Crystallization with Variable Temperature: Corrections for the Activation Energy

Abstract

The Nakamura-Avrami method has been revised to derive reliable solutions for describing the kinetics of crystallization on heating with variable temperature. The corresponding numerical solutions for first-order phase-boundarycontrolled growth were computed to evaluate the errors that should be expected when using simple approximate solutions. The relative differences increased as the average dimensionless temperature increased; thus, a method was proposed to obtain correct values for the activation energy and pre-exponential factors. Our analysis of the effects of heating rate on the crystallization peak is consistent with the Kissinger equation, even for dimensionality values of >1. Numerical solutions were also used to demonstrate the validity of the Kissinger equation.

A theoretical method for analyzing the glass-crystal transformation observed by DSC in the continuous heating regime. Application to the Sb0.16As0.36Se0.48 semiconducting alloy

“…In this case, the temperature dependence of extended volume fraction involves a range of particles that are nucleated at different temperatures and, thus, grow to different final sizes when the sample is subjected to continuous heating. By considering the quoted fact of nucleation and crystal growth simultaneous, which agrees with literature [10],…”

“…(4) and (5) [10,23,24]. In the present work, a theoretical method has been developed to integrate Eq.…”

“…In this regime, the glasses crystallize a constant temperature. The other is so-called non-isothermal regime [8][9][10][11][12] in which glass samples are heated up at a fixed heating rate. Generally, an isothermal experiment takes longer time than a non-isothermal experiment, but isothermal experimental data can be interpreted by the well-established Johnson-Mehl-Avrami (JMA) kinetic equation [13][14][15][16].…”

A study on the variations in the density of nucleated particles with the maximum crystallization rate and with the corresponding temperature, by using differential scanning calorimetry

“…Also, since in many glass systems the crystal growth rates are extremely small at nucleation temperatures, one can often assume that the volume fraction crystallized during the isothermal nucleation step is virtually zero (see Fig. 1) [19]. Thus, the condition of "site saturation" [24,25] is physically realistic.…”

“…The theoretical basis for interpreting DTA or DSC results is provided by the formal theory of transformation kinetics [13][14][15][16][17][18][19][20]. This theory is largely independent of the particular models used in detailed descriptions of the transformation mechanisms, and supposes that the crystal growth rate, in general, is anisotropic.…”