Abstract: This paper investigates the possible benefits for counting atoms of different chemical nature when analysing multiple 2D scanning transmission electron microscopy (STEM) images resulting from independent annular dark field (ADF) detector regimes. To reach this goal, the principles of statistical detection theory are used to quantify the probability of error when determining the number of atoms in atomic columns consisting of multiple types of elements. In order to apply this theory, atom-counting is formulated as a statistical hypothesis test, where each hypothesis corresponds to a specific number of atoms of each atom type in an atomic column. The probability of error, which is limited by the unavoidable presence of electron counting noise, can then be computed from scattering-cross sections extracted from multiple ADF STEM images. Minimisation of the probability of error as a function of the inner and outer angles of a specified number of independent ADF collection regimes results in optimal experimental designs. Based on simulations of spherical Au@Ag and Au@Pt core–shell nanoparticles, we investigate how the combination of two non-overlapping detector regimes helps to improve the probability of error when unscrambling two types of atoms. In particular, the combination of a narrow low angle ADF detector with a detector formed by the remaining annular collection regime is found to be optimal. The benefit is more significant if the atomic number Z difference becomes larger. In
addition, we show the benefit of subdividing the detector regime into three collection areas for heterogeneous nanostructures based on a structure consisting of three types of elements, e.g., a mixture of Au, Ag and Al atoms. Finally, these results are compared with the probability of error resulting when one would ultimately use a pixelated 4D STEM detector and how this could help to further reduce the incident electron dose.

Abstract: Advanced materials often consist of multiple elements which are arranged in a complicated structure. Quantitative scanning transmission electron microscopy is useful to determine the composition and thickness of nanostructures at the atomic scale. However, significant difficulties remain to quantify mixed columns by comparing the resulting atomic resolution images and spectroscopy data with multislice simulations where dynamic scattering needs to be taken into account. The combination of the computationally intensive nature of these simulations and the enormous amount of possible mixed column configurations for a given composition indeed severely hamper the quantification process. To overcome these challenges, we here report the development of an incoherent non-linear method for the fast prediction of ADF-EDX scattering cross-sections of mixed columns under channelling conditions. We first explain the origin of the ADF and EDX incoherence from scattering physics suggesting a linear dependence between those two signals in the case of a high-angle ADF detector. Taking EDX as a perfect incoherent reference mode, we quantitatively examine the ADF longitudinal incoherence under different microscope conditions using multislice simulations. Based on incoherent imaging, the atomic lensing model previously developed for ADF is now expanded to EDX, which yields ADF-EDX scattering cross-section predictions in good agreement with multislice simulations for mixed columns in a core–shell nanoparticle and a high entropy alloy. The fast and accurate prediction of ADF-EDX scattering cross-sections opens up new opportunities to explore the wide range of ordering possibilities of heterogeneous materials with multiple elements.

Abstract: To understand the structure–property relationship of nanostructures, reliably quantifying parameters, such as the number of atoms along the projection direction, is important. Advanced statistical methodologies have made it possible to count the number of atoms for monotype crystalline nanoparticles from a single ADF STEM image. Recent developments enable one to simultaneously acquire multiple ADF STEM images. Here, we present an extended statistics-based method for atom counting from a combination of multiple statistically independent ADF STEM images reconstructed from non-overlapping annular detector collection regions which improves the accuracy and allows one to retrieve precise atom-counts, especially for images acquired with low electron doses and multiple element structures.

Abstract: A new tungsten bronze in the SbWO system has been prepared in a solid state reaction from Sb2O3, WO3 and W metal powder. The average structure was determined by single crystal X-ray diffraction. SbxWO3+y (x ∼ 0.11) crystallizes in the orthorhombic space group Pm21n (no. 31), a = 27.8135(9) Å, b = 7.3659(2) Å and c = 3.8672(1) Å. The structure belongs to the (n)-ITB class of intergrowth tungsten bronzes. It contains slabs of hexagonal channels formed by six WO6 octahedra. These slabs are separated by three layers of WO6 octahedra that are arranged in a WO3-type fashion. The WO6 octahedra share all vertices to build up a three-dimensional framework. The hexagonal channels are filled with Sb atoms to ∼80% and additional O atoms. The atoms are shifted out of the center of the channels. Exit-wave reconstruction of focal series of high resolution-transmission-electron-microscope (HRTEM) images combined with statistical paramäeter estimation techniques allowed to study local ordering in the channels. Sb atoms in neighbouring channels tend to be displaced in the same direction, which is in agreement with total energy calculations on ordered structure models, but the ratio of the occupation of the two possible Sb sites varies from channel to channel. The structure of SbxWO3+y exhibits pronounced local modulations.