Differentiating electron diffuse scattering via 4D-STEM spatial fluctuation and correlation analysis in complex FCC alloys

Complex face-centered-cubic (FCC) alloys frequently display chemical short-range ordering (CSRO), which can be detected through the analysis of diffuse scattering. However, the interpretation of diffuse scattering is complicated by the presence of defects and thermal diffuse scattering, making it extremely challenging to distinguish CSRO using conventional scattering techniques. This complexity has sparked intense debates regarding the origin of specific diffuse-scattering signals, such as those observed at 1/3{422} and 1/2{311} positions. To address this challenge, we introduce the method of spatial fluctuation and correlation (FluCor) analysis of local diffuse scattering captured using Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM). We demonstrate our methodology using a solution-treated (CrCoNi)₉₃Al₄Ti₂Nb medium-entropy alloy (MEA) and show that the FluCor analysis can differentiate diffuse scattering of different origins. The results reveal two sets of overlapping diffuse-scattering signals at the 1/3{422} and 1/2{311} positions in the studied MEA and link both to non-CSRO origins. Specifically, the heterogeneous-domain diffuse-scattering signals are attributed to nanoscale planar defects, while the homogeneous diffuse-scattering of the matrix is best explained by thermal-diffuse scattering. The principles underlying our fluctuation and correlation analysis of diffuse scattering are general and broadly applicable to order-disordered crystals, including various complex alloy systems. This versatility promises to yield valuable insights into the interplay between microstructural characteristics and CSRO behavior in a wide range of materials, potentially resolving long-standing debates in the field.