Three-dimensional Monte Carlo simulation of grain growth in zone-refined iron

The evolution of the grain structure and topological-class distributions in zone-refined iron were modeled using a three-dimensional (3-D) Monte Carlo (MC) model. The effect of grain size on topological features was examined. The relationship between the topological features of grains and the geometry of their surrounding grains was studied. In particular, the average number of sides of the grains was related to the average number of sides of their neighbors. Both the computed grain-size distribution and the topological-class distribution were found to be invariant with time. A linear relationship existed between the average grain size and the average number of sides of grains. The number of sides of grains was inversely proportional to the average number of sides of the neighboring grains. The computed average grain size, grain-size distribution, and topological-class distribution agreed well with the corresponding independent experimental data. The results indicate significant promise for understanding grain growth and topological features using 3-D MC simulation.