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Scanning transmission electron microscopy (STEM) is widely used for imaging, diffraction, and spectroscopy of materials down to atomic resolution. Recent advances in detector technology and computational methods have enabled many experiments that record a full image of the STEM probe for many probe positions, either in diffraction space or real space. In this paper, we review the use of these four-dimensional STEM experiments for virtual diffraction imaging, phase, orientation and strain mapping, measurements of medium-range order, thickness and tilt of samples, and phase contrast imaging methods, including differential phase contrast, ptychography, and others.

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.

Structure plays a vital role in determining materials properties. In lithium ion cathode materials, the crystal structure defines the dimensionality and connectivity of interstitial sites, thus determining lithium ion diffusion kinetics. In most conventional cathode materials that are well-ordered, the average structure as seen in diffraction dictates the lithium ion diffusion pathways. Here, we show that this is not the case in a class of recently discovered high-capacity lithium-excess rocksalts. An average structure picture is no longer satisfactory to understand the performance of such disordered materials. Cation short-range order, hidden in diffraction, is not only ubiquitous in these long-range disordered materials, but fully controls the local and macroscopic environments for lithium ion transport. Our discovery identifies a crucial property that has previously been overlooked and provides guidelines for designing and engineering cation-disordered cathode materials.

Traditional metallic alloys are mixtures of elements where the atoms of minority species tend to distribute randomly if they are below their solubility limit, or lead to the formation of secondary phases if they are above it. Recently, the concept of medium/high entropy alloys (MEA/HEA) has expanded this view, as these materials are single-phase solid solutions of generally equiatomic mixtures of metallic elements that have been shown to display enhanced mechanical properties. However, the question has remained as to how random these solid solutions actually are, with the influence of chemical short-range order (SRO) suggested in computational simulations but not seen experimentally. Here we report the first direct observation of SRO in the CrCoNi MEA using high resolution and energy-filtered transmission electron microscopy. Increasing amounts of SRO give rise to both higher stacking fault energy and hardness. These discoveries suggest that the degree of chemical ordering at the nanometer scale can be tailored through thermomechanical processing, providing a new avenue for tuning the mechanical properties of MEA/HEAs.

The mechanical properties of materials depend strongly on crystal structure and defect configuration. Here we measure the strength of suspended single-crystal and bicrystal graphene membranes prepared by chemical vapour deposition. Membranes of interest are first characterized by transmission electron microscopy and subsequently tested using atomic force microscopy. Single-crystal membranes prepared by chemical vapour deposition show strengths comparable to previous results of single-crystal membranes prepared by mechanical exfoliation. Grain boundaries with large mismatch angles in polycrystalline specimens have higher strengths than their low angle counterparts. Remarkably, these large angle grain boundaries show strength comparable to that of single-crystal graphene. To investigate this enhanced strength, we employ aberration-corrected high-resolution transmission electron microscopy to explicitly map the atomic-scale strain fields in suspended graphene. The high strength is attributed to the presence of low atomic-scale strain in the carbon-carbon bonds at the boundary.

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 1-3. 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. Over the years, a number of experimental and computational methods have been used to investigate nucleation processes 4-17 , but it remains unachievable to experimentally determine the 3D atomic structure and dynamics of early stage nuclei. Here, we develop 4D atomic electron tomography (AET) to study early stage nucleation at 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 a few atoms 2 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 differ from classical nucleation theory (CNT) 1,2,18 , indicating a theory beyond CNT is needed to describe early stage nucleation at the atomic scale. Looking forward, we anticipate that 4D AET opens the door to study 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 4D atomic resolution. AET is a powerful method to determine the 3D atomic structure of materials without the assumption of crystallinity 19 and has been applied to study dislocations, stacking faults, grain boundaries, atomic displacement, strain tensor, chemical order/disorder and point defects with unprecedented 3D detail 20-26. But all of these studies were of static structures. To probe the 4D atomic structure of early stage nucleation, we have tracked the same nuclei at different times and applied AET to determine their 3D atomic coordinates and species at each time (Methods). We used FePt nanoparticles as a model system because binary alloys have been widely used to study phase transitions 2 and FePt is a very promising material for next generation magnetic recording media 25,27. As-synthesized FePt nanoparticles form a chemically disordered face-centred cubic (fcc) structure (A1 phase) 27. With annealing, the A1 phase Author contributions J.M. conceived and directed the project; F.S. and H.Z. prepared the samples; J.Z.,

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...