Monte Carlo simulation of first-order phase transformations with mutual blocking of anisotropically growing particles up to all relevant orders

A numerical model of first-order phase transformations is presented that considers the mutual blocking of growing particles up to all relevant orders. It is applicable for nucleation and growth problems in any space dimensions, even in the case of highly anisotropic growth. Illustrative Monte Carlo simulations were carried out in two dimensions for random elliptical growth of a fixed number of particles and simultaneous nucleation and growth. It is demonstrated that the Johnson-Mehl-Avrami-Kolmogorov model is not applicable under such circumstances. In contrast, the mean-field treatment proposed by Birnie and Weinberg on the basis of strictly radial growth and first-order blocking is in a fair agreement with our simulations for preexisting nuclei.