Analytical modeling of recrystallization considers two arrangements of nuclei: a) random, b) “periodic”. If nucleation departs from these extremes, no exact analytical treatment is available. When classical Johnson-Mehl, Avrami, Kolmogorov approach is used there is often the doubt whether the nucleation is truly random. Therefore, it would be of some interest to assess to what extent the exact analytical theory is valid if the nucleation departs from randomness. In this work, recrystallization is simulated using cellular automata in two dimensions in order to investigate the effect of nuclei distribution on the kinetics. Simulations are carried out for nuclei distribution ranging from periodic to random. The effect of departure from the exact analytical solutions is assessed by means of the overall kinetics and the microstructural path.

Recrystallization of an iron single crystal was reported in detail by Vandermeer and Rath (V&R). We present predictions of recrystallization based on cellular automata (CA) simulations, and compare them with the data and analysis from V&R's study. Agreement is found between our CA simulations and V&R's results, provided that the CA simulations were carried out using a sufficient dynamic range for time, precision spatial dimensionalization, and accommodation of grain shape effects inherent in CA techniques.

Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA). In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recently obtained by Rios and Villa supposing that the intensity is a harmonic function of the spatial coordinate. The simulated data gives very good agreement with the analytical solution provided that the correct shape factor for the growing CA grains is used. This good agreement is auspicious because the analytical expressions were derived and thus are exact only if the shape of the growing regions is spherical.

In recent papers Rios and Villa resorted to developments in stochastic geometry to revisit theclassical KJMA theory and generalize it for situations in which nuclei were located in space accordingto both homogeneous and inhomogeneous Poisson point processes as well as according to Materncluster process and surface and bulk nucleation in small specimens. Rigorous mathematical methodswere employed to ensure the reliability of the new expressions. These results are briefly described.Analytical expression for inhomogeneous Poisson point process nucleation gives very good agreementwith Cellular Automata simulations. Cellular Automata simulations complement the analyticalsolutions by showing the corresponding microstructural evolution. These new results considerablyexpand the range of situations for which analytical solutions are available.