Kissinger plot

Fig. 1.28 Kissinger plot for dehydrogenation of as-received LiAlH. Energy of activation for the decomposition LiAlH —> /4 LijAlH + 2/3A1 + (peak III in Fig. 1.27)...

K. Matusita and S. Sakka, Kinetic-Study on Crystallization of Glass by Differential Thermal-Analysis - Criterion on Application of Kissinger Plot , J. Non-Cryst. Solids, 38-39, 741-46 (1980). 

Matusita, K Sakka, S. (1980). Kinetic study on Crystallization of glass by differential thermal analysis - criterion on application of Kissinger plot. Journal cf Non-Crystlline Solids, Vol. 38-39, pp. 741-7 ISSN 0022-3093... 

Ozawa and Kissinger plots are the most commonly used equations to calculate non-isothermal kinetic data, such as Avrami constant, n and crystallization activation energy, Ea, respectively (Celikbilek et al., 2011 Kissinger, 1956 Ozawa, 1971 Prasad Varma, 2005). 

Fig. 24. The Kissinger plots for determining Ea associated with the first exotherm of the prenucleated 0.90Te02-0.10W03 sample (Oehkbilek et aL, 2011)...

By using the values of glass transition, Tg, crystallization onset, Tx, and crystallization p>eak, Tp, temperatures a Kissinger plot yields approximate straight fines as shown in Fig. 30. From... 

Table 2. Avrami exponent (n) and activation energy of crystallization (Ext) in terms of incubation time during isothermal annealing and the activation energy of crystallization (Eiso) determined from a Kissinger plot for the ball-milled amorphous Ti5oCui8Ni22Al4Sn6 alloy and its composite containing 10 vol.% TiC Reprinted from (Zhang, et al., 2006a), with permission from American Institute of Physics.

Figure 42. Kissinger plots of PEN and PEN/CNT 2.0 nanocomposites under (a) nitrogen and (b) air.

Another, rather popular method of kinetic data analysis is based on expressing the maximum value (index max) on the dependence of a vs. T, for which it holds, a = 0 = a, ax [E/RT /ZJ exp(-E/RTmux) df(a)/da]. The result provides simple but rather useful dependence, often called Kissinger plot and known since 1959 [505], which in various modifications and reproves shows the basic proportionality In (( )/Tn,) = (E/R) (1/Tm). 

The value of can be easily determined from the classical Kissinger plot [3,505] for a series of peak apexes at different heating rates irrespective of the value of exponent, /-. 

This In[g(a)/T ] versus lAT plots (refer Fig. 4.3) for evaluating the activation energy has been compared with the widely used Kissinger plot [4, 5] (refer Fig. 4.4). The activation energy computed from the Kissinger plot is 130 kJ/mole. The difference in the evaluated activation energy values can be explained on the basis of the fact that irrespective of the reaction order, Kissinger relationship. 

Fig. 4.4 Kissinger plot to estimate the activation energy of the reaction. The activation energy of the reaction evaluated from the slope of the line is 130 kJ/mole...

Fig-3 Kissinger plot with the use of the modified Kissinger equation for PP blends with various talc contents... 

For those unfamiliar with the "Kissinger Charts" (Figure 5) for tabulating electrochemical information, a detailed explanation is available on request to the authors. In brief, the box for each compound is plotted between the cyclic voltammetric peak potential (E ) and the potential at half the peak current... 

Because (1 - is a constant for a given value of n, a value for 7i, may be obtained from the slope of a plot of ln(/ /r , against l/r ,ax for a series of experiments at different heating rates, ft,. Augis and Bennett [65] modified the Kissinger treatment for use with the Avrami - Erofeev (or JMAEK) model (An). They plotted - TJ) against l/7] ax where is the initial temperature at the... 

Fig. 5.5 Example data set used for calculation of reaction activation energies (BCYlOSp, per-ovskite formation on heating) change in DTA peak temperature with changing heating rate (a) and the same data plotted in the form of the Kissinger equation (b) (the slope of the tine is -E/R, where E is the activation energy and R is the universal gas constant...

It follows from eq. (12) that values of the activation energy A E can be obtained from the slope of plots of n(sT ) versus Later on Boswell (1980) showed that it is more appropriate to derive AE values from plots of ln(57 ) versus T. An example of such a plot is shown in fig. 13 for Dy6oCo4o (Buschow, 1982a). In practice the AE values derived from plots according to Kissinger do not differ much from those derived from plots proposed by Boswell. 

Fig. 13. Kissinger-Boswell plot of the crystallization temperature in amorphous Dyo o °o.40 studied as a function of the heating rate i (bottom and right-hand scales). The level scheme on the left-hand side indicates the relative energies of the crystalline state (c), the amorphous state (a), and the transitional or activated state (t).

Fig. 7. Plot of ln[-ln(l- a)] Vs. 1000/T for diff. heating rates, a) Modified Kissinger method...

Fig. 28. Plot of the (a) Kissinger and (b) Augis Bennett equations for the crystallization in...

Kissinger relationship, the most extensively used method in kinetic studies since 1957 [13], was in use to determine the energy of activation and the order of reaction, from plots of the logarithms of the heating rate against the temperature inverse at the maximum reaction rate in isothermal conditions. This method is usually based on the Differential Scanning Calorimetry (DSC) analysis of formation or decomposition processes and in relation to these processes the endothermic and exothermic peak positions are related to the heating rate. 

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