Quantifying Chemical and Structural Order in Scanning Transmission Electron Microscopy (STEM) Datasets Using Spatial Statistics

Short-range chemical and structural order are important factors for controlling material properties in a wide range of materials, from complex oxides [1] to multi-principal component alloys [2]. Studying these phenomena at the nanoscale, however, can be challenging due to global averaging of local structure or mixed chemical/structural correlations in the case of X-ray or neutron diffraction [3-6]. Direct imaging in scanning transmission electron microscopy (STEM) provides a local probe of chemistry and structure that has been used to identify ordering [7, 8], yet at extremely local length scales (<1 nm), projection of the structure can introduce “pseudo-SRO” image contrast. Unambiguously distinguishing SRO from a random distribution or unraveling correlations in chemistry and structure thus becomes challenging, requiring a statistical approach. In this presentation, we will demonstrate how spatial statistics tools can be used to quantify short-range order (SRO) in atomic-resolution scanning transmission electron microscopy (STEM) images. First, we adopt a near-neighbor based autocorrelation to identify the overall presence of order. Applying this technique to chemical and structural order in a case study ordered system, we show how the type of order and length scale of correlation can be quickly determined [9]. Additionally, we apply these techniques to measure non-random chemical SRO in the BCC-TiVNbHf refractory high-entropy alloy (RHEA). Using simulated STEM images of ordered (B2) and disordered (A2) structures (Fig. 1b, c), we show that large atomic number differences and local random fluctuations introduce “pseudo-SRO” image contrast (Fig. 1a). We compare experiment with these “baselines” of order and disorder using the Moran's I autocorrelations at increasing neighbor shells. Experiment is demonstrated to be inconsistent with a random distribution, and statistically significant sublattice order is shown to exist in TiVNbHf. Finally, the addition of Al is shown to enhance SRO degree and length scale (Fig. 1d), consistent with predicted mixing and binary formation enthalpies as well as observations in other Al-containing RHEAs [10]. High-angle annular dark-field STEM images and associated normalized intensity maps of (a) TiVNbHfAl from experiment, (b) simulated image of a random structure, (c) simulated image of a fully B2-ordered structure. (d) Moran's I autocorrelation at various near-neighbor shells showing different degrees of ordered intensity.