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The development of fast pixelated direct electron detectors allows the collection of full scattering information at every scanning point in Scanning Transmission Electron Microscopy (STEM). With two scanning directions (x, y) and two momentum dimensions (kx, ky), this results in a four-dimensional dataset, thus the technique is colloquially referred to as 4D-STEM. 4D diffraction data is not readily interpretable, so it must be processed into a more interpretable two-dimensional image. While traditional imaging modes like high-angle angular dark field and bright field images can be replicated, new methods of processing the diffraction data like Center-of-Mass (COM) imaging can quantitatively measure electric field or other properties of the sample. Thus, a better understanding of what information is stored and where in the diffraction pattern will better inform how we can extract quantitative information from the 4D diffraction dataset. In the first part of this thesis, I go over theoretical calculations for diffraction patterns for a variety of samples. By demonstrating how contrast and movement of the bright disk is affected by sample size compared to probe size, I show how the virtual detector geometry of COM imaging affects what length-scale of electromagnetic field is being measured rather than electric versus magnetic fields. Simulations of multiple scattering demonstrate the signal-to-noise efficiency of second moment imaging for thicker biological samples. Finally, a theoretical calculation of polarity contribution in nanobeam electron diffraction (NBED) from 2D materials makes explicit the origin and Z-dependence of the violation of Friedel’s Law even in monolayer samples. In the second part of my thesis, I go over new imaging modes. By understanding how tilt affects placement of diffracted disks in a 2D material, I quantitatively map the in-plane rotation, out-of-plane tilt, and strain in a corrugated sheet of MoS2. Finally, I show how supervised machine learning can be used for high-resolution phase retrieval as a faster, more transferable process than ptychography to demonstrate its capability as a powerful tool for guiding further 4D-STEM characterization development.

The goal of microscopy is to take position-resolved data of things invisible & small and transform that data into something meaningful & macroscopic. In the case of scanning transmission electron microscopy (STEM) we generate position resolved data by raster scanning a focused beam of highly accelerated electrons—also called the probe or the incident beam—on a thin sample and measuring the properties of the electrons that pass through the sample. If we know certain properties of the incident electrons, say their momentum, and then measure that property after having interacted with the sample, we can infer properties about the sample, such as the scattering potential & therefore the locations of the atoms within the sample. We then generate an image where the pixel values represent the measured properties. Obtaining an image that represents the properties of a material lets us understand & convey what is happening in ways that few other forms of science communication can. In this Dissertation, I discuss the concepts behind momentum-resolved STEM (4D-STEM); first with a general presentation of the limiting factors, followed by a more in-depth look at how we refine our measurements and the process by which we transform them into meaningful representations. I show that brightness preservation serves as a better optimization metric than aberration minimization. Finally, I discuss a new physically motivated data transformation that simplifies analysis of 4D-STEM data for high-precision strain measurement & robust grain identification.

Hydrogen fuel cells in fuel cell electric vehicles (FCEVs) are a promising technology to reduce, and eventually eliminate, carbon dioxide emissions from transportation. The Pt nanoparticles used to catalyze the fuel cell’s electrochemical reactions are an important limiting factor because at present levels, the cost of the Pt catalyst will prevent widespread adoption of FCEVs. Catalysts must be developed to reduce the amount of Pt while meeting vehicle power demands even after many years of use. Strategically improving catalysts requires detailed and statistically robust characterization of their microscopic structure to understand the connections between catalyst synthesis, structure, performance, and durability. This dissertation presents the development and application of (scanning) transmission electron microscopy ((S)TEM) techniques to guide advancement of catalysts through nanostructural characterization. We develop a robust strain mapping technique for complex catalyst specimens. We deploy a new exit wave power cepstrum (EWPC) transform to nanobeam electron diffraction (NBED) patterns to enable precise, high-throughput, dose-efficient strain measurement. This approach is suitable for statistically representative measurements of many particles without special requirements such as zone-axis orientation. We apply this strain mapping technique to core-shell Pt-Co nanoparticles in combination with a continuum elastic theory model and demonstrate two mechanisms contributing to the relaxation of strain at the catalyst surface: lattice dislocations and Poisson expansion due to the spherical geometry. Comparison with electrochemical measurements suggests that the geometrical Poisson relaxation accounts for the activity of catalysts with thin shells, but catalysts with thick shells experience additional activity loss from dislocation-driven relaxation. We then turn to the larger-scale catalyst structure, investigating the impact of porous carbon support morphology, local reactant transport, and catalyst durability. Using statistical analysis of STEM images, we compare Pt and Pt-Co catalysts on porous and solid carbon supports. Comparison of 3D tomographic images and electrochemical accessibility measurements indicated that carbon pores prevent ionomer adsorption for particles embedded within them, improving the catalyst activity, while allowing proton access through condensed water. By comparing images and composition maps before and after electrochemical stability tests, we find that porous carbon supports suppress Pt particle coalescence, accounting for improved overall durability.

Transmission electron microscopy is a ubiquitous tool for materials and biological characterization from the micron to atomic scales. While the most common use of transmission electron microscopy is to determine atomic-scale structures, from the protein signatures of Alzheimer’s disease to the arrangement of atoms within a transistor, the scattered electron beam encodes a wealth of information about the structure, chemistry, electrical, optical, and magnetic properties of matter. Conventional electron detectors, however, discard much of this information. A next frontier of atomic scale characterization of matter will be to detect, analyze, and utilize these new scattering signals. Here, a new generation of direct imaging detectors have already enabled pioneering work for cryo-electron microscopy to solve structures of biomolecules, giving us an atomic-scale view into the intricate workings of life and winning the Nobel Prize in Chemistry in 2017. To go beyond traditional electron microscopy techniques, new detectors must also be developed for diffraction imaging. During my PhD at Cornell, I developed and co-invented the Electron Microscope Pixel Array Detector (EMPAD), a fast, highly efficient “universal” detector for the electron microscope that is designed to re-capture and harness this missing information. The EMPAD is poised to have broad scientific and technological impact: we have licensed the EMPAD design to FEI, a subsidiary of Thermo Fisher Scientific. Moreover, in the two years since the first paper was published demonstrating the use of the EMPAD, initial studies applying the EMPAD to various materials and biological systems have demonstrated its broad, cross-disciplinary impact. In my dissertation, I will talk about: previous works on diffraction imaging and STEM diffraction detectors available in the field (Chapter 1), the capabilities of the EMPAD (Chapter 2), the EMPAD’s use for imaging magnetic fields and magnetic phases in FeGe thin films (Chapter 3), and new physics from ferroelectric polarization vortices (Chapter 4). In Chapter 5, I will discuss the future works that can be done with EMPAD. In fact, it is extremely encouraging to know that the imaging examples described in this thesis only represent a small fraction of the potential impact the EMPAD can achieve for the field of electron microscopy.

Two-dimensional layered crystals are a promising class of materials for post-silicon electronics. Due to their atomic thinness, flexibility, and versatile electrical properties (i.e. conductors, semiconductors, and insulators), we can envision future ultra-small, flexible computers completely comprised of various two-dimensional materials. For this application, lateral heterostructures of two-dimensional materials play a major role in the realization of wholly two- dimensional devices, as they are the fundamental elements in a circuit, such as p-n junctions and metal-semiconductor contacts. This dissertation will employ transmission electron microscopy and related techniques to address how different two-dimensional materials merge to form lateral heterostructures, specifically between two distinct two-dimensional semiconductors (analogous to p-n junctions) and two-dimensional conductor- semiconductor heterostructures (analogous to metal-semiconductor contacts). Within the heterostructures between two semiconductors, Chapter 2 and 3 will discuss atomically sharp interfaces and gradual interfaces in lateral heterostructures, respectively. Chapter 4 will describe the conductor-semiconductor interconnects between two-dimensional materials with dissimilar lattice structures. Our results demonstrate how the strain is relaxed in epitaxial lateral heterostructures, as well as how the heterostructure between crystallographically distinct two-dimensional materials forms. These findings can unravel how to use or engineer distortions in two-dimensional lateral heterojunctions, predict the mechanical strength and devices performance, and inform the mechanism of chemical synthesis at the interface between atomically thin films.

Aberration-corrected optics have made transmission electron microscopy a widespread and essential tool for 2D/3D material characterization at the atomic scale. With the rapid development of hardware and novel experimental techniques, there is an increasing demand for advanced algorithms to work with new experimental data or improve existing techniques. In this dissertation, we investigate a variety of image reconstruction algorithms for tomography and ptychography - two fast growing areas in electron microscopy. Using experimental and simulated data, we examine the limitations of advanced reconstruction algorithms and propose new methods to improve existing methods. Chapter 1 provides an overview of transmission electron microscopy and introduces some basic concepts in imaging science. Chapter 2 takes a more in-depth discussion of elastic scattering in STEM and how beam propagation can be described analytically and computationally. The next two chapters focus on electron tomography, a technique that reconstructs the 3D structure of the object. Chapter 3 describes the experimental setup and demonstrates an efficient Fourier-based reconstruction framework that works well with novel experimental techniques, including dual-axis tomography and through-focal tomography. In Chapter 4, we investigate the popular sparsity-exploiting reconstruction algorithms - exploring their practical limitations in the context of electron tomography. Chapter 5 introduces electron ptychography, a diffractive imaging technique that is enabled by the recent development of a high dynamic range detector. Here we demonstrate a full-field ptychographic reconstruction that doubles the spatial resolution of the traditional lens limitations. Finally, in Chapter 6 we further study the practical limitations of ptychography and propose new strategies for reconstructions.

Scanning transmission electron microscopy (STEM) is a key tool in the advancement of materials science. As nanoscale materials and atomically sharp interfaces become increasingly technologically relevant, STEM provides feedback on the individual atoms, defects and interfaces that matter in the material. Two areas where STEM characterization is critical for materials advancement are electrochemical energy materials, such as battery electrodes and fuel cell electrocatalysts, and complex oxide materials, which exhibit a diverse array of properties. Electrochemical energy systems, including battery electrodes and electrocatalysts for fuel cells, are critical for the future of clean transportation. For these materials, investigation of the nanoscale processes which occur in liquid electrolytes is critical for understanding their performance in real devices. Encapsulating a thin layer of liquid in the TEM for in situ characterization is an exciting approach for gaining a detailed understanding of the underlying mechanisms of energy conversion and storage. The first half of this dissertation discusses the development and use of liquid-cell and electrochemical-cell TEM. First, I discuss the limitations and opportunities of EELS in thick liquids. I further discuss an electrochemical cell for the TEM, and its application to fuel cell electrocatalysts and battery materials. I was able to observe Pt-Ni octahedral catalyst particles degrade and lose their shape, and detect lithium ions move in a charging and discharging battery cathode (LiFePO4) with nanoscale detail by mapping the electronic structure. The second part of the dissertation focuses on complex oxides, which host a wide range of electronic and magnetic properties. Oxide interfaces, such as thin-film heterostructures and domain walls, are often atomically abrupt and produce novel functionalities. In particular, ferroelectric domain walls are rich sources of emergent phenomena – such as two-dimensional conductive sheets that form in an otherwise insulating solid – due to their unusual electronic properties or symmetry breaking. We probed how ferroelectric distortions change at domain walls with STEM for ErMnO3. From the STEM images, we calculated the order parameter at many domain walls in ErMnO3 to create a statistical picture of the ferroelectricity at these topological defects, and also observed how the order parameter changes near vortex structures. We further apply these methods to lutetium ferrite superlattices, where we use feedback from STEM to design a near-room-temperature multiferroic material in which ferroelectricity enhances the magnetism. We find that there are confined charged domain walls in the superlattice that additionally boost magnetism.

The transmission electron microscope (TEM) is a powerful tool for characterizing the nanoscale and atomic structure of materials, offering insights into their fundamental physical properties. However, TEM characterization requires very thin samples of material to be placed in a high vacuum environment, and exposed to electron radiation. The high vacuum will induce some materials to evaporate or sublimate, preventing them from being accurately characterized, radiation may damage the sample, causing mass loss, or altering its structure, and structurally delicate samples may collapse and break apart when they are thinned for TEM imaging. This dissertation discusses three different projects in which each of these three difficulties pose challenges to TEM characterization of samples. Firstly, we outline strategies for minimizing radiation damage when characterizing materials in TEM at atomic resolution. We consider types of radiation damage, such as vacancy enhanced displacement, that are not included in some previous discussions of beam damage, and we consider how to minimize damage when using new imaging techniques such as annular bright-field scanning TEM. Our methodology emphasizes the general principle that variation of both signal strength and damage cross section must be considered when choosing an experimental electron beam voltage to minimize damage. Secondly, we consider samples containing sulfur, which is prone to sublimation in high vacuum. TEM is routinely used to attempt to characterize the sulfur distribution in lithium-sulfur battery electrodes, but sublimation artifacts can give misleading results. We demonstrate that sulfur sublimation can be suppressed by using cryogenic TEM to characterize sulfur at very low temperatures, or by using the recently developed airSEM to characterize sulfur without exposing it to vacuum. Finally, we discuss the characterization of aging cadmium yellow paint from early 20th century art masterpieces. The binding medium holding paint particles together bends and curls as sample thickness is reduced to ~100 nm, making high resolution characterization challenging. We acquire lattice resolution images of the pigment particles through the binder using high voltage zero-loss energy filtered TEM, allowing us to measure the pigment particle size and determine the pigment crystal structure, providing insight into why the paint is aging and how it was synthesized.