On some limitations of the Johnson–Mehl–Avrami–Kolmogorov equation

Abstract Some limitations of the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation used widely for describing kinetics of phase transformation are demonstrated using probabilistic analysis and Monte Carlo simulations. The JMAK equation predicts correctly the real transformed fraction only if the number of the growing nuclei in the controlled volume is large. If the number of growing nuclei is small, the transformed fraction predicted by the JMAK equation deviates significantly from the real transformed fraction, no matter how large the volume of the controlled volume is. As an alternative, another equation should be applied, which for any number of the growing nuclei predicts correctly the true amount of transformed fraction.