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Heterogeneous nanocatalysts play a crucial role in both the chemical and energy industries. Despite substantial advancements in theoretical, computational and experimental studies, identifying their active sites remains a major challenge. Here we utilize atomic electron tomography to determine the three-dimensional atomic structure of PtNi and Mo-doped PtNi nanocatalysts for the electrochemical oxygen reduction reaction. We then employ the experimental atomic structures as input to first-principles-trained machine learning to identify the active sites of the nanocatalysts. Through the analysis of the structure–activity relationships, we formulate an equation termed the local environment descriptor, which balances the strain and ligand effects to provide physical and chemical insights into active sites in the oxygen reduction reaction. The ability to determine the three-dimensional atomic structure and chemical composition of realistic nanoparticles, combined with machine learning, could transform our fundamental understanding of the active sites of catalysts and guide the rational design of optimal nanocatalysts. (Figure presented.)

Deciphering the three-dimensional atomic structure of solid-solid interfaces in core-shell nanomaterials is the key to understand their catalytical, optical and electronic properties. Here, we probe the three-dimensional atomic structures of palladium-platinum core-shell nanoparticles at the single-atom level using atomic resolution electron tomography. We quantify the rich structural variety of core-shell nanoparticles with heteroepitaxy in 3D at atomic resolution. Instead of forming an atomically-sharp boundary, the core-shell interface is found to be atomically diffuse with an average thickness of 4.2 Å, irrespective of the particle's morphology or crystallographic texture. The high concentration of Pd in the diffusive interface is highly related to the free Pd atoms dissolved from the Pd seeds, which is confirmed by atomic images of Pd and Pt single atoms and sub-nanometer clusters using cryogenic electron microscopy. These results advance our understanding of core-shell structures at the fundamental level, providing potential strategies into precise nanomaterial manipulation and chemical property regulation.

Liquids and solids are two fundamental states of matter. However, our understanding of their three-dimensional atomic structure is mostly based on physical models. Here we use atomic electron tomography to experimentally determine the three-dimensional atomic positions of monatomic amorphous solids, namely a Ta thin film and two Pd nanoparticles. We observe that pentagonal bipyramids are the most abundant atomic motifs in these amorphous materials. Instead of forming icosahedra, the majority of pentagonal bipyramids arrange into pentagonal bipyramid networks with medium-range order. Molecular dynamics simulations further reveal that pentagonal bipyramid networks are prevalent in monatomic metallic liquids, which rapidly grow in size and form more icosahedra during the quench from the liquid to the glass state. These results expand our understanding of the atomic structures of amorphous solids and will encourage future studies on amorphous-crystalline phase and glass transitions in non-crystalline materials with three-dimensional atomic resolution.

Liquids and solids are two fundamental states of matter. However, our understanding of their three-dimensional atomic structure is mostly based on physical models. Here we use atomic electron tomography to experimentally determine the three-dimensional atomic positions of monatomic amorphous solids, namely a Ta thin film and two Pd nanoparticles. We observe that pentagonal bipyramids are the most abundant atomic motifs in these amorphous materials. Instead of forming icosahedra, the majority of pentagonal bipyramids arrange into pentagonal bipyramid networks with medium-range order. Molecular dynamics simulations further reveal that pentagonal bipyramid networks are prevalent in monatomic metallic liquids, which rapidly grow in size and form more icosahedra during the quench from the liquid to the glass state. These results expand our understanding of the atomic structures of amorphous solids and will encourage future studies on amorphous-crystalline phase and glass transitions in non-crystalline materials with three-dimensional atomic resolution.

Amorphous solids such as glass, plastics and amorphous thin films are ubiquitous in our daily life and have broad applications ranging from telecommunications to electronics and solar cells1-4. However, owing to the lack of long-range order, the three-dimensional (3D) atomic structure of amorphous solids has so far eluded direct experimental determination5-15. Here we develop an atomic electron tomography reconstruction method to experimentally determine the 3D atomic positions of an amorphous solid. Using a multi-component glass-forming alloy as proof of principle, we quantitatively characterize the short- and medium-range order of the 3D atomic arrangement. We observe that, although the 3D atomic packing of the short-range order is geometrically disordered, some short-range-order structures connect with each other to form crystal-like superclusters and give rise to medium-range order. We identify four types of crystal-like medium-range order-face-centred cubic, hexagonal close-packed, body-centred cubic and simple cubic-coexisting in the amorphous sample, showing translational but not orientational order. These observations provide direct experimental evidence to support the general framework of the efficient cluster packing model for metallic glasses10,12-14,16. We expect that this work will pave the way for the determination of the 3D structure of a wide range of amorphous solids, which could transform our fundamental understanding of non-crystalline materials and related phenomena.

Biominerals such as seashells, coral skeletons, bone, and tooth enamel are optically anisotropic crystalline materials with unique nanoscale and microscale organization that translates into exceptional macroscopic mechanical properties, providing inspiration for engineering new and superior biomimetic structures. Using Seriatopora aculeata coral skeleton as a model, here, we experimentally demonstrate X-ray linear dichroic ptychography and map the c-axis orientations of the aragonite (CaCO3) crystals. Linear dichroic phase imaging at the oxygen K-edge energy shows strong polarization-dependent contrast and reveals the presence of both narrow (35°) c-axis angular spread in the coral samples. These X-ray ptychography results are corroborated by four-dimensional (4D) scanning transmission electron microscopy (STEM) on the same samples. Evidence of co-oriented, but disconnected, corallite subdomains indicates jagged crystal boundaries consistent with formation by amorphous nanoparticle attachment. We expect that the combination of X-ray linear dichroic ptychography and 4D STEM could be an important multimodal tool to study nano-crystallites, interfaces, nucleation, and mineral growth of optically anisotropic materials at multiple length scales.

Next-generation nano- and quantum devices have increasingly complex 3D structure. As the dimensions of these devices shrink to the nanoscale, their performance is often governed by interface quality or precise chemical or dopant composition. Here, we present the first phase-sensitive extreme ultraviolet imaging reflectometer. It combines the excellent phase stability of coherent high-harmonic sources, the unique chemical sensitivity of extreme ultraviolet reflectometry, and state-of-the-art ptychography imaging algorithms. This tabletop microscope can nondestructively probe surface topography, layer thicknesses, and interface quality, as well as dopant concentrations and profiles. High-fidelity imaging was achieved by implementing variable-angle ptychographic imaging, by using total variation regularization to mitigate noise and artifacts in the reconstructed image, and by using a high-brightness, high-harmonic source with excellent intensity and wavefront stability. We validate our measurements through multiscale, multimodal imaging to show that this technique has unique advantages compared with other techniques based on electron and scanning probe microscopies.

Through numerical simulations, we demonstrate the combination of ptychography and atomic electron tomography as an effective method for low dose imaging of individual low-Z atoms in three dimensions. After generating noisy diffraction patterns with multislice simulations of an aberration-corrected scanning transmission electron microscope through a 5-nm zinc-oxide nanoparticle, we have achieved three-dimensional (3D) imaging of individual zinc and oxygen atoms and their defects by performing tomography on ptychographic projections. The methodology has also been simulated in 2D materials, resolving individual sulfur atoms in vertical WS2/WSe2 van der Waals heterostructure with a low total electron dose where annular-dark-field images fail to resolve. We envision that the development of this method could be instrumental in studying the precise 3D atomic structures of radiation sensitive systems and low-Z atomic structures such as 2D heterostructures, catalysts, functional oxides, and glasses.

Atomic electron tomography (AET) has become a powerful tool for atomic-scale structural characterization in three and four dimensions. It provides the ability to correlate structures and properties of materials at the single-atom level. With recent advances in data acquisition methods, iterative three-dimensional (3D) reconstruction algorithms, and post-processing methods, AET can now determine 3D atomic coordinates and chemical species with sub-Angstrom precision, and reveal their atomic-scale time evolution during dynamical processes. Here, we review the recent experimental and algorithmic developments of AET and highlight several groundbreaking experiments, which include pinpointing the 3D atom positions and chemical order/disorder in technologically relevant materials and capturing how atoms rearrange during early nucleation at four-dimensional atomic resolution.

Multimodal microscopy that combines complementary nanoscale imaging techniques is critical for extracting comprehensive chemical, structural, and functional information, particularly for heterogeneous samples. X-ray microscopy can achieve high-resolution imaging of bulk materials with chemical, magnetic, electronic, and bond orientation contrast, while electron microscopy provides atomic-scale spatial resolution with quantitative elemental composition. Here, we combine x-ray ptychography and scanning transmission x-ray spectromicroscopy with three-dimensional energy-dispersive spectroscopy and electron tomography to perform structural and chemical mapping of an Allende meteorite particle with 15-nm spatial resolution. We use textural and quantitative elemental information to infer the mineral composition and discuss potential processes that occurred before or after accretion. We anticipate that correlative x-ray and electron microscopy overcome the limitations of individual imaging modalities and open up a route to future multiscale nondestructive microscopies of complex functional materials and biological systems.

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.

Multiple twinning to form fivefold twinned nanoparticles in crystal growth is common and has attracted broad attention ranging from crystallography research to physical chemistry and materials science. Lattice-misfit strain and defects in multiple twinned nanoparticles (MTP) are key to understand and tailor their electronic properties. However, the structural defects and related strain distributions in MTPs are poorly understood in three dimensions (3D). Here, we show the 3D atomic misfit and strain relief mechanism in fivefold twinned icosahedral nanoparticles with amorphization and dislocations by using atomic resolution electron tomography. We discover a two-sided heterogeneity in variety of structural characteristics. A nearly ideal crystallographic fivefold face is always found opposite to a less ordered face, forming Janus-like icosahedral nanoparticles with two distinct hemispheres. The disordered amorphous domains release a large amount of strain. Molecular dynamics simulations further reveal the Janus-like icosahedral nanoparticles are prevalent in the MTPs formed in liquid-solid phase transition. This work provides insights on the atomistic models for the modelling of formation mechanisms of fivefold twinned structures and computational simulations of lattice distortions and defects. We anticipate it will inspire future studies on fundamental problems such as twin boundary migration and kinetics of structures in 3D at atomic level. The crystallographically forbidden fivefold symmetry in icosahedra remains a long-standing mystery. Here, the authors resolve the three-dimensional atomic structure of Janus-like icosahedral nanoparticles with atomic resolution by electron tomography. [ABSTRACT FROM AUTHOR]

Amorphous materials such as glass, polymer and amorphous alloy have broad applications ranging from daily life to extreme conditions due to their unique properties in elasticity, strength and electrical resistivity. A better understanding of atomic structure of amorphous materials will provide invaluable information for their further engineering and applications. However, experimentally determining the three-dimensional (3D) atomic structure of amorphous materials has been a long-standing problem. Due to the disordered atomic arrangement, amorphous materials do not have any translational and rotational symmetry at long-range scale. Conventional characterization methods, such as the scattering and the microscopy imaging, can only provide the statistic structural information which is averaged over the macroscopic region. The knowledge of the 3D atomic structure of amorphous materials is limited. Recently atomic resolution electron tomography (AET) has proven an increasingly powerful tool for atomic scale structural characterization without any crystalline assumptions, which opens a door to determine the 3D structure of various amorphous materials. In this review, we summarize the state-of-art characterization methods for the exploration of atomic structures of amorphous materials in the past few decades, including X-ray/neutron diffraction, nano-beam and angstrom-beam electron diffraction, fluctuation electron microscopy, high-resolution scanning/transmission electron microscopy, and atom probe tomography. From experimental data and theoretical descriptions, 3D structures of various amorphous materials have been built up. Particularly, we introduce the principles and recent progress of AET, and highlight the most recent groundbreaking feat accomplished by AET, i.e., the first experimental determination of all 3D atomic positions in a multi-component glass-forming alloy and the 3D atomic packing in amorphous solids. We also discuss the new opportunities and challenges for characterizing the chemical and structural defects in amorphous materials.

We report quantitative characterization of the high temperature oxidation process by using electron tomography and energy-dispersive X-ray spectroscopy. As a proof of principle, we performed 3D imaging of the oxidation layer of a model system (Mo3Si) at nanoscale resolution with elemental specificity and probed the oxidation kinetics as a function of the oxidation time and the elevated temperature. Our tomographic reconstructions provide detailed 3D structural information of the surface oxidation layer of the Mo3Si system, revealing the evolution of oxidation behavior of Mo3Si from early stage to mature stage. Based on the relative rate of oxidation of Mo3Si, the volatilization rate of MoO3 and reactive molecular dynamics simulations, we propose a model to explain the mechanism of the formation of the porous silica structure during the oxidation process of Mo3Si. We expect that this 3D quantitative characterization method can be applied to other material systems to probe their structure-property relationships in different environments.

Tomography has made a radical impact on diverse fields ranging from the study of 3D atomic arrangements in matter to the study of human health in medicine. Despite its very diverse applications, the core of tomography remains the same, that is, a mathematical method must be implemented to reconstruct the 3D structure of an object from a number of 2D projections. Here, we present the mathematical implementation of a tomographic algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE), for high-resolution 3D reconstruction from a limited number of 2D projections. GENFIRE first assembles a 3D Fourier grid with oversampling and then iterates between real and reciprocal space to search for a global solution that is concurrently consistent with the measured data and general physical constraints. The algorithm requires minimal human intervention and also incorporates angular refinement to reduce the tilt angle error. We demonstrate that GENFIRE can produce superior results relative to several other popular tomographic reconstruction techniques through numerical simulations and by experimentally reconstructing the 3D structure of a porous material and a frozen-hydrated marine cyanobacterium. Equipped with a graphical user interface, GENFIRE is freely available from our website and is expected to find broad applications across different disciplines.

Unravelling the influence of strain and geometric effects on the electrochemical reduction of carbon dioxide (CO2RR) on Cu-based (or Pd-based) alloys remains challenging due to complex local microenvironment variables. Herein, we employ two PdCu alloys (nanoparticles and nanodendrites) to demonstrate how CO2RR selectivity can shift from CO to HCOO−. Despite sharing consistent phases, exposed crystal facets, and overall oxidative states, these alloys exhibit different local strain profiles due to their distinct geometries. By integrating experimental data, in-situ spectroscopy, and density functional theory calculations, we revealed that CO2 prefers adsorption on tensile-strained areas with carbon-side geometry, following a *COOH-to-CO pathway. Conversely, on some compressive-strained regions induced by the dendrite-like morphology, CO2 adopts an oxygen-side geometry, favoring an *OCHO-to-HCOO pathway due to the downshift of the d -band center. Notably, our findings elucidate a dominant *OCHO-to-HCOO− pathway in catalysts when featuring both adsorption geometries. This research provides a comprehensive model for local environment of bimetallic alloys, and establishes a clear relationship between the CO2RR pathway shift and variation in local strain environments of PdCu alloys. [ABSTRACT FROM AUTHOR]

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.

Metal-oxide interfaces with poor coherency have specific properties comparing to bulk materials and offer broad applications in heterogeneous catalysis, battery, and electronics. However, current understanding of the three-dimensional (3D) atomic metal-oxide interfaces remains limited because of their inherent structural complexity and the limitations of conventional two-dimensional imaging techniques. Here, we determine the 3D atomic structure of metal-oxide interfaces in zirconium-zirconia nanoparticles using atomic-resolution electron tomography. We quantitatively analyze the atomic concentration and the degree of oxidation, and find the coherency and translational symmetry of the interfaces are broken. Atoms at the interface have low structural ordering, low coordination, and elongated bond length. Moreover, we observe porous structures such as Zr vacancies and nano-pores, and investigate their distribution. Our findings provide a clear 3D atomic picture of metal-oxide interface with direct experimental evidence. We anticipate this work could encourage future studies on fundamental problems of oxides, such as interfacial structures in semiconductor and atomic motion during oxidation process. A detailed understanding of metal-oxide interfaces is essential for uncovering their intrinsic properties. Here, the authors investigate the 3D atomic structure of metal-oxide interfaces in Zr-ZrO2 nanoparticles using atomic-resolution electron tomography. [ABSTRACT FROM AUTHOR]