Solving complex nanostructures with ptychographic atomic electron tomography

Transmission electron microscopy (TEM) is essential for determining atomic scale structures in structural biology and materials science. In structural biology, three-dimensional structures of proteins are routinely determined from thousands of identical particles using phase-contrast TEM. In materials science, three-dimensional atomic structures of complex nanomaterials have been determined using atomic electron tomography (AET). However, neither of these methods can determine the three-dimensional atomic structure of heterogeneous nanomaterials containing light elements. Here, we perform ptychographic electron tomography from 34.5 million diffraction patterns to reconstruct an atomic resolution tilt series of a double wall-carbon nanotube (DW-CNT) encapsulating a complex ZrTe sandwich structure. Class averaging the resulting tilt series images and subpixel localization of the atomic peaks reveals a Zr11Te50 structure containing a previously unobserved ZrTe2 phase in the core. The experimental realization of atomic resolution ptychographic electron tomography will allow for the structural determination of a wide range of beam-sensitive nanomaterials containing light elements.

Analysis of Strain and Defects in Tellurium-WSe2 Moiré Heterostructures Using Scanning Nanodiffraction

In recent years, there has been an increasing focus on 2D nongraphene materials that range from insulators to semiconductors to metals. As a single-elemental van der Waals semiconductor, tellurium (Te) has captivating anisotropic physical properties. Recent work demonstrated growth of ultrathin Te on WSe2 with the atomic chains of Te aligned with the armchair directions of the substrate using physical vapor deposition (PVD). In this system, a moiré superlattice is formed where micrometer-scale Te flakes sit on top of the continuous WSe2 film. Here, we determined the precise orientation of the Te flakes with respect to the substrate and detailed structure of the resulting moiré lattice by combining electron microscopy with image simulations. We directly visualized the moiré lattice using center of mass-differential phase contrast (CoM-DPC). We also investigated the local strain within the Te/WSe2 layered materials using scanning nanodiffraction techniques. There is a significant tensile strain at the edges of flakes along the direction perpendicular to the Te chain direction, which is an indication of the preferred orientation for the growth of Te on WSe2. In addition, we observed local strain relaxation regions within the Te film, specifically attributed to misfit dislocations, which we characterize as having a screw-like nature. The detailed structural analysis gives insight into the growth mechanisms and strain relaxation in this moiré heterostructure.

Resolution of Virtual Depth Sectioning from Four-Dimensional Scanning Transmission Electron Microscopy

One approach to three-dimensional structure determination using the wealth of scattering data in four-dimensional (4D) scanning transmission electron microscopy (STEM) is the parallax method proposed by Ophus et al. (2019. Advanced phase reconstruction methods enabled by 4D scanning transmission electron microscopy, Microsc Microanal25, 10-11), which determines the scattering matrix and uses it to synthesize a virtual depth-sectioning reconstruction of the sample structure. Drawing on an equivalence with a hypothetical confocal imaging mode, we derive contrast transfer and point spread functions for this parallax method applied to weakly scattering objects, showing them identical to earlier depth-sectioning STEM modes when only bright field signal is used, but that improved depth resolution is possible if dark field signal can be used. Through a simulation-based study of doped Si, we show that this depth resolution is preserved for thicker samples, explore the impact of shot noise on the parallax reconstructions, discuss challenges to making use of dark field signal, and identify cases where the interpretation of the parallax reconstruction breaks down.

Simultaneous Successive Twinning Captured by Atomic Electron Tomography

Shape-controlled synthesis of multiply twinned nanostructures is heavily emphasized in nanoscience, in large part due to the desire to control the size, shape, and terminating facets of metal nanoparticles for applications in catalysis. Direct control of the size and shape of solution-grown nanoparticles relies on an understanding of how synthetic parameters alter nanoparticle structures during synthesis. However, while outcome populations can be effectively studied with standard electron microscopy methods, transient structures that appear during some synthetic routes are difficult to study using conventional high resolution imaging methods due to the high complexity of the 3D nanostructures. Here, we have studied the prevalence of transient structures during growth of multiply twinned particles and employed atomic electron tomography to reveal the atomic-scale three-dimensional structure of a Pd nanoparticle undergoing a shape transition. By identifying over 20 000 atoms within the structure and classifying them according to their local crystallographic environment, we observe a multiply twinned structure consistent with a simultaneous successive twinning from a decahedral to icosahedral structure.

Scattering Matrix Determination in Crystalline Materials from 4D Scanning Transmission Electron Microscopy at a Single Defocus Value

Recent work has revived interest in the scattering matrix formulation of electron scattering in transmission electron microscopy as a stepping stone toward atomic-resolution structure determination in the presence of multiple scattering. We discuss ways of visualizing the scattering matrix that make its properties clear. Through a simulation-based case study incorporating shot noise, we shown how regularizing on this continuity enables the scattering matrix to be reconstructed from 4D scanning transmission electron microscopy (STEM) measurements from a single defocus value. Intriguingly, for crystalline samples, this process also yields the sample thickness to nanometer accuracy with no a priori knowledge about the sample structure. The reconstruction quality is gauged by using the reconstructed scattering matrix to simulate STEM images at defocus values different from that of the data from which it was reconstructed.

py4DSTEM: A Software Package for Four-Dimensional Scanning Transmission Electron Microscopy Data Analysis

Scanning transmission electron microscopy (STEM) allows for imaging, diffraction, and spectroscopy of materials on length scales ranging from microns to atoms. By using a high-speed, direct electron detector, it is now possible to record a full two-dimensional (2D) image of the diffracted electron beam at each probe position, typically a 2D grid of probe positions. These 4D-STEM datasets are rich in information, including signatures of the local structure, orientation, deformation, electromagnetic fields, and other sample-dependent properties. However, extracting this information requires complex analysis pipelines that include data wrangling, calibration, analysis, and visualization, all while maintaining robustness against imaging distortions and artifacts. In this paper, we present py4DSTEM, an analysis toolkit for measuring material properties from 4D-STEM datasets, written in the Python language and released with an open-source license. We describe the algorithmic steps for dataset calibration and various 4D-STEM property measurements in detail and present results from several experimental datasets. We also implement a simple and universal file format appropriate for electron microscopy data in py4DSTEM, which uses the open-source HDF5 standard. We hope this tool will benefit the research community and help improve the standards for data and computational methods in electron microscopy, and we invite the community to contribute to this ongoing project.

A Fast Algorithm for Scanning Transmission Electron Microscopy Imaging and 4D-STEM Diffraction Simulations

Scanning transmission electron microscopy (STEM) is an extremely versatile method for studying materials on the atomic scale. Many STEM experiments are supported or validated with electron scattering simulations. However, using the conventional multislice algorithm to perform these simulations can require extremely large calculation times, particularly for experiments with millions of probe positions as each probe position must be simulated independently. Recently, the plane-wave reciprocal-space interpolated scattering matrix (PRISM) algorithm was developed to reduce calculation times for large STEM simulations. Here, we introduce a new method for STEM simulation: partitioning of the STEM probe into “beamlets,” given by a natural neighbor interpolation of the parent beams. This idea is compatible with PRISM simulations and can lead to even larger improvements in simulation time, as well requiring significantly less computer random access memory (RAM). We have performed various simulations to demonstrate the advantages and disadvantages of partitioned PRISM STEM simulations. We find that this new algorithm is particularly useful for 4D-STEM simulations of large fields of view. We also provide a reference implementation of the multislice, PRISM, and partitioned PRISM algorithms.