Modification of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution

TL;DR

This paper derives a quasi-exact analytical solution to Avrami's phase transformation model under continuous heating, extending the classical isothermal equation to non-isothermal conditions with different activation energies.

Contribution

It introduces a modified Kolmogorov-Johnson-Mehl-Avrami equation for non-isothermal experiments and provides an analytical solution considering different activation energies.

Findings

Derived a quasi-exact solution for non-isothermal transformation kinetics.

Extended the classical Avrami model to continuous heating conditions.

Identified a constant parameter linking isothermal and non-isothermal rate equations.

Abstract

Avrami's model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avrami's model when the transformation takes place under continuous heating. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami transformation rate equation. The corresponding non-isothermal Kolmogorov-Johnson-Mehl-Avrami transformation rate equation only differs from the one obtained under isothermal conditions by a constant parameter, which only depends on the ratio between nucleation and growth rate activation energies. Consequently, a minor correction allows us to extend the Kolmogorov-Johnson-Mehl-Avrami transformation rate equation to continuous heating conditions.