Restatement of the Avrami equation in its nonlinear form, presentation of a convenient method of applying it, and application of the analysis to experimental results are presented. The physical meaning of the model parameters and advantages of applying the nonlinear equation are discussed.
The Avrami model of solid-state reactions or transformations has frequently been presented and compared With other stochastic models. The equation often applied is shown to be merely a simplification of the full Awami model equation (FAME). A convenient proceffure for application of the FAME to the kinetics of solid-state reactions is proposed.Several stochastic models have been proposed to describe the kinetics of phase transformations or chemical reactions in solids.Erofeyev [1 ] discussed the probability of molecular events and reactions in a collection containing a large enough number of molecules to permit the use of statistics. To apply this to solid-state reactions he had to introduce a few simplifying assumptions which can never be true. For example, he neglected intercollisions between the growing nuclei of the product phase. The Erofeyev equationis the same in form as that proposed previously by Johanson-Mehl and Kolmogorov, and expresses a relation between the fractional conversion f and the reaction time t. Mampel [2] assumed the random nucleation of the product phase grains, as well as limitation of the growth of these grains as a result of their intercollisions. Though these assumptions are quite acceptable, Mampel was not able to solve the problem. Nevertheless, in the case of spherical grains, he suggested three separate equations for the initial, the intermediate and the final stage of the reaction, respectively. the problem seems to have been generally solved by Avrami [3]. He found a relation between the real and the idealized case, analysing all the unreal cases by Volterra methods. To prove the resulting equation, Avrami had to assume that the product grains are randomly distributed throughout the whole substrate phase, or even only throughout the transformation zone. With the additional assumption kg/kn = const, concerning the linear growth John Wiley & Sons, Limited, Chichester Akaddmiai Kiad6, Budapest
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