Abstract: 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.

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: 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.

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: A real-time image reconstruction method for scanning transmission electron microscopy (STEM) is proposed. With an algorithm requiring only the center of mass of the diffraction pattern at one probe position at a time, it is able to update the resulting image each time a new probe position is visited without storing any intermediate diffraction patterns. The results show clear features at high spatial frequency, such as atomic column positions. It is also demonstrated that some common post-processing methods, such as band-pass filtering, can be directly integrated in the real-time processing flow. Compared with other reconstruction methods, the proposed method produces high-quality reconstructions with good noise robustness at extremely low memory and computational requirements. An efficient, interactive open source implementation of the concept is further presented, which is compatible with frame-based, as well as event-based camera/file types. This method provides the attractive feature of immediate feedback that microscope operators have become used to, for example, conventional high-angle annular dark field STEM imaging, allowing for rapid decision-making and fine-tuning to obtain the best possible images for beam-sensitive samples at the lowest possible dose.

Abstract: In this study, we explore the possibility to use deep learning for the reconstruction of phase images from 4D scanning transmission electron microscopy (4D-STEM) data. The process can be divided into two main steps. First, the complex electron wave function is recovered for a convergent beam electron diffraction pattern (CBED) using a convolutional neural network (CNN). Subsequently, a corresponding patch of the phase object is recovered using the phase object approximation. Repeating this for each scan position in a 4D-STEM dataset and combining the patches by complex summation yields the full-phase object. Each patch is recovered from a kernel of 3x3 adjacent CBEDs only, which eliminates common, large memory requirements and enables live processing during an experiment. The machine learning pipeline, data generation, and the reconstruction algorithm are presented. We demonstrate that the CNN can retrieve phase information beyond the aperture angle, enabling super-resolution imaging. The image contrast formation is evaluated showing a dependence on the thickness and atomic column type. Columns containing light and heavy elements can be imaged simultaneously and are distinguishable. The combination of super-resolution, good noise robustness, and intuitive image contrast characteristics makes the approach unique among live imaging methods in 4D-STEM.

Abstract: In the present paper, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. In order to count the number of atoms, it is assumed that the total scattered intensity scales with the number of atoms per atom column. These intensities are quantitatively determined using model-based statistical parameter estimation theory. The distribution describing the probability that intensity values are generated by atomic columns containing a specific number of atoms is inferred on the basis of the experimental scattered intensities. Finally, the number of atoms per atom column is quantified using this estimated probability distribution. The number of atom columns available in the observed STEM image, the number of components in the estimated probability distribution, the width of the components of the probability distribution, and the typical shape of a criterion to assess the number of components in the probability distribution directly affect the accuracy and precision with which the number of atoms in a particular atom column can be estimated. It is shown that single atom sensitivity is feasible taking the latter aspects into consideration.

Abstract: In materials science, high angle annular dark field scanning transmission electron microscopy is often used for tomography at the nanometer scale. In this work, it is shown that a thickness dependent, non-linear damping of the recorded intensities occurs. This results in an underestimated intensity in the interior of reconstructions of homogeneous particles, which is known as the cupping artifact. In this paper, this non-linear effect is demonstrated in experimental images taken under common conditions and is reproduced with a numerical simulation. Furthermore, an analytical derivation shows that these non-linearities can be inverted if the imaging is done quantitatively, thus preventing cupping in the reconstruction.

Abstract: This paper is the second part of a two-part paper on direct structure inversion from exit waves. In the first part, a method has been proposed to quantitatively determine structure parameters with atomic resolution such as atom column positions, surface profile and the number of atoms in the atom columns. In this part, the theory will be demonstrated by means of a Au[110] exit wave reconstructed from a set of focal-series images. The procedures to analyze the experimentally reconstructed exit wave in terms of quantitative structure information are described in detail.

Abstract: 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.

Abstract: We propose an improved image simulation procedure for atomic-resolution annular dark-field scanning transmission electron microscopy (STEM) based on the multislice formulation, which takes thermal diffuse scattering fully into account. The improvement with regard to the classical frozen phonon approach is realized by separating the lattice configuration statistics from the dynamical scattering so as to avoid repetitive calculations. As an example, the influence of phonon scattering on the image contrast is calculated and investigated. STEM image simulation of crystals can be applied with reasonable computing times to problems involving a large number of atoms and thick or large supercells.

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: A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has different effects on the transfer of the linear and non-linear terms, such that the non-linear imaging contributions are damped less than the linear imaging contributions at high spatial frequencies. This will be important when coherent aberrations such as spherical aberration and defocus are reduced.