Direct Imaging of the Crystalline Domains and Their Orientation in the PS-b-PEO Block Copolymer with 4D-STEM.

The arrangement of crystalline domains in semicrystalline polymers is key to understanding how to optimize the nanostructured morphology for enabling better properties. For example, in polystyrene-b-poly(ethylene oxide) (PS-b-PEO), the degree of crystallinity and arrangement of the crystallites within the PEO phase plays a crucial role in determining the physical properties of the electrolyte. Here, we used four-dimensional scanning transmission electron microscopy to directly visualize the crystal domains within the PEO-rich region of the PS-b-PEO block copolymer and show the relative angle of the domain with respect to the PEO-PS interface. As demonstrated here, our analysis method is applicable to other electron-beam sensitive materials, especially semicrystalline polymers, to unveil their local phase condition and distribution.

Direct Measurement of the Thermal Expansion Coefficient of Epitaxial WSe2 by Four-Dimensional Scanning Transmission Electron Microscopy.

Current reports of thermal expansion coefficients (TEC) of two-dimensional (2D) materials show large discrepancies that span orders of magnitude. Determining the TEC of any 2D material remains difficult due to approaches involving indirect measurement of samples that are atomically thin and optically transparent. We demonstrate a methodology to address this discrepancy and directly measure TEC of nominally monolayer epitaxial WSe2 using four-dimensional scanning transmission electron microscopy (4D-STEM). Experimentally, WSe2 from metal-organic chemical vapor deposition (MOCVD) was heated through a temperature range of 18-564 °C using a barrel-style heating sample holder to observe temperature-induced structural changes without additional alterations or destruction of the sample. By combining 4D-STEM measurements with quantitative structural analysis, the thermal expansion coefficient of nominally monolayer polycrystalline epitaxial 2D WSe2 was determined to be (3.5 ± 0.9) × 10-6 K-1 and (5.7 ± 2) × 10-5 K-1 for the in- and out-of-plane TEC, respectively, and (3.6 ± 0.2) × 10-5 K-1 for the unit cell volume TEC, in good agreement with historically determined values for bulk crystals.

How the AI-assisted discovery and synthesis of a ternary oxide highlights capability gaps in materials science.

Exploratory synthesis has been the main generator of new inorganic materials for decades. However, our Edisonian and bias-prone processes of synthetic exploration alone are no longer sufficient in an age that demands rapid advances in materials development. In this work, we demonstrate an end-to-end attempt towards systematic, computer-aided discovery and laboratory synthesis of inorganic crystalline compounds as a modern alternative to purely exploratory synthesis. Our approach initializes materials discovery campaigns by autonomously mapping the synthetic feasibility of a chemical system using density functional theory with AI feedback. Following expert-driven down-selection of newly generated phases, we use solid-state synthesis and in situ characterization via hot-stage X-ray diffraction in order to realize new ternary oxide phases experimentally. We applied this strategy in six ternary transition-metal oxide chemistries previously considered well-explored, one of which culminated in the discovery of two novel phases of calcium ruthenates. Detailed characterization using room temperature X-ray powder diffraction, 4D-STEM and SQUID measurements identifies the structure and composition and confirms distinct properties, including distinct defect concentrations, of one of the new phases formed in our experimental campaigns. While the discovery of a new material guided by AI and DFT theory represents a milestone, our procedure and results also highlight a number of critical gaps in the process that can inform future efforts towards the improvement of AI-coupled methodologies.

Heterogeneity in Cation Exchange Ag+ Doping of CdSe Nanocrystals.

Cation exchange is becoming extensively used for nanocrystal (NC) doping in order to produce NCs with unique optical and electronic properties. However, despite its ever-increasing use, the relationships between the cation exchange process, its doped NC products, and the resulting NC photophysics are not well characterized. For example, similar doping procedures on NCs with the same chemical compositions have resulted in quite different photophysics. Through a detailed single molecule investigation of a postsynthesis Ag+ doping of CdSe NCs, a number of species were identified within a single doped NC sample, suggesting the differences in the optical properties of the various synthesis methods are due to the varied contributions of each species. Electrostatic force microscopy (EFM), electron energy loss spectroscopy (EELS) mapping, and single molecule photoluminescence (PL) studies were used to identify four possible species resulting from the Ag+-CdSe cation exchange doping process. The heterogeneity of these samples shows the difficulty in controlling a postsynthesis cation exchange method to produce homogeneous samples needed for use in any potential application. Additionally, the heterogeneity in the doped samples demonstrates that significant care must be taken in describing the ensemble or average characteristics of the sample.

The emergence of three-dimensional chiral domain walls in polar vortices.

Chirality or handedness of a material can be used as an order parameter to uncover the emergent electronic properties for quantum information science. Conventionally, chirality is found in naturally occurring biomolecules and magnetic materials. Chirality can be engineered in a topological polar vortex ferroelectric/dielectric system via atomic-scale symmetry-breaking operations. We use four-dimensional scanning transmission electron microscopy (4D-STEM) to map out the topology-driven three-dimensional domain walls, where the handedness of two neighbor topological domains change or remain the same. The nature of the domain walls is governed by the interplay of the local perpendicular (lateral) and parallel (axial) polarization with respect to the tubular vortex structures. Unique symmetry-breaking operations and the finite nature of domain walls result in a triple point formation at the junction of chiral and achiral domain walls. The unconventional nature of the domain walls with triple point pairs may result in unique electrostatic and magnetic properties potentially useful for quantum sensing applications.

Spatially resolved structural order in low-temperature liquid electrolyte.

Determining the degree and the spatial extent of structural order in liquids is a grand challenge. Here, we are able to resolve the structural order in a model organic electrolyte of 1 M lithium hexafluorophosphate (LiPF6) dissolved in 1:1 (v/v) ethylene carbonate:diethylcarbonate by developing an integrated method of liquid-phase transmission electron microscopy (TEM), cryo-TEM operated at -30°C, four-dimensional scanning TEM, and data analysis based on deep learning. This study reveals the presence of short-range order (SRO) in the high-salt concentration domains of the liquid electrolyte from liquid phase separation at the low temperature. Molecular dynamics simulations suggest the SRO originates from the Li+-(PF6-)n (n > 2) local structural order induced by high LiPF6 salt concentration.

Multiscale hierarchical structures from a nanocluster mesophase.

Spontaneous hierarchical self-organization of nanometre-scale subunits into higher-level complex structures is ubiquitous in nature. The creation of synthetic nanomaterials that mimic the self-organization of complex superstructures commonly seen in biomolecules has proved challenging due to the lack of biomolecule-like building blocks that feature versatile, programmable interactions to render structural complexity. In this study, highly aligned structures are obtained from an organic-inorganic mesophase composed of monodisperse Cd37S18 magic-size cluster building blocks. Impressively, structural alignment spans over six orders of magnitude in length scale: nanoscale magic-size clusters arrange into a hexagonal geometry organized inside micrometre-sized filaments; self-assembly of these filaments leads to fibres that then organize into uniform arrays of centimetre-scale bands with well-defined surface periodicity. Enhanced patterning can be achieved by controlling processing conditions, resulting in bullseye and 'zigzag' stacking patterns with periodicity in two directions. Overall, we demonstrate that colloidal nanomaterials can exhibit a high level of self-organization behaviour at macroscopic-length scales.

Automated Crystal Orientation Mapping in py4DSTEM using Sparse Correlation Matching.

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 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 demonstrate 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.

Correlative image learning of chemo-mechanics in phase-transforming solids.

Constitutive laws underlie most physical processes in nature. However, learning such equations in heterogeneous solids (for example, due to phase separation) is challenging. One such relationship is between composition and eigenstrain, which governs the chemo-mechanical expansion in solids. Here we developed a generalizable, physically constrained image-learning framework to algorithmically learn the chemo-mechanical constitutive law at the nanoscale from correlative four-dimensional scanning transmission electron microscopy and X-ray spectro-ptychography images. We demonstrated this approach on LiXFePO4, a technologically relevant battery positive electrode material. We uncovered the functional form of the composition-eigenstrain relation in this two-phase binary solid across the entire composition range (0 ≤ X ≤ 1), including inside the thermodynamically unstable miscibility gap. The learned relation directly validates Vegard's law of linear response at the nanoscale. Our physics-constrained data-driven approach directly visualizes the residual strain field (by removing the compositional and coherency strain), which is otherwise impossible to quantify. Heterogeneities in the residual strain arise from misfit dislocations and were independently verified by X-ray diffraction line profile analysis. Our work provides the means to simultaneously quantify chemical expansion, coherency strain and dislocations in battery electrodes, which has implications on rate capabilities and lifetime. Broadly, this work also highlights the potential of integrating correlative microscopy and image learning for extracting material properties and physics.

Electric field control of chirality.

Polar textures have attracted substantial attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second-harmonic generation­based 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 nonchiral 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.

The mesoscale order of nacreous pearls.

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 a cross-section at high resolution, we show that 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 µm) despite persistent fluctuations and topological defects. For longer distances (>25 tablets , ∼8.5 µm), the frequency spectrum of nacre tablets follows [Formula: see text] behavior, suggesting that growth is coupled to external stochastic processes-a universality found across disparate natural phenomena, which now includes pearls.

Crystallization by Amorphous Particle Attachment: On the Evolution of Texture.

Crystallization by particle attachment (CPA) is a gradual process where each step has its own thermodynamic and kinetic constrains defining a unique pathway of crystal growth. An important example is biomineralization of calcium carbonate through amorphous precursors that are morphed into shapes and textural patterns that cannot be envisioned by the classical monomer-by-monomer approach. Here, a mechanistic link between the collective kinetics of mineral deposition and the emergence of crystallographic texture is established. Using the prismatic ultrastructure in bivalve shells as a model, a fundamental leap is made in the ability to analytically describe the evolution of form and texture of biological mineralized tissues and to design the structure and crystallographic properties of synthetic materials formed by CPA.

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.

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.