Statistical characterization of segregation-driven inhomogeneities in metallic microstructures employing fast first-order variograms

The microstructure is the centerpiece connecting thermodynamic, compositional, and kinetic stochasticity with macroscopic behavior. As such, its thorough description is of fundamental importance: Microscopical spatial composition fluctuations can critically undermine or improve material performance. Still, both traditional and modern, state-of-the-art statistical microstructural characterization methods overlook micro and mesosegregations. Instead, they generally focus on microconstituent and grain examination. Segregation effects are thus commonly described on a case-by-case basis or employing parameters that lack spatial interpretation. We propose fast first-order variograms as a convenient statistical tool to comprehensively describe chemical segregations in metallic materials. First-order variograms are physically meaningful descriptors capable of revealing spatial variations and correlations. In particular, we discuss the derivation, application, advantages, and limits of their fast computation using the fast Fourier transform, which brings a substantial speed increase over the method-of-moments estimation. Furthermore, we compare them to popular texture characterization techniques borrowed from image processing and analysis. With this work, we establish a simple-to-use, yet powerful method to characterize the severeness of micro and mesosegregations and, thus, to quantify their influence on material behavior.