Transmission electron microscopy is a powerful imaging tool that has found broad application in materials science, nanoscience and biology. With the introduction of aberration-corrected electron lenses, both the spatial resolution and the image quality in transmission electron microscopy have been significantly improved and resolution below 0.5 ångströms has been demonstrated. To reveal the three-dimensional (3D) structure of thin samples, electron tomography is the method of choice, with cubic-nanometre resolution currently achievable. Discrete tomography has recently been used to generate a 3D atomic reconstruction of a silver nanoparticle two to three nanometres in diameter, but this statistical method assumes prior knowledge of the particle's lattice structure and requires that the atoms fit rigidly on that lattice. Here we report the experimental demonstration of a general electron tomography method that achieves atomic-scale resolution without initial assumptions about the sample structure. By combining a novel projection alignment and tomographic reconstruction method with scanning transmission electron microscopy, we have determined the 3D structure of an approximately ten-nanometre gold nanoparticle at 2.4-ångström resolution. Although we cannot definitively locate all of the atoms inside the nanoparticle, individual atoms are observed in some regions of the particle and several grains are identified in three dimensions. The 3D surface morphology and internal lattice structure revealed are consistent with a distorted icosahedral multiply twinned particle. We anticipate that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic-scale resolution, but also to improve the spatial resolution and image quality in other tomography fields.

Dislocations and their interactions strongly influence many material properties, ranging from the strength of metals and alloys to the efficiency of light-emitting diodes and laser diodes. Several experimental methods can be used to visualize dislocations. Transmission electron microscopy (TEM) has long been used to image dislocations in materials, and high-resolution electron microscopy can reveal dislocation core structures in high detail, particularly in annular dark-field mode. A TEM image, however, represents a two-dimensional projection of a three-dimensional (3D) object (although stereo TEM provides limited information about 3D dislocations). X-ray topography can image dislocations in three dimensions, but with reduced resolution. Using weak-beam dark-field TEM and scanning TEM, electron tomography has been used to image 3D dislocations at a resolution of about five nanometres (refs 15, 16). Atom probe tomography can offer higher-resolution 3D characterization of dislocations, but requires needle-shaped samples and can detect only about 60 per cent of the atoms in a sample. Here we report 3D imaging of dislocations in materials at atomic resolution by electron tomography. By applying 3D Fourier filtering together with equal-slope tomographic reconstruction, we observe nearly all the atoms in a multiply twinned platinum nanoparticle. We observed atomic steps at 3D twin boundaries and imaged the 3D core structure of edge and screw dislocations at atomic resolution. These dislocations and the atomic steps at the twin boundaries, which appear to be stress-relief mechanisms, are not visible in conventional two-dimensional projections. The ability to image 3D disordered structures such as dislocations at atomic resolution is expected to find applications in materials science, nanoscience, solid-state physics and chemistry.

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...