Real-space Distribution Research Articles

Coordinate-based simulation of pair distance distribution functions for small and large molecular assemblies: implementation and applications.

X-ray scattering has become a major tool in the structural characterization of nanoscale materials. Thanks to the widely available experimental and computational atomic models, coordinate-based X-ray scattering simulation has played a crucial role in data interpretation in the past two decades. However, simulation of real-space pair distance distribution functions (PDDFs) from small- and wide-angle X-ray scattering, SAXS/WAXS, has been relatively less exploited. This study presents a comparison of PDDF simulation methods, which are applied to molecular structures that range in size from β-cyclo-dextrin [1 kDa molecular weight (MW), 66 non-hydrogen atoms] to the satellite tobacco mosaic virus capsid (1.1 MDa MW, 81 960 non-hydrogen atoms). The results demonstrate the power of interpretation of experimental SAXS/WAXS from the real-space view, particularly by providing a more intuitive method for understanding of partial structure contributions. Furthermore, the computational efficiency of PDDF simulation algorithms makes them attractive as approaches for the analysis of large nanoscale materials and biological assemblies. The simulation methods demonstrated in this article have been implemented in stand-alone software, SolX 3.0, which is available to download from https://12idb.xray.aps.anl.gov/solx.html.

Efficient end-to-end simulation of time-dependent coherent X-ray scattering experiments.

Physical optics simulations for beamlines and experiments allow users to test experiment feasibility and optimize beamline settings ahead of beam time in order to optimize valuable beam time at synchrotron light sources like NSLS-II. Further, such simulations also help to develop and test experimental data processing methods and software in advance. The Synchrotron Radiation Workshop (SRW) software package supports such complex simulations. We demonstrate how recent developments in SRW significantly improve the efficiency of physical optics simulations, such as end-to-end simulations of time-dependent X-ray photon correlation spectroscopy experiments with partially coherent undulator radiation (UR). The molecular dynamics simulation code LAMMPS was chosen to model the sample: a solution of silica nanoparticles in water at room temperature. Real-space distributions of nanoparticles produced by LAMMPS were imported into SRW and used to simulate scattering patterns of partially coherent hard X-ray UR from such a sample at the detector. The partially coherent UR illuminating the sample can be represented by a set of orthogonal coherent modes obtained by simulation of emission and propagation of this radiation through the coherent hard X-ray (CHX) scattering beamline followed by a coherent-mode decomposition. GPU acceleration is added for several key functions of SRW used in propagation from sample to detector, further improving the speed of the calculations. The accuracy of this simulation is benchmarked by comparison with experimental data.

Investigations of Chemical Element Distributions in Soil, North Macedonia—A Review

This review article considers the following aspects: naturally distributed chemical elements and their enrichments, and the increased occurrence of PTEs due to anthropogenic and urban activities, as well as due to the geochemical uniqueness of certain geochemical landscapes, depending on the lithological environment. The review article is the result of many years of successful cooperation between the Geological Survey of Slovenia and the Faculty of Natural Sciences in Skopje, Ss. Cyril and Methodius University in Skopje, as well as several other institutions from North Macedonia, Russia and Romania but, also, through the voluntary and enthusiastic work of Prof. Trajče Stafilov’s PhD and Master’s students. To create the Geochemical Atlas, the territory of North Macedonia was covered with 995 sampling locations, but 16 separate areas with soil contamination were additionally sampled. The total sum of all collected soil samples was 3983 from 2449 different sampling sites in the period from 2006 to 2017. The analyses were performed at the Institute of Chemistry, Faculty of Natural Sciences in Skopje, at the Ss. Cyril and Methodius University in Skopje, North Macedonia, at the Research Institute for Analytical Instrumentation (ICIA), Cluj-Napoca, Romania, at the Joint Institute for Nuclear Research in Dubna, Moscow Region, Russia, and at Acme Labs in Vancouver, Canada. The sum of all analysed soil samples in all four mentioned laboratories was 7991 from 2006 to 2017. Using advanced mathematical methods such as multivariate statistical methods (HCA, FA, PCA) and artificial neural networks–multilayer perceptron (ANN-MP), predictions were made about the concentrations of potentially toxic elements (PTEs) and their distribution in real space. In less than two decades (2007–2023) of fruitful collaboration, a large number of scientific works have been published: 188 scientific publications, 8 geochemical atlases and 23 chapters in monographs.

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.

Dense random packing of disks with a power-law size distribution in thermodynamic limit.

The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases infinitely, while the mean density of the disk centers and the range of the size distribution are kept constant. We investigate the structure factor dependence on momentum transfer across various number of disks and extrapolate these findings to the thermodynamic limit. The fractal power-law decay of the structure factor is recovered in reciprocal space within the fractal range, which corresponds to the range of the size distribution in real space. The fractal exponent coincides with the exponent of the power-law size distribution as was shown previously by the authors of the work of Cherny et al. [J. Chem. Phys. 158(4), 044114 (2023)]. The dependence of the structure factor on density is examined. As is found, the power-law exponent remains unchanged but the fractal range shrinks when the packing fraction decreases. Additionally, the finite-size effects are studied at extremely low momenta of the order of the inverse system size. We show that the structure factor is parabolic in this region and calculate the prefactor analytically. The obtained results reveal fractal-like properties of the packing and can be used to analyze small-angle scattering from such systems.

Microscopic nonlinear optical response: Analysis and calculations with the Floquet-Bloch formalism.

We analyze microscopic nonlinear optical response of periodic structures within the Floquet-Bloch formalism. The analysis is focused on the real-space distributions of optically induced charge and electron current density within the unit cell of a crystal. We demonstrate that the time-reversal symmetry of a crystal determines the phases of the temporal oscillations of these distributions. We further analyze their spatial symmetries and connection to macroscopic optical response. We illustrate our study with ab initio calculations that combine density functional theory with the Floquet-Bloch formalism. The calculations provide time-dependent optically induced charge distributions and electron current densities within the unit cells of a crystal with inversion symmetry and a crystal without inversion symmetry in response to a strong-field excitation. The real-space, microscopic view on nonlinear optical response provides insightful information about the strong field-matter interaction.

Pressure Dependence of Intra- and Interlayer Excitons in 2H-MoS2 Bilayers.

The optical and electronic properties of multilayer transition metal dichalcogenides differ significantly from their monolayer counterparts due to interlayer interactions. The separation of individual layers can be tuned in a controlled way by applying pressure. Here, we use a diamond anvil cell to compress bilayers of 2H-MoS2 in the gigapascal range. By measuring optical transmission spectra, we find that increasing pressure leads to a decrease in the energy splitting between the A and the interlayer exciton. Comparing our experimental findings with ab initio calculations, we conclude that the observed changes are not due to the commonly assumed hydrostatic compression. This effect is attributed to the MoS2 bilayer adhering to the diamond, which reduces the in-plane compression. Moreover, we demonstrate that the distinct real-space distributions and resulting contributions from the valence band account for the different pressure dependencies of the inter- and intralayer excitons in compressed MoS2 bilayers.

Topological analysis of information-theoretic quantities in density functional theory.

We have witnessed considerable research interest in the recent literature about the development and applications of quantities from the information-theoretic approach (ITA) in density functional theory. These ITA quantities are explicit density functionals, whose local distributions in real space are continuous and well-behaved. In this work, we further develop ITA by systematically analyzing the topological behavior of its four representative quantities, Shannon entropy, two forms of Fisher information, and relative Shannon entropy (also called information gain or Kullback-Leibler divergence). Our results from their topological analyses for 103 molecular systems provide new insights into bonding interactions and physiochemical properties, such as electrophilicity, nucleophilicity, acidity, and aromaticity. We also compare our results with those from the electron density, electron localization function, localized orbital locator, and Laplacian functions. Our results offer a new methodological approach and practical tool for applications that are especially promising for elucidating chemical bonding and reactivity propensity.

Symmetry-mode analysis for local structure investigations using pair distribution function data

Symmetry-adapted distortion modes provide a natural way of describing distorted structures derived from higher-symmetry parent phases. Structural refinements using symmetry-mode amplitudes as fit variables have been used for at least ten years in Rietveld refinements of the average crystal structure from diffraction data; more recently, this approach has also been used for investigations of the local structure using real-space pair distribution function (PDF) data. Here, the value of performing symmetry-mode fits to PDF data is further demonstrated through the successful application of this method to two topical materials: TiSe2, where a subtle but long-range structural distortion driven by the formation of a charge-density wave is detected, and MnTe, where a large but highly localized structural distortion is characterized in terms of symmetry-lowering displacements of the Te atoms. The analysis is performed using fully open-source code within the DiffPy framework via two packages developed for this work: isopydistort, which provides a scriptable interface to the ISODISTORT web application for group theoretical calculations, and isopytools, which converts the ISODISTORT output into a DiffPy-compatible format for subsequent fitting and analysis. These developments expand the potential impact of symmetry-adapted PDF analysis by enabling high-throughput analysis and removing the need for any commercial software.

2D imaging spin-filter for NanoESCA based on Au/Ir(001) or Fe(001)-p(1×1)O

A two-dimensional imaging spin-filter for photo-emission electron microscopy is described. The spin-filter is capable of imaging the electron spin polarization of either real space or momentum space electron distributions. As a scattering target either Au/Ir(001) comes into use, where spin sensitivity results from using spin–orbit scattering or Fe(001)-p(1×1)O that exploits exchange interaction. Both scattering targets were characterized with respect to their working points and Sherman function in a separate setup. Spin-polarization images of secondary electrons from the magnetic domains of a poly-crystalline iron sample are shown using both scattering targets. Images with a spin-filter using Au/Ir(001) show more than 104 discrete detection channels which increases the effective two-dimensional figure-of-merit (FoM) of this spin-filter by four orders of magnitude compared to single-channel spin detectors. Using the exchange scattering target two spin-components have been imaged for the first time. A method to detect all three spin-components is also outlined.

Effect of surface polarization and structural deformation on the formation and stabilization of polarons in two-dimensional Ruddlesden–Popper metal halide perovskites

First-principles density-functional theory calculations were performed to reveal the effect of surface polarization and structural deformation on the formation and stabilization of the polaron in two-dimensional Ruddlesden–Popper perovskites. Our results revealed that the orientational distribution of organic cations induces surface polarization. The surface dipole moment can be well featured by the c axis distances between N and the nearest I atoms. Structural deformation and surface dipole moments result in separate real-space distributions of hole and electron polarons. Our results also reveal that the structural deformation of the [PbI6] sublattices and surface polarization are closely related to the reorientation of organic cations and can be effectively modulated by it. This reorientation significantly impacts the stabilization of polarons. Our understandings provide insight into the nature of polarons in two-dimensional Ruddlesden–Popper perovskites and general guidance for the proper selection of organic cations in two-dimensional perovskites for suitable applications in photovoltaic and optoelectronic devices.

Revealing Intramolecular Isotope Effects with Chemical-Bond Precision.

Isotope substitution of a molecule not only changes its vibrational frequencies but also changes its vibrational distributions in real-space. Quantitatively measuring the isotope effects inside a polyatomic molecule requires both energy and spatial resolutions at the single-bond level, which has been a long-lasting challenge in macroscopic techniques. By achieving ångström resolution in tip-enhanced Raman spectroscopy (TERS), we record the corresponding local vibrational modes of pentacene and its fully deuterated form, enabling us to identify and measure the isotope effect of each vibrational mode. The measured frequency ratio νH/νD varies from 1.02 to 1.33 in different vibrational modes, indicating different isotopic contributions of H/D atoms, which can be distinguished from TERS maps in real-space and well described by the potential energy distribution simulations. Our study demonstrates that TERS can serve as a non-destructive and highly sensitive methodology for isotope detection and recognition with chemical-bond precision.

Extended q-Range X-Ray Scattering Reveals High-Resolution Structural Details of Biomacromolecules in Aqueous Solutions.

We communicate a feasibility study for high-resolution structural characterization of biomacromolecules in aqueous solution from X-ray scattering experiments measured over a range of scattering vectors (q) that is approximately two orders of magnitude wider than used previously for such systems. Scattering data with such an extended q-range enables the recovery of the underlying real-space atomic pair distribution function, which facilitates structure determination. We demonstrate the potential of this method for biomacromolecules using several types of cyclodextrins (CD) as model systems. We successfully identified deviations of the tilting angles for the glycosidic units in CDs in aqueous solutions relative to their values in the crystalline forms of these molecules. Such level of structural detail is inaccessible from standard small angle scattering measurements. Our results call for further exploration of ultra-wide-angle X-ray scattering measurements for biomacromolecules.

Equilibrium current distributions and W∞ gauge theory in quantum Hall systems of conventional electrons and Dirac electrons

In equilibrium planer systems of Hall electrons, such as GaAs heterostructures and graphene, support two species of current counterflowing along the system edges, as observed recently in experiment using a nanoscale magnetometer. We examine distinct origins and distinctive features of these equilibrium currents, with the Coulombic many-body effects taken into account, and derive their real-space distributions. Our basic tool of analysis is a reformulation of quantum Hall systems as a ${W}_{\ensuremath{\infty}}$ gauge theory, which allows one to diagonalize the total Hamiltonian according to the resolutions of external probes. These equilibrium currents are deeply tied to the orbital magnetization in quantum Hall systems. Special attention is drawn to the case of graphene, especially the neutral $(\ensuremath{\nu}=0)$ ground state and its intrinsic diamagnetic response that combines with the equilibrium currents to govern the orbital magnetization and its oscillations with filling.

Orbital degree of freedom induced multiple sets of second-order topological states in two-dimensional breathing Kagome crystals

The lattice geometry induced second-order topological corner states in breathing Kagome lattice have attracted enormous research interests, while the realistic breathing Kagome materials identified as second-order topological insulators are still lacking. Here, we report by first-principles calculations the second-order topological states emerging in two-dimensional d-orbital breathing Kagome crystals, i.e., monolayer niobium/tantalum chalcogenide halides M3QX7 (M = Nb, Ta; Q = S, Se, Te; X = Cl, Br, I). We find that the orbital degree of freedom of d orbitals can give rise to multiple sets of corner states. Combining fraction corner anomaly, orbital components and real space distribution of the corner states, we can also identify the topology of these corner states. Our work not only extends the lattice geometry induced second-order topological states to realistic materials, but also builds a clear and complete picture on their multiple sets of second-order topological states.

Phase diagram of twisted bilayer graphene at filling factor ν=±3

We study the correlated insulating phases of twisted bilayer graphene (TBG) in the absence of lattice strain at integer filling $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}3$. Using the self-consistent Hartree-Fock method on a particle-hole symmetric model and allowing translation symmetry breaking terms, we obtain the phase diagram with respect to the ratio of $AA$ interlayer hopping $({w}_{0})$ and $AB$ interlayer hopping $({w}_{1})$. When the interlayer hopping ratio is close to the chiral limit (${w}_{0}/{w}_{1}\ensuremath{\lesssim}0.5$), a quantum anomalous Hall state with Chern number ${\ensuremath{\nu}}_{c}=\ifmmode\pm\else\textpm\fi{}1$ can be observed consistent with previous studies. Around the realistic value ${w}_{0}/{w}_{1}\ensuremath{\approx}0.8$, we find a spin and valley polarized, translation symmetry breaking, state with ${C}_{2z}T$ symmetry, a charge gap and a doubling of the moir\'e unit cell, dubbed the ${C}_{2z}T$ stripe phase. The real-space total charge distribution of this ${C}_{2z}T$ stripe phase in the flat band limit does not have modulation between different moir\'e unit cells, although the charge density in each layer is modulated, and the translation symmetry is strongly broken. Other symmetries, including ${C}_{2z}, {C}_{2x}$, particle-hole symmetry $P$, and the topology of the ${C}_{2z}T$ stripe phase, are also discussed in detail. We observed braiding and annihilation of the Dirac nodes by continuously turning on the order parameter to its fully self-consistent value, and provide a detailed explanation of the mechanism for the charge gap opening despite preserving ${C}_{2z}T$ and valley $\mathrm{U}(1)$ symmetries. In the transition region between the quantum anomalous Hall phase and the ${C}_{2z}T$ stripe phase, we find an additional competing state with comparable energy corresponding to a phase with a tripling of the moir\'e unit cell.

Dielectric properties of V2O3 and (V0.989Cr0.011)2O3 from temperature-dependent ac impedance measurements

The dielectric properties of the various insulating phases in pure ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ and ${({\mathrm{V}}_{0.989}{\mathrm{Cr}}_{0.011})}_{2}{\mathrm{O}}_{3}$ crystals have been investigated. Large dielectric constants on the scale of ${10}^{3}$ were obtained, which were attributed to the backflow effect of normal carriers and also the periodic charge configuration relevant to V-V dimers in an antiferromagnetic insulating state or the bond contraction of V-Cr-V in a paramagnetic insulating phase. We propose that if Cr dopants are arranged nearly uniformly, the charge density of ${({\mathrm{V}}_{0.989}{\mathrm{Cr}}_{0.011})}_{2}{\mathrm{O}}_{3}$ in the paramagnetic insulating phase will exhibit a doping-induced wavelike distribution in real space, and thus the polarization of the system will be enhanced.

A new thermography using inelastic scattering analysis of wavelength-resolved neutron transmission imaging

Thermography using energy-dependent neutron transmission imaging can non-invasively and non-destructively visualize a real-space distribution of interior temperatures of a material in a container. Previously, resonance absorption broadening analysis and Bragg-edge shift analysis using energy-resolved neutron transmission have been developed, however some issues remain, e.g., imaging efficiency, substance limitation and temperature sensitivity. For this reason, we propose a new neutron thermography using the temperature dependence of inelastic scattering of cold neutrons. This method has some advantages, for example, the imaging efficiency is high because cold neutrons are measured with moderate wavelength resolution, and light elements can be analysed in principle. We investigated the feasibility of this new neutron thermography at pulsed neutron time-of-flight imaging instruments at ISIS in the United Kingdom and HUNS in Japan. A Rietveld-type transmission spectrum analysis program (RITS) was employed to refine temperature and atomic displacement parameters from the inelastic scattering cross-section analysis. Finally, we demonstrated interior thermography of an α-Fe sample of 10 mm thickness inside a vacuum chamber by using a neutron time-of-flight imaging detector at the compact accelerator-driven pulsed neutron source HUNS.

Atomic-Scale Mapping and Quantification of Local Ruddlesden-Popper Phase Variations.

The Ruddlesden-Popper (An+1BnO3n+1) compounds are highly tunable materials whose functional properties can be dramatically impacted by their structural phase n. The negligible differences in formation energies for different n can produce local structural variations arising from small stoichiometric deviations. Here, we present a Python analysis platform to detect, measure, and quantify the presence of different n-phases based on atomic-resolution scanning transmission electron microscopy (STEM) images. We employ image phase analysis to identify horizontal Ruddlesden-Popper faults within the lattice images and quantify the local structure. Our semiautomated technique considers effects of finite projection thickness, limited fields of view, and lateral sampling rates. This method retains real-space distribution of layer variations allowing for spatial mapping of local n-phases to enable quantification of intergrowth occurrence and qualitative description of their distribution suitable for a wide range of layered materials.

All-Optically Controlled Topological Current Switcher Based on Silicene-Like Nanoribbons

Low-dimensional topological insulator materials, such as silicene-like 2-D materials, have wide applications in electronic, spintronic, and optoelectronic nanodevice, by utilizing their topologically protected edge states. In theoretical studies, Floquet theorem is usually employed in the nanosystems under light irradiation with high-frequency approximation, which may not be accessible in experimental research. In this work, we study the quasienergy spectra and edge-state transport of silicene-like nanoribbons under low-frequency light irradiation (in visible wavelengths), by extracting the zero-photon component from the nonperturbative Floquet bands. These silicene-like nanoribbons undergo topological phase transition from quantum spin Hall (QSH) to quantum anomalous Hall (QAH) insulator under circularly polarized light, accompanied by helical edge modes to chiral ones. The propagation direction of edge-mode current in QAH nanoribbons can be switched by left-/right-circularly polarized (LCP/RCP) light, and such a current-switching effect is then confirmed in heterojunction composed of QSH and QAH nanoribbons. Based on the all-optically controlled current-switching effect, we design a three-terminal current switcher, with one input terminal, two output ones, and central device irradiated by LCP/RCP light. Conductance and real-space local current distribution of the proposed nanosystem reveal that the input current can indeed be switched into specific output terminal by LCP/RCP light. The proposed current switcher changes the electron movement very quickly, and we believe that it would have potential applications in high-speed photoelectric nanodevices.