Non-random nucleation and the Avrami kinetics

The theory available for obtaining the time evolution of the transformation for a nucleation and growth process, the well- known Kolmogorov- Johnson- Mehl and Avrami kinetic equation, is not accomplished for non- random nucleation processes. However, non- random nucleation protocols are very common; for example in first- order phase transitions where position- dependent nucleation protocols arise from the modification of the nucleation rates in the regions around the growing grains. The present paper attempts to study the effect of these position- dependent nucleation protocols in the overall kinetics of the transformation. Monte Carlo simulations of such processes are performed, and the deviations of the resulting kinetics of the transformation from the Avrami equation are analysed in detail. Consideration of the different effects resulting from the nucleation protocol allows us to model the transformation. A modified Avrami equation is obtained and compared with Monte Carlo simulations, giving excellent agreement. The modelling procedure enables us to extend the validity of the Avrami formulation beyond its limits of applicability.