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aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range.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: 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.

Abstract: Tomography with high angular annular dark field scanning transmission electron microscopy at atomic resolution can be greatly improved if one is able to take advantage of prior knowledge. In this paper we present a reconstruction technique that explicitly takes into account the microscope parameters and the atomic nature of the projected object. This results in a more accurate estimate of the atomic positions and in a good resistance to noise. The reconstruction is a maximum likelihood estimator of the object. Moreover, the limits to the precision have been explored, allowing for a prediction of the amount of expected noise in the reconstruction for a certain experimental setup. We believe that the proposed reconstruction technique can be generalized to other tomographic experiments.

Abstract: We report an innovative method to explore the optimal experimental settings to detect light atoms from scanning transmission electron microscopy (STEM) images. Since light elements play a key role in many technologically important materials, such as lithium-battery devices or hydrogen storage applications, much effort has been made to optimize the STEM technique in order to detect light elements. Therefore, classical performance criteria, such as contrast or signal-to-noise ratio, are often discussed hereby aiming at improvements of the direct visual interpretability. However, when images are interpreted quantitatively, one needs an alternative criterion, which we derive based on statistical detection theory. Using realistic simulations of technologically important materials, we demonstrate the benefits of the proposed method and compare the results with existing approaches.

Abstract: The 3D morphology and distribution of lenticular Ni4Ti3 precipitates in the austenitic B2 matrix of a binary Ni51Ti49 alloy has been investigated by a slice-and-view procedure in a dual-beam focused ion beam/scanning electron microscope system. Due to the weak contrast of the precipitates, proper imaging conditions need to be selected first to allow for semi-automated image treatment. Knowledgeable imaging is further needed to ensure that all variants of the precipitates are observed with equal probability, regardless of sample orientation. Finally, a volume ratio of 10.2% for the Ni4Ti3 precipitates could be calculated, summed over all variants, which yields a net composition of Ni50.27Ti49.73 for the matrix, leading to an increase of 125 degrees for the martensitic start temperature. Also, the expected relative orientation of the different variants of the precipitates could be confirmed.

Abstract: It is not straightforward to determine resolution for a 3D reconstruction when performing an electron tomography experiment. Different contributions such as missing wedge and misalignment add up and often influence the final resolution in an anisotropic manner. The conventional resolution measures can not be used for all of the reconstruction techniques, especially for iterative techniques which are more commonly used for electron tomography in materials science. Here we define a quantitative resolution measure that determines the resolution in three orthogonal directions of the reconstruction. As an application we use this measure to determine the optimum number of simultaneous iterative reconstruction technique (SIRT) iterations to reconstruct the gold nanoparticles, based on a high angle annular dark field STEM (HAADF-STEM) tilt series.

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: The three-dimensional (3D) structure and chemical composition of bamboo-like carbon nanotubes including the catalyst particles that are. used during their growth are studied by discrete electron tomography in combination with energy-filtered transmission electron microscopy. It is found that cavities are present in the catalyst particles. Furthermore, only a small percentage of the catalyst particles consist of pure Cu, since a large volume fraction of the particles is oxidized to CU(2)0. These volume fractions are determined quantitatively from 3D reconstructions obtained by discrete tomography.

Abstract: Determining the three-dimensional (3D) arrangement of atoms in crystalline nanoparticles is important for nanometre-scale device engineering and also for applications involving nanoparticles, such as optoelectronics or catalysis. A nanoparticles physical and chemical properties are controlled by its exact 3D morphology, structure and composition1. Electron tomography enables the recovery of the shape of a nanoparticle from a series of projection images2, 3, 4. Although atomic-resolution electron microscopy has been feasible for nearly four decades, neither electron tomography nor any other experimental technique has yet demonstrated atomic resolution in three dimensions. Here we report the 3D reconstruction of a complex crystalline nanoparticle at atomic resolution. To achieve this, we combined aberration-corrected scanning transmission electron microscopy5, 6, 7, statistical parameter estimation theory8, 9 and discrete tomography10, 11. Unlike conventional electron tomography, only two images of the targeta silver nanoparticle embedded in an aluminium matrixare sufficient for the reconstruction when combined with available knowledge about the particles crystallographic structure. Additional projections confirm the reliability of the result. The results we present help close the gap between the atomic resolution achievable in two-dimensional electron micrographs and the coarser resolution that has hitherto been obtained by conventional electron tomography.

Abstract: Recording the electron energy loss spectroscopy data cube with a series of energy filtered images is a dose inefficient process because the energy slit blocks most of the electrons. When recording the data cube by scanning an electron probe over the sample, perfect dose efficiency is attained; but due to the low current in nanoprobes, this often is slower, with a smaller field of view. In W. Van den Broek et al. [Ultramicroscopy, 106 (2006) 269], we proposed a new method to record the data cube, which is more dose efficient than an energy filtered series. It produces a set of projections of the data cube and then tomographically reconstructs it. In this article, we demonstrate these projections in practice, we present a simple geometrical model that allows for quantification of the projection angles and we present the first successful experimental reconstruction, all on a standard post-column instrument.