Abstract: We present a computational imaging mode for large scale electron microscopy data, which retrieves a complex wave from noisy/sparse intensity recordings using a deep learning approach and subsequently reconstructs an image of the specimen from the Convolutional Neural Network (CNN) predicted exit waves. We demonstrate that an appropriate forward model in combination with open data frameworks can be used to generate large synthetic datasets for training. In combination with augmenting the data with Poisson noise corresponding to varying dose-values, we effectively eliminate overfitting issues. The U-NET[1] based architecture of the CNN is adapted to the task at hand and performs well while maintaining a relatively small size and fast performance. The validity of the approach is confirmed by comparing the reconstruction to well-established methods using simulated, as well as real electron microscopy data. The proposed method is shown to be effective particularly in the low dose range, evident by strong suppression of noise, good spatial resolution, and sensitivity to different atom types, enabling the simultaneous visualisation of light and heavy elements and making different atomic species distinguishable. Since the method acts on a very local scale and is comparatively fast it bears the potential to be used for near-real-time reconstruction during data acquisition.

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: Inelastic excitation as exploited in Electron Energy Loss Spectroscopy (EELS) contains a rich source of information that is revealed in the scattering process. To accurately quantify core-loss EELS, it is common practice to fit the observed spectrum with scattering cross-sections calculated using experimental parameters and a Generalized Oscillator Strength (GOS) database [1].   The GOS is computed using Fermi’s Golden Rule and orbitals of bound and excited states. Previously, the GOS was based on Hartree-Fock solutions [2], but more recently Density Functional Theory (DFT) has been used [3]. In this work, we have chosen to use the Dirac equation to incorporate relativistic effects and have performed calculations using Flexible Atomic Code (FAC) [4]. This repository contains a tabulated GOS database based on Dirac solutions for computing double differential cross-sections under experimental conditions.   We hope the Dirac-based GOS database can benefit the EELS community for both academic use and industry integration.   Database Details: – Covers all elements (Z: 1-108) and all edges – Large energy range: 0.01 – 4000 eV – Large momentum range: 0.05 -50 Å-1 – Fine log sampling: 128 points for energy and 256 points for momentum – Data format: GOSH [3]   Calculation Details: – Single atoms only; solid-state effects are not considered – Unoccupied states before continuum states of ionization are not considered; no fine structure – Plane Wave Born Approximation – Frozen Core Approximation is employed; electrostatic potential remains unchanged for orthogonal states when – core-shell electron is excited – Self-consistent Dirac–Fock–Slater iteration is used for Dirac calculations; Local Density Approximation is assumed for electron exchange interactions; continuum states are normalized against asymptotic form at large distances – Both large and small component contributions of Dirac solutions are included in GOS – Final state contributions are included until the contribution of the previous three states falls below 0.1%. A convergence log is provided for reference.   Version 1.1 release note: – Update to be consistent with GOSH data format [3], all the edges are now within a single hdf5 file. A notable change in particular, the sampling in momentum is in 1/m, instead of previously in 1/Å. Great thanks to Gulio Guzzinati for his suggestions and sending conversion script.  Version 1.2 release note: – Add “File Type / File version” information [1] Verbeeck, J., and S. Van Aert. Ultramicroscopy 101.2-4 (2004): 207-224. [2] Leapman, R. D., P. Rez, and D. F. Mayers. The Journal of Chemical Physics 72.2 (1980): 1232-1243. [3] Segger, L, Guzzinati, G, & Kohl, H. Zenodo (2023). doi:10.5281/zenodo.7645765 [4] Gu, M. F. Canadian Journal of Physics 86(5) (2008): 675-689.

Abstract: Supplementary information for the article “In-situ Plasma Studies using a Direct Current Microplasma in a Scanning Electron Microscope” containing the videos of in-situ SEM imaging (mp4 files), raw data/images, and Jupyter notebooks (ipynb files) for data treatment and plots. Link to the preprint: https://doi.org/10.48550/arXiv.2308.15123 Explanation of the data files can be found in the Information.pdf file. The Videos folder contains the in-situ SEM image series mentioned in the paper. If there are any questions/bugs, feel free to contact me at lukas.grunewaldatuantwerpen.be

Abstract: Even at low temperatures, metal nanoparticles (NPs) possess atomic dynamics that are key for their properties but challenging to elucidate. Recent experimental advances allow obtaining atomic-resolution snapshots of the NPs in realistic regimes, but data acquisition limitations hinder the experimental reconstruction of the atomic dynamics present within them. Molecular simulations have the advantage that these allow directly tracking the motion of atoms over time. However, these typically start from ideal/perfect NP structures and, suffering from sampling limits, provide results that are often dependent on the initial/putative structure and remain purely indicative. Here, by combining state-of-the-art experimental and computational approaches, how it is possible to tackle the limitations of both approaches and resolve the atomistic dynamics present in metal NPs in realistic conditions is demonstrated. Annular dark-field scanning transmission electron microscopy enables the acquisition of ten high-resolution images of an Au NP at intervals of 0.6 s. These are used to reconstruct atomistic 3D models of the real NP used to run ten independent molecular dynamics simulations. Machine learning analyses of the simulation trajectories allow resolving the real-time atomic dynamics present within the NP. This provides a robust combined experimental/computational approach to characterize the structural dynamics of metal NPs in realistic conditions. Experimental and computational techniques are bridged to unveil atomic dynamics in gold nanoparticles (NPs), using annular dark-field scanning transmission electron microscopy and molecular dynamics simulations informed by machine learning. The approach provides unprecedented insights into the real-time structural behaviors of NPs, merging state-of-the-art techniques to accurately characterize their dynamics under realistic conditions. image

Abstract: Because of its low hysteresis, high dielectric constant, and strong piezoelectric response, Pb(Mg1/3Nb2/3)O-3-PbTiO3 (PMN-PT) thin films have attracted considerable attention for the application in PiezoMEMS, field-effect transistors, and energy harvesting and storage devices. However, it remains a great challenge to fabricate phase-pure, pyrochlore-free PMN-PT thin films. In this study, we demonstrate that a high deposition rate, combined with a tensile mismatched template layer can stabilize the perovskite phase of PMN-PT films and prevent the nucleation of passive pyrochlore phases. We observed that an accelerated deposition rate promoted mixing of the B-site cation and facilitated relaxation of the compressively strained PMN-PT on the SrTiO3 (STO) substrate in the initial growth layer, which apparently suppressed the initial formation of pyrochlore phases. By employing La-doped-BaSnO3 (LBSO) as the tensile mismatched buffer layer, 750 nm thick phase-pure perovskite PMN-PT films were synthesized. The resulting PMN-PT films exhibited excellent crystalline quality close to that of the STO substrate.

Abstract: The concept of resolution in high-resolution electron microscopy (HREM) is the power to resolve neighboring atoms. Since the resolution is related to the width of the point spread function of the microscope, it could in principle be determined from the image of a point object. However, in electron microscopy there are no ideal point objects. The smallest object is an individual atom. If the width of an atom is much smaller than the resolution of the microscope, this atom can still be considered as a point object. As the resolution of the microscope enters the sub-Å regime, information about the microscope is strongly entangled with the information about the atoms in HREM images. Therefore, we need to find an alternative method to determine the resolution in an object-independent way. In this work we propose to use the image wave of a crystalline object in zone axis orientation. Under this condition, the atoms of a column act as small lenses so that the electron beam channels through the atom column periodically. Because of this focusing, the image wave of the column can be much more peaked than the constituting atoms and can thus be a much more sensitive probe to measure the resolution. Our approach is to use the peakiness of the image wave of the atom column to determine the resolution. We will show that the resolution can be directly linked to the total curvature of the atom column wave. Moreover, we can then directly obtain the resolution of the microscope given that the contribution from the object is known, which is related to the bounding energy of the atom. The method is applied on an experimental CaTiO3 image wave.

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: 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: 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: 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: 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.