Abstract: Depth sectioning in high angular annular dark field scanning transmission electron microscopy is considered a candidate for three-dimensional characterization on the atomic scale. However at present the depth resolution is still far from the atomic level, due to strong limitations in the opening angle of the beam. In this paper we introduce a new, parameter based tomographic reconstruction algorithm that allows to make maximal use of the prior knowledge about the constituent atom types and the microscope settings, so as to retrieve the atomic positions and push the resolution to the atomic level in all three dimensions.

Abstract: Over the last two decades, three-dimensional (3D) imaging by transmission electron microscopy or “electron tomography” has evolved into a powerful tool to investigate a variety of nanomaterials in different fields, such as life sciences, chemistry, solid-state physics, and materials science. Most of these results were obtained with nanometer-scale resolution, but different approaches have recently pushed the resolution to the atomic level. Such information is a prerequisite to understand the specific relationship between the atomic structure and the physicochemical properties of (nano) materials. We provide an overview of the latest progress in the field of atomic-resolution electron tomography. Different imaging and reconstruction approaches are presented, and state-of-the-art results are discussed. This article demonstrates the power and importance of electron tomography with atomic-scale resolution.

Abstract: Statistical parameter estimation theory is proposed as a method to quantify electron microscopy images. It aims at obtaining precise and accurate values for the unknown structure parameters including, for example, atomic column positions and types. In this theory, observations are purely considered as data planes, from which structure parameters have to be determined using a parametric model describing the images. The method enables us to measure positions of atomic columns with a precision of the order of a few picometers even though the resolution of the electron microscope is one or two orders of magnitude larger. Moreover, small differences in averaged atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark field scanning transmission electron microscopy images. Finally, it is shown how to optimize the experimental design so as to attain the highest precision. As an example, the optimization of the probe size for nanoparticle radius measurements is considered. It is also shown how to quantitatively balance signal-to-noise ratio and resolution by adjusting the probe size.

Abstract: In this study, we explore the possibility to use deep learning for the reconstruction of phase images from 4D scanning transmission electron microscopy (4D-STEM) data. The process can be divided into two main steps. First, the complex electron wave function is recovered for a convergent beam electron diffraction pattern (CBED) using a convolutional neural network (CNN). Subsequently, a corresponding patch of the phase object is recovered using the phase object approximation. Repeating this for each scan position in a 4D-STEM dataset and combining the patches by complex summation yields the full-phase object. Each patch is recovered from a kernel of 3x3 adjacent CBEDs only, which eliminates common, large memory requirements and enables live processing during an experiment. The machine learning pipeline, data generation, and the reconstruction algorithm are presented. We demonstrate that the CNN can retrieve phase information beyond the aperture angle, enabling super-resolution imaging. The image contrast formation is evaluated showing a dependence on the thickness and atomic column type. Columns containing light and heavy elements can be imaged simultaneously and are distinguishable. The combination of super-resolution, good noise robustness, and intuitive image contrast characteristics makes the approach unique among live imaging methods in 4D-STEM.

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.

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.

Abstract: The maximum a posteriori (MAP) probability rule for atom column detection can also be used as a tool to evaluate the relation between scanning transmission electron microscopy (STEM) image quality and atom detectability. In this chapter, a new image-quality measure is proposed that correlates well with atom detectability, namely the integrated contrast-to-noise ratio (ICNR). Furthermore, the working principle of the MAP probability rule is described in detail showing a close relation to the principles of model-selection methods.

Abstract: The present contribution gives a review of recent quantification work of atom displacements, atom site occupations and level of crystallinity in various systems and based on aberration corrected HR(S)TEM images. Depending on the case studied, picometer range precisions for individual distances can be obtained, boundary widths at the unit cell level determined or statistical evolutions of fractions of the ordered areas calculated. In all of these cases, these quantitative measures imply new routes for the applications of the respective materials.

Abstract: Nowadays, aberration corrected transmission electron microscopy (TEM) is a popular method to characterise nanomaterials at the atomic scale. Here, atomically resolved images of nanomaterials are acquired, where the contrast depends on the illumination, imaging and detector conditions of the microscope. Visualization of light elements is possible when using low angle annular dark field (LAADF) STEM, annular bright field (ABF) STEM, integrated differential phase contrast (iDPC) STEM, negative spherical aberration imaging (NCSI) and imaging STEM (ISTEM). In this work, images of a NdGaO3-La0.67Sr0.33MnO3 (NGO-LSMO) interface are quantitatively evaluated by using statistical parameter estimation theory. For imaging light elements, all techniques are providing reliable results, while the techniques based on interference contrast, NCSI and ISTEM, are less robust in terms of accuracy for extracting heavy column locations. In term of precision, sample drift and scan distortions mainly limits the STEM based techniques as compared to NCSI. Post processing techniques can, however, partially compensate for this. In order to provide an outlook to the future, simulated images of NGO, in which the unavoidable presence of Poisson noise is taken into account, are used to determine the ultimate precision. In this future counting noise limited scenario, NCSI and ISTEM imaging will provide more precise values as compared to the other techniques, which can be related to the mechanisms behind the image recording.