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: The local structure of Bi4W2/3Mn1/3O8Cl is determined using quantitative transmission electron microscopy. The electron exit wave, which is closely related to the projected crystal potential, is reconstructed and used as a starting point for statistical parameter estimation. This method allows us to refine all atomic positions on a local scale, including those of the light atoms, with a precision in the picometer range. Using this method one is no longer restricted to the information limit of the electron microscope. Our results are in good agreement with x-ray powder diffraction data demonstrating the reliability of the method. Moreover, it will be shown that local effects can be interpreted using this approach.

Abstract: In order to fully exploit structure–property relations of nanomaterials, three-dimensional (3D) characterization at the atomic scale is often required. In recent years, the resolution of electron tomography has reached the atomic scale. However, such tomography typically requires several projection images demanding substantial electron dose. A newly developed alternative circumvents this by counting the number of atoms across a single projection. These atom counts can be used to create an initial atomic model with which an energy minimization can be applied to obtain a relaxed 3D reconstruction of the nanoparticle. Here, we compare, at the atomic scale, this single projection reconstruction approach with tomography and find an excellent agreement. This new approach allows for the characterization of beam-sensitive materials or where the acquisition of a tilt series is impossible. As an example, the utility is illustrated by the 3D atomic scale characterization of a nanodumbbell on an in situ heating holder of limited tilt range.

Abstract: Starting from the gas phase, small clusters can be produced and deposited with huge flexibility with regard to composition, materials choice and cluster size. Despite many advances in experimental characterization, a detailed morphology of such clusters is still lacking. Here we present an atomic scale observation as well as the dynamical behaviour of ultrasmall germanium clusters. Using quantitative scanning transmission electron microscopy in combination with ab initio calculations, we are able to characterize the transition between different equilibrium geometries of a germanium cluster consisting of less than 25 atoms. Seven-membered rings, trigonal prisms and some smaller subunits are identified as possible building blocks that stabilize the structure.

Abstract: Reconstructed exit waves are useful to quantify unknown structure parameters such as the position and composition of the atom columns at atomic scale. Existing techniques provide a complex wave in a flat plane which is close to the plane where the electrons leave the atom columns. However, due to local deviation in the flatness of the exit surface, there will be an offset between the plane of reconstruction and the actual exit of a specific atom column. Using the channelling theory, it has been shown that this defocus offset can in principle be determined atom column-by-atom column. As such, the surface roughness could be quantified at atomic scale. However, the outcome strongly depends on the initial plane of reconstruction especially in a crystalline structure. If this plane is further away from the true exit, the waves of the atom columns become delocalized and interfere mutually which strongly complicates the interpretation of the exit wave in terms of the local structure. In this paper, we will study the delocalization with defocus using the channelling theory in a more systematic way.

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: In thispaperweinvestigatewhichprobesizemaximizesthethroughputwhenmeasuringtheradiusof nanoparticlesinhighangleannulardarkfieldscanningtransmissionelectronmicroscopy(HAADFSTEM). The sizeandthecorrespondingcurrentoftheelectronprobedeterminetheprecisionoftheestimateofa particlesradius.Maximizingthroughputmeansthatamaximumnumberofparticlesshouldbeimaged withinagiventimeframe,sothataprespecifiedprecisionisattained.WeshowthatBayesianstatistical experimentaldesignisaveryusefulapproachtodeterminetheoptimalprobesizeusingacertainamount of priorknowledgeaboutthesample.Thedependenceoftheoptimalprobesizeonthedetectorgeometry and thediameter,variabilityandatomicnumberoftheparticlesisinvestigated.Anexpressionforthe optimalprobesizeintheabsenceofanykindofpriorknowledgeaboutthespecimenisderivedaswell.

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.

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 atom-counting diagnosed by combining a thorough statistical method and detailed image simulations.

Abstract: A new tungsten bronze in the SbWO system has been prepared in a solid state reaction from Sb2O3, WO3 and W metal powder. The average structure was determined by single crystal X-ray diffraction. SbxWO3+y (x ∼ 0.11) crystallizes in the orthorhombic space group Pm21n (no. 31), a = 27.8135(9) Å, b = 7.3659(2) Å and c = 3.8672(1) Å. The structure belongs to the (n)-ITB class of intergrowth tungsten bronzes. It contains slabs of hexagonal channels formed by six WO6 octahedra. These slabs are separated by three layers of WO6 octahedra that are arranged in a WO3-type fashion. The WO6 octahedra share all vertices to build up a three-dimensional framework. The hexagonal channels are filled with Sb atoms to ∼80% and additional O atoms. The atoms are shifted out of the center of the channels. Exit-wave reconstruction of focal series of high resolution-transmission-electron-microscope (HRTEM) images combined with statistical paramäeter estimation techniques allowed to study local ordering in the channels. Sb atoms in neighbouring channels tend to be displaced in the same direction, which is in agreement with total energy calculations on ordered structure models, but the ratio of the occupation of the two possible Sb sites varies from channel to channel. The structure of SbxWO3+y exhibits pronounced local modulations.

Abstract: We report a method to reliably count the number of atoms from high-angle annular dark field scanning transmission electron microscopy images. A model-based analysis of the experimental images is used to measure scattering cross sections at the atomic level. The high sensitivity of these measurements in combination with a thorough statistical analysis enables us to count atoms with single-atom sensitivity. The validity of the results is confirmed by means of detailed image simulations. We will show that the method can be applied to nanocrystals of arbitrary shape, size, and atom type without the need for a priori knowledge about the atomic structure.