4 for the isothermal nucleation and growth process x ⳱ 1 − exp(−Kt n)
,
where x is the volume fraction transformed at time t, n is a quantity called the “kinetic exponent,” which depends on the mechanism of transformation and the growth geometry, and K is a cluster of numerical and growth constants which is dif
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