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) arrangement of atoms in crystalline nanoparticles is important for nanometre-scale device engineering and also for applications involving nanoparticles, such as optoelectronics or catalysis. A nanoparticles physical and chemical properties are controlled by its exact 3D morphology, structure and composition1. Electron tomography enables the recovery of the shape of a nanoparticle from a series of projection images2, 3, 4. Although atomic-resolution electron microscopy has been feasible for nearly four decades, neither electron tomography nor any other experimental technique has yet demonstrated atomic resolution in three dimensions. Here we report the 3D reconstruction of a complex crystalline nanoparticle at atomic resolution. To achieve this, we combined aberration-corrected scanning transmission electron microscopy5, 6, 7, statistical parameter estimation theory8, 9 and discrete tomography10, 11. Unlike conventional electron tomography, only two images of the targeta silver nanoparticle embedded in an aluminium matrixare sufficient for the reconstruction when combined with available knowledge about the particles crystallographic structure. Additional projections confirm the reliability of the result. The results we present help close the gap between the atomic resolution achievable in two-dimensional electron micrographs and the coarser resolution that has hitherto been obtained by conventional electron tomography.

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: 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: In materials science, high angle annular dark field scanning transmission electron microscopy is often used for tomography at the nanometer scale. In this work, it is shown that a thickness dependent, non-linear damping of the recorded intensities occurs. This results in an underestimated intensity in the interior of reconstructions of homogeneous particles, which is known as the cupping artifact. In this paper, this non-linear effect is demonstrated in experimental images taken under common conditions and is reproduced with a numerical simulation. Furthermore, an analytical derivation shows that these non-linearities can be inverted if the imaging is done quantitatively, thus preventing cupping in the reconstruction.

Abstract: In order to interpret the amplitude and phase of the exit wave in terms of mass and position of the atoms, one has to invert the dynamic scattering of the electrons in the object so as to obtain a starting structure which can then be used as a seed for further quantitative structure refinement. This is especially challenging in case of a zone axis condition when the interaction of the electrons with the atom column is very strong. Based on the channelling theory we will show that the channelling map not only yields a circle on the Argand plot but also a circular defocus curve for every column. The former gives the number of atoms in each column, while the latter provides the defocus value for each column, which reveals the surface roughness at the exit plane with single atom sensitivity.

Abstract: In this paper, it has been investigated how to measure atom column positions as accurately and precisely as possible using a focal series of images. In theory, it is expected that the precision would considerably improve using a maximum likelihood estimator based on the full series of focal images. As such, the theoretical lower bound on the variances of the unknown atom column positions can be attained. However, this approach is numerically demanding. Therefore, maximum likelihood estimation has been compared with the results obtained by fitting a model to a reconstructed exit wave rather than to the full series of focal images. Hence, a real space model-based exit wave reconstruction technique based on the channelling theory is introduced. Simulations show that the reconstructed complex exit wave contains the same amount of information concerning the atom column positions as the full series of focal images. Only for thin samples, which act as weak phase objects, this information can be retrieved from the phase of the reconstructed complex exit wave.

Abstract: A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has different effects on the transfer of the linear and non-linear terms, such that the non-linear imaging contributions are damped less than the linear imaging contributions at high spatial frequencies. This will be important when coherent aberrations such as spherical aberration and defocus are reduced.

Abstract: Statistical parameter estimation theory is proposed as a method to quantify electron microscopy images. It aims at obtaining precise and accurate values for the unknown structure parameters including, for example, atomic column positions and types. In this theory, observations are purely considered as data planes, from which structure parameters have to be determined using a parametric model describing the images. The method enables us to measure positions of atomic columns with a precision of the order of a few picometers even though the resolution of the electron microscope is one or two orders of magnitude larger. Moreover, small differences in averaged atomic number, which cannot be distinguished visually, can be quantified using high-angle annular dark field scanning transmission electron microscopy images. Finally, it is shown how to optimize the experimental design so as to attain the highest precision. As an example, the optimization of the probe size for nanoparticle radius measurements is considered. It is also shown how to quantitatively balance signal-to-noise ratio and resolution by adjusting the probe size.

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.