The effect of probe inaccuracies on the quantitative model-based analysis of high angle annular dark field scanning transmission electron microscopy images

Real-time simulations of ADF STEM probe position-integrated scattering cross-sections for single element fcc crystals in zone axis orientation using a densely connected neural network

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.

A decade of atom-counting in STEM: From the first results toward reliable 3D atomic models from a single projection

Quantitative structure determination is needed in order to study and understand nanomaterials at the atomic scale. Materials characterisation resulting in precise structural information is a crucial point to understand the structure-property relation of materials. Counting the number of atoms and retrieving the 3D atomic structure of nanoparticles plays an important role here. In this paper, an overview will be given of the atom-counting methodology and its applications over the past decade. The procedure to count the number of atoms will be discussed in detail and it will be shown how the performance of the method can be further improved. Furthermore, advances toward mixed element nanostructures, 3D atomic modelling based on the atom-counting results, and quantifying the nanoparticle dynamics will be highlighted.

Modelling ADF STEM images using elliptical Gaussian peaks and its effects on the quantification of structure parameters in the presence of sample tilt

A small sample tilt away from a main zone axis orientation results in an elongation of the atomic columns in ADF STEM images. An often posed research question is therefore whether the ADF STEM image intensities of tilted nanomaterials should be quantified using a parametric imaging model consisting of elliptical rather than the currently used symmetrical peaks. To this purpose, simulated ADF STEM images corresponding to different amounts of sample tilt are studied using a parametric imaging model that consists of superimposed 2D elliptical Gaussian peaks on the one hand and symmetrical Gaussian peaks on the other hand. We investigate the quantification of structural parameters such as atomic column positions and scattering cross sections using both parametric imaging models. In this manner, we quantitatively study what can be gained from this elliptical model for quantitative ADF STEM, despite the increased parameter space and computational effort. Although a qualitative improvement can be achieved, no significant quantitative improvement in the estimated structure parameters is achieved by the elliptical model as compared to the symmetrical model. The decrease in scattering cross sections with increasing sample tilt is even identical for both types of parametric imaging models. This impedes direct comparison with zone axis image simulations. Nonetheless, we demonstrate how reliable atom-counting can still be achieved in the presence of small sample tilt.

Advances and Applications of Atomic-Resolution Scanning Transmission Electron Microscopy

Although scanning transmission electron microscopy (STEM) images of individual heavy atoms were reported 50 years ago, the applications of atomic-resolution STEM imaging became wide spread only after the practical realization of aberration correctors on field-emission STEM/TEM instruments to form sub-Ångstrom electron probes. The innovative designs and advances of electron optical systems, the fundamental understanding of electron–specimen interaction processes, and the advances in detector technology all played a major role in achieving the goal of atomic-resolution STEM imaging of practical materials. It is clear that tremendous advances in computer technology and electronics, image acquisition and processing algorithms, image simulations, and precision machining synergistically made atomic-resolution STEM imaging routinely accessible. It is anticipated that further hardware/software development is needed to achieve three-dimensional atomic-resolution STEM imaging with single-atom chemical sensitivity, even for electron-beam-sensitive materials. Artificial intelligence, machine learning, and big-data science are expected to significantly enhance the impact of STEM and associated techniques on many research fields such as materials science and engineering, quantum and nanoscale science, physics and chemistry, and biology and medicine. This review focuses on advances of STEM imaging from the invention of the field-emission electron gun to the realization of aberration-corrected and monochromated atomic-resolution STEM and its broad applications.

Combining quantitative ADF STEM with SiNx membrane-based MEMS devices: A simulation study with Pt nanoparticles

Computer simulations are used to assess the influence of a 20-nm-thick SiN_x membrane on the quantification of atomic-resolution annular dark-field (ADF) scanning transmission electron microscopy images of Pt nanoparticles. The discussions include the effect of different nanoparticle/membrane arrangements, accelerating voltage, nanoparticle thickness and the presence of adjacent atomic columns on the accuracy with which the number of Pt atoms in each atom column can be counted. The results, which are based on the use of ADF scattering cross-sections, show that an accuracy of better than a single atom is attainable at 200 and 300 kV. At 80kV, the scattering in a typical SiN_x membrane is sufficiently strong that the best possible atom counting accuracy is reduced to +/- 2 atoms. The implications of the work for quantitative studies of Pt nanoparticles imaged through SiN_x membranes are discussed.

Aberration-corrected STEM imaging of 2D materials: Artifacts and practical applications of threefold astigmatism

High-resolution scanning transmission electron microscopy (HR-STEM) with spherical aberration correction enables researchers to peer into two-dimensional (2D) materials and correlate the material properties with those of single atoms. The maximum intensity of corrected electron beam is confined in the area having sub-angstrom size. Meanwhile, the residual threefold astigmatism of the electron probe implies a triangular shape distribution of the intensity, whereas its tails overlap and thus interact with several atomic species simultaneously. The result is the resonant modulation of contrast that interferes the determination of phase transition of 2D materials. Here, we theoretically reveal and experimentally determine the origin of resonant modulation of contrast and its unintended impact on violating the power-law dependence of contrast on coordination modes between transition metal and chalcogenide atoms. The finding illuminates the correlation between atomic contrast, spatially inequivalent chalcogenide orientation, and residual threefold astigmatism on determining the atomic structure of emerging 2D materials.

Unscrambling Mixed Elements using High Angle Annular Dark Field Scanning Transmission Electron Microscopy

The development of new nanocrystals with outstanding physicochemical properties requires a full three-dimensional (3D) characterization at the atomic scale. For homogeneous nanocrystals, counting the number of atoms in each atomic column from high angle annular dark field scanning transmission electron microscopy images has been shown to be a successful technique to get access to this 3D information. However, technologically important nanostructures often consist of more than one chemical element. In order to extend atom counting to heterogeneous materials, a new atomic lensing model is presented. This model takes dynamical electron diffraction into account and opens up new possibilities for unraveling the 3D composition at the atomic scale. Here, the method is applied to determine the 3D structure of Au@Ag core-shell nanorods, but it is applicable to a wide range of heterogeneous complex nanostructures.

Advanced electron crystallography through model-based imaging

The increasing need for precise determination of the atomic arrangement of non-periodic structures in materials design and the control of nanostructures explains the growing interest in quantitative transmission electron microscopy. The aim is to extract precise and accurate numbers for unknown structure parameters including atomic positions, chemical concentrations and atomic numbers. For this purpose, statistical parameter estimation theory has been shown to provide reliable results. In this theory, observations are considered purely as data planes, from which structure parameters have to be determined using a parametric model describing the images. As such, the positions of atom columns can be measured with a precision of the order of a few picometres, even though the resolution of the electron microscope is still one or two orders of magnitude larger. Moreover, small differences in average atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark-field scanning transmission electron microscopy images. In addition, this theory allows one to measure compositional changes at interfaces, to count atoms with single-atom sensitivity, and to reconstruct atomic structures in three dimensions. This feature article brings the reader up to date, summarizing the underlying theory and highlighting some of the recent applications of quantitative model-based transmisson electron microscopy.

Quantitative STEM normalisation: The importance of the electron flux

Annular dark-field (ADF) scanning transmission electron microscopy (STEM) has become widely used in quantitative studies based on the opportunity to directly compare experimental and simulated images. This comparison merely requires the experimental data to be normalised and expressed in units of 'fractional beam-current'. However, inhomogeneities in the response of electron detectors can complicate this normalisation. The quantification procedure becomes both experiment and instrument specific, requiring new simulations for the particular response of each instrument's detector, and for every camera-length used. This not only impedes the comparison between different instruments and research groups, but can also be computationally very time consuming. Furthermore, not all image simulation methods allow for the inclusion of an inhomogeneous detector response. In this work, we propose an alternative method for normalising experimental data in order to compare these with simulations that consider a homogeneous detector response. To achieve this, we determine the electron flux distribution reaching the detector by means of a camera-length series or a so-called atomic column cross-section averaged convergent beam electron diffraction (XSACBED) pattern. The result is then used to determine the relative weighting of the detector response. Here we show that the results obtained by this new electron flux weighted (EFW) method are comparable to the currently used method, while considerably simplifying the needed simulation libraries. The proposed method also allows one to obtain a metric that describes the quality of the detector response in comparison with the 'ideal' detector response.

Rapid estimation of catalyst nanoparticle morphology and atomic-coordination by high-resolution Z-contrast electron microscopy

Heterogeneous nanoparticle catalyst development relies on an understanding of their structure-property relationships, ideally at atomic resolution and in three-dimensions. Current transmission electron microscopy techniques such as discrete tomography can provide this but require multiple images of each nanoparticle and are incompatible with samples that change under electron irradiation or with surveying large numbers of particles to gain significant statistics. Here, we make use of recent advances in quantitative dark-field scanning transmission electron microscopy to count the number atoms in each atomic column of a single image from a platinum nanoparticle. These atom-counts, along with the prior knowledge of the face-centered cubic geometry, are used to create atomistic models. An energy minimization is then used to relax the nanoparticle's 3D structure. This rapid approach enables high-throughput statistical studies or the analysis of dynamic processes such as facet-restructuring or particle damage.