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: Recently, the maximum a posteriori (MAP) probability rule has been proposed as an objective and quantitative method to detect atom columns and even single atoms from high-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images. The method combines statistical parameter estimation and model-order selection using a Bayesian framework and has been shown to be especially useful for the analysis of the structure of beam-sensitive nanomaterials. In order to avoid beam damage, images of such materials are usually acquired using a limited incoming electron dose resulting in a low contrast-to-noise ratio (CNR) which makes visual inspection unreliable. This creates a need for an objective and quantitative approach. The present paper describes the methodology of the MAP probability rule, gives its step-by-step derivation and discusses its algorithmic implementation for atom column detection. In addition, simulation results are presented showing that the performance of the MAP probability rule to detect the correct number of atomic columns from HAADF STEM images is superior to that of other model-order selection criteria, including the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). Moreover, the MAP probability rule is used as a tool to evaluate the relation between STEM image quality measures and atom detectability resulting in the introduction of the so-called integrated CNR (ICNR) as a new image quality measure that better correlates with atom detectability than conventional measures such as signal-to-noise ratio (SNR) and CNR.

Abstract: High-resolution transmission electron microscopy (TEM) of organic crystals, such as Lead Phthalocyanine (PbPc), is very challenging since these materials are prone to electron beam damage leading to the breakdown of the crystal structure during investigation. Quantification of the damage is imperative to enable high-resolution imaging of PbPc crystals with minimum structural changes. In this work, we performed a detailed electron diffraction study to quantitatively measure degradation of PbPc crystals upon electron beam irradiation. Our study is based on the quantification of the fading intensity of the spots in the electron diffraction patterns. At various incident dose rates (e/Å2/s) and acceleration voltages, we experimentally extracted the decay rate (1/s), which directly correlates with the rate of beam damage. In this manner, a value for the critical dose (e/Å2) could be determined, which can be used as a measure to quantify beam damage. Using the same methodology, we explored the influence of cryogenic temperatures, graphene TEM substrates, and graphene encapsulation in prolonging the lifetime of the PbPc crystal structure during TEM investigation. The knowledge obtained by diffraction experiments is then translated to real space high-resolution TEM imaging of PbPc.

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 contribution several advanced electron microscopy techniques are employed in order to describe chemical and structural features of the nano- and microstructure of a Ni45.5Ti45.5Nb9 alloy. A line-up of Nb-rich nano-precipitates is found in the Ni-Ti-rich austenite of as-cast material. Concentration changes of the matrix after annealing are correlated with changes in the transformation temperatures. The formation of rows and plates of larger Nb-rich precipitates and particles is described. The interaction of a twinned martensite plate with a Nb-rich nano-precipitate is discussed and the substitution of Nb atoms on the Ti-sublattice in the matrix is confirmed.

Abstract: Structural analysis of metal clusters confined in nanoporous materials is typically performed by X-ray-driven techniques. Although X-ray analysis has proved its strength in the characterization of metal clusters, it provides averaged structural information. Therefore, we here present an alternative workflow for bringing the characterization of confined metal clusters towards the local scale. This workflow is based on the combination of aberration-corrected transmission electron microscopy (TEM), TEM image simulations, and powder X-ray diffraction (XRD) with advanced statistical techniques. In this manner, we were able to characterize the clustering of Pb atoms in Linde Type A (LTA) zeolites with Pb loadings as low as 5 wt%. Moreover, individual Pb clusters could be directly detected. The proposed methodology thus enables a local-scale characterization of confined metal clusters in zeolites. This is important for further elucidation of the connection between the structure and the physicochemical properties of such systems.

Abstract: 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.

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: Tailoring the properties of oxide-based nanocomposites is of great importance for a wide range of materials relevant for energy technology. YBa2Cu3O7−δ (YBCO) superconducting thin films containing nanosized BaHfO3 (BHO) particles yield a significant improvement of the magnetic flux pinning properties and a reduced anisotropy of the critical current density. These films were prepared by chemical solution deposition (CSD) on (100) SrTiO3 (STO) substrates yielding critical current densities up to 3.6 MA cm−2 at 77 K and self-field. Transport in-field J c measurements demonstrated a high pinning force maximum of around 6 GN/m3 for a sample annealed at T = 760 °C that has a doping of 12 mol% of BHO. This sample was investigated by scanning transmission electron microscopy (STEM) in combination with electron energy-loss spectroscopy (EELS) yielding strain and spectral maps. Spherical BHO nanoparticles of 15 nm in size were found in the matrix, whereas the particles at the interface were flat. A 2 nm diffusion layer containing Ti was found at the YBCO (BHO)/STO interface. Local lattice deformation mapping at the atomic scale revealed crystal defects induced by the presence of both sorts of BHO nanoparticles, which can act as pinning centers for magnetic flux lines. Two types of local lattice defects were identified and imaged: (i) misfit edge dislocations and (ii) Ba-Cu-Cu-Ba stacking faults (Y-248 intergrowths). The local electronic structure and charge transfer were probed by high energy resolution monochromated electron energy-loss spectroscopy. This technique made it possible to distinguish superconducting from non-superconducting areas in nanocomposite samples with atomic resolution in real space, allowing the identification of local pinning sites on the order of the coherence length of YBCO (~1.5 nm) and the determination of 0.25 nm dislocation cores.

Abstract: In quantitative scanning transmission electron microscopy (STEM), scattering cross-sections have been shown to be very sensitive to the number of atoms in a column and its composition. They correspond to the integrated intensity over the atomic column and they outperform other measures. As compared to atomic column peak intensities, which saturate at a given thickness, scattering cross-sections increase monotonically. A study of the electron wave propagation is presented to explain the sensitivity of the scattering cross-sections. Based on the multislice algorithm, we analyse the wave propagation inside the crystal and its link to the scattered signal for the different probe positions contained in the scattering cross-section for detector collection in the low-, middle- and high-angle regimes. The influence to the signal from scattering of neighbouring columns is also discussed.

Abstract: 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.

Abstract: In this paper, we investigate to what extent high resolution transmission electron microscopy images can be used to measure the mass, in terms of thickness, and surface profile, corresponding to the defocus offset, of an object at the atomic scale. Therefore, we derive an expression for the statistical precision with which these object parameters can be estimated in a quantitative analysis. Evaluating this expression as a function of the microscope settings allows us to derive the optimal microscope design. Acquiring three-dimensional structure information in terms of thickness turns out to be much more difficult than obtaining two-dimensional information on the projected atom column positions. The attainable precision is found to be more strongly affected by processes influencing the image contrast, such as phonon scattering, than by the specific choice of microscope settings. For a realistic incident electron dose, it is expected that atom columns can be distinguished with single atom sensitivity up to a thickness of the order of the extinction distance. A comparable thickness limit is determined to measure surface steps of one atom. An increase of the electron dose shifts the limiting thickness upward due to an increase in the signal-to-noise ratio.

Abstract: After a short review of electron tomography techniques for materials science, this overview will cover some recent results on different shape memory and nanostructured metallic systems obtained by various three-dimensional (3D) electron imaging techniques. In binary NiTi, the 3D morphology and distribution of Ni4Ti3 precipitates are investigated by using FIB/SEM slice-and-view yielding 3D data stacks. Different quantification techniques will be presented including the principal ellipsoid for a given precipitate, shape classification following a Zingg scheme, particle distribution function, distance transform and water penetration. The latter is a novel approach to quantifying the expected matrix transformation in between the precipitates. The different samples investigated include a single crystal annealed with and without compression yielding layered and autocatalytic precipitation, respectively, and a polycrystal revealing different densities and sizes of the precipitates resulting in a multistage transformation process. Electron tomography was used to understand the interaction between focused ion beam-induced Frank loops and long dislocation structures in nanobeams of Al exhibiting special mechanical behaviour measured by on-chip deposition. Atomic resolution electron tomography is demonstrated on Ag nanoparticles in an Al matrix.

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.

Abstract: 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 Cramer-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.