Abstract: An efficient model-based estimation algorithm is introduced in order 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 the 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, is investigated. The highest attainable precision is reached even for low dose images. Furthermore, advantages of the model- based approach taking into account overlap between neighbouring columns are highlighted. 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: 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: 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.

Abstract: Zinc is routinely employed in the synthesis of InP quantum dots (QDs) to improve the photoluminescence efficiency and carrier mobility of the resulting In(Zn)P alloy nanostructures. The exact location of Zn in the final structures and the mechanism by which it enhances the optoelectronic properties of the QDs is debated. We use synchrotron X-ray absorbance spectroscopy to show that the majority of Zn in In(Zn)P QDs is located at their surface as Zn-carboxylates. However, a small amount of Zn is present inside the bulk of the QDs with the consequent contraction of their lattice, as confirmed by combining high resolution high-angle annular dark-field imaging scanning transmission electron microscopy (HAADF-STEM) with statistical parameter estimation theory. We further demonstrate that the Zn content and its incorporation into the QDs can be tuned by the ligation of commonly employed Zn carboxylate precursors: the use of highly reactive Zn-acetate leads to the formation of undesired Zn3P2 and the final nanostructures being characterized by broad optical features, whereas Zn-carboxylates with longer carbon chains lead to InP crystals with much lower zinc content and narrow optical features. These results can explain the differences between structural and optical properties of In(Zn)P samples reported across the literature, and provide a rational method to tune the amount of Zn in InP nanocrystals and to drive the incorporation of Zn either as surface Zn-carboxylate, as a substitutional dopant inside the InP crystal lattice, or even predominantly as Zn3P2.

Abstract: We propose a new method to measure atomic scale dynamics of nanoparticles from experimental high-resolution annular dark field scanning transmission electron microscopy images. By using the so-called hidden Markov model, which explicitly models the possibility of structural changes, the number of atoms in each atomic column can be quantified over time. This newly proposed method outperforms the current atom-counting procedure and enables the determination of the probabilities and cross sections for surface diffusion. This method is therefore of great importance for revealing and quantifying the atomic structure when it evolves over time via adatom dynamics, surface diffusion, beam effects, or during in situ experiments.

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: In this chapter, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high-resolution annular dark-field (ADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. We show that this method can be applied to nanocrystals of arbitrary shape, size, and atom type. The validity of the atom-counting results is confirmed by means of detailed image simulations and it is shown that the high sensitivity of our method enables us to count atoms with single atom sensitivity.

Abstract: This chapter provides an overview of statistical and quantitative methodologies that have pushed (scanning) transmission electron microscopy ((S)TEM) toward accurate and precise measurements of unknown structure parameters for understanding the relation between the structure of a material and its properties. Hereby, statistical parameter estimation theory has extensively been used which enabled not only measuring atomic column positions, but also quantifying the number of atoms, and detecting atomic columns as accurately and precisely as possible from experimental images. As a general conclusion, it can be stated that advanced statistical techniques are ideal tools to perform quantitative electron microscopy at the atomic scale. In the future, statistical methods will continue to be developed and novel quantification procedures will open up new possibilities for studying material structures at the atomic scale.

Abstract: In this chapter, the principles of statistical parameter estimation theory for a quantitative analysis of atomic-resolution electron microscopy images are introduced. Within this framework, electron microscopy images are described by a parametric statistical model. Here, parametric models are introduced for different types of electron microscopy images: reconstructed exit waves, annular dark-field (ADF) scanning transmission electron microscopy (STEM) images, and simultaneously acquired ADF and annular bright-field (ABF) STEM images. Furthermore, the Cramér-Rao lower bound (CRLB) is introduced, i.e. a theoretical lower bound on the variance of any unbiased estimator. This CRLB is used to quantify the precision of the structure parameters of interest, such as the atomic column positions and the integrated atomic column intensities.

Abstract: Advances in controlling energy migration pathways in core-shell lanthanide (Ln)-based hetero-nanocrystals (HNCs) have relied heavily on assumptions about how optically active centers are distributed within individual HNCs. In this article, it is demonstrated that different types of interface patterns can be formed depending on shell growth conditions. Such interface patterns are not only identified but also characterized with spatial resolution ranging from the nanometer- to the atomic-scale. In the most favorable cases, atomic-scale resolved maps of individual particles are obtained. It is also demonstrated that, for the same type of core-shell architecture, the interface pattern can be engineered with thicknesses of just 1 nm up to several tens of nanometers. Total alloying between the core and shell domains is also possible when using ultra-small particles as seeds. Finally, with different types of interface patterns (same architecture and chemical composition of the core and shell domains) it is possible to modify the output color (yellow, red, and green-yellow) or change (improvement or degradation) the absolute upconversion quantum yield. The results presented in this article introduce an important paradigm shift and pave the way toward the emergence of a new generation of core-shell Ln-based HNCs with better control over their atomic-scale organization.

Abstract: A new methodology is presented to count the number of atoms in multimetallic nanocrystals by combining energy dispersive X-ray spectroscopy (EDX) and high angle annular dark field scanning transmission electron microscopy (HAADF STEM). For this purpose, the existence of a linear relationship between the incoherent HAADF STEM and EDX images is exploited. Next to the number of atoms for each element in the atomic columns, the method also allows quantification of the error in the obtained number of atoms, which is of importance given the noisy nature of the acquired EDX signals. Using experimental images of an Au@Ag core–shell nanorod, it is demonstrated that 3D structural information can be extracted at the atomic scale. Furthermore, simulated data of an Au@Pt core–shell nanorod show the prospect to characterize heterogeneous nanostructures with adjacent atomic numbers.

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: 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.