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Medium- and high-entropy alloys (M/HEAs) mix several principal elements with near-equiatomic composition and represent a model-shift strategy for designing previously unknown materials in metallurgy 1 – 8 , catalysis 9 – 14 and other fields 15 – 18 . One of the core hypotheses of M/HEAs is lattice distortion 5 , 19 , 20 , which has been investigated by different numerical and experimental techniques 21 – 26 . However, determining the three-dimensional (3D) lattice distortion in M/HEAs remains a challenge. Moreover, the presumed random elemental mixing in M/HEAs has been questioned by X-ray and neutron studies 27 , atomistic simulations 28 – 30 , energy dispersive spectroscopy 31 , 32 and electron diffraction 33 , 34 , which suggest the existence of local chemical order in M/HEAs. However, direct experimental observation of the 3D local chemical order has been difficult because energy dispersive spectroscopy integrates the composition of atomic columns along the zone axes 7 , 32 , 34 and diffuse electron reflections may originate from planar defects instead of local chemical order 35 . Here we determine the 3D atomic positions of M/HEA nanoparticles using atomic electron tomography 36 and quantitatively characterize the local lattice distortion, strain tensor, twin boundaries, dislocation cores and chemical short-range order (CSRO). We find that the high-entropy alloys have larger local lattice distortion and more heterogeneous strain than the medium-entropy alloys and that strain is correlated to CSRO. We also observe CSRO-mediated twinning in the medium-entropy alloys, that is, twinning occurs in energetically unfavoured CSRO regions but not in energetically favoured CSRO ones, which represents, to our knowledge, the first experimental observation of correlating local chemical order with structural defects in any material. We expect that this work will not only expand our fundamental understanding of this important class of materials but also provide the foundation for tailoring M/HEA properties through engineering lattice distortion and local chemical order. Atomic electron tomography is used to determine the 3D atomic positions and chemical species of medium- and high-entropy alloy nanoparticles and quantitatively characterize the local lattice distortion, strain tensor, twin boundaries, dislocation cores and chemical short-range order.

Crystallography has been fundamental to the development of many fields of science over the last century. However, much of our modern science and technology relies on materials with defects and disorders, and their three-dimensional (3D) atomic structures are not accessible to crystallography. One method capable of addressing this major challenge is atomic electron tomography. By combining advanced electron microscopes and detectors with powerful data analysis and tomographic reconstruction algorithms, it is now possible to determine the 3D atomic structure of crystal defects such as grain boundaries, stacking faults, dislocations, and point defects, as well as to precisely localize the 3D coordinates of individual atoms in materials without assuming crystallinity. Here we review the recent advances and the interdisciplinary science enabled by this methodology. We also outline further research needed for atomic electron tomography to address long-standing unresolved problems in the physical sciences.

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 diseases 1 – 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 processes 4 – 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 theory 1 , 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. Atomic electron tomography captures crystal nucleation in four dimensions in FePt nanoparticles, with the observed early-stage nucleation not consistent with classical nucleation theory.

Exchange bias is a property of widespread technological utility, but its underlying mechanism remains elusive, in part because it is rooted in the interaction of coexisting order parameters in the presence of complex magnetic disorder. Here we show that a giant exchange bias housed within a spin-glass phase arises in a disordered antiferromagnet. The magnitude and robustness of the exchange bias emerges from a convolution of two energetic landscapes, namely the highly degenerate landscape of the spin glass biased by the sublattice spin configuration of the antiferromagnet. The former provides a source of uncompensated moment, whereas the latter provides a mechanism for its pinning, which leads to the exchange bias. Tuning the relative strengths of the spin-glass and antiferromagnetic order parameters reveals a principle for tailoring the exchange bias, with potential applications to spintronic technologies.Coexistence of a spin-glass phase with antiferromagnetism in an intercalated crystal produces a large exchange bias effect. This is due to the interplay of disorder and frustration.

An understanding of how facets of a nanocrystal develop is critical for controlling nanocrystal shape and designing novel functional materials. However, the atomic pathways of nanocrystal facet development are mostly unknown because of the lack of direct observation. We report the imaging of platinum nanocube growth in a liquid cell using transmission electron microscopy with high spatial and temporal resolution. The growth rates of all low index facets are similar until the {100} facets stop growth. The continuous growth of the rest facets leads to a nanocube. Our calculation shows that the much lower ligand mobility on the {100} facets is responsible for the arresting of {100} growing facets. These findings shed light on nanocrystal shape-control mechanisms and future design of nanomaterials.

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 Zr 11 Te 50 structure containing a previously unobserved ZrTe 2 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. Transmission electron microscopy is essential for three-dimensional atomic structure determination, but solving complex heterogeneous structures containing light elements remains challenging. Here, authors solve a complex nanostructure using atomic resolution ptychographic electron tomography.

Knowledge about the synthesis, growth mechanisms, and physical properties of colloidal nanoparticles has been limited by technical impediments. We introduce a method for determining three-dimensional (3D) structures of individual nanoparticles in solution. We combine a graphene liquid cell, high-resolution transmission electron microscopy, a direct electron detector, and an algorithm for single-particle 3D reconstruction originally developed for analysis of biological molecules. This method yielded two 3D structures of individual platinum nanocrystals at near-atomic resolution. Because our method derives the 3D structure from images of individual nanoparticles rotating freely in solution, it enables the analysis of heterogeneous populations of potentially unordered nanoparticles that are synthesized in solution, thereby providing a means to understand the structure and stability of defects at the nanoscale.

The three-dimensional coordinates of more than 23,000 atoms in an iron-platinum nanoparticle are determined with 22 picometre precision to correlate chemical order/disorder and crystal defects with magnetic properties. Material properties at the single-atom level FePt nanoparticles have practical potential in fields as diverse as catalysis and magnetic storage media. But far from being pristine crystalline materials, these nanoparticles are structurally heterogeneous with grain boundaries and other crystal defects. In this paper, Jianwei Miao and colleagues reveal the complex atomic-scale structure of a single FePt nanoparticle containing more than 22,000 atoms. They do this by generating a high-resolution tomographic tilt series of 68 images of the nanoparticle and reconstructing it using a new algorithm, achieving resolution with 22 picometre precision. The resulting structure reveals the complexity of the nanoparticle, and the chemistry and crystal structure of the grains within the material. When analysing the order/disorder character, the authors find that the grains are more ordered towards the core of the nanoparticle and less ordered towards the surface. They use data from the boundary between two grains to calculate local magnetocrystalline anisotropy energies using density functional theory, revealing how these energies vary across the grain with order parameter and across a grain boundary. 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 1 , 2 , 3 . Such disruption in periodicity strongly affects material properties and functionality 1 , 2 , 3 . Despite rapid development of quantitative material characterization methods 1 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 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 19 , 20 ; 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.

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.

Multicomponent nanocrystal superlattices represent an interesting class of material that derives emergent properties from mesoscale structure, yet their programmability can be limited by the alkyl-chain-based ligands decorating the surfaces of the constituent nanocrystals. Polymeric ligands offer distinct advantages, as they allow for more precise tuning of the effective size and ‘interaction softness’ through changes to the polymer’s molecular weight, chemical nature, architecture, persistence length and surrounding solvent. Here we show the formation of 10 different binary nanocrystal superlattices (BNSLs) with both two- and three-dimensional order through independent adjustment of the core size of spherical nanocrystals and the molecular weight of densely grafted polystyrene ligands. These polymer-brush-based ligands introduce new energetic contributions to the interparticle potential that stabilizes various BNSL phases across a range of length scales and interparticle spacings. Our study opens the door for nanocrystals to become modular elements in the design of functional particle brush solids with controlled nanoscale interfaces and mesostructures. Binary nanocrystal superlattice metamaterials are arousing significant interest due to their potential for use in functional devices. Here, the authors endow the nanoparticles with polymer brushes which enable control over their spacings and thus mesoscale structure and properties.