Generalized kinetics of overall phase transition in terms of logistic equation

I. Avramov; J. Šesták

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arXiv · 1510.02250

Generalized kinetics of overall phase transition in terms of logistic equation

I. Avramov·J. Šesták

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Abstract

We summarize and to discuss briefly the geometrical practice of modeling attitudes so far popular in treating reaction kinetics of solid-state processes. The model equations existing in the literature have been explored to describe the thermal decomposition and crystallization data and are deeply questioned and analyzed showing that under such a simple algebraic representation, the reacting system is thus classified as a set of geometrical bodies (spheres) where each and every one reaction interface is represented by similar and smooth characteristics of reaction curve. It brings an unsolved question whether the sharp and even boundary factually exists or if it resides jointly just inside the global whole of the sample entirety preventing individual particles from having their individual reaction front. Most of the derived expressions are specified in an averaged generalization in terms of the three and two parameters equation (so called JMAK and SB models) characterized by a combination of power exponents m, n and p as summarized in a lucid Table. As an alternative the logistic equation is proposed powered with fractal exponents standing for the interfaces to be identified with an underlying principle of defects. Unfortunately, many of the solutions for the standard kinetic equations are truncated by infinite series, unfriendly to mathematical solutions. Based on the assumption that transformation rate is a product of two functions f(α)k(t), we propose a fundamentally new method to analyze the individual mechanism of each process.The idea is to plot the experimental data in coordinates the transformation rate against f(α).

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I. Avramov, J. Šesták. 2015-10-08. Generalized kinetics of overall phase transition in terms of logistic equation. https://arxiv.org/abs/1510.02250

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