Analytics on large microstructure datasets using two-point spatial correlations: Coarsening of dendritic structures

Abstract We extend the existing framework [1–4] of two-point spatial correlations to allow for the quantification, analyses, interpretation and visualization of microstructure coarsening measured by time-resolved X-ray computed tomography. Specifically, extensions were made to facilitate (i) the incorporation of nonconventional local attributes such as solid-liquid interface, interface curvature, and interface velocity in the description of the local state, and (ii) the efficient computation of bulk spatial correlations when the local attributes are sparsely defined only at special locations in the three-dimensional volume (e.g., solid-liquid interfaces). We have explored multiple variants of spatial correlations, including Pearson correlation coefficients and two-point joint probabilities, and examined their relative merits in providing useful new insights into the coarsening process. Algorithmic enhancements needed to carry out these computations on the large datasets produced in the experiments are also described. The results demonstrate the remarkable ability of these new protocols in automated (unbiased) capture of the four-fold symmetry of the dendritic microstructure, and in providing quantitative and reliable estimates of the characteristic lengths associated with the dendritic microstructure (including the secondary and tertiary dendrite arm spacings, secondary dendrite arm diameter, and the solute diffusion length). These estimated quantities agree well with the direct measurements from the microstructure. The results also indicate that interfaces with high negative and near-zero mean curvature ( H ) have long range spatial auto-correlations, whereas all values of the interfacial normal velocity ( V ) are only auto-correlated in the short range in space. For mid-range (positive) values of H and non-extreme values of V , the spatial distributions are essentially random.