On the Use of JMAK Theory to Describe Mechanical Amorphization: A Comparison between Experiments, Numerical Solutions and Simulations

The kinetics of amorphization during ball milling is generally analyzed using two different approaches: the classical Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory and Delogu and Cocco's model for which a region deterministically transforms after it reaches a certain number of collisions. The application of JMAK analysis to the latter model predicts Avrami exponents to be higher than the experimental ones (typically close to one). We develop simulations based on the probabilistic character of the nucleation phenomenon and concave growth of the amorphous phase in the core of a nanocrystal. The predictions of our simulations are in good agreement with the low Avrami exponents and with the size evolution of the remaining crystallites found experimentally. From these values, the parameters involved in the simulated model (growth rate and probability of nucleation) can be estimated.