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

A procedure has been developed to obtain an evolution equation with the temperature for the actual transformed volume fraction under non-isothermal regime and to calculate the kinetic parameters in glassy solids. Once an extended volume of transformed material has been defined and spatially random transformed regions have been assumed, a general expression of the extended volume fraction has been obtained as a function of the temperature, bearing in mind the case presented in the practice of a kinetic exponent with a larger value than 4. This unexpected value is justified assuming that both the nucleation frequency and the crystal growth rate depend on time as a power law. Moreover, considering impingement effect and from the quoted expression, the actual volume fraction transformed has been deduced. The kinetic parameters have been obtained, by assuming that the reaction rate constant is a temperature function of Arrhenius type and using the following considerations: the condition of maximum crystallization rate and the quoted maximum rate. The theoretical model developed and the Johnson-Mehl-Avrami model have been applied to the crystallization kinetics of the Ag0.16As0.42Se0.42 glassy alloy, which presents two exothermic peaks. The second peak gives for the kinetic exponent values enough larger than 4 in both models. The quoted values do not fulfil the assumptions of the Avrami model and it is necessary to resort to the hypotheses of the developed model to justify the unexpectedly high value of the kinetic exponent. Moreover, the experimental curve of the transformed fraction shows a better agreement with the theoretical curve of the developed model than with the corresponding curve of the Avrami model, confirming the reliability of the theoretical model developed in order to analyze the transformation kinetics of the above-mentioned glassy alloy.