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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

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