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Diffraction is the most common method to solve for unknown or partially known crystal structures. However, it remains a challenge to determine the crystal structure of a new material that may have nanoscale size or heterogeneities. Here we train an architecture of hierarchical random forest models capable of predicting the crystal system, space group, and lattice parameters from one or more unknown 2D electron diffraction patterns. Our initial model correctly identifies the crystal system of a simulated electron diffraction pattern from a 20 nm thick specimen of arbitrary orientation 67% of the time. We achieve a topline accuracy of 79% when aggregating predictions from 10 patterns of the same material but different zone axes. The space group and lattice predictions range from 70-90% accuracy and median errors of 0.01-0.5 angstroms, respectively, for cubic, hexagonal, trigonal and tetragonal crystal systems while being less reliable on orthorhombic and monoclinic systems. We apply this architecture to a 4D-STEM scan of gold nanoparticles, where it accurately predicts the crystal structure and lattice constants. These random forest models can be used to significantly accelerate the analysis of electron diffraction patterns, particularly in the case of unknown crystal structures. Additionally, due to the speed of inference, these models could be integrated into live TEM experiments, allowing real-time labeling of a specimen.

Scanning transmission electron microscopy (STEM) has been extensively used for imaging complex materials down to atomic resolution. The most commonly employed STEM modality, annular dark-field imaging, produces easily-interpretable contrast, but is dose-inefficient and produces little to no discernible contrast for light elements and weakly-scattering samples. An alternative is to use STEM phase retrieval imaging, enabled by high speed detectors able to record full images of a diffracted STEM probe over a grid of scan positions. Phase retrieval imaging in STEM is highly dose-efficient, enabling the measurement of the structure of beam-sensitive materials such as biological samples. Here, we comprehensively describe the theoretical background, algorithmic implementation details, and perform both simulated and experimental tests for three iterative phase retrieval STEM methods: focused-probe differential phase contrast, defocused-probe parallax imaging, and a generalized ptychographic gradient descent method implemented in two and three dimensions. We discuss the strengths and weaknesses of each of these approaches by comparing the transfer of information using analytical expressions and numerical results for a white-noise model. This presentation of STEM phase retrieval methods aims to make these methods more approachable, reproducible, and more readily adoptable for many classes of samples., Comment: 25 pages, 14 figures, 1 table

We describe the development, operation, and application of the 4D Camera -- a 576 by 576 pixel active pixel sensor for scanning/transmission electron microscopy which operates at 87,000 Hz. The detector generates data at approximately 480 Gbit/s which is captured by dedicated receiver computers with a parallelized software infrastructure that has been implemented to process the resulting 10 - 700 Gigabyte-sized raw datasets. The back illuminated detector provides the ability to detect single electron events at accelerating voltages from 30 - 300 keV. Through electron counting, the resulting sparse data sets are reduced in size by 10 - 300x compared to the raw data, and open-source sparsity-based processing algorithms offer rapid data analysis. The high frame rate allows for large and complex 4D-STEM experiments to be accomplished with typical STEM scanning parameters.

Implementation of a fast, robust, and fully-automated pipeline for crystal structure determination and underlying strain mapping for crystalline materials is important for many technological applications. Scanning electron nanodiffraction offers a procedure for identifying and collecting strain maps with good accuracy and high spatial resolutions. However, the application of this technique is limited, particularly in thick samples where the electron beam can undergo multiple scattering, which introduces signal nonlinearities. Deep learning methods have the potential to invert these complex signals, but previous implementations are often trained only on specific crystal systems or a small subset of the crystal structure and microscope parameter phase space. In this study, we implement a Fourier space, complex-valued deep neural network called FCU-Net, to invert highly nonlinear electron diffraction patterns into the corresponding quantitative structure factor images. We trained the FCU-Net using over 200,000 unique simulated dynamical diffraction patterns which include many different combinations of crystal structures, orientations, thicknesses, microscope parameters, and common experimental artifacts. We evaluated the trained FCU-Net model against simulated and experimental 4D-STEM diffraction datasets, where it substantially out-performs conventional analysis methods. Our simulated diffraction pattern library, implementation of FCU-Net, and trained model weights are freely available in open source repositories, and can be adapted to many different diffraction measurement problems., Comment: 17 pages, 7 figures

Crystalline materials used in technological applications are often complex assemblies composed of multiple phases and differently oriented grains. Robust identification of the phases and orientation relationships from these samples is crucial, but the information extracted from the diffraction condition probed by an electron beam is often incomplete. We therefore have developed an automated crystal orientation mapping (ACOM) procedure which uses a converged electron probe to collect diffraction patterns from multiple locations across a complex sample. We provide an algorithm to determine the orientation of each diffraction pattern based on a fast sparse correlation method. We test the speed and accuracy of our method by indexing diffraction patterns generated using both kinematical and dynamical simulations. We have also measured orientation maps from an experimental dataset consisting of a complex polycrystalline twisted helical AuAgPd nanowire. From these maps we identify twin planes between adjacent grains, which may be responsible for the twisted helical structure. All of our methods are made freely available as open source code, including tutorials which can be easily adapted to perform ACOM measurements on diffraction pattern datasets., Comment: 14 pages, 7 figures

Lithium iron phosphate (LixFePO4), a cathode material used in rechargeable Li-ion batteries, phase separates upon de/lithiation under equilibrium. The interfacial structure and chemistry within these cathode materials affects Li-ion transport, and therefore battery performance. Correlative imaging of LixFePO4 was performed using four-dimensional scanning transmission electron microscopy (4D-STEM), scanning transmission X-ray microscopy (STXM), and X-ray ptychography in order to analyze the local structure and chemistry of the same particle set. Over 50,000 diffraction patterns from 10 particles provided measurements of both structure and chemistry at a nanoscale spatial resolution (16.6-49.5 nm) over wide (several micron) fields-of-view with statistical robustness.LixFePO4 particles at varying stages of delithiation were measured to examine the evolution of structure and chemistry as a function of delithiation. In lithiated and delithiated particles, local variations were observed in the degree of lithiation even while local lattice structures remained comparatively constant, and calculation of linear coefficients of chemical expansion suggest pinning of the lattice structures in these populations. Partially delithiated particles displayed broadly core-shell-like structures, however, with highly variable behavior both locally and per individual particle that exhibited distinctive intermediate regions at the interface between phases, and pockets within the lithiated core that correspond to FePO4 in structure and chemistry.The results provide insight into the LixFePO4 system, subtleties in the scope and applicability of Vegards law (linear lattice parameter-composition behavior) under local versus global measurements, and demonstrate a powerful new combination of experimental and analytical modalities for bridging the crucial gap between local and statistical characterization., Comment: 17 pages, 4 figures

Polar textures have attracted significant attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second harmonic generation based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric-field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field. The emergence of chirality from the combination of non-chiral materials and subsequent control of the handedness with an electric field has far-reaching implications for new electronics based on chirality as a field controllable order parameter., Comment: 19 pages, 4 figures Supplement: 27 pages, 13 figures

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 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 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., Comment: 15 pages, 7 figures

A pearl's distinguished beauty and toughness are attributable to the periodic stacking of aragonite tablets known as nacre. Nacre has naturally occurring mesoscale periodicity that remarkably arises in the absence of discrete translational symmetry. Gleaning the inspiring biomineral design of a pearl requires quantifying its structural coherence and understanding the stochastic processes that influence formation. By characterizing the entire structure of pearls (~3 mm) in cross-section at high resolution, we show nacre has medium-range mesoscale periodicity. Self-correcting growth mechanisms actively remedy disorder and topological defects of the tablets and act as a countervailing process to long-range disorder. Nacre has a correlation length of roughly 16 tablets (~5.5 um) despite persistent fluctuations and topological defects. For longer distances (> 25 tablets, ~8.5 um), the frequency spectrum of nacre tablets follows f^(-1.5) behavior suggesting growth is coupled to external stochastic processes-a universality found across disparate natural phenomena which now includes pearls., Comment: 19 pages, 4 figures, PNAS 118(42)

One of the primary uses for transmission electron microscopy (TEM) is to measure diffraction pattern images in order to determine a crystal structure and orientation. In nanobeam electron diffraction (NBED) we scan a moderately converged electron probe over the sample to acquire thousands or even millions of sequential diffraction images, a technique that is especially appropriate for polycrystalline samples. However, due to the large Ewald sphere of TEM, excitation of Bragg peaks can be extremely sensitive to sample tilt, varying strongly for even a few degrees of sample tilt for crystalline samples. In this paper, we present multibeam electron diffraction (MBED), where multiple probe forming apertures are used to create mutiple STEM probes, all of which interact with the sample simultaneously. We detail designs for MBED experiments, and a method for using a focused ion beam (FIB) to produce MBED apertures. We show the efficacy of the MBED technique for crystalline orientation mapping using both simulations and proof-of-principle experiments. We also show how the angular information in MBED can be used to perform 3D tomographic reconstruction of samples without needing to tilt or scan the sample multiple times. Finally, we also discuss future opportunities for the MBED method., Comment: 14 pages, 6 figures

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 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, from data wrangling to calibration to analysis to 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 have also implemented 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, helps to move the developing standards for data and computational methods in electron microscopy, and invite the community to contribute to this ongoing, fully open-source project., Comment: 32 pages, 18 figures

Magic-sized clusters (MSCs) are renowned for their identical size and closed-shell stability that inhibit conventional nanoparticle (NP) growth processes. Though MSCs have been of increasing interest, understanding the reaction pathways toward their nucleation and stabilization is an outstanding issue. In this work, we demonstrate that high concentration synthesis (1000 mM) promotes a well-defined reaction pathway to form high-purity MSCs (greater than 99.9 percent). The MSCs are resistant to typical growth and dissolution processes. Based on insights from in-situ X-ray scattering analysis, we attribute this stability to the accompanying production of a large, hexagonal organic-inorganic mesophase (greater than 100 nm grain size) that arrests growth of the MSCs and prevents NP growth. At intermediate concentrations (500 mM), the MSC mesophase forms, but is unstable, resulting in NP growth at the expense of the assemblies. These results provide an alternate explanation for the high stability of MSCs. Whereas the conventional mantra has been that the stability of MSCs derives from the precise arrangement of the inorganic structures (i.e., closed-shell atomic packing), we demonstrate that anisotropic clusters can also be stabilized by self-forming fibrous mesophase assemblies. At lower concentration (less than 200 mM or greater than 16 acid-to-metal), MSCs are further destabilized and NPs formation dominates that of MSCs. Overall, the high concentration approach intensifies and showcases inherent concentration-dependent surfactant phase behavior that is not accessible in conventional (i.e., dilute) conditions. This work provides not only a robust method to synthesize, stabilize, and study identical MSC products, but also uncovers an underappreciated stabilizing interaction between surfactants and clusters., Comment: main text - 24 pages, 8 figures. SI - 35 pages, 30 figures, 6 tables

Combining multiple fast image acquisitions to mitigate scan noise and drift artifacts has proven essential for picometer precision, quantitative analysis of atomic resolution scanning transmission electron microscopy (STEM) data. For very low signal-to-noise ratio (SNR) image stacks - frequently required for undistorted imaging at liquid nitrogen temperatures - image registration is particularly delicate, and standard approaches may either fail, or produce subtly specious reconstructed lattice images. We present an approach which effectively registers and averages image stacks which are challenging due to their low-SNR and propensity for unit cell misalignments. Registering all possible image pairs in a multi-image stack leads to significant information surplus. In combination with a simple physical picture of stage drift, this enables identification of incorrect image registrations, and determination of the optimal image shifts from the complete set of relative shifts. We demonstrate the effectiveness of our approach on experimental, cryogenic STEM datasets, highlighting subtle artifacts endemic to low-SNR lattice images and how they can be avoided. High-SNR average images with information transfer out to 0.72 A are achieved at 300 kV and with the sample cooled to near liquid nitrogen temperature., Comment: 25 pages, 5 figures

Incommensurate charge order in hole-doped oxides is intertwined with exotic phenomena such as colossal magnetoresistance, high-temperature superconductivity, and electronic nematicity. Here, we map at atomic resolution the nature of incommensurate order in a manganite using scanning transmission electron microscopy at room temperature and cryogenic temperature ($\sim$ 93K). In diffraction, the ordering wavevector changes upon cooling, a behavior typically associated with incommensurate order. However, using real space measurements, we discover that the underlying ordered state is lattice-commensurate at both temperatures. The cations undergo picometer-scale ($\sim $6-11 pm) transverse displacements, which suggests that charge-lattice coupling is strong and hence favors lattice-locked modulations. We further unearth phase inhomogeneity in the periodic lattice displacements at room temperature, and emergent phase coherence at 93K. Such local phase variations not only govern the long range correlations of the charge-ordered state, but also results in apparent shifts in the ordering wavevector. These atomically-resolved observations underscore the importance of lattice coupling and provide a microscopic explanation for putative "incommensurate" order in hole-doped oxides.

In complex electronic materials, coupling between electrons and the atomic lattice gives rise to remarkable phenomena, including colossal magnetoresistance and metal-insulator transitions. Charge-ordered phases are a prototypical manifestation of charge-lattice coupling, in which the atomic lattice undergoes periodic lattice displacements (PLDs). Here we directly map the picometer scale PLDs at individual atomic columns in the room temperature charge-ordered manganite Bi$_{0.35}$Sr$_{0.18}$Ca$_{0.47}$MnO$_3$ using aberration corrected scanning transmission electron microscopy (STEM). We measure transverse, displacive lattice modulations of the cations, distinct from existing manganite charge-order models. We reveal locally unidirectional striped PLD domains as small as $\sim$5 nm, despite apparent bidirectionality over larger length scales. Further, we observe a direct link between disorder in one lattice modulation, in the form of dislocations and shear deformations, and nascent order in the perpendicular modulation. By examining the defects and symmetries of PLDs near the charge-ordering phase transition, we directly visualize the local competition underpinning spatial heterogeneity in a complex oxide., Comment: Main text: 20 pages, 4 figures. Supplemental Information: 27 pages, 14 figures

Charge density waves (CDW) and their concomitant periodic lattice distortions (PLD) govern the electronic properties in many layered transition-metal dichalcogenides. In particular, 1T-TaS2 undergoes a metal-to-insulator phase transition as the PLD becomes commensurate with the crystal lattice. Here we directly image PLDs of the nearly-commensurate (NC) and commensurate (C) phases in thin exfoliated 1T-TaS2 using atomic resolution scanning transmission electron microscopy at room and cryogenic temperature. At low temperatures, we observe commensurate PLD superstructures, suggesting ordering of the CDWs both in- and out-of-plane. In addition, we discover stacking transitions in the atomic lattice that occur via one bond length shifts. Interestingly, the NC PLDs exist inside both the stacking domains and their boundaries. Transitions in stacking order are expected to create fractional shifts in the CDW between layers and may be another route to manipulate electronic phases in layered dichalcogenides., Comment: 4 figures in Proceedings of the National Academy of Sciences of the United States of America, 2016