Evaluation of time-dependent grain-size populations for nucleation and growth kinetics

A theoretical calculation of time-dependent grain-size populations of an emerging phase driven by nucleation and growth kinetics is performed. A statistical mean-field model is presented for a completely degenerated system, based on the same assumptions as the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model, that is to say, randomly distributed active nucleation sites which grow isotropically and collision resulting in a growth stop at the interface. Dependence of the kinetic parameters (nucleation and growth rates) on macroscopic and/or microscopic variables and on time is considered. The differential form of the KJMA model is applied to each grain-size population, providing a detailed microstructure development. As a result of this calculation, grain-size distributions are obtained. The validity of the model is tested by comparing the grain-size distributions obtained for a kinetically controlled process with a numerical Monte Carlo simulation. Imaging of the microstructure obtained by Monte Carlo is also shown. Finally, the model is computed with different kinetic conditions and the results are presented.