Functional form of the Kolmogorov–Johnson–Mehl–Avrami kinetics for non-isothermal phase transformations at constant heating rate

Abstract

An analytical computation is presented for determining the functional form of the Kolmogorov–Johnson–Mehl–Avrami (KJMA) kinetics in the case of non-isothermal transformations under linear temperature variation. Differently to previous modeling, in the present computation no approximate expression of the exponential integral is employed. The mathematical derivation holds true independently of the activation energy values for nucleation and growth and, in the limiting case of zero heating rate, reduces to the isothermal kinetics. The present computation demonstrates that the transformation rate factorizes in the product of temperature-dependent and volume fraction-dependent functions. In the framework of the KJMA theory this result is exact and implies that the KJMA kinetics is fully consistent with the requirement for the applicability of the multiple-scan analysis techniques, widely employed in thermochemistry. In the limit of large values of the reduced activation energies, the non-isothermal kinetics yields the KJMA transformation rate equation.