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: Over the last decade, scanning transmission electron microscopy has become one of the most powerful tools to characterise nanomaterials at the atomic scale. Often, the ultimate goal is to retrieve the three-dimensional structure, which is very challenging since small species are typically sensitive to electron irradiation. Nevertheless, measuring individual atomic positions is crucial to understand the relation between the structure and physicochemical properties of these (nano)materials. In this review, we highlight the latest approaches that are available to reveal the 3D atomic structure of small species. Finally, we will provide an outlook and will describe future challenges where the limits of electron microscopy will be pushed even further.

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: Scheelite related compounds (A',A '') [(B',B '')O-4], with B', B '' = W and/or Mo are promising new light-emitting materials for photonic applications, including phosphor converted LEDs (light-emitting diodes). In this paper, the creation and ordering of A-cation vacancies and the effect of cation substitutions in the scheelite-type framework are investigated as a factor for controlling the scheelite-type structure and luminescent properties. CaGd2(1-x)Eu2x(MoO4)(4(1-y))(WO4)(4y) (0 <= x <= 1, 0 <= y <= 1) solid solutions with scheelite-type structure were synthesized by a solid state method, and their structures were investigated using a combination of transmission electron microscopy techniques and powder X-ray diffraction. Within this series all complex molybdenum oxides have (3 + 2)D incommensurately modulated structures with superspace group I4(1)/a(alpha,beta,0)00(-beta,alpha,0)00, while the structures of all tungstates are (3 + 1)D incommensurately modulated with superspace group I2/b(alpha beta 0)00. In both cases the modulation arises because of cation-vacancy ordering at the A site. The prominent structural motif is formed by columns of A-site vacancies running along the c-axis. These vacant columns occur in rows of two or three aligned along the [110] direction of the scheelite subcell. The replacement of the smaller Gd3+ by the larger Eu3+ at the A-sublattice does not affect the nature of the incommensurate modulation, but an increasing replacement of Mo6+ by W6+ switches the modulation from (3 + 2)D to (3 + 1)D regime. Thus, these solid solutions can be considered as a model system where the incommensurate modulation can be monitored as a function of cation nature while the number of cation vacancies at the A sites remain constant upon the isovalent cation replacement. All compounds' luminescent properties were measured, and the optical properties were related to the structural properties of the materials. CaGd2(1-x)(MoO4)(4(1-y))(WO4)(4y) phosphors emit intense red light dominated by the D-5(0)-F-7(2) transition at 612 nm, along with other transitions from the D-5(1) and D-5(0) excited states. The intensity of the 5D0-7F2 transition reaches a maximum at x = 0.5 for y = 0 and 1.

Abstract: Various strategies have been proposed to engineer the band gap of metal halide perovskite nanocrystals (NCs) while preserving their structure and composition and thus ensuring spectral stability of the emission color. An aspect that has only been marginally investigated is how the type of surface passivation influences the structural/color stability of AMX3 perovskite NCs composed of two different M2+ cations. Here, we report the synthesis of blue-emitting Cs-oleate capped CsCdxPb1–xBr3 NCs, which exhibit a cubic perovskite phase containing Cd-rich domains of Ruddlesden–Popper phases (RP phases). The RP domains spontaneously transform into pure orthorhombic perovskite ones upon NC aging, and the emission color of the NCs shifts from blue to green over days. On the other hand, postsynthesis ligand exchange with various Cs-carboxylate or ammonium bromide salts, right after NC synthesis, provides monocrystalline NCs with cubic phase, highlighting the metastability of RP domains. When NCs are treated with Cs-carboxylates (including Cs-oleate), most of the Cd2+ ions are expelled from NCs upon aging, and the NCs phase evolves from cubic to orthorhombic and their emission color changes from blue to green. Instead, when NCs are coated with ammonium bromides, the loss of Cd2+ ions is suppressed and the NCs tend to retain their blue emission (both in colloidal dispersions and in electroluminescent devices), as well as their cubic phase, over time. The improved compositional and structural stability in the latter cases is ascribed to the saturation of surface vacancies, which may act as channels for the expulsion of Cd2+ ions from NCs.

Abstract: Modern TEM enables the investigation of nanostructures at the atomic scale. However, TEM images are only two-dimensional (2D) projections of a three-dimensional (3D) object. Electron tomography can overcome this limitation. The technique is increasingly focused towards quantitative measurements and reaching atomic resolution in 3D has been the ultimate goal for many years. Therefore, one needs to optimize the acquisition of the data, the 3D reconstruction techniques as well as the quantification methods. Here, we will review a broad range of methodologies and examples. Finally, we will provide an outlook and will describe future challenges in the field of electron tomography.

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: The increasing need for precise determination of the atomic arrangement of non-periodic structures in materials design and the control of nanostructures explains the growing interest in quantitative transmission electron microscopy. The aim is to extract precise and accurate numbers for unknown structure parameters including atomic positions, chemical concentrations and atomic numbers. For this purpose, statistical parameter estimation theory has been shown to provide reliable results. In this theory, observations are considered purely as data planes, from which structure parameters have to be determined using a parametric model describing the images. As such, the positions of atom columns can be measured with a precision of the order of a few picometres, even though the resolution of the electron microscope is still one or two orders of magnitude larger. Moreover, small differences in average atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark-field scanning transmission electron microscopy images. In addition, this theory allows one to measure compositional changes at interfaces, to count atoms with single-atom sensitivity, and to reconstruct atomic structures in three dimensions. This feature article brings the reader up to date, summarizing the underlying theory and highlighting some of the recent applications of quantitative model-based transmisson electron microscopy.

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: 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.