Short-range order and its impact on the CrCoNi medium-entropy alloy.

Traditional metallic alloys are mixtures of elements in which the atoms of minority species tend to be distributed randomly if they are below their solubility limit, or to form secondary phases if they are above it. The concept of multiple-principal-element alloys has recently expanded this view, as these materials are single-phase solid solutions of generally equiatomic mixtures of metallic elements. This group of materials has received much interest owing to their enhanced mechanical properties1-5. They are usually called medium-entropy alloys in ternary systems and high-entropy alloys in quaternary or quinary systems, alluding to their high degree of configurational entropy. However, the question has remained as to how random these solid solutions actually are, with the influence of short-range order being suggested in computational simulations but not seen experimentally6,7. Here we report the observation, using energy-filtered transmission electron microscopy, of structural features attributable to short-range order in the CrCoNi medium-entropy alloy. Increasing amounts of such order give rise to both higher stacking-fault energy and hardness. These findings suggest that the degree of local ordering at the nanometre scale can be tailored through thermomechanical processing, providing a new avenue for tuning the mechanical properties of medium- and high-entropy alloys.

Design and synthesis of multigrain nanocrystals via geometric misfit strain.

The impact of topological defects associated with grain boundaries (GB defects) on the electrical, optical, magnetic, mechanical and chemical properties of nanocrystalline materials1,2 is well known. However, elucidating this influence experimentally is difficult because grains typically exhibit a large range of sizes, shapes and random relative orientations3-5. Here we demonstrate that precise control of the heteroepitaxy of colloidal polyhedral nanocrystals enables ordered grain growth and can thereby produce material samples with uniform GB defects. We illustrate our approach with a multigrain nanocrystal comprising a Co3O4 nanocube core that carries a Mn3O4 shell on each facet. The individual shells are symmetry-related interconnected grains6, and the large geometric misfit between adjacent tetragonal Mn3O4 grains results in tilt boundaries at the sharp edges of the Co3O4 nanocube core that join via disclinations. We identify four design principles that govern the production of these highly ordered multigrain nanostructures. First, the shape of the substrate nanocrystal must guide the crystallographic orientation of the overgrowth phase7. Second, the size of the substrate must be smaller than the characteristic distance between the dislocations. Third, the incompatible symmetry between the overgrowth phase and the substrate increases the geometric misfit strain between the grains. Fourth, for GB formation under near-equilibrium conditions, the surface energy of the shell needs to be balanced by the increasing elastic energy through ligand passivation8-10. With these principles, we can produce a range of multigrain nanocrystals containing distinct GB defects.

Observing crystal nucleation in four dimensions using atomic electron tomography.

Nucleation plays a critical role in many physical and biological phenomena that range from crystallization, melting and evaporation to the formation of clouds and the initiation of neurodegenerative diseases1-3. However, nucleation is a challenging process to study experimentally, especially in its early stages, when several atoms or molecules start to form a new phase from a parent phase. A number of experimental and computational methods have been used to investigate nucleation processes4-17, but experimental determination of the three-dimensional atomic structure and the dynamics of early-stage nuclei has been unachievable. Here we use atomic electron tomography to study early-stage nucleation in four dimensions (that is, including time) at atomic resolution. Using FePt nanoparticles as a model system, we find that early-stage nuclei are irregularly shaped, each has a core of one to a few atoms with the maximum order parameter, and the order parameter gradient points from the core to the boundary of the nucleus. We capture the structure and dynamics of the same nuclei undergoing growth, fluctuation, dissolution, merging and/or division, which are regulated by the order parameter distribution and its gradient. These experimental observations are corroborated by molecular dynamics simulations of heterogeneous and homogeneous nucleation in liquid-solid phase transitions of Pt. Our experimental and molecular dynamics results indicate that a theory beyond classical nucleation theory1,2,18 is needed to describe early-stage nucleation at the atomic scale. We anticipate that the reported approach will open the door to the study of many fundamental problems in materials science, nanoscience, condensed matter physics and chemistry, such as phase transition, atomic diffusion, grain boundary dynamics, interface motion, defect dynamics and surface reconstruction with four-dimensional atomic resolution.

Uneven Strain Distribution Induces Consecutive Dislocation Slipping, Plane Gliding, and Subsequent Detwinning of Penta-Twinned Nanoparticles.

Twin structures possess distinct physical and chemical properties by virtue of their specific twin configuration. However, twinning and detwinning processes are not fully understood on the atomic scale. Integrating in situ high resolution transmission electron microscopy and molecular dynamic simulations, we find tensile strain in the asymmetrical 5-fold twins of Au nanoparticles leads to twin boundary migration through dislocation sliding (slipping of an atomic layer) along twin boundaries and dislocation reactions at the 5-fold axis under an electron beam. Migration of one or two layers of twin planes is governed by energy barriers, but overall, the total energy, including surface, lattice strain, and twin boundary energy, is relaxed after consecutive twin boundary migration, leading to a detwinning process. In addition, surface rearrangement of 5-fold twinned nanoparticles can aid in the detwinning process.

A method for crystallographic mapping of an alpha-beta titanium alloy with nanometre resolution using scanning precession electron diffraction and open-source software libraries.

An approach for the crystallographic mapping of two-phase alloys on the nanoscale using a combination of scanned precession electron diffraction and open-source python libraries is introduced in this paper. This method is demonstrated using the example of a two-phase α/ß titanium alloy. The data were recorded using a direct electron detector to collect the patterns, and recently developed algorithms to perform automated indexing and analyse the crystallography from the results. Very high-quality mapping is achieved at a 3 nm step size. The results show the expected Burgers orientation relationships between the α laths and ß matrix, as well as the expected misorientations between α laths. A minor issue was found that one area was affected by 180° ambiguities in indexing occur due to this area being aligned too close to a zone axis of the α with twofold projection symmetry (not present in 3D) in the zero-order Laue Zone, and this should be avoided in data acquisition in the future. Nevertheless, this study demonstrates a good workflow for the analysis of nanocrystalline two- or multi-phase materials, which will be of widespread use in analysing two-phase titanium and other systems and how they evolve as a function of thermomechanical treatments.

Energy Funneling in a Noninteger Two-Dimensional Perovskite.

Energy funneling is a phenomenon that has been exploited in optoelectronic devices based on low-dimensional materials to improve their performance. Here, we introduce a new class of two-dimensional semiconductor, characterized by multiple regions of varying thickness in a single confined nanostructure with homogeneous composition. This "noninteger 2D semiconductor" was prepared via the structural transformation of two-octahedron-layer-thick (n = 2) 2D cesium lead bromide perovskite nanosheets; it consisted of a central n = 2 region surrounded by edge-lying n = 3 regions, as imaged by electron microscopy. Thicker noninteger 2D CsPbBr3 nanostructures were obtained as well. These noninteger 2D perovskites formed a laterally coupled quantum well band alignment with virtually no strain at the interface and no dielectric barrier, across which unprecedented intramaterial funneling of the photoexcitation energy was observed from the thin to the thick regions using time-resolved absorption and photoluminescence spectroscopy.

Mapping Nanoscale Electrostatic Field Fluctuations around Graphene Dislocation Cores Using Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM).

Defects in crystalline lattices cause modulation of the atomic density, and this leads to variations in the associated electrostatics at the nanoscale. Mapping these spatially varying charge fluctuations using transmission electron microscopy has typically been challenging due to complicated contrast transfer inherent to conventional phase contrast imaging. To overcome this, we used four-dimensional scanning transmission electron microscopy (4D-STEM) to measure electrostatic fields near point dislocations in a monolayer. The asymmetry of the atomic density in a (1,0) edge dislocation core in graphene yields a local enhancement of the electric field in part of the dislocation core. Through experiment and simulation, the increased electric field magnitude is shown to arise from "long-range" interactions from beyond the nearest atomic neighbor. These results provide insights into the use of 4D-STEM to quantify electrostatics in thin materials and map out the lateral potential variations that are important for molecular and atomic bonding through Coulombic interactions.

Enabling Oxidation Protection and Carrier-Type Switching for Bismuth Telluride Nanoribbons via in Situ Organic Molecule Coating.

Thermoelectric materials with high electrical conductivity and low thermal conductivity (e.g., Bi2Te3) can efficiently convert waste heat into electricity; however, in spite of favorable theoretical predictions, individual Bi2Te3 nanostructures tend to perform less efficiently than bulk Bi2Te3. We report a greater-than-order-of-magnitude enhancement in the thermoelectric properties of suspended Bi2Te3 nanoribbons, coated in situ to form a Bi2Te3/F4-TCNQ core-shell nanoribbon without oxidizing the core-shell interface. The shell serves as an oxidation barrier but also directly functions as a strong electron acceptor and p-type carrier donor, switching the majority carriers from a dominant n-type carrier concentration (∼1021 cm-3) to a dominant p-type carrier concentration (∼1020 cm-3). Compared to uncoated Bi2Te3 nanoribbons, our Bi2Te3/F4-TCNQ core-shell nanoribbon demonstrates an effective chemical potential dramatically shifted toward the valence band (by 300-640 meV), robustly increased Seebeck coefficient (∼6× at 250 K), and improved thermoelectric performance (10-20× at 250 K).

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.

Deciphering chemical order/disorder and material properties at the single-atom level.

Perfect crystals are rare in nature. Real materials often contain crystal defects and chemical order/disorder such as grain boundaries, dislocations, interfaces, surface reconstructions and point defects. Such disruption in periodicity strongly affects material properties and functionality. Despite rapid development of quantitative material characterization methods, correlating three-dimensional (3D) atomic arrangements of chemical order/disorder and crystal defects with material properties remains a challenge. On a parallel front, quantum mechanics calculations such as density functional theory (DFT) have progressed from the modelling of ideal bulk systems to modelling 'real' materials with dopants, dislocations, grain boundaries and interfaces; but these calculations rely heavily on average atomic models extracted from crystallography. To improve the predictive power of first-principles calculations, there is a pressing need to use atomic coordinates of real systems beyond average crystallographic measurements. Here we determine the 3D coordinates of 6,569 iron and 16,627 platinum atoms in an iron-platinum nanoparticle, and correlate chemical order/disorder and crystal defects with material properties at the single-atom level. We identify rich structural variety with unprecedented 3D detail including atomic composition, grain boundaries, anti-phase boundaries, anti-site point defects and swap defects. We show that the experimentally measured coordinates and chemical species with 22 picometre precision can be used as direct input for DFT calculations of material properties such as atomic spin and orbital magnetic moments and local magnetocrystalline anisotropy. This work combines 3D atomic structure determination of crystal defects with DFT calculations, which is expected to advance our understanding of structure-property relationships at the fundamental level.

Measurement of Atomic Modulation Direction Using the Azimuthal Variation of First-Order Laue Zone Electron Diffraction.

We show that diffraction intensity into the first-order Laue zone (FOLZ) of a crystal can have a strong azimuthal dependence, where this FOLZ ring appears solely because of unidirectional atom position modulation. Such a modulation was already known to cause the appearance of elliptical columns in atom-resolution images, but we show that measurement of the angle via four-dimensional scanning transmission electron microscopy (4DSTEM) is far more reliable and allows the measurement of the modulation direction with a precision of about 1° and an accuracy of about 3°. This method could be very powerful in characterizing atomic structures in three dimensions by 4DSTEM, especially in cases where the structure is found only in nanoscale regions or crystals.

Defect Contrast with 4D-STEM: Understanding Crystalline Order with Virtual Detectors and Beam Modification.

Material properties strongly depend on the nature and concentration of defects. Characterizing these features may require nano- to atomic-scale resolution to establish structure-property relationships. 4D-STEM, a technique where diffraction patterns are acquired at a grid of points on the sample, provides a versatile method for highlighting defects. Computational analysis of the diffraction patterns with virtual detectors produces images that can map material properties. Here, using multislice simulations, we explore different virtual detectors that can be applied to the diffraction patterns that go beyond the binary response functions that are possible using ordinary STEM detectors. Using graphene and lead titanate as model systems, we investigate the application of virtual detectors to study local order and in particular defects. We find that using a small convergence angle with a rotationally varying detector most efficiently highlights defect signals. With experimental graphene data, we demonstrate the effectiveness of these detectors in characterizing atomic features, including vacancies, as suggested in simulations. Phase and amplitude modification of the electron beam provides another process handle to change image contrast in a 4D-STEM experiment. We demonstrate how tailored electron beams can enhance signals from short-range order and how a vortex beam can be used to characterize local symmetry.

Design of Electrostatic Aberration Correctors for Scanning Transmission Electron Microscopy.

In a scanning transmission electron microscope (STEM), producing a high-resolution image generally requires an electron beam focused to the smallest point possible. However, the magnetic lenses used to focus the beam are unavoidably imperfect, introducing aberrations that limit resolution. Modern STEMs overcome this by using hardware aberration correctors comprised of many multipole elements, but these devices are complex, expensive, and can be difficult to tune. We demonstrate a design for an electrostatic phase plate that can act as an aberration corrector. The corrector is comprised of annular segments, each of which is an independent two-terminal device that can apply a constant or ramped phase shift to a portion of the electron beam. We show the improvement in image resolution using an electrostatic corrector. Engineering criteria impose that much of the beam within the probe-forming aperture be blocked by support bars, leading to large probe tails for the corrected probe that sample the specimen beyond the central lobe. We also show how this device can be used to create other STEM beam profiles such as vortex beams and probes with a high degree of phase diversity, which improve information transfer in ptychographic reconstructions.

Ultrasensitive Sub-monolayer Palladium Induced Chirality Switching and Topological Evolution of Skyrmions.

Chiral spin textures are fundamentally interesting, with promise for device applications. Stabilizing chirality is conventionally achieved by introducing Dzyaloshinskii-Moriya interaction (DMI) in asymmetric multilayers, where the thickness of each layer is at least a few monolayers. Here we report an ultrasensitive chirality switching in (Ni/Co)n multilayer induced by capping with only 0.22 monolayer of Pd. Using spin-polarized low-energy electron microscopy, we monitor the gradual evolution of domain walls from left-handed to right-handed Néel walls and quantify the DMI induced by the Pd capping layer. We also observe the chiral evolution of a skyrmion during the DMI switching, where no significant topological protection is found as the skyrmion winding number varies. This corresponds to a minimum energy cost of <1 attojoule during the skyrmion chirality switching. Our results demonstrate the detailed chirality evolution within skyrmions during the DMI sign switching, which is relevant to practical applications of skyrmionic devices.

Visualizing Grain Statistics in MOCVD WSe2 through Four-Dimensional Scanning Transmission Electron Microscopy.

Using four-dimensional scanning transmission electron microscopy, we demonstrate a method to visualize grains and grain boundaries in WSe2 grown by metal organic chemical vapor deposition (MOCVD) directly onto silicon dioxide. Despite the chemical purity and uniform thickness and texture of the MOCVD-grown WSe2, we observe a high density of small grains that corresponds with the overall selenium deficiency we measure through ion beam analysis. Moreover, reconstruction of grain information permits the creation of orientation maps that demonstrate the nucleation mechanism for new layers-triangular domains with the same orientation as the layer underneath induces a tensile strain increasing the lattice parameter at these sites.

Strong Structural and Electronic Coupling in Metavalent PbS Moiré Superlattices.

Moiré superlattices are twisted bilayer materials in which the tunable interlayer quantum confinement offers access to new physics and novel device functionalities. Previously, moiré superlattices were built exclusively using materials with weak van der Waals interactions, and synthesizing moiré superlattices with strong interlayer chemical bonding was considered to be impractical. Here, using lead sulfide (PbS) as an example, we report a strategy for synthesizing moiré superlattices coupled by strong chemical bonding. We use water-soluble ligands as a removable template to obtain free-standing ultrathin PbS nanosheets and assemble them into direct-contact bilayers with various twist angles. Atomic-resolution imaging shows the moiré periodic structural reconstruction at the superlattice interface due to the strong metavalent coupling. Electron energy loss spectroscopy and theoretical calculations collectively reveal the twist-angle-dependent electronic structure, especially the emergent separation of flat bands at small twist angles. The localized states of flat bands are similar to well-arranged quantum dots, promising an application in devices. This study opens a new door to the exploration of deep energy modulations within moiré superlattices alternative to van der Waals twistronics.

Strain fields in twisted bilayer graphene.

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles <2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moiré heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anisotropically in saddle-point regions, generating distinctive striped strain phases. Our results establish the reconstruction mechanics underpinning the twist-angle-dependent electronic behaviour of twisted bilayer graphene and provide a framework for directly visualizing structural relaxation, disorder and strain in moiré materials.

4D-STEM of Beam-Sensitive Materials.

ConspectusScanning electron nanobeam diffraction, or 4D-STEM (four-dimensional scanning transmission electron microscopy), is a flexible and powerful approach to elucidate structure from "soft" materials that are challenging to image in the transmission electron microscope because their structure is easily damaged by the electron beam. In a 4D-STEM experiment, a converged electron beam is scanned across the sample, and a pixelated camera records a diffraction pattern at each scan position. This four-dimensional data set can be mined for various analyses, producing maps of local crystal orientation, structural distortions, crystallinity, or different structural classes. Holding the sample at cryogenic temperatures minimizes diffusion of radicals and the resulting damage and disorder caused by the electron beam. The total fluence of incident electrons can easily be controlled during 4D-STEM experiments by careful use of the beam blanker, steering of the localized electron dose, and by minimizing the fluence in the convergent beam thus minimizing beam damage. This technique can be applied to both organic and inorganic materials that are known to be beam-sensitive; they can be highly crystalline, semicrystalline, mixed phase, or amorphous.One common example is the case for many organic materials that have a π-π stacking of polymer chains or rings on the order of 3.4-4.2 Å separation. If these chains or rings are aligned in some regions, they will produce distinct diffraction spots (as would other crystalline spacings in this range), though they may be weak or diffuse for disordered or weakly scattering materials. We can reconstruct the orientation of the π-π stacking, the degree of π-π stacking in the sample, and the domain size of the aligned regions. This Account summarizes illumination conditions and experimental parameters for 4D-STEM experiments with the goal of producing images of structural features for materials that are beam-sensitive. We will discuss experimental parameters including sample cooling, probe size and shape, fluence, and cameras. 4D-STEM has been applied to a variety of materials, not only as an advanced technique for model systems, but as a technique for the beginning microscopist to answer materials science questions. It is noteworthy that the experimental data acquisition does not require an aberration-corrected TEM but can be produced on a variety of instruments with the right attention to experimental parameters.

Nanoscale oxygen defect gradients in UO2+x surfaces.

Oxygen defects govern the behavior of a range of materials spanning catalysis, quantum computing, and nuclear energy. Understanding and controlling these defects is particularly important for the safe use, storage, and disposal of actinide oxides in the nuclear fuel cycle, since their oxidation state influences fuel lifetimes, stability, and the contamination of groundwater. However, poorly understood nanoscale fluctuations in these systems can lead to significant deviations from bulk oxidation behavior. Here we describe the use of aberration-corrected scanning transmission electron microscopy and electron energy loss spectroscopy to resolve changes in the local oxygen defect environment in [Formula: see text] surfaces. We observe large image contrast and spectral changes that reflect the presence of sizable gradients in interstitial oxygen content at the nanoscale, which we quantify through first-principles calculations and image simulations. These findings reveal an unprecedented level of excess oxygen incorporated in a complex near-surface spatial distribution, offering additional insight into defect formation pathways and kinetics during [Formula: see text] surface oxidation.

Analysis of Interpretable Data Representations for 4D-STEM Using Unsupervised Learning.

Understanding the structure of materials is crucial for engineering devices and materials with enhanced performance. Four-dimensional scanning transmission electron microscopy (4D-STEM) is capable of mapping nanometer-scale local crystallographic structure over micron-scale field of views. However, 4D-STEM datasets can contain tens of thousands of images from a wide variety of material structures, making it difficult to automate detection and classification of structures. Traditional automated analysis pipelines for 4D-STEM focus on supervised approaches, which require prior knowledge of the material structure and cannot describe anomalous or deviant structures. In this article, a pipeline for engineering 4D-STEM feature representations for unsupervised clustering using non-negative matrix factorization (NMF) is introduced. Each feature is evaluated using NMF and results are presented for both simulated and experimental data. It is shown that some data representations more reliably identify overlapping grains. Additionally, real space refinement is applied to identify spatially distinct sample regions, allowing for size and shape analysis to be performed. This work lays the foundation for improved analysis of nanoscale structural features in materials that deviate from expected crystallographic arrangement using 4D-STEM.