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: Semiconductor heterostructures are used for the fabrication of optoelectronic devices. Performance of such devices is governed by their chemical morphology. The composition distribution of quantum wells and dots is influenced by kinetic growth processes which are not understood completely at present. To obtain more information about these effects, methods for composition determination with a spatial resolution at a near atomic scale are necessary. In this paper we focus on the present state of the composition evaluation by the lattice fringe analysis (CELFA) technique and explain the basic ideas, optimum imaging conditions, precision and accuracy.

Abstract: Quantitative atomic resolution annular dark field scanning transmission electron microscopy (ADF STEM) has become a powerful technique for nanoparticle atom-counting. However, a lot of nanoparticles provide a severe characterisation challenge because of their limited size and beam sensitivity. Therefore, quantitative ADF STEM may greatly benefit from statistical detection theory in order to optimise the instrumental microscope settings such that the incoming electron dose can be kept as low as possible whilst still retaining single-atom precision. The principles of detection theory are used to quantify the probability of error for atom-counting. This enables us to decide between different image performance measures and to optimise the experimental detector settings for atom-counting in ADF STEM in an objective manner. To demonstrate this, ADF STEM imaging of an industrial catalyst has been conducted using the near-optimal detector settings. For this experiment, we discussed the limits for atom-counting diagnosed by combining a thorough statistical method and detailed image simulations.

Abstract: Quantitative atomic resolution annular dark field scanning transmission electron microscopy (ADF STEM) has become a powerful technique for nanoparticle atom-counting. However, a lot of nanoparticles provide a severe characterisation challenge because of their limited size and beam sensitivity. Therefore, quantitative ADF STEM may greatly benefit from statistical detection theory in order to optimise the instrumental microscope settings such that the incoming electron dose can be kept as low as possible whilst still retaining single-atom precision. The principles of detection theory are used to quantify the probability of error for atom-counting. This enables us to decide between different image performance measures and to optimise the experimental detector settings for atom-counting in ADF STEM in an objective manner. To demonstrate this, ADF STEM imaging of an industrial catalyst has been conducted using the near-optimal detector settings. For this experiment, we discussed the limits for atomcounting diagnosed by combining a thorough statistical method and detailed image simulations.

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: By combining statistical parameter estimation and model-order selection using a Bayesian framework, the maximum a posteriori (MAP) probability rule is proposed in this chapter as an objective and quantitative method to detect atom columns from high-resolution scanning transmission electron microscopy (HRSTEM) images. The validity and usefulness of this approach is demonstrated to both simulated and experimental annular dark-field (ADF) STEM images, but also to simultaneously acquired annular bright-field (ABF) and ADF STEM image data.

Abstract: An efficient model-based estimation algorithm is introduced 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 overlap between neighboring columns, enabling the analysis of a large field of view. To provide end-users with this well-established quantification method, a user friendly program, StatSTEM, is developed which is freely available under a GNU public license. In this chapter, this efficient algorithm is applied to three different nanostructures for which the analysis of a large field of view is required.

Abstract: The maximum a posteriori (MAP) probability rule for atom column detection can also be used as a tool to evaluate the relation between scanning transmission electron microscopy (STEM) image quality and atom detectability. In this chapter, a new image-quality measure is proposed that correlates well with atom detectability, namely the integrated contrast-to-noise ratio (ICNR). Furthermore, the working principle of the MAP probability rule is described in detail showing a close relation to the principles of model-selection methods.

Abstract: In this chapter, the principles of detection theory are used to quantify the probability of error for atom counting from high-resolution scanning transmission electron microscopy (HRSTEM) images. Binary and multiple hypothesis testing have been investigated in order to determine the limits to the precision with which the number of atoms in a projected atomic column can be estimated. The probability of error has been calculated when using STEM images, scattering cross-sections or peak intensities as a criterion to count atoms. Based on this analysis, we conclude that scattering cross-sections perform almost equally well as images and perform better than peak intensities. Furthermore, the optimal STEM detector design can be derived for atom counting using the expression of the probability of error. We show that for very thin objects the low-angle annular dark-field (LAADF) regime is optimal and that for thicker objects the optimal inner detector angle increases.

Abstract: Determining the three-dimensional (3D) atomic structure of nanoparticles (NPs) is critical to understand their structure-dependent properties. It is hereby important to perform such analyses under conditions relevant for the envisioned application. Here, we investigate the 3D structure of supported Au NPs at high temperature, which is of importance to understand their behavior during catalytic reactions. To overcome limitations related to conventional high-resolution electron tomography at high temperature, 3D characterization of NPs with atomic resolution has been performed by applying atom-counting using atomic resolution annular darkfield scanning transmission electron microscopy (ADF STEM) images followed by structural relaxation. However, at high temperatures, thermal displacements, which affect the ADF STEM intensities, should be taken into account. Moreover, it is very likely that the structure of a NP investigated at elevated temperature deviates from a ground state configuration, which is difficult to determine using purely computational energy minimization approaches. In this paper, we therefore propose an optimized approach using an iterative local minima search algorithm followed by molecular dynamics (MD) structural relaxation of candidate structures associated with each local minimum. In this manner, it becomes possible to investigate the 3D atomic structure of supported NPs, which may deviate from their ground state configuration.

Abstract: We present a computational imaging mode for large scale electron microscopy data, which retrieves a complex wave from noisy/sparse intensity recordings using a deep learning approach and subsequently reconstructs an image of the specimen from the Convolutional Neural Network (CNN) predicted exit waves. We demonstrate that an appropriate forward model in combination with open data frameworks can be used to generate large synthetic datasets for training. In combination with augmenting the data with Poisson noise corresponding to varying dose-values, we effectively eliminate overfitting issues. The U-NET[1] based architecture of the CNN is adapted to the task at hand and performs well while maintaining a relatively small size and fast performance. The validity of the approach is confirmed by comparing the reconstruction to well-established methods using simulated, as well as real electron microscopy data. The proposed method is shown to be effective particularly in the low dose range, evident by strong suppression of noise, good spatial resolution, and sensitivity to different atom types, enabling the simultaneous visualisation of light and heavy elements and making different atomic species distinguishable. Since the method acts on a very local scale and is comparatively fast it bears the potential to be used for near-real-time reconstruction during data acquisition.