Abstract: A new methodology is presented to count the number of atoms in multimetallic nanocrystals by combining energy dispersive X-ray spectroscopy (EDX) and high angle annular dark field scanning transmission electron microscopy (HAADF STEM). For this purpose, the existence of a linear relationship between the incoherent HAADF STEM and EDX images is exploited. Next to the number of atoms for each element in the atomic columns, the method also allows quantification of the error in the obtained number of atoms, which is of importance given the noisy nature of the acquired EDX signals. Using experimental images of an Au@Ag core–shell nanorod, it is demonstrated that 3D structural information can be extracted at the atomic scale. Furthermore, simulated data of an Au@Pt core–shell nanorod show the prospect to characterize heterogeneous nanostructures with adjacent atomic numbers.

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 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: A hybrid statistics-simulations based method for atom-counting from annular dark field scanning transmission electron microscopy (ADF STEM) images of monotype crystalline nanostructures is presented. Different atom-counting methods already exist for model-like systems. However, the increasing relevance of radiation damage in the study of nanostructures demands a method that allows atom-counting from low dose images with a low signal-to-noise ratio. Therefore, the hybrid method directly includes prior knowledge from image simulations into the existing statistics-based method for atom-counting, and accounts in this manner for possible discrepancies between actual and simulated experimental conditions. It is shown by means of simulations and experiments that this hybrid method outperforms the statistics-based method, especially for low electron doses and small nanoparticles. The analysis of a simulated low dose image of a small nanoparticle suggests that this method allows for far more reliable quantitative analysis of beam-sensitive materials.

Abstract: The development of new nanocrystals with outstanding physicochemical properties requires a full threedimensional (3D) characterization at the atomic scale. For homogeneous nanocrystals, counting the number of atoms in each atomic column from high angle annular dark field scanning transmission electron microscopy images has been shown to be a successful technique to get access to this 3D information. However, technologically important nanostructures often consist of more than one chemical element. In order to extend atom counting to heterogeneous materials, a new atomic lensing model is presented. This model takes dynamical electron diffraction into account and opens up new possibilities for unraveling the 3D composition at the atomic scale. Here, the method is applied to determine the 3D structure of Au@Ag core-shell nanorods, but it is applicable to a wide range of heterogeneous complex nanostructures.

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: 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.