An integral method to analyze the glass-crystal transformation kinetics by differential scanning calorimetry under non-isothermal regime. Application to the crystallization of the Ge0.08Sb0.15Se0.77 chalcogenide glass

In this article, a theoretical procedure has been developed for the kinetic study of the glass-crystal transformations under continuous heating regime in materials involving formation and growth of nuclei, obtaining the corresponding parameters: kinetic exponent, activation energy, and pre-exponential frequency. It is an integral procedure, which is based on a transformation rate independent of the thermal history of the material and assumes that the quoted rate depends only on the transformed fraction, x, across the f(x) function, and temperature, considering that these variables are independent ones. Therefore, the transformation rate is expressed as the product of two separable functions of absolute temperature and the transformed fraction. The quoted f(x) function corresponds to a theoretical method that we have developed and recently published, whose details are given in the Sect. "Basic theory" of this study. The above-mentioned integral procedure considers the same pair of temperatures for the different heating rates and obtains a constant value for temperature integral and, therefore, a plot of a function of the transformed fraction versus the reciprocal of the heating rate leads to a straight line with an intercept of zero, if the value of kinetic exponent is correctly chosen. The process may be repeated for other pairs of temperatures and, consequently, other straight lines will be obtained. By using different values of kinetic exponent for each of the quoted lines, it is taken the best correlation coefficient to choose the quoted exponent more suitable. On the other hand, by using the first mean value theorem to approach the temperature integral, one obtains a relationship between a function of the temperature and other function of the transformed fraction. The logarithmic form of the quoted relationship leads to a straight line, whose slope and intercept allow the obtaining of the activation energy and of the pre-exponential frequency. In addition, this study applies the quoted procedure to the analysis of the crystallization kinetics of the Ge0.08Sb0.15Se0.77 glassy alloy resulting in ranges of variation both of the kinetic exponent, n, with the temperature and of the activation energy, E, with the crystallized fraction, which contain the values of n and E, obtained according to the already quoted theoretical method, that we have developed and recently published. This fact shows the reliability of the theoretical procedure described in this article to analyze the glass-crystal transformation kinetics of glassy alloy.