Monte Carlo simulations of phase transformations caused by nucleation and subsequent anisotropic growth: Extension of the Johnson-Mehl-Avrami-Kolmogorov theory

Monte Carlo (MC) simulations of isothermal phase transformations were performed based on a temperature- and time-dependent nucleation rate and a temperature-dependent and time-independent anisotropic growth rate (linear growth). One- or two-dimensional anisotropic growth in two-dimensional space is considered and nucleation occurs randomly throughout space. The MC simulations show that parallel growth of anisotropically growing transformation products with identical convex shape can be described accurately by the kinetic theory due to Johnson, Mehl, Avrami, and Kolmogorov (JMAK), but nonparallel anisotropic growth, orthogonal in the present work, incorporating blocking up to all relevant orders leads to hard impingement that results in strong deviations from JMAK kinetics. A transparent analytical description extending on, but incorporating the JMAK theory has been developed that turns out to accurately reproduce the numerical results of all present MC simulation, leading to improved understanding of how impingement should be incorporated in JMAK theory.