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: 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aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range.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: 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: A model-based method is proposed to relatively quantify the chemical composition of atomic columns using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. The method is based on a quantification of the total intensity of the scattered electrons for the individual atomic columns using statistical parameter estimation theory. In order to apply this theory, a model is required describing the image contrast of the HAADF STEM images. Therefore, a simple, effective incoherent model has been assumed which takes the probe intensity profile into account. The scattered intensities can then be estimated by fitting this model to an experimental HAADF STEM image. These estimates are used as a performance measure to distinguish between different atomic column types and to identify the nature of unknown columns with good accuracy and precision using statistical hypothesis testing. The reliability of the method is supported by means of simulated HAADF STEM images as well as a combination of experimental images and electron energy-loss spectra. It is experimentally shown that statistically meaningful information on the composition of individual columns can be obtained even if the difference in averaged atomic number Z is only 3. Using this method, quantitative mapping at atomic resolution using HAADF STEM images only has become possible without the need of simultaneously recorded electron energy loss spectra.

Abstract: We propose a new method to measure atomic scale dynamics of nanoparticles from experimental high-resolution annular dark field scanning transmission electron microscopy images. By using the so-called hidden Markov model, which explicitly models the possibility of structural changes, the number of atoms in each atomic column can be quantified over time. This newly proposed method outperforms the current atom-counting procedure and enables the determination of the probabilities and cross sections for surface diffusion. This method is therefore of great importance for revealing and quantifying the atomic structure when it evolves over time via adatom dynamics, surface diffusion, beam effects, or during in situ experiments.

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: Investigating domain boundaries and their effects on the behaviour of materials automatically implies the need for detailed knowledge on the structural aspects of the atomic configurations at these interfaces. Not only in view of nearest neighbour interactions but also at a larger scale, often surpassing the unit cell, the boundaries can contain structural elements that do not exist in the bulk. In the present contribution, a number of special boundaries resulting from phase transformations or crystal growth and those recently investigated by advanced transmission electron microscopy techniques in different systems will be reviewed. These include macrotwins between microtwinned martensite plates in NiAl, austenite-single variant martensite habit planes in low hysteresis NiTiPd, nanotwins in non-textured nanostructured Pd and ferroelastic domain boundaries in CaTiO3. In all discussed cases these boundaries play an essential role in the properties of the respective materials.

Abstract: We introduce a Bayesian genetic algorithm for reconstructing atomic models of monotype crystalline nanoparticles from a single projection using Z-contrast imaging. The number of atoms in a projected atomic column obtained from annular dark field scanning transmission electron microscopy images serves as an input for the initial three-dimensional model. The algorithm minimizes the energy of the structure while utilizing a priori information about the finite precision of the atom-counting results and neighbor-mass relations. The results show promising prospects for obtaining reliable reconstructions of beam-sensitive nanoparticles during dynamical processes from images acquired with sufficiently low incident electron doses.

Abstract: Advanced electron microscopy techniques, including scanning electron microscopes (SEM), scanning transmission electron microscopes (STEM), and transmission electron microscopes (TEM), have revolutionized imaging capabilities. However, achieving high-quality experimental images remains a challenge due to various distortions stemming from the instrumentation and external factors. These distortions, introduced at different stages of imaging, hinder the extraction of reliable quantitative insights. In this paper, we will discuss the main sources of distortion in TEM and S(T)EM images, develop models to describe them, and propose a method to correct these distortions using a convolutional neural network. We validate the effectiveness of our method on a range of simulated and experimental images, demonstrating its ability to significantly enhance the signal-to-noise ratio. This improvement leads to a more reliable extraction of quantitative structural information from the images. In summary, our findings offer a robust framework to enhance the quality of electron microscopy images, which in turn supports progress in structural analysis and quantification in materials science and biology.

Abstract: Electron tomography is essential for investigating the three-dimensional (3D) structure of nanomaterials. However, many of these materials, such as metal-organic frameworks (MOFs), are extremely sensitive to electron radiation, making it difficult to acquire a series of projection images for electron tomography without inducing electron-beam damage. Another significant challenge is the high contrast in high-angle annular dark field scanning transmission electron microscopy that can be expected for nanocomposites composed of a metal nanoparticle and an MOF. This strong contrast leads to so-called metal artifacts in the 3D reconstruction. To overcome these limitations, we here present low-dose electron tomography based on four-dimensional scanning transmission electron microscopy (4D-STEM) data sets, collected using an ultrafast and highly sensitive direct electron detector. As a proof of concept, we demonstrate the applicability of the method for an Au nanostar embedded in a ZIF-8 MOF, which is of great interest for applications in various fields, including drug delivery.

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: The conventional approach to object reconstruction through electron tomography is to reduce the three-dimensional problem to a series of independent two-dimensional slice-by-slice reconstructions. However, at atomic resolution the image of a single atom extends over many such slices and incorporating this image as prior knowledge in tomography or depth sectioning therefore requires a fully three-dimensional treatment. Unfortunately, the size of the three-dimensional projection operator scales highly unfavorably with object size and readily exceeds the available computer memory. In this paper, it is shown that for incoherent image formation the memory requirement can be reduced to the fundamental lower limit of the object size, both for tomography and depth sectioning. Furthermore, it is shown through multislice calculations that high angle annular dark field scanning transmission electron microscopy can be sufficiently incoherent for the reconstruction of single element nanocrystals, but that dynamical diffraction effects can cause classification problems if more than one element is present. (C) 2014 Elsevier B.V. All rights reserved.