ab initio description of bonding for transmission electron microscopy

Uncovering the Atomic Structure of Substitutional Platinum Dopants in MoS2 with Single-Sideband Ptychography

We substitute individual Pt atoms into monolayer MoS2 and study the resulting atomic structures with single-sideband ptychography (SSB) supported by ab initio simulations. We demonstrate that while high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) imaging provides excellent Z-contrast, distinguishing some defect types such as single and double sulfur vacancies remains challenging due to their low relative contrast difference. However, SSB with its nearly linear Z-contrast and high phase sensitivity enables reliable identification of these defect configurations, as well as various Pt dopant structures at significantly lower electron doses. Our findings uncover the precise atomic placement and highlight the potential of SSB for detailed structural analysis of dopant-modified 2D materials while minimizing beam-induced damage, offering new pathways for understanding and engineering atomic-scale features in 2D systems.

Direct Quantifying Charge Transfer by 4D-STEM: A Study on Perfect and Defective Hexagonal Boron Nitride

Four-dimensional scanning transmission electron microscopy (4D-STEM) offers an attractive approach to simultaneously obtain precise structural determinations and capture details of local electric fields and charge densities. However, accurately extracting quantitative data at the atomic scale poses challenges, primarily due to probe propagation and size-related effects, which may even lead to misinterpretations of qualitative effects. In this study, we present a comprehensive analysis of electric fields and charge densities in both pristine and defective h-BN flakes. Through a combination of experiments and first-principle simulations, we demonstrate that while precise charge quantification at individual atomic sites is hindered by probe effects, 4D-STEM can directly measure charge transfer phenomena at the monolayer edge with sensitivity down to a few tenths of an electron and a spatial resolution on the order of a few angstroms.

GPAW: An open Python package for electronic structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Mean inner potential of elemental crystals from density-functional theory calculations: Efficient computation and trends

The mean inner potential (V0) of crystals plays an important role in electron microscopy. In a few cases, it has been measured experimentally, using mostly electron holography; however, it is not uncommon to find reports that disagree by a few volts regarding the mean inner potential of the same material. Different levels of theory have also been used to estimate its value, often by building the crystal as a superposition of isolated atoms or ions-an independent-atom approximation that does not take bonding into account. In a few cases, density-functional theory (DFT) calculations were done to capture such bonding, frequently using computer-intensive all-electron approaches. In this article, we describe in detail a faster implementation based on postprocessing files produced by a DFT code that relies on the projector-augmented wave method. We deployed this approach to compute values of V0 for 44 elemental solids, and we provide the first quantum-mechanical calculation of the mean inner potential beyond the independent-atom approximation for many of them. We also report instances in which different surface terminations for the same material led to differences in V0 of more than 3 V, highlighting the dependence of the mean inner potential on the boundary conditions of the sample. Finally, by comparing our values of V0 with other material properties, we show that it correlates mostly linearly with the mass density, that it can be used to compute a good approximation to the orbital diamagnetic contribution to the magnetic susceptibility, and that it provides a simple route to compute atomic scattering amplitudes for forward scattering of electrons.

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.

Moiré Superlattice Structure of Pleated Trilayer Graphene Imaged by 4D Scanning Transmission Electron Microscopy

Moiré superlattices in graphene arise from rotational twists in stacked 2D layers, leading to specific band structures, charge density and interlayer electron and excitonic interactions. The periodicities in bilayer graphene moiré lattices are given by a simple moiré basis vector that describes periodic oscillations in atomic density. The addition of a third layer to form trilayer graphene generates a moiré lattice comprised of multiple harmonics that do not occur in bilayer systems, leading to nontrivial crystal symmetries. Here, we use atomic resolution 4D-scanning transmission electron microscopy to study atomic structure in bilayer and trilayer graphene moiré superlattices and use 4D-STEM to map the electric fields to show subtle variations in the long-range moiré patterns. We show that monolayer graphene folded into an S-bend graphene pleat produces trilayer moiré superlattices with both small (<2°) and larger twist angles (7-30°). Annular in-plane electric field concentrations are detected in high angle bilayers due to overlapping rotated graphene hexagons in each layer. The presence of a third low angle twisted layer in S-bend trilayer graphene, introduces a long-range modulation of the atomic structure so that no real space unit cell is detected. By directly imaging trilayer moiré harmonics that span from picoscale to nanoscale using 4D-STEM, we gain insights into the complex spatial distributions of atomic density and electric fields in trilayer twisted layered materials.

Machine learning in electron microscopy for advanced nanocharacterization: current developments, available tools and future outlook

In the last few years, electron microscopy has experienced a new methodological paradigm aimed to fix the bottlenecks and overcome the challenges of its analytical workflow. Machine learning and artificial intelligence are answering this call providing powerful resources towards automation, exploration, and development. In this review, we evaluate the state-of-the-art of machine learning applied to electron microscopy (and obliquely, to materials and nano-sciences). We start from the traditional imaging techniques to reach the newest higher-dimensionality ones, also covering the recent advances in spectroscopy and tomography. Additionally, the present review provides a practical guide for microscopists, and in general for material scientists, but not necessarily advanced machine learning practitioners, to straightforwardly apply the offered set of tools to their own research. To conclude, we explore the state-of-the-art of other disciplines with a broader experience in applying artificial intelligence methods to their research (e.g., high-energy physics, astronomy, Earth sciences, and even robotics, videogames, or marketing and finances), in order to narrow down the incoming future of electron microscopy, its challenges and outlook.

Event driven 4D STEM acquisition with a Timepix3 detector: Microsecond dwell time and faster scans for high precision and low dose applications

Four dimensional scanning transmission electron microscopy (4D STEM) records the scattering of electrons in a material in great detail. The benefits offered by 4D STEM are substantial, with the wealth of data it provides facilitating for instance high precision, high electron dose efficiency phase imaging via centre of mass or ptychography based analysis. However the requirement for a 2D image of the scattering to be recorded at each probe position has long placed a severe bottleneck on the speed at which 4D STEM can be performed. Recent advances in camera technology have greatly reduced this bottleneck, with the detection efficiency of direct electron detectors being especially well suited to the technique. However even the fastest frame driven pixelated detectors still significantly limit the scan speed which can be used in 4D STEM, making the resulting data susceptible to drift and hampering its use for low dose beam sensitive applications. Here we report the development of the use of an event driven Timepix3 direct electron camera that allows us to overcome this bottleneck and achieve 4D STEM dwell times down to 100 ns; orders of magnitude faster than what has been possible with frame based readout. We characterize the detector for different acceleration voltages and show that the method is especially well suited for low dose imaging and promises rich datasets without compromising dwell time when compared to conventional STEM imaging.