Monte‐Carlo based algorithm for reconstruction of oriented microstructure

Abstract Despite the development of three‐dimensional imaging techniques in materials science, most of the microstructural data is taken from two‐dimensional sections. It includes images produced by optical, scanning, and transmission electron microscopy. Due to the stochastic indefinite characteristics of such sections, it is a challenge to reproduce three‐dimensional microstructure characteristics quantitatively. Several analytical techniques were developed in stereology to overcome such limitations. Nevertheless, available analytical techniques are restricted to limiting cases of entirely random or fully coaxial orientation of microstructural features. On the other hand, achieving ideal coaxiality of such inclusions in actual technological conditions is not achievable. In this work, the Monte‐Carlo‐based optimization algorithm is constructed to overcome the limitations of existing stereometric models. This algorithm considers information from longitudinal and transverse sets of images. Orientations, as well as size distributions, are taken into account. The model operates under the assumption of log‐normal distribution of 3d size characteristics and von Mises distributions of angles. Then, a derivation‐free optimization algorithm is used to match histograms of simulated and observed sections. The method for estimating the initial values of optimized variables is proposed, based on the existing analytic solutions. The reconstruction algorithm is then applied to estimate three‐dimensional angle and size distributions of inclusion of phase in near‐eutectic alloy, produced by directional solidification technique. Finally, the algorithm's convergence is discussed, as well as its limitations and future developments.