Using a total of 297 segmented sections, we reconstructed the three-dimensional (3D) structure of pure iron and obtained the largest dataset of 16254 3D complete grains reported to date. The mean values of equivalent sphere radius and face number of pure iron were observed to be consistent with those of Monte Carlo simulated grains, phase-field simulated grains, Ti-alloy grains, and Ni-based super alloy grains. In this work, by finding a balance between automatic methods and manual refinement, we developed an interactive segmentation method to segment serial sections accurately in the reconstruction of the 3D microstructure; this approach can save time as well as substantially eliminate errors. The segmentation process comprises four operations: image preprocessing, breakpoint detection based on mathematical morphology analysis, optimized automatic connection of the breakpoints, and manual refinement by artificial evaluation.

•We investigated topological grain forms by large-scale serial sectioning experiment.•We simulate 3-D grain growth in large scale with Monte Carlo method.•Noticeable topological bias between pure iron and Monte Carlo grains is observed.•Monte Carlo grains have the lowest average dispersion for the distribution of edges per face.Topological forms of three-dimensional grains were investigated by means of large-scale serial sectioning experiment (16,254 pure iron grains) and Monte Carlo-Potts model simulation (150,428 simulation grains). Noticeable topological bias among pure iron grains, Monte Carlo grains and other type of cells is observed in terms of the most frequent grain forms. Moreover, Monte Carlo structure has lower average dispersion for edge distributions of grains than pure iron microstructure, Poisson-Voronoi structure and isolated convex polyhedra, which indicates that some differences in kinetics or evolution processes may play a role in such topological differentiation.

•We simulate 3D normal grain growth in large scale with Monte Carlo method.•We conduct serial sectioning experiment to get topological data of 3D grains.•The increase in dimension has dampening effect on affinity of contacting grains.•The affinity properties in genuine 2D system and 3D one are different.The topologies of contacting grains were investigated based on large grain datasets from 2D and 3D Monte Carlo simulation, 3D reconstruction of pure iron, and the cross sections of these 3D microstructures. In all systems, the results show the expected trends of high affinity for contact between few- and many-faced or edged grains and avoidance of contact between grains in similar face or edge classes. However, this correlation appears relatively stronger in genuine 2D system than in 2D cross-sectional system and 3D system. This result indicates that the increase in dimension has dampening effect on the contact affinity of curvature-driven grain-growth structure.

The selective abnormal growth of Goss grains in magnetic sheets of Fe-3%Si (grade Hi-B) induced by second-phase particles (AlN and MnS) was studied using a modified Monte Carlo Potts model. The starting microstructures for the simulations were generated from electron backscatter diffraction (EBSD) orientation imaging maps of recrystallized samples. In the simulation, second-phase particles were assumed to be randomly distributed in the initial microstructures and the Zener drag effect of particles on Goss grain boundaries was assumed to be selectively invalid because of the unique properties of Goss grain boundaries. The simulation results suggest that normal growth of the matrix grains stagnates because of the pinning effect of particles on their boundaries. During the onset of abnormal grain growth, some Goss grains with concave boundaries in the initial microstructure grow fast abnormally and other Goss grains with convex boundaries shrink and eventually disappear.

•We simulate 2D grain growth in large scale with Monte Carlo method.•We investigated the short- and long-range topological correlations of grains.•The generalized Aboav–Weaire law is verified by data of 103,849 grains.•The edge distribution in grain’s jth neighbor layer follows Lognormal function.In order to understand the topological properties in grain networks, Monte Carlo-Potts model is employed to simulate the normal grain growth in a large scale of 10,000 × 10,000. The topological analysis of 103,849 simulated grains shows strong support to the generalized Aboav–Weaire relationship, which is consistent with the experimental observation in single-phase materials. It was found that the grain size and edge distribution in the system follow Weibull and Lognormal functions, respectively. The mean grain area is related to the edge number by a curve slightly concave upward. For different edge class n, the edge distribution in its first-nearest neighbor layer follows Lognormal function with different parameters, while the edge distributions in the neighbor layers beyond the first follow a same Lognormal function.