Johnson-Mehl-Avrami kinetic model

The different combinations of nucleation, growth, and impingement processes give rise to the Johnson-Mehl-Avrami kinetic model [4], which results in the following equation... 

After switching from fast cooling to isothermal conditions at time zero, the measured heat flow rate exponentially approaches a constant value (-10.3 mW) with a time constant of about 3 seconds for this DSC. The observed crystallization peak is often symmetric, and then the time of the peak maximum (nunimum) is a measure of crystallization half time. Integration of the peak yields the enthalpy change, which can be transformed into relative crystallinity by dividing by the limiting value at infinite time. To obtain development of absolute crystallinity (mass fraction) the curve has to be divided by the enthalpy difference between crystal and liquid at the crystallization temperature, which is available from ATHAS-DB [124], The commonly applied Kolmogorov-Johnson-Mehl-Avrami (KJMA) model for the kinetic analysis of isothermal crystallization data is based on volume fractions. Therefore, the mass fraction crystallinity, Wc, as always obtained from DSC, should be transformed into volume crystallinity. 

Most reconstructive transitions take place by processes of formation and growth of nuclei of the product phase and the kinetics are often described by the model developed by Johnson, Mehl, Avrami and Erofeev (see Chapter 3). These reactions are, therefore, identical with other decompositions and represent simple chemical changes. Studies are often relatively difficult and greater interest has been directed towards the experimentally more accessible reactions that jdeld gaseous products. 

The kinetic evolution is usually represented by a sigmoid-type curve. Such a typical curve is given in Figure 9 for the case of displacement reaction, Ni + CuO Cu -F NiO realized in planetary ball mill [58]. Author of this overview analyzed these experimental results by one of the most frequently used kinetic model applied to various solid-state reactions, namely Johnson-Mehl-Avrami equation ... 

The common method for modeling both isothermal and non-isothermal crystallization kinetics from amorphous solids is the Johnson-Mehl-Avrami -Kolmogorov... 

It follows that the so-called empirical kinetic model function can be generally described by all-purpose, three-exponent relation, first introduced by (and often named after the authors as) Sestdk and Berggren (SB) equation [480], h(q) = (/ ( - a) [-In (1 - a)f AX is practically applicable as either form, SB equation, oT (1 - a) , and/or modified Johnson, Mehl, Avrami, Yerofeev and Kolmogorov (JMAYK) equation, (1 - a) [-In (1 - a)f (related to its original form, - ln(l - a) = (krtf, through the exponentsp and r,. Q.,p (1 - 1/r ). 

Many mathematical models have bees advanced relating nucleation and nuclei growth rates to the overall kinetics of phase transformation, such as Johnson and Mehl [427], Avrami [428], Yerofyeyev [429], Kolmogorov [430] as well as Jacobs-Tompkins [431] or Mampel [432] and were agreeably suinmarized elsewhere [1,3,413,144, 421,422,423,426,43 I ]. 

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