Kolmogorov–Johnson–Mehl–Avrami kinetics for non-isothermal phase transformations ruled by diffusional growth

Abstract

We report on the functional form of the rate of the transformed volume fraction in non-isothermal phase transitions occurring by nucleation and diffusional growth. The microscopic growth rate is computed by solving the diffusion problem for time-dependent diffusion coefficient. The growth law is further employed in the Kolmogorov–Johnson–Mehl–Avrami (KJMA) theory for describing the time dependence of the transformed volume at constant heating rate. It is demonstrated that the transformation rate separates in the product of volume fraction and actual temperature functions. In the framework of the KJMA approach this factorization is exact. It is also shown that for real systems (due to the high values of the reduced activation energies for nucleation and growth), the kinetics is in excellent agreement with the stretched exponential function appropriate for isothermal transformations.