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Metal-oxide interfaces with poor coherency have unique properties comparing to the bulk materials and offer broad applications in the fields of 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 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. 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., Comment: 35 pages, 4 main figures, 17 Supplementary figures

Icosahedral nanoparticles composed of fivefold twinned tetrahedra have broad applications. The strain relief mechanism and angular deficiency in icosahedral multiply twinned particles are poorly understood in three dimensions. Here, we resolved the three-dimensional atomic structures of Janus icosahedral nanoparticles using atomic resolution electron tomography. A geometrically fivefold face consistently corresponds to a less ordered face like two hemispheres. We quantify rich structural variety of icosahedra including bond orientation order, bond length, strain tensor; and packing efficiency, atom number, solid angle of each tetrahedron. These structural characteristics exhibit two-sided distribution. Edge dislocations near the axial atoms and small disordered domains fill the angular deficiency. Our findings provide new insights how the fivefold symmetry can be compensated and the geometrically-necessary internal strains relived in multiply twinned particles., Comment: 30 pages, 5 figures

Medium- and high-entropy alloys (M/HEAs) mix multiple principal elements with near-equiatomic composition and represent a paradigm-shift strategy for designing new materials for metallurgy, catalysis, and other fields. One of the core hypotheses of M/HEAs is lattice distortion. However, experimentally determining the 3D local lattice distortion in M/HEAs remains a challenge. Additionally, the presumed random elemental mixing in M/HEAs has been questioned by atomistic simulations, energy dispersive x-ray spectroscopy (EDS), and electron diffraction, which suggest the existence of local chemical order in M/HEAs. However, the 3D local chemical order has eluded direct experimental observation since the EDS elemental maps integrate the composition of atomic columns along the zone axes, and the diffuse reflections/streaks in electron diffraction of M/HEAs may originate from planar defects. Here, we determine the 3D atomic positions of M/HEA nanocrystals using atomic electron tomography, and quantitatively characterize the local lattice distortion, strain tensor, twin boundaries, dislocation cores, and chemical short-range order (CSRO) with unprecedented 3D detail. We find that the local lattice distortion and strain tensor in the HEAs are larger and more heterogeneous than in the MEAs. We observe CSRO-mediated twinning in the MEAs. that is, twinning occurs in energetically unfavoured CSRO regions but not in energetically favoured CSRO ones. This observation confirms the atomistic simulation results of the bulk CrCoNi MEA and represents the first experimental evidence of correlating local chemical order with structural defects in any material system. We expect that this work will not only expand our fundamental understanding of this important class of materials, but also could provide the foundation for tailoring M/HEA properties through lattice distortion and local chemical order., Comment: 35 pages, 13 figures

Deciphering the three-dimensional atomic structure of solid-solid interfaces in core-shell nanomaterials is the key to understand their remarkable 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 successfully quantify the rich structural variety of core-shell nanoparticles including bond length, coordination number, local bond orientation order, grain boundary, and five-fold symmetry, all in 3D at atomic resolution. Instead of forming an atomically-sharp boundary, the core-shell interface is atomically diffuse with an average thickness of 4.2 A, irrespective of the particle's size, morphology, or crystallographic texture. The high concentration of Pd in the interface is highly related to the electric double layers of the Pd seeds. These results advance our understanding of core-shell structures at the fundamental level, providing potential strategies into nanomaterial manipulation and chemical property regulation., Comment: 41 pages, 18 figures

Alloy nanocatalysts have found broad applications ranging from fuel cells to catalytic converters and hydrogenation reactions. Despite extensive studies, identifying the active sites of nanocatalysts remains a major challenge due to the heterogeneity of the local atomic environment. Here, we advance atomic electron tomography to determine the 3D local atomic structure, surface morphology and chemical composition of PtNi and Mo-doped PtNi nanocatalysts. Using machine learning trained by density functional theory calculations, we identify the catalytic active sites for the oxygen reduction reaction from experimental 3D atomic coordinates, which are corroborated by electrochemical measurements. By quantifying the structure-activity relationship, we discover a local environment descriptor to explain and predict the catalytic active sites at the atomic level. The ability to determine the 3D atomic structure and chemical species coupled with machine learning is expected to expand our fundamental understanding of a wide range of nanocatalysts., Comment: 37 pages, 16 figures

Biominerals such as seashells, corals skeletons, bone, and enamel are optically anisotropic crystalline materials with unique nano- and micro-scale organization that translates into exceptional macroscopic mechanical properties, providing inspiration for engineering new and superior biomimetic structures. Here we use particles of Seriatopora aculeata coral skeleton as a model and demonstrate, for the first time, x-ray linear dichroic ptychography. We map the aragonite (CaCO3) crystal c-axis orientations in coral skeleton with 35 nm spatial resolution. Linear dichroic phase imaging at the O K-edge energy shows strong polarization-dependent contrast and reveals the presence of both narrow (< 35{\deg}) and wide (> 35{\deg}) c-axis angular spread in sub-micrometer coral particles. These x-ray ptychography results were corroborated using 4D scanning transmission electron nano-diffraction on the same particles. Evidence of co-oriented but disconnected corallite sub-domains indicates jagged crystal boundaries consistent with formation by amorphous nanoparticle attachment. Looking forward, we anticipate that x-ray linear dichroic ptychography can be applied to study nano-crystallites, interfaces, nucleation and mineral growth of optically anisotropic materials with sub-ten nanometers spatial resolution in three dimensions.

Liquids and solids are two fundamental states of matter. However, due to the lack of direct experimental determination, our understanding of the 3D atomic structure of liquids and amorphous solids remained speculative. Here we advance atomic electron tomography to determine for the first time the 3D atomic positions in monatomic amorphous materials, including 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 networks that extend to medium-range scale. Molecular dynamic simulations further reveal that pentagonal bipyramid networks are prevalent in monatomic amorphous liquids, which rapidly grow in size and form icosahedra during the quench from the liquid state to glass state. The experimental method and results are expected to advance the study of the amorphous-crystalline phase transition and glass transition at the single-atom level.

Nucleation plays a critical role in many physical and biological phenomena ranging from crystallization, melting and evaporation to the formation of clouds and the initiation of neurodegenerative diseases. However, nucleation is a challenging process to study in experiments especially in the early stage when several atoms/molecules start to form a new phase from its parent phase. Here, we advance atomic electron tomography to study early stage nucleation at 4D atomic resolution. Using FePt nanoparticles as a model system, we reveal that early stage nuclei are irregularly shaped, each has a core of one to 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 differ from classical nucleation theory (CNT) and to explain them we propose the order parameter gradient (OPG) model. We show the OPG model generalizes CNT and energetically favours diffuse interfaces for small nuclei and sharp interfaces for large nuclei. We further corroborate this model using molecular dynamics simulations of heterogeneous and homogeneous nucleation in liquid-solid phase transitions of Pt. We anticipate that the OPG model is applicable to different nucleation processes and our experimental method opens the door to study the structure and dynamics of materials with 4D atomic resolution., Comment: 42 pages, 5 figures, 12 supplementary figures and one supplementary table

Correlating 3D arrangements of atoms and defects with material properties and functionality forms the core of several scientific disciplines. Here, we determined the 3D coordinates of 6,569 iron and 16,627 platinum atoms in a model iron-platinum nanoparticle system to correlate 3D atomic arrangements and chemical order/disorder with material properties at the single-atom level. We identified rich structural variety and chemical order/disorder including 3D atomic composition, grain boundaries, anti-phase boundaries, anti-site point defects and swap defects. We show for the first time that experimentally measured 3D atomic coordinates and chemical species with 22 pm precision can be used as direct input for first-principles calculations of material properties such as atomic magnetic moments and local magnetocrystalline anisotropy. This work not only opens the door to determining 3D atomic arrangements and chemical order/disorder of a wide range of nanostructured materials with high precision, but also will transform our understanding of structure-property relationships at the most fundamental level., Comment: 21 pages, 4 figures