Abstract: This study sheds light on the prerequisites, possibilities, limitations and interpretation of high-resolution differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM). We draw particular attention to the well-established DPC technique based on segmented annular detectors and its relation to recent developments based on pixelated detectors. These employ the expectation value of the momentum transfer as a reliable measure of the angular deflection of the STEM beam induced by an electric field in the specimen. The influence of scattering and propagation of electrons within the specimen is initially discussed separately and then treated in terms of a two-state channeling theory. A detailed simulation study of GaN is presented as a function of specimen thickness and bonding. It is found that bonding effects are rather detectable implicitly, e.g., by characteristics of the momentum flux in areas between the atoms than by directly mapping electric fields and charge densities. For strontium titanate, experimental charge densities are compared with simulations and discussed with respect to experimental artifacts such as scan noise. Finally, we consider practical issues such as figures of merit for spatial and momentum resolution, minimum electron dose, and the mapping of larger-scale, built-in electric fields by virtue of data averaged over a crystal unit cell. We find that the latter is possible for crystals with an inversion center. Concerning the optimal detector design, this study indicates that a sampling of 5mrad per pixel is sufficient in typical applications, corresponding to approximately 10x10 available pixels.

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aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range.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: A straightforward application of the theoretical framework presented by Verbeeck et al. [Ultramicroscopy 102 (2005) 239] is presented to explain the energy-filtered electron-diffracted beam holography experiments published by Herring [Ultramicroscopy 104 (2005) 261]. It is shown that the theory is in agreement with all experimental findings, which leads to the interpretation that the experiments are mainly measuring the angular coherence of the source image rather than exposing details on the coherence properties of inelastic scattering. A change in experimental parameters is proposed, which could result in interesting information about the coherence in all inelastic scattering process. (c) 2006 Elsevier B.V. All rights reserved.

Abstract: Inelastic image simulation software is presented, implementing the double channeling approximation which takes into account the combination of multiple elastic and single inelastic scattering in a crystal. The approach is described with a density matrix formalism. Two applications in high resolution energy filtered (EFTEM) transmission electron microscopy (TEM) images are presented: thickness-defocus maps for SrTiO3 and exit plane intensities for an (LaAlO3)3(SrTiO3)3 multilayer system. Both systems show a severe breakdown in direct interpretability which becomes worse for higher acceleration voltages, thicker samples and lower excitation edge energies. Since this effect already occurs in the exit plane intensity, it is a fundamental limit and image simulations in EFTEM are indispensable just as they are indispensable for elastic high resolution TEM images.

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: In this paper, it has been investigated how to measure atom column positions as accurately and precisely as possible using a focal series of images. In theory, it is expected that the precision would considerably improve using a maximum likelihood estimator based on the full series of focal images. As such, the theoretical lower bound on the variances of the unknown atom column positions can be attained. However, this approach is numerically demanding. Therefore, maximum likelihood estimation has been compared with the results obtained by fitting a model to a reconstructed exit wave rather than to the full series of focal images. Hence, a real space model-based exit wave reconstruction technique based on the channelling theory is introduced. Simulations show that the reconstructed complex exit wave contains the same amount of information concerning the atom column positions as the full series of focal images. Only for thin samples, which act as weak phase objects, this information can be retrieved from the phase of the reconstructed complex exit wave.

Abstract: We present a quantitative method which allows us to reliably measure dynamic changes in the atomic structure of monatomic crystalline nanomaterials from a time series of atomic resolution annular dark field scanning transmission electron microscopy images. The approach is based on the so-called hidden Markov model and estimates the number of atoms in each atomic column of the nanomaterial in each frame of the time series. We discuss the origin of the improved performance for time series atom-counting as compared to the current state-of-the-art atom-counting procedures, and show that the so-called transition probabilities that describe the probability for an atomic column to lose or gain one or more atoms from frame to frame are particularly important. Using these transition probabilities, we show that the method can also be used to estimate the probability and cross section related to structural changes. Furthermore, we explore the possibilities for applying the method to time series recorded under variable environmental conditions. The method is shown to be promising for a reliable quantitative analysis of dynamic processes such as surface diffusion, adatom dynamics, beam effects, or in situ experiments.

Abstract: <script type='text/javascript'>document.write(unpmarked('In this paper, both the frozen lattice (FL) and the absorptive potential (AP) approximation models are compared in terms of the integrated intensity and the precision with which atomic columns can be located from an image acquired using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM). The comparison is made for atoms of Cu, Ag, and Au. The integrated intensity is computed for both an isolated atomic column and an atomic column inside an FCC structure. The precision has been computed using the so-called Cramer-Rao Lower Bound (CRLB), which provides a theoretical lower bound on the variance with which parameters can be estimated. It is shown that the AP model results into accurate measurements for the integrated intensity only for small detector ranges under relatively low angles and for small thicknesses. In terms of the attainable precision, both methods show similar results indicating picometer range precision under realistic experimental conditions. (C) 2017 Elsevier B.V. All rights reserved.'));

Abstract: Advanced materials often consist of multiple elements which are arranged in a complicated structure. Quantitative scanning transmission electron microscopy is useful to determine the composition and thickness of nanostructures at the atomic scale. However, significant difficulties remain to quantify mixed columns by comparing the resulting atomic resolution images and spectroscopy data with multislice simulations where dynamic scattering needs to be taken into account. The combination of the computationally intensive nature of these simulations and the enormous amount of possible mixed column configurations for a given composition indeed severely hamper the quantification process. To overcome these challenges, we here report the development of an incoherent non-linear method for the fast prediction of ADF-EDX scattering cross-sections of mixed columns under channelling conditions. We first explain the origin of the ADF and EDX incoherence from scattering physics suggesting a linear dependence between those two signals in the case of a high-angle ADF detector. Taking EDX as a perfect incoherent reference mode, we quantitatively examine the ADF longitudinal incoherence under different microscope conditions using multislice simulations. Based on incoherent imaging, the atomic lensing model previously developed for ADF is now expanded to EDX, which yields ADF-EDX scattering cross-section predictions in good agreement with multislice simulations for mixed columns in a core–shell nanoparticle and a high entropy alloy. The fast and accurate prediction of ADF-EDX scattering cross-sections opens up new opportunities to explore the wide range of ordering possibilities of heterogeneous materials with multiple elements.

Abstract: Several different projection mechanisms that all make use of inelastically scattered electrons are used for electron tomography. The advantages and the disadvantages of these methods are compared to HAADFSTEM tomography, which is considered as the standard electron tomography technique in materials science. The different inelastic setups used are energy filtered transmission electron microscopy (EFTEM), thickness mapping based on the log-ratio method and bulk plasmon mapping. We present a comparison that can be used to select the best inelastic signal for tomography, depending on different parameters such as the beam stability and nature of the sample. The appropriate signal will obviously also depend on the exact information which is requested.