Extension of the Johnson-Mehl-Avrami-Kolmogorov theory incorporating anisotropic growth studied by Monte Carlo simulations

An analytical theory has been developed, based on Monte Carlo (MC) simulations, describing the kinetics of isothermal phase transformations proceeding by nucleation and subsequent growth for d-1 dimensional growth in d dimensional space (with d 2 or 3). This type of growth is of interest since it is generally anisotropic, leads to hard impingement, and obtains strong deviations from the traditional Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory. Within the MC simulations 1D growth can occur with equal probability in two or three different nonparallel orientations in 2D space. In 3D space 2D growth can occur with equal probability in three (or two) different orthogonal orientations. The MC simulations show that initially always a regime is present where JMAK theory prevails, but that after a well-defined critical time a transition to a blocking regime occurs. Both regimes are characterized by clearly different, but nearly constant values of the Avrami exponent which depend on the dimensionality of growth and space and on the time dependence of nucleation. The dependence of the critical time and of the extended fraction within the blocking regime (based on the concept of the extended volume of the JMAK theory) on the nucleation and growth parameters has been extensively analyzed and all results of the MC simulations have been captured within the analytical theory.