Reciprocal Space Information Research Articles

Measurement of residual elastic strain in rolled-up amorphous nanomembranes using nanobeam electron diffraction

Amorphous nanomembranes play a crucial role in flexible electronics due to their ability to create intricate 3D structures through strain engineering. To better understand the formation of these structures, accurately mapping the local elastic strain distribution is essential. In this study, we conducted position-sensitive nanobeam electron diffraction investigations on various rolled-up amorphous nanomembranes. By analyzing the diffraction rings obtained from different locations on the amorphous samples, we extracted anisotropic structure information in reciprocal space and determined the local strain distributions in real space. Our analysis revealed that particle-assisted dry-released samples exhibited higher strain values than pure amorphous samples. This suggests that nanoparticles introduce additional strain through dewetting effects, thereby facilitating the formation of self-rolling 3D structures.

Direct observation of quadrupolar strain fields surrounding Eshelby inclusions in metallic glasses.

For decades, scanning/transmission electron microscopy (S/TEM) techniques have been employed to analyze shear bands in metallic glasses and understand their formation in order to improve the mechanical properties of metallic glasses. However, due to a lack of direct information in reciprocal space, conventional S/TEM cannot characterize the local strain and atomic structure of amorphous materials, which are key to describe the deformation of glasses. For this work, we applied 4-dimensional STEM to map and directly correlate the local strain and the atomic structure at the nanometer scale in deformed metallic glasses. We observe residual strain fields with quadrupolar symmetry concentrated at dilated Eshelby inclusions. The strain fields percolate in a vortex-like manner building up the shear band. This provides a new understanding of the formation of shear bands in metallic glass. This article is protected by copyright. All rights reserved.

Phone2SAS: 3D scanning by smartphone aids the realization of small-angle scattering.

Small-angle scattering (SAS) is a powerful tool for the detailed structural analysis of objects at the nanometer scale. In contrast to techniques such as electron microscopy, SAS data are presented as reciprocal space information, which hinders the intuitive interpretation of SAS data. This study presents a workflow: (1) creating objects, (2) 3D scanning, (3) the representation of the object as point clouds on a laptop, (4) computation of a distance distribution function, and (5) computation of SAS, executed via the computer program Phone2SAS. This enables us to realize SAS and perform the interactive modeling of SAS of the object of interest. Because 3D scanning is easily accessible through smartphones, this workflow driven by Phone2SAS contributes to the widespread use of SAS. The application of Phone2SAS for the structural assignment of SAS to Y-shaped antibodies is reported in this study.

Visualization of single crosslinks and heterogeneity in polymer networks

At the very heart of any polymer networks are the crosslinks that interconnect neighboring chains and lock them in position to resist stress. The crosslinks and their spatial heterogeneity are expected to dictate network architecture, origin of elasticity, and transmission from macroscopic forces to local responses. Yet, direct confirmations of these predictions have been elusive largely because the traditional experimental means are limited to ensemble-averaged or reciprocal-space information. In this perspective, we call attention to the very recent developments that managed to visualize the crosslinks on a single-molecule level, which further localized their static, equilibrium positions in space and tracked their fluctuations around the equilibrium positions in time. Hopefully, these real-space information with unprecedent details can allow us to fully understand networks of complexity and to correlate macroscopic properties to nanoscopic structures.

Ultrafast Imaging of Molecular Dynamics Using Ultrafast Low-Frequency Lasers, X-ray Free Electron Lasers, and Electron Pulses.

The requirement of high space-time resolution and brightness is a great challenge for imaging atomic motion and making molecular movies. Important breakthroughs in ultrabright tabletop laser, X-ray, and electron sources have enabled the direct imaging of evolving molecular structures in chemical processes, and recent experimental advances in preparing ultrafast laser and electron pulses resulted in molecular imaging with femtosecond time resolution. This Perspective presents an overview of the versatile imaging methods of molecular dynamics. High-order harmonic generation imaging and photoelectron diffraction imaging are based on laser-induced ionization and rescattering processes. Coulomb explosion imaging retrieves molecular structural information by detecting the momentum vectors of fragmented ions. Diffraction imaging encodes molecular structural and electronic information in reciprocal space. We also present various applications of these ultrafast imaging methods in resolving laser-induced nuclear and electronic dynamics.

Neutron Radiography and Computed Tomography of Biological Systems at the Oak Ridge National Laboratory's High Flux Isotope Reactor.

Neutrons have historically been used for a broad range of biological applications employing techniques such as small-angle neutron scattering, neutron spin echo, diffraction, and inelastic scattering. Unlike neutron scattering techniques that obtain information in reciprocal space, attenuation-based neutron imaging measures a signal in real space that is resolved on the order of tens of micrometers. The principle of neutron imaging follows the Beer-Lambert law and is based on the measurement of the bulk neutron attenuation through a sample. Greater attenuation is exhibited by some light elements (most notably, hydrogen), which are major components of biological samples. Contrast agents such as deuterium, gadolinium, or lithium compounds can be used to enhance contrast in a similar fashion as it is done in medical imaging, including techniques such as optical imaging, magnetic resonance imaging, X-ray, and positron emission tomography. For biological systems, neutron radiography and computed tomography have increasingly been used to investigate the complexity of the underground plant root network, its interaction with soils, and the dynamics of water flux in situ. Moreover, efforts to understand contrast details in animal samples, such as soft tissues and bones, have been explored. This manuscript focuses on the advances in neutron bioimaging such as sample preparation, instrumentation, data acquisition strategy, and data analysis using the High Flux Isotope Reactor CG-1D neutron imaging beamline. The aforementioned capabilities will be illustrated using a selection of examples in plant physiology(herbaceous plant/root/soil system)and biomedical applications(rat femur and mouse lung).

Quantifying Information via Shannon Entropy in Spatially Structured Optical Beams.

While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to assess the amount and quality of information inside a noisy optical channel. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations. Some of these approaches are limited to a certain alphabet, while others tend to fall short when considering optical beams with a nontrivial structure, such as Hermite-Gauss, Laguerre-Gauss, and other modes with a nontrivial structure. Here, we propose a new definition of the classical Shannon information via the Wigner distribution function, while respecting the Heisenberg inequality. Following this definition, we calculate the amount of information in Gaussian, Hermite-Gaussian, and Laguerre-Gaussian laser modes in juxtaposition and experimentally validate it by reconstruction of the Wigner distribution function from the intensity distribution of structured laser beams. We experimentally demonstrate the technique that allows to infer field structure of the laser beams in singular optics to assess the amount of contained information. Given the generality, this approach of defining information via analyzing the beam complexity is applicable to laser modes of any topology that can be described by well-behaved functions. Classical Shannon information, defined in this way, is detached from a particular alphabet, i.e., communication scheme, and scales with the structural complexity of the system. Such a synergy between the Wigner distribution function encompassing the information in both real and reciprocal space and information being a measure of disorder can contribute into future coherent detection algorithms and remote sensing.

Determination of the 3D Atomic Structures of Nanoparticles

The 3D atomic arrangements of materials determine the free energy landscape, thus governing the physical and catalytic properties of those materials. The 3D structures of nanoparticles can deviate from the periodic atomic arrangement of their bulk counterparts due to the dominance of surface dangling bonds, defects, and dislocations. One approach to understand the structure of nanoparticles and their resulting unique properties involves precise probing of the 3D positions of all constituent atoms of individual nanoparticles. The 3D electron tomography and Brownian one particle reconstruction allow investigation of the 3D atomic positions of nanoparticles. Both methods use transmission electron microscopy (TEM) or scanning TEM (STEM) images of nanoparticles with different projection angles and collect their phase information in reciprocal space to reconstruct the 3D structure of the particles. The thus‐reconstructed 3D maps of metal nanoparticles are highly resolved, facilitating the determination of their atomic coordinates. Grain boundary, dislocation, and lattice expansion are observed on the 3D atomic maps. On the basis of the 3D atomic maps, the physical properties of individual nanoparticles can be accurately predicted, enabling purpose‐driven synthesis.

Sensitivity of pair statistics on pair potentials in many-body systems.

We study the sensitivity and practicality of Henderson's theorem in classical statistical mechanics, which states that the pair potential v(r) that gives rise to a given pair correlation function g2(r) [or equivalently, the structure factor S(k)] in a classical many-body system at number density ρ and temperature T is unique up to an additive constant. While widely invoked in inverse-problem studies, the utility of the theorem has not been quantitatively scrutinized to any large degree. We show that Henderson's theorem has practical shortcomings for disordered and ordered phases for certain densities and temperatures. Using proposed sensitivity metrics, we identify illustrative cases in which distinctly different potential functions give very similar pair correlation functions and/or structure factors up to their corresponding correlation lengths. Our results reveal that due to a limited range and precision of pair information in either direct or reciprocal space, there is effective ambiguity of solutions to inverse problems that utilize pair information only, and more caution must be exercised when one claims the uniqueness of any resulting effective pair potential found in practice. We have also identified systems that possess virtually identical pair statistics but have distinctly different higher-order correlations. Such differences should be reflected in their individually distinct dynamics (e.g., glassy behaviors). Finally, we prove a more general version of Henderson's theorem that extends the uniqueness statement to include potentials that involve two- and higher-body interactions.

Large field-of-view scanning small-angle X-ray scattering of mammalian cells.

X-ray imaging is a complementary method to electron and fluorescence microscopy for studying biological cells. In particular, scanning small-angle X-ray scattering provides overview images of whole cells in real space as well as local, high-resolution reciprocal space information, rendering it suitable to investigate subcellular nanostructures in unsliced cells. One persisting challenge in cell studies is achieving high throughput in reasonable times. To this end, afastscanning mode is used to image hundreds of cells in a single scan. A way ofdealing with the vast amount of data thus collected is suggested, including asegmentation procedure and three complementary kinds of analysis, i.e. characterization of the cell population as a whole, of single cells and of different parts of the same cell. The results show that short exposure times, which enable faster scans and reduce radiation damage, still yield information in agreement with longer exposure times.

Quantitative analysis of spectroscopic low energy electron microscopy data: High-dynamic range imaging, drift correction and cluster analysis

For many complex materials systems, low-energy electron microscopy (LEEM) offers detailed insights into morphology and crystallography by naturally combining real-space and reciprocal-space information. Its unique strength, however, is that all measurements can easily be performed energy-dependently. Consequently, one should treat LEEM measurements as multi-dimensional, spectroscopic datasets rather than as images to fully harvest this potential. Here we describe a measurement and data analysis approach to obtain such quantitative spectroscopic LEEM datasets with high lateral resolution. The employed detector correction and adjustment techniques enable measurement of true reflectivity values over four orders of magnitudes of intensity. Moreover, we show a drift correction algorithm, tailored for LEEM datasets with inverting contrast, that yields sub-pixel accuracy without special computational demands. Finally, we apply dimension reduction techniques to summarize the key spectroscopic features of datasets with hundreds of images into two single images that can easily be presented and interpreted intuitively. We use cluster analysis to automatically identify different materials within the field of view and to calculate average spectra per material. We demonstrate these methods by analyzing bright-field and dark-field datasets of few-layer graphene grown on silicon carbide and provide a high-performance Python implementation.

Real-time coherent diffraction inversion using deep generative networks

Phase retrieval, or the process of recovering phase information in reciprocal space to reconstruct images from measured intensity alone, is the underlying basis to a variety of imaging applications including coherent diffraction imaging (CDI). Typical phase retrieval algorithms are iterative in nature, and hence, are time-consuming and computationally expensive, making real-time imaging a challenge. Furthermore, iterative phase retrieval algorithms struggle to converge to the correct solution especially in the presence of strong phase structures. In this work, we demonstrate the training and testing of CDI NN, a pair of deep deconvolutional networks trained to predict structure and phase in real space of a 2D object from its corresponding far-field diffraction intensities alone. Once trained, CDI NN can invert a diffraction pattern to an image within a few milliseconds of compute time on a standard desktop machine, opening the door to real-time imaging.

Resonant soft X-ray scattering reveals cellulose microfibril spacing in plant primary cell walls

Cellulose microfibrils are crucial for many of the remarkable mechanical properties of primary cell walls. Nevertheless, many structural features of cellulose microfibril organization in cell walls are not yet fully described. Microscopy techniques provide direct visualization of cell wall organization, and quantification of some aspects of wall microstructure is possible through image processing. Complementary to microscopy techniques, scattering yields structural information in reciprocal space over large sample areas. Using the onion epidermal wall as a model system, we introduce resonant soft X-ray scattering (RSoXS) to directly quantify the average interfibril spacing. Tuning the X-ray energy to the calcium L-edge enhances the contrast between cellulose and pectin due to the localization of calcium ions to homogalacturonan in the pectin matrix. As a consequence, RSoXS profiles reveal an average center-to-center distance between cellulose microfibrils or microfibril bundles of about 20 nm.

Determination of rhombohedral structure of BiFeO3 single-domain-like films grown on SrTiO3 and LaAlO3 substrates by X-ray diffraction using

The crystal structure of bismuth ferrite (BiFeO3; BFO) epitaxial films was analyzed by X-ray diffraction (XRD) using a two-dimensional detector. The diffraction spots hex (hexagonal notation was used for the rhombohedral structure in this study) specific to the rhombohedral structure (space group: R3c), which clearly separated from the diffractions in other crystal symmetries of BFO, was used for determining the crystal symmetry. The BFO films on the SrTiO3 substrates were unambiguously identified as R3c with the hex diffraction spot, whereas highly strained BFO films (space group: Cm) on the LaAlO3 substrates did not show the diffraction spot. The structure of a single-domain-like sample with R3c could not be determined using variants, i.e., degrees of freedom for crystal orientation, whereas the Bragg’s diffraction of hex can be used to unambiguously distinguish R3c from other space groups. It was proposed that electron diffraction complemented by nondestructive and high-resolution XRD is highly effective to obtain wide-area reciprocal space information for identifying low-symmetric-complex materials such as BFO.

TEM Observation of Nano-Scale Hydrogel Network Structure

Hydrogel, containing large amount of water inside its polymer network, is one of the most attractive biomaterials, because of its similarities with living tissues such as, high water content, low friction and flexibility. These unique features come from complicated polymer network structure, and until now great effort have been put in to clarify nano scale structure of hydrogel. Especially, many researchers tried to investigate by using scattering techniques. However, scattering data just presents limited information in reciprocal space and “real” polymer network structure is still not well understood due to difficulty on direct observation of hydrogel polymer. In this study, we adopt an idea to stain polymer network by using inhomogeneous nucleation, nucleation starts from the functional group of additive. If we carried out inhomogeneous nucleation in the hydrogel, mineral crystals easily forms complex with hydrogel network and this mineral distribution should represent the original polymer structure. Therefore, the purpose of this study is to stain hydrogel polymer network with mineral and to observe its nano-scale structure by using transmission electron microscope (TEM). Double network hydrogel was synthesized by two step UV radical polymerization.1 2-acrylamido-2-methyl propanesulfonic acid (AMPS), which contains sulfonic functional group, was used for 1st polymer network. Then, mineral bernalite (Fe(OH)3), whose nucleation accelerates by sulfonic group, was mineralized into DN gel. Fig.1 shows TEM image of mineralized DN gel and its schematic image. Nano scale hydrogel polymer network structure was successfully observed and this structure well agreed with previous prediction from neutron scattering method. This is the world’s first direct observation of polymer network. Mineralized crystal size was several nm in diameter, which is same scale of polymer blob. It indicates that we observed mineral crystals surrounded by individual polymer blobs. The detailed results will be presented in conference. In conclusion, we succeeded direct observation of hydrogel polymer network using TEM. This is a very challenging study not only for understanding hydrogel, but also for visualization polymer network, which is one of biggest dream of polymer scientists.

Imaging nanoscale lattice variations by machine learning of x-ray diffraction microscopy data

We present a novel methodology based on machine learning to extract lattice variations in crystalline materials, at the nanoscale, from an x-ray Bragg diffraction-based imaging technique. By employing a full-field microscopy setup, we capture real space images of materials, with imaging contrast determined solely by the x-ray diffracted signal. The data sets that emanate from this imaging technique are a hybrid of real space information (image spatial support) and reciprocal lattice space information (image contrast), and are intrinsically multidimensional (5D). By a judicious application of established unsupervised machine learning techniques and multivariate analysis to this multidimensional data cube, we show how to extract features that can be ascribed physical interpretations in terms of common structural distortions, such as lattice tilts and dislocation arrays. We demonstrate this ‘big data’ approach to x-ray diffraction microscopy by identifying structural defects present in an epitaxial ferroelectric thin-film of lead zirconate titanate.

Quantitative Neutron Dark-field Imaging through Spin-Echo Interferometry

Neutron dark-field imaging constitutes a seminal progress in the field of neutron imaging as it combines real space resolution capability with information provided by one of the most significant neutron scattering techniques, namely small angle scattering. The success of structural characterizations bridging the gap between macroscopic and microscopic features has been enabled by the introduction of grating interferometers so far. The induced interference pattern, a spatial beam modulation, allows for mapping of small-angle scattering signals and hence addressing microstructures beyond direct spatial resolution of the imaging system with high efficiency. However, to date the quantification in the small angle scattering regime is severely limited by the monochromatic approach. To overcome such drawback we here introduce an alternative and more flexible method of interferometric beam modulation utilizing a spin-echo technique. This novel method facilitates straightforward quantitative dark-field neutron imaging, i.e. the required quantitative microstructural characterization combined with real space image resolution. For the first time quantitative microstructural reciprocal space information from small angle neutron scattering becomes available together with macroscopic image information creating the potential to quantify several orders of magnitude in structure sizes simultaneously.

Combining phase information in reciprocal space for molecular replacement with partial models.

ARCIMBOLDO allows ab initio phasing of macromolecular structures below atomic resolution by exploiting the location of small model fragments combined with density modification in a multisolution frame. The model fragments can be either secondary-structure elements predicted from the sequence or tertiary-structure fragments. The latter can be derived from libraries of typical local folds or from related structures, such as a low-homology model that is unsuccessful in molecular replacement. In all ARCIMBOLDO applications, fragments are searched for sequentially. Correct partial solutions obtained after each fragment-search stage but lacking the necessary phasing power can, if combined, succeed. Here, an analysis is presented of the clustering of partial solutions in reciprocal space and of its application to a set of different cases. In practice, the task of combining model fragments from an ARCIMBOLDO run requires their referral to a common origin and is complicated by the presence of correct and incorrect solutions as well as by their not being independent. The F-weighted mean phase difference has been used as a figure of merit. Clustering perfect, non-overlapping fragments dismembered from test structures in polar and nonpolar space groups shows that density modification before determining the relative origin shift enhances its discrimination. In the case of nonpolar space groups, clustering of ARCIMBOLDO solutions from secondary-structure models is feasible. The use of partially overlapping search fragments provides a more favourable circumstance and was assessed on a test case. Applying the devised strategy, a previously unknown structure was solved from clustered correct partial solutions.

Exploring fibrous materials with micro/nanobeam scanning diffraction techniques

Fibrous materials play an important role in many fields of research spanning from industrial applications to life sciences. They are typically organized in hierarchical arrangements of structural features on multiple length scales. Employing focused monochromatic x-rays combined with scanning diffraction, such samples can be studied obtaining rich information in reciprocal space (molecular to mesoscale level) and direct space simultaneously [1][2]. The resolution of the latter is mainly limited by the focal spot size ranging from a few microns down to 100 nm and less. The arrival of fast, sensitive pixel array detectors during the past years and the availability of high performance focusing optics enable in-situ studies on weakly scattering specimen like single polymer fibers and bio-composite materials (e.g. wood, bone tissue, ...) controlling environmental parameters such as humidity, temperature, and mechanical deformation. In this contribution we will present in a first part the state of the art of instrumentation for such experiments at the ESRF Microfocus Beamline, illustrated with recent examples. The figure below shows an example of a single fiber diffraction pattern of a high performance polymer (KEVLAR®) obtained from a 20 ms exposure with a 1.5 micron beam (Frelon CCD detector, 2k x 2k pixels, 13 keV photon energy). In the second part, future opportunities for scanning diffraction experiments emerging from potential upgrades of 3rd generation synchrotron radiation sources, as currently explored at the ESRF and elsewhere, will be discussed.

Why powder diffractionists need help from electron crystallography

Although X-ray powder diffraction (XPD) is used as a routine tool for solving crystal structures of polycrystalline materials, its weakness is obvious: not only is the phase information lost during the diffraction experiment, but reflections with similar d-spacings, which are well-separated in a single-crystal measurement, overlap in a powder pattern. These effects increase the difficulty of structure solution especially when dealing with complex structures. Compared to XPD, the advantages from electron microscopy are: (1) single-crystal electron diffraction data, either in 2-dimensional or 3-dimensional form, can be obtained from a very tiny crystallite in a powder sample; and (2) high-resolution images can be collected and used to extract phase information in reciprocal space or to provide a direct view of structural features (ordered and disordered) [1]. With the extra information supplied by electron microscopy, the limits of structure determination for polycrystalline materials can be extended [2]. Here we will present a few examples to demonstrate why powder diffractionists need help from electron microscopy and how to integrate these two techniques into the structure determination process.