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The resolution of transmission electron microscopes allows the imaging of single atoms and determination of their locations in a plane. Here, the authors present a tomographic method to recover the three-dimensional shape of a crystalline particle without the need for sample rotation.

Intensities in high-resolution phase-contrast images from electron microscopes build up discretely in time by detecting single electrons. A wave description of pulse-like coherent-inelastic interaction of an electron with matter implies a time-dependent coexistence of coherent partial waves. Their superposition forms a wave package by phase decoherence of 0.5 - 1 radian with Heisenbergs energy uncertainty ΔEH = ħ/2 Δt-1 matching the energy loss ΔE of a coherent-inelastic interaction and sets the interaction time Δt. In these circumstances, the product of Planck's constant and the speed of light hc is given by the product of the expression for temporal coherence λ2/Δλ and the energy loss ΔE. Experimentally, the self-coherence length was measured by detecting the energy-dependent localization of scattered, plane matter waves in surface proximity exploiting the Goos-Hänchen shift. Chromatic-aberration Cc-corrected electron microscopy on boron nitride (BN) proves that the coherent crystal illumination and phase contrast are lost if the self-coherence length shrinks below the size of the crystal unit cell at ΔE > 200 eV. In perspective, the interaction time of any matter wave compares with the lifetime of a virtual particle of any elemental interaction, suggesting the present concept of coherent-inelastic interactions of matter waves might be generalizable., Competing Interests: Conflict of Interest. The authors declare that they have no competing interest., (Published by Oxford University Press on behalf of the Microscopy Society of America 2024.)

The relation between the energy-dependent particle and wave descriptions of electron-matter interactions on the nanoscale was analyzed by measuring the delocalization of an evanescent field from energy-filtered amplitude images of sample/vacuum interfaces with a special aberration-corrected electron microscope. The spatial field extension coincided with the energy-dependent self-coherence length of propagating wave packets that obeyed the time-dependent Schrödinger equation, and underwent a Goos-Hänchen shift. The findings support the view that wave packets are created by self-interferences during coherent-inelastic Coulomb interactions with a decoherence phase close to Δ φ = 0.5 rad. Due to a strictly reciprocal dependence on energy, the wave packets shrink below atomic dimensions for electron energy losses beyond 1000 eV, and thus appear particle-like. Consequently, our observations inevitably include pulse-like wave propagations that stimulate structural dynamics in nanomaterials at any electron energy loss, which can be exploited to unravel time-dependent structure-function relationships on the nanoscale.

Modifiers are commonly used in natural, biological, and synthetic crystallization to tailor the growth of diverse materials. Here, we identify tautomers as a new class of modifiers where the dynamic interconversion between solute and its corresponding tautomer(s) produces native crystal growth inhibitors. The macroscopic and microscopic effects imposed by inhibitor-crystal interactions reveal dual mechanisms of inhibition where tautomer occlusion within crystals that leads to natural bending, tunes elastic modulus, and selectively alters the rate of crystal dissolution. Our study focuses on ammonium urate crystallization and shows that the keto-enol form of urate, which exists as a minor tautomer, is a potent inhibitor that nearly suppresses crystal growth at select solution alkalinity and supersaturation. The generalizability of this phenomenon is demonstrated for two additional tautomers with relevance to biological systems and pharmaceuticals. These findings offer potential routes in crystal engineering to strategically control the mechanical or physicochemical properties of tautomeric materials., (© 2023. The Author(s).)

Advances in electron microscopy have enabled visualizations of the three-dimensional (3D) atom arrangements in nano-scale objects. The observations are, however, prone to electron-beam-induced object alterations, so tracking of single atoms in space and time becomes key to unravel inherent structures and properties. Here, we introduce an analytical approach to quantitatively account for atom dynamics in 3D atomic-resolution imaging. The approach is showcased for a Co-Mo-S nanocrystal by analysis of time-resolved in-line holograms achieving ~1.5 Å resolution in 3D. The analysis reveals a decay of phase image contrast towards the nanocrystal edges and meta-stable edge motifs with crystallographic dependence. These findings are explained by beam-stimulated vibrations that exceed Debye-Waller factors and cause chemical transformations at catalytically relevant edges. This ability to simultaneously probe atom vibrations and displacements enables a recovery of the pristine Co-Mo-S structure and establishes, in turn, a foundation to understand heterogeneous chemical functionality of nanostructures, surfaces and molecules., (© 2021. The Author(s).)

This article summarizes core aspects of beam-sample interactions in research that aims at exploiting the ability to detect single atoms at atomic resolution by mid-voltage transmission electron microscopy. Investigating the atomic structure of catalytic Co 3 O 4 nanocrystals underscores how indispensable it is to rigorously control electron dose rates and total doses to understand native material properties on this scale. We apply in-line holography with variable dose rates to achieve this goal. Genuine object structures can be maintained if dose rates below ~100 e/Å 2 s are used and the contrast required for detection of single atoms is generated by capturing large image series. Threshold doses for the detection of single atoms are estimated. An increase of electron dose rates and total doses to common values for high resolution imaging of solids stimulates object excitations that restructure surfaces, interfaces, and defects and cause grain reorientation or growth. We observe a variety of previously unknown atom configurations in surface proximity of the Co 3 O 4 spinel structure. These are hidden behind broadened diffraction patterns in reciprocal space but become visible in real space by solving the phase problem. An exposure of the Co 3 O 4 spinel structure to water vapor or other gases induces drastic structure alterations that can be captured in this manner.

It is now established that the 3D structure of homogeneous nanocrystals can be recovered from in-line hologram of single projections. The method builds on a quantitative contrast interpretation of electron exit wave functions. Since simulated exit wave functions of single and bilayers of graphene reveal the atomic structure of carbon-based materials with sufficient resolution, we explore theoretically how the approach can be expanded beyond periodic carbon-based materials to include non-periodic molecular structures. We show here theoretically that the 3D atomic structure of randomly oriented oleic acid molecules can be recovered from a single projection.

Resolution and sensitivity of the latest generation aberration-corrected transmission electron microscopes allow the vast majority of single atoms to be imaged with sub-Ångstrom resolution and their locations determined in an image plane with a precision that exceeds the 1.9-pm wavelength of 300 kV electrons. Such unprecedented performance allows expansion of electron microscopic investigations with atomic resolution into the third dimension. Here we report a general tomographic method to recover the three-dimensional shape of a crystalline particle from high-resolution images of a single projection without the need for sample rotation. The method is compatible with low dose rate electron microscopy, which improves on signal quality, while minimizing electron beam-induced structure modifications even for small particles or surfaces. We apply it to germanium, gold and magnesium oxide particles, and achieve a depth resolution of 1-2 Å, which is smaller than inter-atomic distances.

The atomic structure of graphene edges is critical in determining the electrical, magnetic and chemical properties of truncated graphene structures, notably nanoribbons. Unfortunately, graphene edges are typically far from ideal and suffer from atomic-scale defects, structural distortion and unintended chemical functionalization, leading to unpredictable properties. Here we report that graphene edges fabricated by electron beam-initiated mechanical rupture or tearing in high vacuum are clean and largely atomically perfect, oriented in either the armchair or zigzag direction. We demonstrate, via aberration-corrected transmission electron microscopy, reversible and extended pentagon-heptagon (5-7) reconstruction at zigzag edges, and explore experimentally and theoretically the dynamics of the transitions between configuration states. Good theoretical-experimental agreement is found for the flipping rates between 5-7 and 6-6 zigzag edge states. Our study demonstrates that simple ripping is remarkably effective in producing atomically clean, ideal terminations, thus providing a valuable tool for realizing atomically tailored graphene and facilitating meaningful experimental study.

The TEAM 0.5 electron microscope is employed to demonstrate atomic resolution phase contrast imaging and focal series reconstruction with acceleration voltages between 20 and 300 kV and a variable dose rate. A monochromator with an energy spread of ≤0.1 eV is used for dose variation by a factor of 1,000 and to provide a beam-limiting aperture. The sub-Ångstrøm performance of the instrument remains uncompromised. Using samples obtained from silicon wafers by chemical etching, the [200] atom dumbbell distance of 1.36 Å can be resolved in single images and reconstructed exit wave functions at 300, 80, and 50 kV. At 20 kV, atomic resolution <2 Å is readily available but limited by residual lens aberrations at large scattering angles. Exit wave functions reconstructed from images recorded under low dose rate conditions show sharper atom peaks as compared to high dose rate. The observed dose rate dependence of the signal is explained by a reduction of beam-induced atom displacements. If a combined sample and instrument instability is considered, the experimental image contrast can be matched quantitatively to simulations. The described development allows for atomic resolution transmission electron microscopy of interfaces between soft and hard materials over a wide range of voltages and electron doses.

The study of first-order structural transformations has been of great interest to scientists in many disciplines. Expectations from phase-transition theory are that the system fluctuates between two equilibrium structures near the transition point and that the region of transition broadens in small crystals. We report the direct observation of structural fluctuations within a single nanocrystal using transmission electron microscopy. We observed trajectories of structural transformations in individual nanocrystals with atomic resolution, which reveal details of the fluctuation dynamics, including nucleation, phase propagation, and pinning of structural domains by defects. Such observations provide crucial insight for the understanding of microscopic pathways of phase transitions.

Understanding of colloidal nanocrystal growth mechanisms is essential for the syntheses of nanocrystals with desired physical properties. The classical model for the growth of monodisperse nanocrystals assumes a discrete nucleation stage followed by growth via monomer attachment, but has overlooked particle-particle interactions. Recent studies have suggested that interactions between particles play an important role. Using in situ transmission electron microscopy, we show that platinum nanocrystals can grow either by monomer attachment from solution or by particle coalescence. Through the combination of these two processes, an initially broad size distribution can spontaneously narrow into a nearly monodisperse distribution. We suggest that colloidal nanocrystals take different pathways of growth based on their size- and morphology-dependent internal energies.

Although the physics of materials at surfaces and edges has been extensively studied, the movement of individual atoms at an isolated edge has not been directly observed in real time. With a transmission electron aberration-corrected microscope capable of simultaneous atomic spatial resolution and 1-second temporal resolution, we produced movies of the dynamics of carbon atoms at the edge of a hole in a suspended, single atomic layer of graphene. The rearrangement of bonds and beam-induced ejection of carbon atoms are recorded as the hole grows. We investigated the mechanism of edge reconstruction and demonstrated the stability of the "zigzag" edge configuration. This study of an ideal low-dimensional interface, a hole in graphene, exhibits the complex behavior of atoms at a boundary.

The ability of electron microscopes to analyze all the atoms in individual nanostructures is limited by lens aberrations. However, recent advances in aberration-correcting electron optics have led to greatly enhanced instrument performance and new techniques of electron microscopy. The development of an ultrastable electron microscope with aberration-correcting optics and a monochromated high-brightness source has significantly improved instrument resolution and contrast. In the present work, we report information transfer beyond 50 pm and show images of single gold atoms with a signal-to-noise ratio as large as 10. The instrument's new capabilities were exploited to detect a buried Sigma3 {112} grain boundary and observe the dynamic arrangements of single atoms and atom pairs with sub-angstrom resolution. These results mark an important step toward meeting the challenge of determining the three-dimensional atomic-scale structure of nanomaterials.

It is known that fractures are more likely to occur in altered teeth, particularly following restoration or endodontic repair; consequently, it is important to understand the structure of altered forms of dentin, the most abundant tissue in the human tooth, in order to better define the increased propensity for such fractures. Transparent (or sclerotic) dentin, wherein the dentinal tubules become occluded with mineral as a natural progressive consequence of aging, is one such altered form. In the present study, high-resolution transmission electron microscopy is used to investigate the effect of aging on the mineral phase of dentin. Such studies revealed that the intertubular mineral crystallites were smaller in transparent dentin, and that the intratubular mineral (larger crystals deposited within the tubules) was chemically similar to the surrounding intertubular mineral. Exit-wave reconstructed lattice-plane images suggested that the intratubular mineral had nanometer-size grains. These observations support a "dissolution and reprecipitation" mechanism for the formation of transparent dentin.

Bicrystalline nanowires of hematite (alpha-Fe(2)O(3)) have been successfully synthesized by the oxidation of pure iron. The product was characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy (TEM), high-resolution TEM in combination with focal series reconstruction, energy-dispersive X-ray spectroscopy, and electron energy-loss spectroscopy. The bicrystalline nanowires have diameters of 20-80 nm and lengths up to 20 microm. All of the investigated materials are found to be alpha-Fe(2)O(3) with a rhombohedral crystal structure. Investigations indicate that most of the bicrystalline nanowires are nanotwins with ellipsoidal heads. The orientation relationship between the nanotwins can be described as (110)(M)//(110)(T), [110](M)//[0](T). An energy-filtered TEM investigation indicates that the ellipsoidal head is iron-rich. The growth mechanism of such unique nanostructures is considered to be a solid-phase growth via surface and internal diffusions of molecules from base to tip.

Direct atomic resolution images have been obtained that illustrate how a range of rare-earth atoms bond to the interface between the intergranular phase and the matrix grains in an advanced silicon nitride ceramic. It has been found that each rare-earth atom bonds to the interface at a different location, depending on atom size, electronic configuration, and the presence of oxygen at the interface. This is the key factor to understanding the origin of the mechanical properties in these ceramics and will enable precise tailoring in the future to critically improve the materials' performance in wide-ranging applications.

High-resolution transmission electron microscopy (HR-TEM) has been used as the ultimate method of thickness measurement for thin films. The appearance of phase contrast interference patterns in HR-TEM images has long been confused as the appearance of a crystal lattice by nonspecialists. Relatively easy to interpret crystal lattice images are now directly observed with the introduction of annular dark-field detectors for scanning TEM (STEM). With the recent development of reliable lattice image processing software that creates crystal structure images from phase contrast data, HR-TEM can also provide crystal lattice images. The resolution of both methods has been steadily improved reaching now into the sub-Angstrom region. Improvements in electron lens and image analysis software are increasing the spatial resolution of both methods. Optimum resolution for STEM requires that the probe beam be highly localized. In STEM, beam localization is enhanced by selection of the correct aperture. When STEM measurement is done using a highly localized probe beam, HR-TEM and STEM measurement of the thickness of silicon oxynitride films agree within experimental error. In this article, the optimum conditions for HR-TEM and STEM measurement are discussed along with a method for repeatable film thickness determination. The impact of sample thickness is also discussed. The key result in this article is the proposal of a reproducible method for film thickness determination.