Stochastic Multi-Scale Reconstruction of 3D Microstructure Consisting of Polycrystalline Grains and Second-Phase Particles from 2D Micrographs

An accurate knowledge of the 3D polycrystalline microstructure of a material is crucial to its property prediction, performance optimization, and design. Here, we present a multi-scale computational scheme that allows one to stochastically reconstruct the 3D microstructure of a highly heterogeneous polycrystalline material with large variation in grain size, morphology, and spatial distribution, as well as the distribution of second-phase particles, from single-2D electron back-scattered diffraction (EBSD) micrograph. Specifically, the two-point correlation functions S₂ are employed to statistically characterize grain morphology, orientation, and spatial distribution and are incorporated into the simulated annealing procedure for microstructure reconstruction. During the reconstruction, the original polycrystalline microstructure is coarsened such that the large grains are reconstructed first and the smaller ones are generated later. The second-phase particles are then inserted into the reconstructed polycrystalline material based on the pair-correlation function g₂ sampled from the 2D back-scattered electron micrograph. The utility of our multi-scale scheme is demonstrated by successfully reconstructing a highly heterogeneous polycrystalline Sn-rich solder joint with Cu₆Sn₅ intermetallic particles. The accuracy of our reconstruction is ascertained by comparing the virtual microstructure with the actual 3D structure of the joint obtained via serial sectioning techniques.