Abstract: Statistical parameter estimation theory is proposed as a quantitative method to measure unknown structure parameters from electron microscopy images. Images are then purely considered as data planes from which structure parameters have to be determined as accurately and precisely as possible using a parametric statistical model of the observations. For this purpose, an efficient algorithm is proposed for the estimation of atomic column positions and intensities from high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. Furthermore, the so-called CramérRao lower bound (CRLB) is reviewed to determine the limits to the precision with which continuous parameters such as atomic column positions and intensities can be estimated. Since this lower bound can only be derived for continuous parameters, alternative measures using the principles of detection theory are introduced for problems concerning the estimation of discrete parameters such as atomic numbers. An experimental case study is presented to show the practical use of these measures for the optimization of the experiment design if the purpose is to decide between the presence of specific atom types using STEM images.

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: 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.

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: Quantitative structural and chemical information can be obtained from high angle annular dark field scanning transmission electron microscopy (HAADF STEM) images when using statistical parameter estimation theory. In this approach, we assume an empirical parameterized imaging model for which the total scattered intensities of the atomic columns are estimated. These intensities can be related to the material structure or composition. Since the experimental probe profile is assumed to be known in the description of the imaging model, we will explore how the uncertainties in the probe profile affect the estimation of the total scattered intensities. Using multislice image simulations, we analyze this effect for Cs corrected and non-Cs corrected microscopes as a function of inaccuracies in cylindrically symmetric aberrations, such as defocus and spherical aberration of third and fifth order, and non-cylindrically symmetric aberrations, such as 2-fold and 3-fold astigmatism and coma.

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: 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: A thorough understanding of the three-dimensional (3D) atomic structure and composition of coreshell nanostructures is indispensable to obtain a deeper insight on their physical behavior. Such 3D information can be reconstructed from two-dimensional (2D) projection images using electron tomography. Recently, different electron tomography techniques have enabled the 3D characterization of a variety of nanostructures down to the atomic level. However, these methods have all focused on the investigation of nanomaterials containing only one type of chemical element. Here, we combine statistical parameter estimation theory with compressive sensing based tomography to determine the positions and atom type of each atom in heteronanostructures. The approach is applied here to investigate the interface in coreshell Au@Ag nanorods but it is of great interest in the investigation of a broad range of nanostructures.

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: 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 atomcounting diagnosed by combining a thorough statistical method and detailed image simulations.

Abstract: The rapid progress in materials science that enables the design of materials down to the nanoscale also demands characterization techniques able to analyze the materials down to the same scale, such as transmission electron microscopy. As Belgium’s foremost electron microscopy group, among the largest in the world, EMAT is continuously contributing to the development of TEM techniques, such as high-resolution imaging, diffraction, electron tomography, and spectroscopies, with an emphasis on quantification and reproducibility, as well as employing TEM methodology at the highest level to solve real-world materials science problems. The lab’s recent contributions are presented here together with specific case studies in order to highlight the usefulness of TEM to the advancement of materials science.

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: 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.

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: 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.