Abstract: Structural analysis of metal clusters confined in nanoporous materials is typically performed by X-ray-driven techniques. Although X-ray analysis has proved its strength in the characterization of metal clusters, it provides averaged structural information. Therefore, we here present an alternative workflow for bringing the characterization of confined metal clusters towards the local scale. This workflow is based on the combination of aberration-corrected transmission electron microscopy (TEM), TEM image simulations, and powder X-ray diffraction (XRD) with advanced statistical techniques. In this manner, we were able to characterize the clustering of Pb atoms in Linde Type A (LTA) zeolites with Pb loadings as low as 5 wt%. Moreover, individual Pb clusters could be directly detected. The proposed methodology thus enables a local-scale characterization of confined metal clusters in zeolites. This is important for further elucidation of the connection between the structure and the physicochemical properties of such systems.

Abstract: We introduce a Bayesian genetic algorithm for reconstructing atomic models of monotype crystalline nanoparticles from a single projection using Z-contrast imaging. The number of atoms in a projected atomic column obtained from annular dark field scanning transmission electron microscopy images serves as an input for the initial three-dimensional model. The algorithm minimizes the energy of the structure while utilizing a priori information about the finite precision of the atom-counting results and neighbor-mass relations. The results show promising prospects for obtaining reliable reconstructions of beam-sensitive nanoparticles during dynamical processes from images acquired with sufficiently low incident electron doses.

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: Quantification of annular dark field (ADF) scanning transmission electron microscopy (STEM) images in terms
of composition or thickness often relies on probe-position integrated scattering cross sections (PPISCS). In
order to compare experimental PPISCS with theoretically predicted ones, expensive simulations are needed for
a given specimen, zone axis orientation, and a variety of microscope settings. The computation time of such
simulations can be in the order of hours using a single GPU card. ADF STEM simulations can be efficiently
parallelized using multiple GPUs, as the calculation of each pixel is independent of other pixels. However, most
research groups do not have the necessary hardware, and, in the best-case scenario, the simulation time will
only be reduced proportionally to the number of GPUs used. In this manuscript, we use a learning approach and
present a densely connected neural network that is able to perform real-time ADF STEM PPISCS predictions as
a function of atomic column thickness for most common face-centered cubic (fcc) crystals (i.e., Al, Cu, Pd, Ag,
Pt, Au and Pb) along [100] and [111] zone axis orientations, root-mean-square displacements, and microscope
parameters. The proposed architecture is parameter efficient and yields accurate predictions for the PPISCS
values for a wide range of input parameters that are commonly used for aberration-corrected transmission
electron microscopes.

Abstract: CsPbI3 is a promising perovskite material for photovoltaic applications in its photoactive perovskite or black phase. However, the material degrades to a photovoltaically inactive or yellow phase at room temperature. Various mitigation strategies are currently being developed to increase the lifetime of the black phase, many of which rely on inducing strains in the material that hinder the black-to-yellow phase transition. Physical insight into how these strategies exactly induce strain as well as knowledge of the spatial extent over which these strains impact the material is crucial to optimize these approaches but is still lacking. Herein, we combine machine learning potential-based molecular dynamics simulations with our in silico strain engineering approach to accurately quantify strained large-scale atomic structures on a nanosecond time scale. To this end, we first model the strain fields introduced by atomic substitutions as they form the most elementary strain sources. We demonstrate that the magnitude of the induced strain fields decays exponentially with the distance from the strain source, following a decay rate that is largely independent of the specific substitution. Second, we show that the total strain field induced by multiple strain sources can be predicted to an excellent approximation by summing the strain fields of each individual source. Finally, through a case study, we illustrate how this additive character allows us to explain how complex strain fields, induced by spatially extended strain sources, can be predicted by adequately combining the strain fields caused by local strain sources. Hence, the strain additivity proposed here can be adopted to further our insight into the complex strain behavior in perovskites and to design strain from the atomic level onward to enhance their sought-after phase stability.

Abstract: In this study, the multi-layer self-assembled molecular network formation of an alkylated tetrathiafulvalene compound is studied at the liquid-solid interface between 1-phenyloctane and graphite. A combined theoretical/experimental approach associating force-field and quantum-chemical calculations with scanning tunnelling microscopy is used to determine the two-dimensional self-assembly beyond the monolayer, but also to further the understanding of the molecular adsorption conformation and its impact on the molecular packing within the assemblies at the monolayer and bilayer level.

Abstract: In this paper, a methodology is presented to count the number of atoms in heterogeneous nanoparticles based on the combination of multiple annular dark field scanning transmission electron microscopy (ADF STEM) images. The different non-overlapping annular detector collection regions are selected based on the principles of optimal statistical experiment design for the atom-counting problem. To count the number of atoms, the total intensities of scattered electrons for each atomic column, the so-called scattering cross-sections, are simultaneously compared with simulated library values for the different detector regions by minimising the squared differences. The performance of the method is evaluated for simulated Ni@Pt and Au@Ag core-shell nanoparticles. Our approach turns out to be a dose efficient alternative for the investigation of beam-sensitive heterogeneous materials as compared to the combination of ADF STEM and energy dispersive X-ray spectroscopy.

Abstract: The concept of resolution in high-resolution electron microscopy (HREM) is the power to resolve neighboring atoms. Since the resolution is related to the width of the point spread function of the microscope, it could in principle be determined from the image of a point object. However, in electron microscopy there are no ideal point objects. The smallest object is an individual atom. If the width of an atom is much smaller than the resolution of the microscope, this atom can still be considered as a point object. As the resolution of the microscope enters the sub-Å regime, information about the microscope is strongly entangled with the information about the atoms in HREM images. Therefore, we need to find an alternative method to determine the resolution in an object-independent way. In this work we propose to use the image wave of a crystalline object in zone axis orientation. Under this condition, the atoms of a column act as small lenses so that the electron beam channels through the atom column periodically. Because of this focusing, the image wave of the column can be much more peaked than the constituting atoms and can thus be a much more sensitive probe to measure the resolution. Our approach is to use the peakiness of the image wave of the atom column to determine the resolution. We will show that the resolution can be directly linked to the total curvature of the atom column wave. Moreover, we can then directly obtain the resolution of the microscope given that the contribution from the object is known, which is related to the bounding energy of the atom. The method is applied on an experimental CaTiO3 image wave.

Abstract: In materials science, high angle annular dark field scanning transmission electron microscopy is often used for tomography at the nanometer scale. In this work, it is shown that a thickness dependent, non-linear damping of the recorded intensities occurs. This results in an underestimated intensity in the interior of reconstructions of homogeneous particles, which is known as the cupping artifact. In this paper, this non-linear effect is demonstrated in experimental images taken under common conditions and is reproduced with a numerical simulation. Furthermore, an analytical derivation shows that these non-linearities can be inverted if the imaging is done quantitatively, thus preventing cupping in the reconstruction.

Abstract: In order to interpret the amplitude and phase of the exit wave in terms of mass and position of the atoms, one has to invert the dynamic scattering of the electrons in the object so as to obtain a starting structure which can then be used as a seed for further quantitative structure refinement. This is especially challenging in case of a zone axis condition when the interaction of the electrons with the atom column is very strong. Based on the channelling theory we will show that the channelling map not only yields a circle on the Argand plot but also a circular defocus curve for every column. The former gives the number of atoms in each column, while the latter provides the defocus value for each column, which reveals the surface roughness at the exit plane with single atom sensitivity.

Abstract: The effects of amorphous layers on the quality of exit wave restorations have been investigated. Two independently developed software implementations for exit wave restoration have been used to simulated focal series of images of SrTiO3 with amorphous carbon layers incorporated. The restored exit waves have been compared both qualitatively and quantitatively. We have shown that amorphous layers have a strong impact on the quantitative measurements of atomic column positions, however, the error in the position measurements is still in the picometer range.