Avrami phenomenological equation

By use of the Poison distribution, Avrami derived the famous Avrami phenomenological equation to treat a kinetic process (Avrami 1939, 1940, 1941). Kolmogorov first discussed the formulation of this equation (Kolmogorov 1937). Johnson and Mehl also made similar derivation independently (Johnson and Mehl 1939). Evans proposed a very concise derivation as introduced below (Evans 1945). 

Equations (6.15) and (6.17) phenomenologically describe the overall growth kinetics after the initial nucleation took place and further nucleation is still occurring. Indeed, the sigmoidal form of the X(t) curve represents a wide variety of transformation reactions. Equation (6.13) is named after Johnson, Mehl, and Avrami [W. A. Johnson, R. E Mehl (1939) M. Avrami (1939)]. Let us finally mention two points. 1) Plotting Vin (1 -X) vs. t should give a straight line with slope km. 2) The time ty of the inflection point (d2X/dt2 = 0) on X(t) is suitable to derive either m or km, namely... 

Apart from empirical determinations of these transformation diagrams, methods of prediction based on nucleation theory and phenomenological growth theory using the Johnson-Mehl-Avrami equation have been devised to estimate TTT diagrams [1.83]. 

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