Abstract: In this chapter, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high-resolution annular dark-field (ADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. We show that this method can be applied to nanocrystals of arbitrary shape, size, and atom type. The validity of the atom-counting results is confirmed by means of detailed image simulations and it is shown that the high sensitivity of our method enables us to count atoms with single atom sensitivity.

Abstract: This chapter provides an overview of statistical and quantitative methodologies that have pushed (scanning) transmission electron microscopy ((S)TEM) toward accurate and precise measurements of unknown structure parameters for understanding the relation between the structure of a material and its properties. Hereby, statistical parameter estimation theory has extensively been used which enabled not only measuring atomic column positions, but also quantifying the number of atoms, and detecting atomic columns as accurately and precisely as possible from experimental images. As a general conclusion, it can be stated that advanced statistical techniques are ideal tools to perform quantitative electron microscopy at the atomic scale. In the future, statistical methods will continue to be developed and novel quantification procedures will open up new possibilities for studying material structures at the atomic scale.

Abstract: In this chapter, the principles of statistical parameter estimation theory for a quantitative analysis of atomic-resolution electron microscopy images are introduced. Within this framework, electron microscopy images are described by a parametric statistical model. Here, parametric models are introduced for different types of electron microscopy images: reconstructed exit waves, annular dark-field (ADF) scanning transmission electron microscopy (STEM) images, and simultaneously acquired ADF and annular bright-field (ABF) STEM images. Furthermore, the Cramér-Rao lower bound (CRLB) is introduced, i.e. a theoretical lower bound on the variance of any unbiased estimator. This CRLB is used to quantify the precision of the structure parameters of interest, such as the atomic column positions and the integrated atomic column intensities.

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: Heterostructures formed by La0.7Sr0.3MnO3/ZnO (LSMO/ZnO) interfaces exhibit extremely interesting electronic properties making them promising candidates for novel oxide p–n junctions, with multifunctional features. In this work, the structure of the interface is studied through a combined experimental/theoretical approach. Heterostructures were grown epitaxially and homogeneously on 4″ silicon wafers, characterized by advanced electron microscopy imaging and spectroscopy and simulated by ab initio density functional theory calculations. The simulation results suggest that the most stable interface configuration is composed of the (001) face of LSMO, with the LaO planes exposed, in contact with the (112̅0) face of ZnO. The ab initio predictions agree well with experimental high-angle annular dark field scanning transmission electron microscopy images and confirm the validity of the suggested structural model. Electron energy loss spectroscopy confirms the atomic sharpness of the interface. From statistical parameter estimation theory, it has been found that the distances between the interfacial planes are displaced from the respective ones of the bulk material. This can be ascribed to the strain induced by the mismatch between the lattices of the two materials employed

Abstract: Anisotropic bimetallic nanoparticles are promising candidates for plasmonic and catalytic applications. Their catalytic performance and plasmonic properties are closely linked to the distribution of the two metals, which can change during applications in which the particles are exposed to heat. Due to this fact, correlating the thermal stability of complex heterogeneous nanoparticles to their microstructural properties is of high interest for the practical applications of such materials. Here, we employ quantitative electron tomography in high-angle annular dark-field scanning transmission electron microscopy (HAADFSTEM) mode to measure the 3D elemental diffusion dynamics in individual anisotropic Au−Ag nanoparticles upon heating in situ. This approach allows us to study the elemental redistribution in complex, asymmetric nanoparticles on a single particle level, which has been inaccessible to other techniques so far. In this work, we apply the proposed method to compare the alloying dynamics of Au−Ag nanoparticles with different shapes and compositions and find that the shape of the nanoparticle does not exhibit a significant effect on the alloying speed whereas the composition does. Finally, comparing the experimental results to diffusion simulations allows us to estimate the diffusion coefficients of the metals for individual nanoparticles.

Abstract: Understanding the thermal stability of bimetallic nanoparticles is of vital importance to preserve their functionalities during their use in a variety of applications. In contrast to well-studied bimetallic systems such as Au@Ag, heat-induced morphological and compositional changes in Au@Pt nanoparticles are insufficiently understood, even though Au@Pt is an important material for catalysis. To investigate the thermal instability of Au@Pt nanorods at temperatures below their bulk melting point, we combined in situ heating with two- and three-dimensional electron microscopy techniques, including three-dimensional energy-dispersive X-ray spectroscopy. The experimental results were used as input for molecular dynamics simulations, to unravel the mechanisms behind the morphological transformation of Au@Pt core–shell nanorods. We conclude that thermal stability is influenced not only by the degree of coverage of Pt on Au but also by structural details of the Pt shell.

Abstract: The synthesis of materials with well-controlled composition and structure improves our understanding of their intrinsic electrical transport properties. Recent developments in atomically controlled growth have been shown to be crucial in enabling the study of new physical phenomena in epitaxial oxide heterostructures. Nevertheless, these phenomena can be influenced by the presence of defects that act as extrinsic sources of both doping and impurity scattering. Control over the nature and density of such defects is therefore necessary to fully understand the intrinsic materials properties and exploit them in future device technologies. Here, it is shown that incorporation of a strontium copper oxide nano-layer strongly reduces the impurity scattering at conducting interfaces in oxide LaAlO3SrTiO3(001) heterostructures, opening the door to high carrier mobility materials. It is proposed that this remote cuprate layer facilitates enhanced suppression of oxygen defects by reducing the kinetic barrier for oxygen exchange in the hetero-interfacial film system. This design concept of controlled defect engineering can be of significant importance in applications in which enhanced oxygen surface exchange plays a crucial role.

Abstract: Direct observations of the ferroelectric domain boundaries in LiNbO3 are performed using high-resolution high-angle annular dark field scanning transmission electron microscopy imaging, revealing a very narrow width of the domain wall between the 180° domains. The domain walls demonstrate local side-way meandering, which results in inclinations even when the overall wall orientation follows the ferroelectric polarization. These local meanders contain kinks with “head-to-head” and “tail-to-tail” dipolar configurations and are therefore locally charged. The charged meanders are confined to a few cation layers along the polarization direction and are separated by longer stretches of straight domain walls.

Abstract: High-resolution aberration-corrected transmission electron microscopy aided by statistical parameter estimation theory is used to quantify localized displacements at a (110) twin boundary in orthorhombic CaTiO3. The displacements are 36 pm for the Ti atoms and confined to a thin layer. This is the first direct observation of the generation of ferroelectricity by interfaces inside this material which opens the door for domain boundary engineering.