Pair distribution analysis of short- and medium-range order of metallic glasses: Direct imaging and diffraction-based approaches

Abstract Pair distribution function (PDF) analysis provides a quantitative framework for resolving short- and medium-range order in glasses. This article summarizes recent advances that extend PDF methods from bulk x-ray and neutron-diffraction methods to local electron microscopy-based characterization for metallic glasses. High-energy x-rays and neutrons offer robust structural averages, while electron-based approaches such as electron PDF (ePDF) enable nanoscale mapping of local order and heterogeneity in metallic glasses. Validated PDF techniques, supported by molecular dynamics simulations, allow direct correlation between real-space pair correlations and the underlying atomic configurations. In particular, ePDF mapping visualizes nanoscale variations in short-range order (SRO), interfacial amorphous phases, and deformation-induced structural changes. Machine learning-assisted analysis enhances the extraction of meaningful structural motifs from large ePDF data sets. Complementary three-dimensional (3D) imaging methods, including atomic electron tomography and ptychography, allow to reconstruct coordinate-resolved 3D atomic models, which can be directly compared with atomistic simulations and can be evaluated locally via PDF analysis. This article provides an overview over recent methodology advances and further introduces possibilities to link multiscale PDF-derived structural information with properties and functionality in metallic glasses. Graphical abstract Pair distribution function (PDF) analysis to characterize short- and medium range order based on bulk X-ray and neutron diffraction, nanometer level resolved employing 4D scanning transmission electron microscopy (STEM) based electron PDF (ePDF) and by employing atomic electron tomography (AET).