Abstract: The three-dimensional (3D) atomic structure of nanomaterials, including strain, is crucial to understand their properties. Here, we investigate lattice strain in Au nanodecahedra using electron tomography. Although different electron tomography techniques enabled 3D characterizations of nanostructures at the atomic level, a reliable determination of lattice strain is not straightforward. We therefore propose a novel model-based approach from which atomic coordinates are measured. Our findings demonstrate the importance of investigating lattice strain in 3D.

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: In the present paper, the principles of detection theory are used to quantify the probability of error for atom-counting from high resolution scanning transmission electron microscopy (HR STEM) images. Binary and multiple hypothesis testing have been investigated in order to determine the limits to the precision with which the number of atoms in a projected atomic column can be estimated. The probability of error has been calculated when using STEM images, scattering cross-sections or peak intensities as a criterion to count atoms. Based on this analysis, we conclude that scattering cross-sections perform almost equally well as images and perform better than peak intensities. Furthermore, the optimal STEM detector design can be derived for atom-counting using the expression for the probability of error. We show that for very thin objects LAADF is optimal and that for thicker objects the optimal inner detector angle increases.

Abstract: Short-wave infrared (SWIR) fluorescence could become the new gold standard in optical imaging for biomedical applications due to important advantages such as lack of autofluorescence, weak photon absorption by blood and tissues, and reduced photon scattering coefficient. Therefore, contrary to the visible and NIR regions, tissues become translucent in the SWIR region. Nevertheless, the lack of bright and biocompatible probes is a key challenge that must be overcome to unlock the full potential of SWIR fluorescence. Although rare-earth-based core-shell nanocrystals appeared as promising SWIR probes, they suffer from limited photoluminescence quantum yield (PLQY). The lack of control over the atomic scale organization of such complex materials is one of the main barriers limiting their optical performance. Here, the growth of either homogeneous (α-NaYF₄) or heterogeneous (CaF₂) shell domains on optically-active α-NaYF₄:Yb:Er (with and without Ce³⁺co-doping) core nanocrystals is reported. The atomic scale organization can be controlled by preventing cation intermixing only in heterogeneous core-shell nanocrystals with a dramatic impact on the PLQY. The latter reached 50% at 60 mW/cm²; one of the highest reported PLQY values for sub-15 nm nanocrystals. The most efficient nanocrystals were utilized for in vivo imaging above 1450 nm.

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: Nanoparticle self-assembly and epitaxy are utilized extensively to make 1D and 2D structures with complex shapes. High-resolution transmission electron microscopy (HRTEM) has shown that single-crystalline interfaces can form, but little is known about the strain and dislocations at these interfaces. Such information is critically important for applications: drastically reducing
dislocation density was the key breakthrough enabling widespread implementation of light-emitting diodes, while strain engineering has been fundamental to modern high-performance transistors, solar cells, and thermoelectrics. In this work, the interfacial defect and strain formation after selfassembly and room temperature epitaxy of 7 nm Pd nanocubes capped with polyvinylpyrrolidone (PVP) is examined. It is observed that, during ligand removal, the cubes move over large distances on the substrate, leading to both spontaneous self-assembly and epitaxy to form single crystals. Subsequently, atomically resolved images are used to quantify the strain and dislocation density at the epitaxial interfaces between cubes with different lateral and angular misorientations. It is shown that dislocation- and strain-free interfaces form when the nanocubes align parallel to each other. Angular misalignment between adjacent cubes does not necessarily lead to grain boundaries but does cause dislocations, with higher densities associated with larger rotations.

Abstract: Quantitative atomic resolution annular dark field scanning transmission electron microscopy (ADF STEM) has become a powerful technique for nanoparticle atom-counting. However, a lot of nanoparticles provide a severe characterisation challenge because of their limited size and beam sensitivity. Therefore, quantitative ADF STEM may greatly benefit from statistical detection theory in order to optimise the instrumental microscope settings such that the incoming electron dose can be kept as low as possible whilst still retaining single-atom precision. The principles of detection theory are used to quantify the probability of error for atom-counting. This enables us to decide between different image performance measures and to optimise the experimental detector settings for atom-counting in ADF STEM in an objective manner. To demonstrate this, ADF STEM imaging of an industrial catalyst has been conducted using the near-optimal detector settings. For this experiment, we discussed the limits for atom-counting diagnosed by combining a thorough statistical method and detailed image simulations.

Abstract: High angle annular dark field scanning transmission electron microscopy (HAADF STEM) images provide sample information which is sensitive to the chemical composition. The image intensities indeed scale with the mean atomic number Z. To some extent, chemically different atomic column types can therefore be visually distinguished. However, in order to quantify the atomic column composition with high accuracy and precision, model-based methods are necessary. Therefore, an empirical incoherent parametric imaging model can be used of which the unknown parameters are determined using statistical parameter estimation theory (Van Aert et al., 2009, [1]). In this paper, it will be shown how this method can be combined with frozen lattice multislice simulations in order to evolve from a relative toward an absolute quantification of the composition of single atomic columns with mixed atom types. Furthermore, the validity of the model assumptions are explored and discussed.

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: Over the last decade, scanning transmission electron microscopy has become one of the most powerful tools to characterise nanomaterials at the atomic scale. Often, the ultimate goal is to retrieve the three-dimensional structure, which is very challenging since small species are typically sensitive to electron irradiation. Nevertheless, measuring individual atomic positions is crucial to understand the relation between the structure and physicochemical properties of these (nano)materials. In this review, we highlight the latest approaches that are available to reveal the 3D atomic structure of small species. Finally, we will provide an outlook and will describe future challenges where the limits of electron microscopy will be pushed even further.

Abstract: An efficient model-based estimation algorithm is introduced to quantify the atomic column positions and intensities from atomic resolution (scanning) transmission electron microscopy ((S)TEM) images. This algorithm uses the least squares estimator on image segments containing individual columns fully accounting for overlap between neighbouring columns, enabling the analysis of a large field of view. For this algorithm, the accuracy and precision with which measurements for the atomic column positions and scattering cross-sections from annular dark field (ADF) STEM images can be estimated, has been investigated. The highest attainable precision is reached even for low dose images. Furthermore, the advantages of the model-based approach taking into account overlap between neighbouring columns are highlighted. This is done for the estimation of the distance between two neighbouring columns as a function of their distance and for the estimation of the scattering cross-section which is compared to the integrated intensity from a Voronoi cell. To provide end-users this well-established quantification method, a user friendly program, StatSTEM, is developed which is freely available under a GNU public license.

Abstract: The atomic lensing model has been proposed as a promising method facilitating atom-counting in heterogeneous nanocrystals [1]. Here, image simulations will validate the model, which describes dynamical diffraction as a superposition of individual atoms focussing the incident electrons. It will be demonstrated that the model is reliable in the annular dark field regime for crystals having columns containing dozens of atoms. By using the principles of statistical detection theory, it will be shown that this model gives new opportunities for detecting compositional differences.

Abstract: A decade ago, a statistics-based method was introduced to count the number of atoms from annular dark-field scanning transmission electron microscopy (ADF STEM) images. In the past years, this method was successfully applied to nanocrystals of arbitrary shape, size, and composition (and its high accuracy and precision has been demonstrated). However, the counting results obtained from this statistical framework are so far presented without a visualization of the actual uncertainty about this estimate. In this paper, we present three approaches that can be used to represent counting results together with their statistical error, and discuss which approach is most suited for further use based on simulations and an experimental ADF STEM image.

Abstract: Au nanoparticles (NPs) deposited on CeO2 are extensively used as thermal catalysts since the morphology of the NPs is expected to be stable at elevated temperatures. Although it is well known that the activity of Au NPs depends on their size and surface structure, their three-dimensional (3D) structure at the atomic scale has not been completely characterized as a function of temperature. In this paper, we overcome the limitations of conventional electron tomography by combining atom counting applied to aberration-corrected scanning transmission electron microscopy images and molecular dynamics relaxation. In this manner, we are able to perform an atomic resolution 3D investigation of supported Au NPs. Our results enable us to characterize the 3D equilibrium structure of single NPs as a function of temperature. Moreover, the dynamic 3D structural evolution of the NPs at high temperatures, including surface layer jumping and crystalline transformations, has been studied.

Abstract: Pt nanoparticles play an essential role in a wide variety of catalytic reactions. The activity of the particles strongly depends on their three-dimensional (3D) structure and exposed facets, as well as on the reactive environment. High-resolution electron microscopy has often been used to characterize nanoparticle catalysts but unfortunately most observations so far have been either performed in vacuum and/or using conventional (2D) in situ microscopy. The latter however does not provide direct 3D morphological information. We have implemented a quantitative methodology to measure variations of the 3D atomic structure of nanoparticles under the flow of a selected gas. We were thereby able to quantify refaceting of Pt nanoparticles with atomic resolution during various oxidation−reduction cycles. In a H2 environment, a more faceted surface morphology of the particles was observed with {100} and {111} planes being dominant. On the other hand, in O2 the percentage of {100} and {111} facets decreased and a significant increase of higher order facets was found, resulting in a more rounded morphology. This methodology opens up new opportunities toward in situ characterization of catalytic nanoparticles because for the first time it enables one to directly measure 3D morphology variations at the atomic scale in a specific gaseous reaction environment.