Probing Compositional Order in Atomic Columns: STEM Simulations Beyond the Virtual Crystal Approximation

Taking advantage of recent advances in parallel computing, we studied compositional disorder along metal-oxygen atomic columns in a complex Mo,V-oxide bronze using multislice frozen-phonon calculations. Commonly, the virtual crystal approximation (VCA) is used to model compositional disorder at crystallographic sites in a unit cell for a number of different theoretical and experimental techniques. In the VCA, a weighted linear sum of atomic properties is used to approximate the model structure. When using the VCA, the extracted V content of Mo,V-O columns from experimental high-angle annular dark-field (HAADF) images will be about half the V content estimated from simulations, considering the distinct cation ordering. This discrepancy is larger than the spread of HAADF signals of different configurational orders at a given V concentration, which can be up to 20%. Certain "isophilic" atomic arrangements along the column can be distinguished from more random ones using HAADF-STEM imaging. The trends and ratios of the simulated intensity spreads due to different compositional ordering along 11 M-O columns along the c-axis of the Mo,V oxide bronze qualitatively match those observed in experimental HAADF-STEM data. Instrumental and sample-based noise adds to the variability but does not significantly distort the relative ratios of column intensity variation. We observed that we only required seven random configurations to represent the intensity variations along columns.