Abstract: Advanced materials often consist of multiple elements which are arranged in a complicated structure. Quantitative scanning transmission electron microscopy is useful to determine the composition and thickness of nanostructures at the atomic scale. However, significant difficulties remain to quantify mixed columns by comparing the resulting atomic resolution images and spectroscopy data with multislice simulations where dynamic scattering needs to be taken into account. The combination of the computationally intensive nature of these simulations and the enormous amount of possible mixed column configurations for a given composition indeed severely hamper the quantification process. To overcome these challenges, we here report the development of an incoherent non-linear method for the fast prediction of ADF-EDX scattering cross-sections of mixed columns under channelling conditions. We first explain the origin of the ADF and EDX incoherence from scattering physics suggesting a linear dependence between those two signals in the case of a high-angle ADF detector. Taking EDX as a perfect incoherent reference mode, we quantitatively examine the ADF longitudinal incoherence under different microscope conditions using multislice simulations. Based on incoherent imaging, the atomic lensing model previously developed for ADF is now expanded to EDX, which yields ADF-EDX scattering cross-section predictions in good agreement with multislice simulations for mixed columns in a core–shell nanoparticle and a high entropy alloy. The fast and accurate prediction of ADF-EDX scattering cross-sections opens up new opportunities to explore the wide range of ordering possibilities of heterogeneous materials with multiple elements.

Abstract: High-resolution transmission electron microscopy (TEM) of organic crystals, such as Lead Phthalocyanine (PbPc), is very challenging since these materials are prone to electron beam damage leading to the breakdown of the crystal structure during investigation. Quantification of the damage is imperative to enable high-resolution imaging of PbPc crystals with minimum structural changes. In this work, we performed a detailed electron diffraction study to quantitatively measure degradation of PbPc crystals upon electron beam irradiation. Our study is based on the quantification of the fading intensity of the spots in the electron diffraction patterns. At various incident dose rates (e/Å2/s) and acceleration voltages, we experimentally extracted the decay rate (1/s), which directly correlates with the rate of beam damage. In this manner, a value for the critical dose (e/Å2) could be determined, which can be used as a measure to quantify beam damage. Using the same methodology, we explored the influence of cryogenic temperatures, graphene TEM substrates, and graphene encapsulation in prolonging the lifetime of the PbPc crystal structure during TEM investigation. The knowledge obtained by diffraction experiments is then translated to real space high-resolution TEM imaging of PbPc.

Abstract: Quantification of annular dark field (ADF) scanning transmission electron microscopy (STEM) images in terms
of composition or thickness often relies on probe-position integrated scattering cross sections (PPISCS). In
order to compare experimental PPISCS with theoretically predicted ones, expensive simulations are needed for
a given specimen, zone axis orientation, and a variety of microscope settings. The computation time of such
simulations can be in the order of hours using a single GPU card. ADF STEM simulations can be efficiently
parallelized using multiple GPUs, as the calculation of each pixel is independent of other pixels. However, most
research groups do not have the necessary hardware, and, in the best-case scenario, the simulation time will
only be reduced proportionally to the number of GPUs used. In this manuscript, we use a learning approach and
present a densely connected neural network that is able to perform real-time ADF STEM PPISCS predictions as
a function of atomic column thickness for most common face-centered cubic (fcc) crystals (i.e., Al, Cu, Pd, Ag,
Pt, Au and Pb) along [100] and [111] zone axis orientations, root-mean-square displacements, and microscope
parameters. The proposed architecture is parameter efficient and yields accurate predictions for the PPISCS
values for a wide range of input parameters that are commonly used for aberration-corrected transmission
electron microscopes.

Abstract: To understand the structure–property relationship of nanostructures, reliably quantifying parameters, such as the number of atoms along the projection direction, is important. Advanced statistical methodologies have made it possible to count the number of atoms for monotype crystalline nanoparticles from a single ADF STEM image. Recent developments enable one to simultaneously acquire multiple ADF STEM images. Here, we present an extended statistics-based method for atom counting from a combination of multiple statistically independent ADF STEM images reconstructed from non-overlapping annular detector collection regions which improves the accuracy and allows one to retrieve precise atom-counts, especially for images acquired with low electron doses and multiple element structures.

Abstract: CsPbI3 is a promising perovskite material for photovoltaic applications in its photoactive perovskite or black phase. However, the material degrades to a photovoltaically inactive or yellow phase at room temperature. Various mitigation strategies are currently being developed to increase the lifetime of the black phase, many of which rely on inducing strains in the material that hinder the black-to-yellow phase transition. Physical insight into how these strategies exactly induce strain as well as knowledge of the spatial extent over which these strains impact the material is crucial to optimize these approaches but is still lacking. Herein, we combine machine learning potential-based molecular dynamics simulations with our in silico strain engineering approach to accurately quantify strained large-scale atomic structures on a nanosecond time scale. To this end, we first model the strain fields introduced by atomic substitutions as they form the most elementary strain sources. We demonstrate that the magnitude of the induced strain fields decays exponentially with the distance from the strain source, following a decay rate that is largely independent of the specific substitution. Second, we show that the total strain field induced by multiple strain sources can be predicted to an excellent approximation by summing the strain fields of each individual source. Finally, through a case study, we illustrate how this additive character allows us to explain how complex strain fields, induced by spatially extended strain sources, can be predicted by adequately combining the strain fields caused by local strain sources. Hence, the strain additivity proposed here can be adopted to further our insight into the complex strain behavior in perovskites and to design strain from the atomic level onward to enhance their sought-after phase stability.

Abstract: In this paper, a methodology is presented to count the number of atoms in heterogeneous nanoparticles based on the combination of multiple annular dark field scanning transmission electron microscopy (ADF STEM) images. The different non-overlapping annular detector collection regions are selected based on the principles of optimal statistical experiment design for the atom-counting problem. To count the number of atoms, the total intensities of scattered electrons for each atomic column, the so-called scattering cross-sections, are simultaneously compared with simulated library values for the different detector regions by minimising the squared differences. The performance of the method is evaluated for simulated Ni@Pt and Au@Ag core-shell nanoparticles. Our approach turns out to be a dose efficient alternative for the investigation of beam-sensitive heterogeneous materials as compared to the combination of ADF STEM and energy dispersive X-ray spectroscopy.

Abstract: The atomic lensing model has been proposed as a promising method facilitating atom-counting in heterogeneous nanocrystals [1]. Here, image simulations will validate the model, which describes dynamical diffraction as a superposition of individual atoms focussing the incident electrons. It will be demonstrated that the model is reliable in the annular dark field regime for crystals having columns containing dozens of atoms. By using the principles of statistical detection theory, it will be shown that this model gives new opportunities for detecting compositional differences.

Abstract: Understanding nanostructures down to the atomic level is the key to optimizing the design of advancedmaterials with revolutionary novel properties. This requires characterization methods capable of quantifying the three-dimensional (3D) atomic structure with the highest possible precision. A successful approach to reach this goal is to count the number of atoms in each atomic column from 2D annular dark field scanning transmission electron microscopy images. To count atoms with single atom sensitivity, a minimum electron dose has been shown to be necessary, while on the other hand beam damage, induced by the high energy electrons, puts a limit on the tolerable dose. An important challenge is therefore to develop experimental strategies to optimize the electron dose by balancing atom-counting fidelity vs the risk of knock-on damage. To achieve this goal, a statistical framework combined with physics-based modeling of the dose-dependent processes is here proposed and experimentally verified. This model enables an investigator to theoretically predict, in advance of an experimental measurement, the optimal electron dose resulting in an unambiguous quantification of nanostructures in their native state with the highest attainable precision.

Abstract: Thickness-driven electronic phase transitions are broadly observed in different types of functional perovskite heterostructures. However, uncertainty remains whether these effects are solely due to spatial confinement, broken symmetry, or rather to a change of structure with varying film thickness. Here, this study presents direct evidence for the relaxation of oxygen-2p and Mn-3d orbital (p-d) hybridization coupled to the layer-dependent octahedral tilts within a La2/3Sr1/3MnO3 film driven by interfacial octahedral coupling. An enhanced Curie temperature is achieved by reducing the octahedral tilting via interface structure engineering. Atomically resolved lattice, electronic, and magnetic structures together with X-ray absorption spectroscopy demonstrate the central role of thickness-dependent p-d hybridization in the widely observed dimensionality effects present in correlated oxide heterostructures.

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: 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: 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 study, a new bottom-up approach is proposed to predict the crystal structure of the substrate-induced polymorph (SIP) of an archetypal molecular semiconductor. In spite of intense efforts, the formation mechanism of SIPs is still not fully understood, and predicting their crystal structure is a very delicate task. Here, we selected lead phthalocyanine (PbPc) as a prototypical molecular material because it is a highly symmetrical yet nonplanar molecule and we demonstrate that the growth and crystal structure of the PbPc SIPs can be templated by the corresponding physisorbed self-assembled molecular networks (SAMNs). Starting from SAMNs of PbPc formed at the solution/graphite interface, the structural and energetic aspects of the assembly were studied by a combination of in situ scanning tunneling microscopy and multiscale computational chemistry approach. Then, the growth of a PbPc SIP on top of the physisorbed monolayer was modeled without prior experimental knowledge, from which the crystal structure of the SIP was predicted. The theoretical prediction of the SIP was verified by determining the crystal structure of PbPc thin films using X-ray diffraction techniques, revealing the formation of a new polymorph of PbPc on the graphite substrate. This study clearly illustrates the correlation between the SAMNs and SIPs, which are traditionally considered as two separate but conceptually connected research areas. This approach is applicable to molecular materials in general to predict the crystal structure of their SIPs.

Abstract: Reducible supports can affect the performance of metal catalysts by the formation of suboxide overlayers upon reduction, a process referred to as the strong metal-support interaction (SMSI). A combination of operando electron microscopy and vibrational spectroscopy revealed that thin TiOx overlayers formed on nickel/titanium dioxide catalysts during 400 degrees C reduction were completely removed under carbon dioxide hydrogenation conditions. Conversely, after 600 degrees C reduction, exposure to carbon dioxide hydrogenation reaction conditions led to only partial reexposure of nickel, forming interfacial sites in contact with TiOx and favoring carbon-carbon coupling by providing a carbon species reservoir. Our findings challenge the conventional understanding of SMSIs and call for more-detailed operando investigations of nanocatalysts at the single-particle level to revisit static models of structure-activity relationships.