Thickness dependence of scattering cross-sections in quantitative scanning transmission electron microscopy

Reliable phase quantification in focused probe electron ptychography of thin materials

Electron ptychography provides highly sensitive, dose efficient phase images which can be corrected for aberrations after the data has been acquired. This is crucial when very precise quantification is required, such as with sensitivity to charge transfer due to bonding. Drift can now be essentially eliminated as a major impediment to focused probe ptychography, which benefits from the availability of easily interpretable simultaneous Z-contrast imaging. However challenges have remained when quantifying the ptychographic phases of atomic sites. The phase response of a single atom has a negative halo which can cause atoms to reduce in phase when brought closer together. When unaccounted for, as in integrating methods of quantification, this effect can completely obscure the effects of charge transfer. Here we provide a new method of quantification that overcomes this challenge, at least for 2D materials, and is robust to experimental parameters such as noise, sample tilt.

Fast generation of calculated ADF-EDX scattering cross-sections under channelling conditions

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.

Atomic-scale detection of individual lead clusters confined in Linde Type A zeolites

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.

Modelling ADF STEM images using elliptical Gaussian peaks and its effects on the quantification of structure parameters in the presence of sample tilt

A small sample tilt away from a main zone axis orientation results in an elongation of the atomic columns in ADF STEM images. An often posed research question is therefore whether the ADF STEM image intensities of tilted nanomaterials should be quantified using a parametric imaging model consisting of elliptical rather than the currently used symmetrical peaks. To this purpose, simulated ADF STEM images corresponding to different amounts of sample tilt are studied using a parametric imaging model that consists of superimposed 2D elliptical Gaussian peaks on the one hand and symmetrical Gaussian peaks on the other hand. We investigate the quantification of structural parameters such as atomic column positions and scattering cross sections using both parametric imaging models. In this manner, we quantitatively study what can be gained from this elliptical model for quantitative ADF STEM, despite the increased parameter space and computational effort. Although a qualitative improvement can be achieved, no significant quantitative improvement in the estimated structure parameters is achieved by the elliptical model as compared to the symmetrical model. The decrease in scattering cross sections with increasing sample tilt is even identical for both types of parametric imaging models. This impedes direct comparison with zone axis image simulations. Nonetheless, we demonstrate how reliable atom-counting can still be achieved in the presence of small sample tilt.

Hidden Markov model for atom-counting from sequential ADF STEM images: Methodology, possibilities and limitations

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.

Control of Knock-On Damage for 3D Atomic Scale Quantification of Nanostructures: Making Every Electron Count in Scanning Transmission Electron Microscopy

Understanding nanostructures down to the atomic level is the key to optimizing the design of advanced materials 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.