A nonextensive statistical approach to the kinetics of phase transformation

Some limitations of Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation, which is used widely for describing kinetics of phase transformation, were demonstrated using probabilistic analysis and Monte Carlo simulations [Acta Mater. 48 (2000) 4217]. As well-known, JMAK equation predicts correctly the real transformed fraction only if the number of the growing nuclei in the controlled volume is large. However JMAK equation seems to fail, if the number of growing nuclei is small, no matter how large the volume of the controlled volume is. In this study, we propose a different equation for describing kinetics of phase transformation, using a nonextensive formalism, namely Tsallis thermostatistics which has been commonly employed to study the various physical systems for a decade.