Element specific atom counting for heterogeneous nanostructures: Combining multiple ADF STEM images for simultaneous thickness and composition determination.

In this paper, a methodology is presented to count the number of atoms in heterogeneous nanoparticles based on the combination of multiple annular dark field scanning transmission electron microscopy (ADF STEM) images. The different non-overlapping annular detector collection regions are selected based on the principles of optimal statistical experiment design for the atom-counting problem. To count the number of atoms, the total intensities of scattered electrons for each atomic column, the so-called scattering cross-sections, are simultaneously compared with simulated library values for the different detector regions by minimising the squared differences. The performance of the method is evaluated for simulated Ni@Pt and Au@Ag core-shell nanoparticles. Our approach turns out to be a dose efficient alternative for the investigation of beam-sensitive heterogeneous materials as compared to the combination of ADF STEM and energy dispersive X-ray spectroscopy.

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.

Optimal experiment design for element specific atom counting using multiple annular dark field scanning transmission electron microscopy detectors.

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.

The atomic lensing model: New opportunities for atom-by-atom metrology of heterogeneous nanomaterials.

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.

A model of defect cluster creation in fragmented cascades in metals based on morphological analysis.

The impacts of ions and neutrons in metals cause cascades of atomic collisions that expand and shrink, leaving microstructure defect debris, i.e. interstitial or vacancy clusters or loops of different sizes. In De Backer et al (2016 Europhys. Lett. 115 26001), we described a method to detect the first morphological transition, i.e. the cascade fragmentation in subcascades, and a model of primary damage combining the binary collision approximation and molecular dynamics (MD). In this paper including W, Fe, Be, Zr and 20 other metals, we demonstrate that the fragmentation energy increases with the atomic number and decreases with the atomic density following a unique power law. Above the fragmentation energy, the cascade morphology can be characterized by the cross pair correlation functions of the multitype point pattern formed by the subcascades. We derive the numbers of pairs of subcascades and observed that they follow broken power laws. The energy where the power law breaks indicates the second morphological transition when cascades are formed by branches decorated by chaplets of small subcascades. The subcascade interaction is introduced in our model of primary damage by adding pairwise terms. Using statistics obtained on hundreds of MD cascades in Fe, we demonstrate that the interaction of subcascades increases the proportion of large clusters in the damage created by high energy cascades. Finally, we predict the primary damage of 500 keV Fe ion in Fe and obtain cluster size distributions when large statistics of MD cascades are not feasible.

Three-dimensional atomic models from a single projection using Z-contrast imaging: verification by electron tomography and opportunities.

In order to fully exploit structure-property relations of nanomaterials, three-dimensional (3D) characterization at the atomic scale is often required. In recent years, the resolution of electron tomography has reached the atomic scale. However, such tomography typically requires several projection images demanding substantial electron dose. A newly developed alternative circumvents this by counting the number of atoms across a single projection. These atom counts can be used to create an initial atomic model with which an energy minimization can be applied to obtain a relaxed 3D reconstruction of the nanoparticle. Here, we compare, at the atomic scale, this single projection reconstruction approach with tomography and find an excellent agreement. This new approach allows for the characterization of beam-sensitive materials or where the acquisition of a tilt series is impossible. As an example, the utility is illustrated by the 3D atomic scale characterization of a nanodumbbell on an in situ heating holder of limited tilt range.

How precise can atoms of a nanocluster be located in 3D using a tilt series of scanning transmission electron microscopy images?

In this paper, we investigate how precise atoms of a small nanocluster can ultimately be located in three dimensions (3D) from a tilt series of images acquired using annular dark field (ADF) scanning transmission electron microscopy (STEM). Therefore, we derive an expression for the statistical precision with which the 3D atomic position coordinates can be estimated in a quantitative analysis. Evaluating this statistical precision as a function of the microscope settings also allows us to derive the optimal experimental design. In this manner, the optimal angular tilt range, required electron dose, optimal detector angles, and number of projection images can be determined.

Atom-counting in High Resolution Electron Microscopy:TEM or STEM - That's the question.

In this work, a recently developed quantitative approach based on the principles of detection theory is used in order to determine the possibilities and limitations of High Resolution Scanning Transmission Electron Microscopy (HR STEM) and HR TEM for atom-counting. So far, HR STEM has been shown to be an appropriate imaging mode to count the number of atoms in a projected atomic column. Recently, it has been demonstrated that HR TEM, when using negative spherical aberration imaging, is suitable for atom-counting as well. The capabilities of both imaging techniques are investigated and compared using the probability of error as a criterion. It is shown that for the same incoming electron dose, HR STEM outperforms HR TEM under common practice standards, i.e. when the decision is based on the probability function of the peak intensities in HR TEM and of the scattering cross-sections in HR STEM. If the atom-counting decision is based on the joint probability function of the image pixel values, the dependence of all image pixel intensities as a function of thickness should be known accurately. Under this assumption, the probability of error may decrease significantly for atom-counting in HR TEM and may, in theory, become lower as compared to HR STEM under the predicted optimal experimental settings. However, the commonly used standard for atom-counting in HR STEM leads to a high performance and has been shown to work in practice.

Depth sectioning combined with atom-counting in HAADF STEM to retrieve the 3D atomic structure.

Aberration correction in scanning transmission electron microscopy (STEM) has greatly improved the lateral and depth resolution. When using depth sectioning, a technique during which a series of images is recorded at different defocus values, single impurity atoms can be visualised in three dimensions. In this paper, we investigate new possibilities emerging when combining depth sectioning and precise atom-counting in order to reconstruct nanosized particles in three dimensions. Although the depth resolution does not allow one to precisely locate each atom within an atomic column, it will be shown that the depth location of an atomic column as a whole can be measured precisely. In this manner, the morphology of a nanoparticle can be reconstructed in three dimensions. This will be demonstrated using simulations and experimental data of a gold nanorod.

Quantification by aberration corrected (S)TEM of boundaries formed by symmetry breaking phase transformations.

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.

Detecting and locating light atoms from high-resolution STEM images: The quest for a single optimal design.

In the present paper, the optimal detector design is investigated for both detecting and locating light atoms from high resolution scanning transmission electron microscopy (HR STEM) images. The principles of detection theory are used to quantify the probability of error for the detection of light atoms from HR STEM images. To determine the optimal experiment design for locating light atoms, use is made of the so-called Cramér-Rao Lower Bound (CRLB). It is investigated if a single optimal design can be found for both the detection and location problem of light atoms. Furthermore, the incoming electron dose is optimised for both research goals and it is shown that picometre range precision is feasible for the estimation of the atom positions when using an appropriate incoming electron dose under the optimal detector settings to detect light atoms.

StatSTEM: An efficient approach for accurate and precise model-based quantification of atomic resolution electron microscopy images.

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.

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.

γ-H2AX foci as in vivo effect biomarker in children emphasize the importance to minimize x-ray doses in paediatric CT imaging.

OBJECTIVES: Investigation of DNA damage induced by CT x-rays in paediatric patients versus patient dose in a multicentre setting. METHODS: From 51 paediatric patients (median age, 3.8 years) who underwent an abdomen or chest CT examination in one of the five participating radiology departments, blood samples were taken before and shortly after the examination. DNA damage was estimated by scoring γ-H2AX foci in peripheral blood T lymphocytes. Patient-specific organ and tissue doses were calculated with a validated Monte Carlo program. Individual lifetime attributable risks (LAR) for cancer incidence and mortality were estimated according to the BEIR VII risk models. RESULTS: Despite the low CT doses, a median increase of 0.13 γ-H2AX foci/cell was observed. Plotting the induced γ-H2AX foci versus blood dose indicated a low-dose hypersensitivity, supported also by an in vitro dose-response study. Differences in dose levels between radiology centres were reflected in differences in DNA damage. LAR of cancer mortality for the paediatric chest CT and abdomen CT cohort was 0.08 and 0.13 ‰ respectively. CONCLUSION: CT x-rays induce DNA damage in paediatric patients even at low doses and the level of DNA damage is reduced by application of more effective CT dose reduction techniques and paediatric protocols. .

Dose limited reliability of quantitative annular dark field scanning transmission electron microscopy for nano-particle atom-counting.

Quantitative annular dark field scanning transmission electron microscopy (ADF STEM) has become a powerful technique to characterise nano-particles on an atomic scale. Because of their limited size and beam sensitivity, the atomic structure of such particles may become extremely challenging to determine. Therefore keeping the incoming electron dose to a minimum is important. However, this may reduce the reliability of quantitative ADF STEM which will here be demonstrated for nano-particle atom-counting. Based on experimental ADF STEM images of a real industrial catalyst, we discuss the limits for counting the number of atoms in a projected atomic column with single atom sensitivity. We diagnose these limits by combining a thorough statistical method and detailed image simulations.

Optimal experimental design for nano-particle atom-counting from high-resolution STEM images.

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.

Hepatic adenomatosis: MR imaging features.

Hepatocellular adenomas are rare benign liver neoplasms that commonly occur in women with a history of oral contraceptives intake for more than 2 years. Hepatic adenomatosis is characterized by the presence of multiple adenomas, arbitrarily > than 10, involving both lobes of the liver, without any history of steroid therapy or glycogen storage disease. Although the adenomas in liver adenomatosis are histologically similar to other adenomas, liver adenomatosis appears to be a separate clinical entity. Adenomas in hepatic adenomatosis may be of the inflammatory, hepatocyte nuclear factor 1alpha-mutated, or beta-catenin-mutated subtype, and accordingly show variable imaging appearances. Hepatic adenomatosis carries the risk of impaired liver function, hemorrhage and malignant degeneration. We report a case with the inflammatory subtype of hepatic adenomatosis in a 39-year-old woman with liver steatosis. The magnetic resonance imaging features using extracellular gadolinium chelates and hepatocyte-targeted contrast agents are described.

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

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.