Comparing the Johnson-Mehl-Avrami-Kolmogorov equations for isothermal and linear heating conditions

We present a derivation of the linear heating Johnson-Mehl-Avrami-Kolmogoro v (JMAK) equation for a constant nucleation rate and diffusion-controlled g rowth, in the hard impingement approximation. The result is compared with t he linear heating JMAK equation for interface-controlled growth, and with t he isothermal JMAK equation. We show that all approximations made in derivi ng the JMAK equations (i.e. including previous work) hold when the activati on energies involved are large compared to the thermal energy, which turns out to be virtually always the case. Finally, we demonstrate in a simple wa y that within the JMAK framework, peak shift methods such as Kissinger anal ysis, Marseglia and Ozawa plots are formally equivalent and may all be used to analyse experimental data. (C) 2001 Elsevier Science B.V. All rights re served.