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.

In 1959, Richard Feynman challenged the electron microscopy community to locate the positions of individual atoms in substances 3 . Over the last 55 years, significant advances have been made in electron microscopy. With the development of aberration-corrected electron optics 4,5 , scanning transmission electron microscopy (STEM) has reached sub-0.5 Å resolution in two dimensions 6 . In a combination of STEM 7-9 and a 3D image reconstruction method known as equal slope tomography (EST) 10,11 , electron tomography has achieved 2.4 Å resolution and was applied to image the 3D core structure of edge and screw dislocations at atomic resolution 12,13 . More recently, transmission electron microscopy (TEM) has been used to determine the 3D atomic structure of gold nanoparticles by averaging 939 particles 14 . Notwithstanding these important developments, Feynman's 1959 challenge  3D localization of the coordinates of individual atoms in a substance without using averaging or a priori knowledge of sample crystallinity  remains elusive. Here, we determine the 3D coordinates of 3,769 individual atoms in a tungsten needle sample with a precision of ~19 picometers and identify a point defect inside the sample in three dimensions. The acquisition of a high-quality tilt series with an aberration-corrected STEM and 3D EST reconstruction allow us to trace individual atomic coordinates from the reconstructed intensity and refine the 3D atomic model. direction from 0 to 180, a tilt series of 62 angles was acquired with equal slope increments ( Supplementary Fig. 1). The 0 (Fig. 1 inset) and 180 images of the tilt series are compared in Supplementary Fig. 2, indicating minimal change of the sample structure throughout the experiment. After correcting sample drift, scan distortion, and performing background subtraction on each image (Methods), the tilt series was aligned to a common rotation axis by a centre of mass method 12 . Only the apex of the needle ( Fig. 1 inset and Supplementary Fig. 1) was used for the EST reconstruction due to the 4 STEM depth of focus and to minimize dynamical scattering. Three different schemes were implemented to reconstruct our experimental data. First, a direct EST reconstruction was performed on the tilt series (termed the raw reconstruction). Second, 3DWiener filtering was applied to the raw reconstruction to reduce the noise 22 . Third, the tilt series images were denoised by a sparsity based algorithm 23 ( Supplementary Fig. 3) and then reconstructed by EST (Methods).The EST reconstruction provides an estimate of the intensity distribution inside the tungsten tip, and further analysis known as atom tracing is needed to determine atomic coordinates. We traced and verified the 3D positions of individual atoms using two independent reconstructions: one using Wiener filtering and the other using sparsity denoising (Methods). During atom tracing, a 3D Gaussian function was fit to each local intensity maximum in both reconstructions. Then, we screened each of these plausible atoms by its fi...

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Single element quasicrystalline monolayers were prepared by deposition of antimony and bismuth on the fivefold surface of icosahedral Al71.5Pd21Mn8.5 and the tenfold surface of decagonal Al71.8Ni14.8Co13.4. Elastic helium atom scattering and low energy electron diffraction of the monolayers show Bragg peaks at the bulk derived positions of the clean surfaces, revealing highly ordered quasicrystalline epitaxial films. Their adatom densities of (0.9+/-0.2)x10(15) cm(-2) and (0.8+/-0.2)x10(15) cm(-2) on Al-Pd-Mn and Al-Ni-Co, respectively, correspond to roughly one adatom per Al atom of the quasicrystalline substrate surfaces.

Highlights A new class of TiO2 nanofiber/red phosphorus (TiO2/RP) nanolayer core/shell heterostructure was fabricated by vaporization-deposition strategy. TiO2/RP exhibits enhanced photocatalytic pure water splitting performance. Decoration of RP extends the optical light harvesting ability.  P 5+ doping induced oxygen vacancies improve the charge separation efficiency.