Abstract: In quantitative scanning transmission electron microscopy (STEM), scattering cross-sections have been shown to be very sensitive to the number of atoms in a column and its composition. They correspond to the integrated intensity over the atomic column and they outperform other measures. As compared to atomic column peak intensities, which saturate at a given thickness, scattering cross-sections increase monotonically. A study of the electron wave propagation is presented to explain the sensitivity of the scattering cross-sections. Based on the multislice algorithm, we analyse the wave propagation inside the crystal and its link to the scattered signal for the different probe positions contained in the scattering cross-section for detector collection in the low-, middle- and high-angle regimes. The influence to the signal from scattering of neighbouring columns is also discussed.

Abstract: The present contribution gives a review of recent quantification work of atom displacements, atom site occupations and level of crystallinity in various systems and based on aberration corrected HR(S)TEM images. Depending on the case studied, picometer range precisions for individual distances can be obtained, boundary widths at the unit cell level determined or statistical evolutions of fractions of the ordered areas calculated. In all of these cases, these quantitative measures imply new routes for the applications of the respective materials.

Abstract: Recently, the maximum a posteriori (MAP) probability rule has been proposed as an objective and quantitative method to detect atom columns and even single atoms from high-resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images. The method combines statistical parameter estimation and model-order selection using a Bayesian framework and has been shown to be especially useful for the analysis of the structure of beam-sensitive nanomaterials. In order to avoid beam damage, images of such materials are usually acquired using a limited incoming electron dose resulting in a low contrast-to-noise ratio (CNR) which makes visual inspection unreliable. This creates a need for an objective and quantitative approach. The present paper describes the methodology of the MAP probability rule, gives its step-by-step derivation and discusses its algorithmic implementation for atom column detection. In addition, simulation results are presented showing that the performance of the MAP probability rule to detect the correct number of atomic columns from HAADF STEM images is superior to that of other model-order selection criteria, including the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). Moreover, the MAP probability rule is used as a tool to evaluate the relation between STEM image quality measures and atom detectability resulting in the introduction of the so-called integrated CNR (ICNR) as a new image quality measure that better correlates with atom detectability than conventional measures such as signal-to-noise ratio (SNR) and CNR.

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: 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: 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: Understanding light–matter interactions in nanomaterials is crucial for
optoelectronic, photonic, and plasmonic applications. Specifically, metal
nanoparticles (NPs) strongly interact with light and can undergo shape
transformations, fragmentation and ablation upon (pulsed) laser excitation.
Despite being vital for technological applications, experimental insight into
the underlying atomistic processes is still lacking due to the complexity of
such measurements. Herein, atomic resolution electron tomography is performed
on the same mesoporous-silica-coated gold nanorod, before and after
femtosecond laser irradiation, to assess the missing information. Combined
with molecular dynamics (MD) simulations based on the experimentally
determined 3D atomic-scale morphology, the complex atomistic rearrangements,
causing shape deformations and defect generation, are unraveled.
These rearrangements are simultaneously driven by surface diffusion, facet
restructuring, and strain formation, and are influenced by subtleties in the
atomic distribution at the surface.

Abstract: Advances in controlling energy migration pathways in core-shell lanthanide (Ln)-based hetero-nanocrystals (HNCs) have relied heavily on assumptions about how optically active centers are distributed within individual HNCs. In this article, it is demonstrated that different types of interface patterns can be formed depending on shell growth conditions. Such interface patterns are not only identified but also characterized with spatial resolution ranging from the nanometer- to the atomic-scale. In the most favorable cases, atomic-scale resolved maps of individual particles are obtained. It is also demonstrated that, for the same type of core-shell architecture, the interface pattern can be engineered with thicknesses of just 1 nm up to several tens of nanometers. Total alloying between the core and shell domains is also possible when using ultra-small particles as seeds. Finally, with different types of interface patterns (same architecture and chemical composition of the core and shell domains) it is possible to modify the output color (yellow, red, and green-yellow) or change (improvement or degradation) the absolute upconversion quantum yield. The results presented in this article introduce an important paradigm shift and pave the way toward the emergence of a new generation of core-shell Ln-based HNCs with better control over their atomic-scale organization.

Abstract: We report a study of scattering dynamics in crystals employing momentum-resolved scanning transmission
electron microscopy under varying illumination conditions. As we perform successive changes of the probe
focus, multiple real-space signals are obtained in dependence of the shape of the incident electron wave.
With support from extensive simulations, each signal is shown to be characterised by an optimum focus for
which the contrast is maximum and which differs among different signals. For instance, a systematic focus
mismatch is found between images formed by high-angle scattering, being sensitive to thickness and chemical
composition, and the first moment in diffraction space, being sensitive to electric fields. It follows that a single
recording at one specific probe focus is usually insufficient to characterise materials comprehensively. Most
importantly, we demonstrate in experiment and simulation that the second moment (

Abstract: A real-time image reconstruction method for scanning transmission electron microscopy (STEM) is proposed. With an algorithm requiring only the center of mass of the diffraction pattern at one probe position at a time, it is able to update the resulting image each time a new probe position is visited without storing any intermediate diffraction patterns. The results show clear features at high spatial frequency, such as atomic column positions. It is also demonstrated that some common post-processing methods, such as band-pass filtering, can be directly integrated in the real-time processing flow. Compared with other reconstruction methods, the proposed method produces high-quality reconstructions with good noise robustness at extremely low memory and computational requirements. An efficient, interactive open source implementation of the concept is further presented, which is compatible with frame-based, as well as event-based camera/file types. This method provides the attractive feature of immediate feedback that microscope operators have become used to, for example, conventional high-angle annular dark field STEM imaging, allowing for rapid decision-making and fine-tuning to obtain the best possible images for beam-sensitive samples at the lowest possible dose.

Abstract: Structural analysis of metal clusters confined in nanoporous materials is typically performed by X-ray-driven techniques. Although X-ray analysis has proved its strength in the characterization of metal clusters, it provides averaged structural information. Therefore, we here present an alternative workflow for bringing the characterization of confined metal clusters towards the local scale. This workflow is based on the combination of aberration-corrected transmission electron microscopy (TEM), TEM image simulations, and powder X-ray diffraction (XRD) with advanced statistical techniques. In this manner, we were able to characterize the clustering of Pb atoms in Linde Type A (LTA) zeolites with Pb loadings as low as 5 wt%. Moreover, individual Pb clusters could be directly detected. The proposed methodology thus enables a local-scale characterization of confined metal clusters in zeolites. This is important for further elucidation of the connection between the structure and the physicochemical properties of such systems.

Abstract: A decade ago, a statistics-based method was introduced to count the number of atoms from annular dark-field scanning transmission electron microscopy (ADF STEM) images. In the past years, this method was successfully applied to nanocrystals of arbitrary shape, size, and composition (and its high accuracy and precision has been demonstrated). However, the counting results obtained from this statistical framework are so far presented without a visualization of the actual uncertainty about this estimate. In this paper, we present three approaches that can be used to represent counting results together with their statistical error, and discuss which approach is most suited for further use based on simulations and an experimental ADF STEM image.