Reciprocal Space Research Articles

Quantum refinement in real and reciprocal space using the Phenix and ORCA software.

X-ray and neutron crystallography, as well as cryogenic electron microscopy (cryo-EM), are the most common methods to obtain atomic structures of biological macromolecules. A feature they all have in common is that, at typical resolutions, the experimental data need to be supplemented by empirical restraints, ensuring that the final structure is chemically reasonable. The restraints are accurate for amino acids and nucleic acids, but often less accurate for substrates, inhibitors, small-molecule ligands and metal sites, for which experimental data are scarce or empirical potentials are harder to formulate. This can be solved using quantum mechanical calculations for a small but interesting part of the structure. Such an approach, called quantum refinement, has been shown to improve structures locally, allow the determination of the protonation and oxidation states of ligands and metals, and discriminate between different interpretations of the structure. Here, we present a new implementation of quantum refinement interfacing the widely used structure-refinement software Phenix and the freely available quantum mechanical software ORCA. Through application to manganese superoxide dismutase and V- and Fe-nitrogenase, we show that the approach works effectively for X-ray and neutron crystal structures, that old results can be reproduced and structural discrimination can be performed. We discuss how the weight factor between the experimental data and the empirical restraints should be selected and how quantum mechanical quality measures such as strain energies should be calculated. We also present an application of quantum refinement to cryo-EM data for particulate methane monooxygenase and show that this may be the method of choice for metal sites in such structures because no accurate empirical restraints are currently available for metals.

Oxygen Vacancy Compensation-Induced Analog Resistive Switching in the SrFeO3-δ/Nb:SrTiO3 Epitaxial Heterojunction for Noise-Tolerant High-Precision Image Recognition.

Neuromorphic computing, inspired by the brain's architecture, promises to surpass the limitations of von Neumann computing. In this paradigm, synaptic devices play a crucial role, with resistive switching memory (memristors) emerging as promising candidates due to their low power consumption and scalability advantages. This study focuses on the development of metal/oxide-semiconductor heterojunctions, which offer several technological advantages and have broad potential for applications in artificial neural synapses. However, constructing high-quality epitaxial interfaces between metal and oxide semiconductors and designing modifiable contact barriers are challenging. Herein, we construct high-quality epitaxial metal/semiconductor interfaces based on the metallicity of the perovskite phase SrFeO3-δ (PV-SFO) and a small Schottky barrier in contact with Nb-doped SrTiO3 (NSTO). X-ray diffraction patterns, reciprocal space mapping results, and cross-sectional transmission electron microscopy images reveal that the prepared PV-SFO film exhibits a perfect single-crystal structure and an excellent epitaxial interface with the NSTO (111) substrate. The corresponding memristor exhibits analog-type resistive-variable characteristics with an ON/OFF ratio of ∼1000, stable data retention after 10,000 s, and no noticeable fluctuation in resistance after 10,000 pulse cycles. Electron energy loss spectroscopy, first-principles calculations, and electrical measurements reveal that compensating or restoring oxygen vacancies at the NSTO surface decreases or increases the contact barrier between PV-SFO and NSTO, respectively, thereby gradually regulating the resistance value. Furthermore, high-quality epitaxial PV-SFO/NSTO devices achieve up to 98.21% recognition accuracy for handwriting recognition tasks using LeNet-5-based network structures and 92.21% accuracy for color images using visual geometry group (VGG) network structures. This work contributes to the advancement of interface-type memristors and provides valuable insights into enhancing synaptic functionality in neuromorphic computing systems.

Large-Area Perovskite Nanocrystal Metasurfaces for Direction-Tunable Lasing.

Perovskite nanocrystals (PNCs) are attractive emissive materials for developing compact lasers. However, manipulation of PNC laser directionality has been difficult, which limits their usage in photonic devices that require on-demand tunability. Here we demonstrate PNC metasurface lasers with engineered emission angles. We fabricated millimeter-scale CsPbBr3 PNC metasurfaces using an all-solution-processing technique based on soft nanoimprinting lithography. By designing band-edge photonic modes at the high-symmetry X point of the reciprocal lattice, we achieved four linearly polarized lasing beams along a polar angle of ∼30° under optical pumping. The device architecture further allows tuning of the lasing emission angles to 0° and ∼50°, respectively, by adjusting the PNC thickness to shift other high-symmetry points (Γ and M) to the PNC emission wavelength range. Our laser design strategies offer prospects for applications in directional optical antennas and detectors, 3D laser projection displays, and multichannel visible light communication.

Influence of device configuration and noise on a machine learning predictor for the selection of nanoparticle small-angle X-ray scattering models.

Small-angle X-ray scattering (SAXS) is a widely used method for nanoparticle characterization. A common approach to analysing nanoparticles in solution by SAXS involves fitting the curve using a parametric model that relates real-space parameters, such as nanoparticle size and electron density, to intensity values in reciprocal space. Selecting the optimal model is a crucial step in terms of analysis quality and can be time-consuming and complex. Several studies have proposed effective methods, based on machine learning, to automate the model selection step. Deploying these methods in software intended for both researchers and industry raises several issues. The diversity of SAXS instrumentation requires assessment of the robustness of these methods on data from various machine configurations, involving significant variations in the q-space ranges and highly variable signal-to-noise ratios (SNR) from one data set to another. In the case of laboratory instrumentation, data acquisition can be time-consuming and there is no universal criterion for defining an optimal acquisition time. This paper presents an approach that revisits the nanoparticle model selection method proposed by Monge et al. [Acta Cryst. (2024), A80, 202-212], evaluating and enhancing its robustness on data from device configurations not seen during training, by expanding the data set used for training. The influence of SNR on predictor robustness is then assessed, improved, and used to propose a stopping criterion for optimizing the trade-off between exposure time and data quality.

The AUREX cell: a versatile operando electrochemical cell for studying catalytic materials using X-ray diffraction, total scattering and X-ray absorption spectroscopy under working conditions.

Understanding the structure-property relationship in electrocatalysts under working conditions is crucial for the rational design of novel and improved catalytic materials. This paper presents the Aarhus University reactor for electrochemical studies using X-rays (AUREX) operando electrocatalytic flow cell, designed as an easy-to-use versatile setup with a minimal background contribution and a uniform flow field to limit concentration polarization and handle gas formation. The cell has been employed to measure operando total scattering, diffraction and absorption spectroscopy as well as simultaneous combinations thereof on a commercial silver electrocatalyst for proof of concept. This combination of operando techniques allows for monitoring of the short-, medium- and long-range structure under working conditions, including an applied potential, liquid electrolyte and local reaction environment. The structural transformations of the Ag electrocatalyst are monitored with non-negative matrix factorization, linear combination analysis, the Pearson correlation coefficient matrix, and refinements in both real and reciprocal space. Upon application of an oxidative potential in an Ar-saturated aqueous 0.1 M KHCO3/K2CO3 electrolyte, the face-centered cubic (f.c.c.) Ag gradually transforms first to a trigonal Ag2CO3 phase, followed by the formation of a monoclinic Ag2CO3 phase. A reducing potential immediately reverts the structure to the Ag (f.c.c.) phase. Following the electrochemical-reaction-induced phase transitions is of fundamental interest and necessary for understanding and improving the stability of electrocatalysts, and the operando cell proves a versatile setup for probing this. In addition, it is demonstrated that, when studying electrochemical reactions, a high energy or short exposure time is needed to circumvent beam-induced effects.

Unconventional spin textures emerging from a universal symmetry theory of spin-momentum locking

Spin textures, i.e., the distribution of spin polarization vectors in reciprocal space, exhibit diverse patterns determined by symmetry constraints, resulting in a variety of spintronic phenomena. Here, we propose a universal theory to comprehensively describe the nature of spin textures by incorporating three symmetry flavors of reciprocal wavevector, atomic orbital, and atomic site. Such an approach enables us to establish a complete classification of spin textures constrained by the little co-group and predict some exotic spin texture types, such as Zeeman-type spin splitting in antiferromagnets and quadratic spin texture. To illustrate the influence of atomic orbitals and sites on spin textures, we predict orbital-dependent spin texture and anisotropic spin-momentum-site locking effects, and corresponding material candidates validated through first-principles calculations. The comprehensive classification and the predicted new spin textures in realistic materials are expected to trigger future spin-based functionalities in electronics.

Structural and electronic transformations in TiO2 induced by electric current

In-situ diffuse neutron scattering experiments revealed that when electric current is passed through single crystals of rutile TiO2 under conditions conducive to flash sintering, it induces the formation of parallel planes of oxygen vacancies. Specifically, a current perpendicular to the c-axis generates planes normal to the (132) reciprocal lattice vector, whereas currents aligned with the c-axis form planes normal to the (132) and to the (225) vector. The concentration of defects increases with incresing current. The structural modifications are linked to the appearance of signatures of interacting Ti3+ moments in magnetic susceptibility, signifying a structural collapse around the vacancy planes. Electrical conductivity measurements of the modified material reveal several electronic transitions between semiconducting states (via a metal-like intermediate state) with the smallest gap being 27 meV. Pristine TiO2 can be restored by heating followed by slow cooling in air. Our work suggests a novel paradigm for achieving switching of electrical conductivity related to the flash phenomenon.

Gate induced metallicity and absence of superconductivity in BSTO/LCO heterostructure

We fabricated Ba0.8Sr0.2TiO3 (BSTO)/La2CuO4 (LCO) heterostructure on SrTiO3 (STO) substrate and investigated its structure and physical properties. X-ray diffraction and reciprocal space mapping confirm the epitaxial growth of BSTO/LCO/STO heterostructure. X-ray photoelectron spectroscopy and UV–Visible spectroscopy measurements reveal a straddling band alignment of the BSTO/LCO heterojunction. Such band alignment facilitates the accumulation of both electrons and holes at the interface. Their movement depends on the direction of the internal field of the BSTO film. Electrical transport measurements have revealed a signature of insulator-to-metal transition (IMT) in response to applied gate voltages ±Vg. Hall measurements confirm the presence of electron and hole type charge carriers under ＋Vg and −Vg, respectively. We have proposed a screening mechanism linked to the polarization state of the BSTO film to explain the observed IMT.

Anomalous relaxation of coarsening foams with viscoelastic continuous phases.

We investigate the ultraslow structural relaxation of ageing foams with rheologically tunable continuous phases. We probe the bubble dynamics associated with pressure-driven foam coarsening using differential dynamic microscopy, which allows characterising the sample dynamics in reciprocal space with imaging experiments. Similar to other out-of-equilibrium jammed soft systems, these foams exhibit compressed exponential relaxations, with a ballistic-like linear dependency of the relaxation rate on the scattering wavevector. By tuning the rheology of the continuous phase, we observe changes in the relaxation shape, where stiffer matrices yield larger compression exponents. Our results corroborate recent real-space observations obtained using bubble tracking, providing a comprehensive overview of structural relaxation in these complex systems, both in direct and reciprocal space.

Growth Conditions and Interfacial Misfit Array in SnTe (111) Films Grown on InP (111)A Substrates by Molecular Beam Epitaxy.

Tin telluride (SnTe) is an IV-VI semiconductor with a topological crystalline insulator band structure, high thermoelectric performance, and in-plane ferroelectricity. Despite its many applications, there has been little work focused on understanding the growth mechanisms of SnTe thin films. In this manuscript, we investigate the molecular beam epitaxy synthesis of SnTe (111) thin films on InP (111)A substrates. We explore the effect of substrate temperature, Te/Sn flux ratio, and growth rate on the film quality. Using a substrate temperature of 340 °C, a Te/Sn flux ratio of 3, and a growth rate of 0.48 Å/s, fully coalesced and single crystalline SnTe (111) epitaxial layers with X-ray rocking curve full-width-at-half-maxima of 0.09° and root-mean-square surface roughness as low as 0.2 nm have been obtained. Despite the 7.5% lattice mismatch between the SnTe (111) film and the InP (111)A substrate, reciprocal space mapping indicates that the 15 nm SnTe layer is fully relaxed. We show that a periodic interfacial misfit (IMF) dislocation array forms at the SnTe/InP heterointerface, where each IMF dislocation is separated by 14 InP lattice sites/13 SnTe lattice sites, providing rapid strain relaxation and yielding the high quality SnTe layer. This is the first report of an IMF array forming in a rock-salt on zinc-blende material system and at an IV-VI on III-V heterointerface, and highlights the potential for SnTe as a buffer layer for epitaxial telluride film growth. This work represents an important milestone in enabling the heterointegration between IV-VI and III-V semiconductors to create multifunctional devices.

Real-Space Tilting Method for Atomic Resolution STEM Imaging of Nanocrystalline Materials.

Atomic-resolution scanning transmission electron microscopy (STEM) characterization requires precise tilting of the specimen to a high symmetric zone axis, which is usually processed in reciprocal space by following the diffraction patterns. However, for small-sized nanocrystalline materials, their diffraction patterns are often too faint to guide the tilting process. Here, a simple and effective tilting method is developed based on the diffraction contrast change of the shadow image in the Ronchigram. The misorientation angle of the specimen can be calculated and tilted to the zone axis based on the position of the shadow image with lowest intensity. This method requires no prior knowledge of the sample and the maximum misorientation angle that can be corrected is >±6.9° with sub-mrad accuracy. It operates in real space, without recording the diffraction patterns of the specimens, making it particularly effective for nanocrystalline materials. Combined with the scripting to control the microscope, the sample can be automatically tilted to the zone axis under low dose conditions (<0.17 e-Å- 2s-1), facilitating the imaging of beam sensitive materials such as zeolites or metal-organic frameworks. This automated tilting method can significantly contribute to the atomic-scale characterization of the nanocrystalline materials by STEM imaging.

Deep learning for symmetry classification using sparse 3D electron density data for inorganic compounds

We report a novel deep learning (DL) method for classifying inorganic compounds using 3D electron density data. We transform Density Functional Theory (DFT)-derived CHGCAR files from the Materials Project (MP) and experimental data from the Inorganic Crystal Structure Database (ICSD) into point clouds and sparse tensors, optimized for use in DL models such as PointNet and Sparse 3D CNN. This approach effectively overcomes the limitations of handling the dense 3D data, a common challenge in DL. Contrasting with traditional 1D or 2D X-ray diffraction (XRD) patterns that necessitate complex reciprocal space analysis, our method utilizes 3D density data for direct interpretation in real lattice space. This shift significantly enhances classification accuracy, outperforming traditional XRD-driven DL methods. We achieve accuracies of 97.28%, 90.77%, and 90.10% for crystal system, extinction group, and space group classifications, respectively. Our 3D electron density-based DL approach not only showcases improved accuracy but also contributes a more intuitive and effective framework for materials discovery.

Real- and reciprocal space characterization of the three-dimensional charge density wave in quasi-one-dimensional CuTe

Real- and reciprocal space characterization of the three-dimensional charge density wave in quasi-one-dimensional CuTe

A spatial phase-shifting method for real-space wave reconstruction of off-axis electron holograms

The Fourier transform with a side-band filter is the well-established method for reconstructing off-axis fringe-type holograms due to its ease of implementation and fast processing. However, this method works in reciprocal space and requires inversion of a side-band sub-region, which can degrade the spatial resolution of reconstructed wave compared to the original hologram. We present a new method, the spatial phase-shifting (SPS) method, for real-space wave reconstruction of off-axis electron holograms. We describe the working principles of the SPS method in analogy to the temporal phase-shifting method. We conducted both hologram simulations and experiments to evaluate its applicability and effectiveness. We compared the wave reconstruction results of the SPS and the conventional Fourier transform method, highlighting the advantages of the newly proposed SPS method. Our results demonstrate that the proposed SPS method is particularly effective for real-space wave reconstruction of small-sized hologram, providing an alternative approach to off-axis type holography wave reconstruction.

Spectral energy transfer on complex networks: a filtering approach

The spectral analysis of dynamical systems is a staple technique for analyzing a vast range of systems. But beyond its analytical utility, it is also the primary lens through which many physical phenomena are defined and interpreted. The turbulent energy cascade in fluid mechanics, a dynamical consequence of the three-dimensional Navier–Stokes equations in which energy “cascades” from large injection scales to smaller dissipation scales, is a well-known example that is precisely defined only in reciprocal space. Related techniques in the context of networked dynamical systems have been employed with great success in deriving reduced order models. But what such techniques gain in analytical tractability, they often lose in interpretability and locality, as the lower degree of freedom system frequently contains information from all nodes of the network. Here, we demonstrate that a network of nonlinear oscillators exhibits spectral energy transfer facilitated by an effective force akin to the Reynolds stress in turbulence, an example of an emergent higher order interaction. Then, introducing a filter-based decomposition motivated by large eddy simulation, we show that such higher order interactions can be localized to individual nodes and study the effects of local topology on such interactions.

Giant resistance switch in twisted transition metal dichalcogenide tunnel junctions

Abstract Resistance switching in multilayer structures are typically based on materials possessing ferroic orders. Here we predict an extremely large resistance switching based on the relative spin-orbit splitting in twisted transition metal dichalcogenide (TMD) monolayers tunnel junctions. Because of the valence band spin splitting which depends on the valley index in the Brillouin zone, the perpendicular electronic transport through the junction depends on the relative reciprocal space overlap of the spin-dependent Fermi surfaces of both layers, which can be tuned by twisting one layer. Our quantum transport calculations reveal a switching resistance larger than 106% when the relative alignment of TMDs goes from 0º to 60º and when the angle is kept fixed at 60º and the Fermi level is varied. By creating vacancies, we evaluate how inter-valley scattering affects the efficiency and find that the resistance switching remains large (104%) for typical values of vacancy concentration. Not only should this resistance switching be observed at room temperature due to the large spin splitting, but our results also show how twist angle engineering and control of van der Waals heterostructures could be used for next-generation memory and electronic applications.&amp;#xD;

Ab initio uncertainty quantification in scattering analysis of microscopy.

Estimating parameters from data is a fundamental problem in physics, customarily done by minimizing a loss function between a model and observed statistics. In scattering-based analysis, it is common to work in the reciprocal space. Researchers often employ their domain expertise to select a specific range of wave vectors for analysis, a choice that can vary depending on the specific case. We introduce another paradigm that defines a probabilistic generative model from the beginning of data processing and propagates the uncertainty for parameter estimation, termed the ab initio uncertainty quantification (AIUQ). As an illustrative example, we demonstrate this approach with differential dynamic microscopy (DDM) that extracts dynamical information through minimizing a loss function for the squared differences of the Fourier-transformed intensities, at a selected range of wave vectors. We first show that the conventional way of estimation in DDM is equivalent to fitting a temporal variogram in the reciprocal space using a latent factor model as the generative model. Then we derive the maximum marginal likelihood estimator, which optimally weighs the information at all wave vectors, therefore eliminating the need to select the range of wave vectors. Furthermore, we substantially reduce the computational cost of computing the likelihood function without approximation, by utilizing the generalized Schur algorithm for Toeplitz covariances. Simulated studies of a wide range of dynamical systems validate that the AIUQ method improves estimation accuracy and enables model selection with automated analysis. The utility of AIUQ is also demonstrated by three distinct sets of experiments: first in an isotropic Newtonian fluid, pushing limits of optically dense systems compared to multiple particle tracking; next in a system undergoing a sol-gel transition, automating the determination of gelling points and critical exponent; and lastly, in discerning anisotropic diffusive behavior of colloids in a liquid crystal. These studies demonstrate that the new approach does not require manually selecting the wave vector range and enables automated analysis.

Spin and orbital magnetism by light in rutile altermagnets

While the understanding of altermagnetism is still at a very early stage, it is expected to play a role in various fields of condensed matter research, for example spintronics, caloritronics and superconductivity. In the field of optical magnetism, it is still unclear to which extent altermagnets as a class can exhibit a distinct behavior. Here we choose RuO2, a prototype metallic altermagnet with a giant spin splitting, and CoF2, an experimentally known insulating altermagnet, to study the light-induced magnetism in rutile altermagnets from first-principles. We demonstrate that in the non-relativisic limit the allowed sublattice-resolved orbital response exhibits symmetries, imposed by altermagnetism, which lead to a drastic canting of light-induced moments. On the other hand, we find that inclusion of spin-orbit interaction enhances the overall effect drastically, introduces a significant anisotropy with respect to the light polarization and strongly suppresses the canting of induced moments. Remarkably, we observe that the moments induced by linearly-polarized laser pulses in light altermagnets can even exceed in magnitude those predicted for heavy ferromagnets exposed to circularly polarized light. By resorting to microscopic tools we interpret our results in terms of the altermagnetic spin splittings and of their reciprocal space distribution. Based on our findings, we speculate that optical excitations may provide a unique tool to switch and probe the magnetic state of rutile altermagnets.

Ultrafast energy-dispersive soft-x-ray diffraction in the water window with a laser-driven source

Time-resolved soft-x-ray-diffraction experiments give access to microscopic processes in a broad range of solid-state materials by probing ultrafast dynamics of ordering phenomena. While laboratory-based high-harmonic generation (HHG) light sources provide the required photon energies, their limited photon flux is distributed over a wide spectral range, rendering typical monochromatic diffraction schemes challenging. Here, we present a scheme for energy-dispersive soft-x-ray diffraction with femtosecond temporal resolution and photon energies across the water window from 200 to 600 eV. The experiment utilizes the broadband nature of the HHG emission to efficiently probe large slices in reciprocal space. As a proof-of-concept, we study the laser-induced structural dynamics of a Mo/Si superlattice in an ultrafast, non-resonant soft-x-ray diffraction experiment. We extract the underlying strain dynamics from the measured shift of its first order superlattice Bragg peak in reciprocal space at photon energies around 500 eV via soft-x-ray scattering simulations.

Current opinion on the prospect of mapping electronic orbitals in the transmission electron microscope: State of the art, challenges and perspectives.

The concept of electronic orbitals has enabled the understanding of a wide range of physical and chemical properties of solids through the definition of, for example, chemical bonding between atoms. In the transmission electron microscope, which is one of the most used and powerful analytical tools for high-spatial-resolution analysis of solids, the accessible quantity is the local distribution of electronic states. However, the interpretation of electronic state maps at atomic resolution in terms of electronic orbitals is far from obvious, not always possible, and often remains a major hurdle preventing a better understanding of the properties of the system of interest. In this review, the current state of the art of the experimental aspects for electronic state mapping and its interpretation as electronic orbitals is presented, considering approaches that rely on elastic and inelastic scattering, in real and reciprocal spaces. This work goes beyond resolving spectral variations between adjacent atomic columns, as it aims at providing deeper information about, for example, the spatial or momentum distributions of the states involved. The advantages and disadvantages of existing experimental approaches are discussed, while the challenges to overcome and future perspectives are explored in an effort to establish the current state of knowledge in this field. The aims of this review are also to foster the interest of the scientific community and to trigger a global effort to further enhance the current analytical capabilities of transmission electron microscopy for chemical bonding and electronic structureanalysis.