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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Capturing CO 2 in Quadrupolar Binding Pockets: Broadband Microwave Spectroscopy of Pyrimidine-(CO 2 ) n , n = 1,2

Pyrimidine has two in-plane CH(δ+)/N̈(δ–)/CH(δ+) binding sites that are complementary to the (δ–/2δ+/δ–) quadrupole moment of CO 2 . For this study, we recorded broadband microwave spectra over the 7.5–17.5 GHz range for pyrimidine-(CO 2 ) n with n = 1 and 2 formed in a supersonic expansion. Based on fits of the rotational transitions, including nuclear hyperfine splitting due to the two 14 N nuclei, we have assigned 313 hyperfine components across 105 rotational transitions for the n = 1 complex and 208 hyperfine components across 105 rotational transitions for the n = 2 complex. The pyrimidine-CO 2 complex is planar, with CO 2 occupying one of the quadrupolar binding sites, forming a structure in which the CO 2 is stabilized in the plane by interactions with the C–H hydrogens adjacent to the nitrogen atom. This structure is closely analogous to that of the pyridine-CO 2 complex studied previously by (Doran, J. L. J. Mol. Struct. 2012, 1019, 191–195). The fit to the n = 2 cluster gives rotational constants consistent with a planar cluster of C 2v symmetry in which the second CO 2 molecule binds in the second quadrupolar binding pocket on the opposite side of the ring. The calculated total binding energy in pyrimidine-CO 2 is –13.7 kJ mol –1 , including corrections for basis set superposition error and zero-point energy, at the CCSD(T)/ 6-311++G(3df,2p) level, while that in pyrimidine-(CO 2 ) 2 is almost exactly double that size, indicating little interaction between the two CO 2 molecules in the two binding sites. The enthalpy, entropy, and free energy of binding are also calculated at 300 K within the harmonic oscillator/rigid-rotor model. This model is shown to lack quantitative accuracy when it is applied to the formation of weakly bound complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Improved Accuracy in Semi-Experimental Structure Determination by Resolving Problems Associated with Rotation of Principal Inertial Axes of Isotopologues: Structures of 1,3-Oxazole ( c -C 3 H 3 NO)

The rotational spectrum of the normal isotopologue of 1,3-oxazole (c-C 3 H 3 NO) was observed from 43 to 750 GHz. Over 3900 transitions for the ground vibrational state are measured, assigned, and least-squares fit to sextic centrifugally distorted-rotor Hamiltonians. The measured frequencies and resulting spectroscopic constants from this extended spectral range, combined with previous measurements of the nuclear quadrupole coupling constants, will facilitate astronomical searches for oxazole across the majority of the range of modern radiotelescopes. Spectra for a set of 30 oxazole isotopologues, which include multiple isotopic substitutions of each atom, are used to determine the first semi-experimental equilibrium ($r$$^{SE}_{e}$) structure and semi-experimental substitution structure ($r$$^{SE}_{e}$), each using CCSD(T) computed values for the vibration–rotation interaction and electron-mass corrections. The large number of isotopologues, including 21 isotopologues observed for the first time, and the redundant substitutions of each atom provide sufficient spectroscopic information to determine the $r$$^{SE}_{e}$ structure with the expected high level of accuracy and precision (0.0001 or 0.0002 Å in bond distances and 0.013 to 0.025° in bond angles). In the course of this study, we analyzed a known issue for some $r$$^{SE}_{e}$ structure determinations of near-oblate asymmetric tops in which inclusion of individual isotopologues degrades the structure determination. We demonstrate that this problem primarily arises from the difference in the values of the computed vibration–rotation interaction corrections as evaluated at the computed re geometry vs the $r$$^{SE}_{e}$ geometry of the “real” molecule. Our solution to this problem substantially improves the $r$$^{SE}_{e}$ structure of oxazole and likely can be generalized to many other molecules.

Chemical structure↗
DOE OSTI2020

Electronic Structure of the Primary Electron Donor P 700 +• in Photosystem I Studied by Multifrequency HYSCORE Spectroscopy at X- and Q-Band

The primary electron donor P 700 of the photosystem I ( PS I) is a heterodimer consisting of two chlorophyll molecules. A series of electron-transfer events immediately following the initial light excitation leads to a stabilization of the positive charge by its cation radical form, P 700 +• . Here, the electronic structure of P 700 +• and, in particular, its asymmetry with respect to the two chlorophyll monomers is of fundamental interest and is not fully understood up to this date. Here, we apply multifrequency X- (9 GHz) and Q-band (35 GHz) hyperfine sublevel correlation (HYSCORE) spectroscopy to investigate the electron spin density distribution in the cation radical P 700 +• of PS I from a thermophilic cyanobacterium Thermosynechococcus elongatus . Six 14 N and two 1 H distinct nuclei have been resolved in the HYSCORE spectra and parameters of the corresponding nuclear hyperfine and quadrupolar hyperfine interactions were obtained by combining the analysis of HYSCORE spectral features with direct numerical simulations. Based on a close similarity of the nuclear quadrupole tensor parameters, all of the resolved 14 N nuclei were assigned to six out of total eight available pyrrole ring nitrogen atoms (i.e., four in each of the chlorophylls), providing direct evidence of spin density delocalization over the both monomers in the heterodimer. Using the obtained experimental values of the 14 N electron-nuclear hyperfine interaction parameters, the upper limit of the electron spin density asymmetry parameter is estimated as R A/B upper = 7.7 ± 0.5, while a tentative assignment of 14 N observed in the HYSCORE spectra yields R B/A = 3.1 ± 0.5.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Spin Decoherence in VOPc@graphene Nanoribbon Complexes

Carbon nanoribbons or nanographene qubit arrays can facilitate quantum-to-quantum transduction between light, charge, and spin, making them an excellent testbed for fundamental science in quantum coherent systems and for the construction of higher-level qubit circuits. Here, in this work, we study spin decoherence due to coupling with a surrounding nuclear spin bath of an electronic molecular spin of a vanadyl phthalocyanine (VOPc) molecule integrated onto an armchair-edged graphene nanoribbon (GNR). Density functional theory (DFT) is used to obtain ground-state atomic configurations. Decay of spin coherence in Hahn echo experiments is then simulated using the cluster correlation expansion method with a spin Hamiltonian involving hyperfine and electric field gradient tensors calculated from DFT. We find that the decoherence time T 2 is anisotropic with respect to magnetic field orientation and determined only by the hydrogen nuclear spins on both VOPc and GNR. Large electron spin echo envelope modulation (ESEEM) due to nitrogen and vanadium nuclear spins is present at specific field ranges and can be completely suppressed by tuning the magnetic field. The relation between these field ranges and the hyperfine interactions is analyzed. The effects of interactions with the nuclear quadrupole moments are also studied, validating the applicability and limitations of the spin Hamiltonian when they are disregarded.

Hamiltonians↗
DOE OSTI2024

Predicting Partial Atomic Charges in Metal–Organic Frameworks: An Extension to Ionic MOFs

Molecular simulation is an invaluable tool to predict and understand the usage of metal–organic frameworks (MOFs) for gas storage and separation applications. Accurate partial atomic charges, commonly obtained from density functional theory (DFT) calculations, are often required to model the electrostatic interactions between the MOF and adsorbates, especially when the adsorbates have dipole or quadrupole moments, such as water and CO 2 . Machine learning (ML) models have been previously employed to predict partial charges and avoid the computational cost associated with DFT calculations. However, previous ML models suffer from small training data sets, which limit their scope of application. In this work, we introduce two novel machine learning models, PACMOF2-neutral and PACMOF2-ionic, aimed at predicting the density-derived electrostatic and chemical (DDEC6) partial atomic charges for both neutral and ionic MOFs. These models not only yield DFT-level accuracy at a fraction of the computational cost but also demonstrate a remarkable improvement in prediction of adsorption, as validated with grand canonical Monte Carlo simulations. Furthermore, the robustness and fast computational time of the PACMOF2 models, along with their transferability to other porous materials such as covalent organic frameworks and zeolites, underscores their potential in high-throughput screening of MOFs for diverse applications.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Tip-Enhanced Multipolar Raman Scattering

We record nanoscale chemical images of thiobenzonitrile (TBN)-functionalized plasmonic gold nanocubes via tip-enhanced Raman spectroscopy (TERS). The spatially averaged optical response is dominated by conventional (dipolar) TERS scattering from TBN but also contains weaker spectral signatures in the 1225-1500 cm-1 region. The weak optical signatures dominate some of the recorded single pixel spectra. We can uniquely assign these Raman forbidden transitions to multipolar Raman scattering, which implicates spatially varying enhanced electric field gradients at plasmonic tip-sample nanojunctions. Specifically, we can assign observations of tip-enhanced electric dipole-magnetic dipole as well as electric dipole-electric quadrupole driven transitions. These signals need to be understood and accounted for in the interpretation of TERS spectral images, particularly in on-going quests aimed at chemical reaction mapping via TERS.

Wang, Chih-Feng↗
DOE OSTI2025

Chemical Vapor Transformation of Lithium Metal: Mechanism and Enhanced Stability

Constructing a stable solid electrolyte interface (SEI) with high productivity and scalability is essential for the practical application of thin Li metal anodes. Here, in this work, we report a chemical vapor transformation (CVT) strategy in which Li metal is exposed to trimethylaluminum (TMA), inducing a rapid and spontaneous surface reaction that forms a robust, multilayered SEI. In situ quartz crystal microbalance (QCM) and quadrupole mass spectrometry (QMS), combined with ex situ X-ray photoelectron spectroscopy (XPS), UV Raman spectroscopy, and density functional theory (DFT) calculations, reveal that TMA removes the native passivation layer, reacts with Li metal, and drives a coupled bulk-surface transformation involving Li–Al interdiffusion. The resulting SEI exhibits a chemically graded structure consisting of an inner Li–Al alloy and an outer amorphous carbon layer formed via demethylation and ligand-exchange pathways. This modified surface exhibits significantly enhanced stability compared to that of bare Li in electrochemical cycling using liquid and solid-state electrolytes. This work unveils a unique surface-mediated bulk transformation mechanism for lithium metal and establishes CVT as a scalable and fundamentally distinct approach for the interfacial engineering of reactive metals.

Li metal↗
DOE OSTI2020

Nanoporous Co/Mn-Mixed Metal Oxides Templated via Polysulfones for Amine Oxidation

Herein, we report syntheses of microporous and mesoporous mixed metal oxides templated via an anionic surfactant. The effects of acid treatment, solvent type, and the amount of metal incorporation were investigated. Two different cobalt–manganese oxide spinels that were synthesized with surface areas as high as 137 m 2 /g were obtained. These nanomaterials indicate 3.8 nm monomodal pore sizes with crystallite sizes of 2.4–3.6 nm. 59 Co MASNMR studies have shown that quadrupole coupling values from 1500 to 5000 kHz with asymmetry values ranging from 0.1 to 1 have been used to identify cobalt oxidation states. Amine oxidation was used as a model reaction, which allowed for imide yields of above 90% from benzylamine homocoupling. Finally, the use of these nanoporous oxides allows for a high-yielding homocoupling of benzylamine.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Active Plasmonics and Active Chiral Plasmonics through Orientation-Dependent Multipolar Interactions

While most active plasmonic efforts focus on responsive metamaterials to modulate optical response, we present a simple alternative based on applied orientation control that can likely be implemented for many passive plasmonic materials. Passive plasmonic motifs are simpler to prepare but cannot be altered postfabrication. Here, we show that such systems can be easily manipulated through substrate orientation control to generate both active plasmonic and active chiral plasmonic responses. Using gold nanocrescents as our model platform, we demonstrate tuning of optical extinction from -21% to +36% at oblique incidence relative to normal incidence. Variation of substrate orientation in relation to incident polarization is also demonstrated to controllably switch chiroptical handedness (e.g., Δg = ± 0.55). These active plasmonic responses arise from the multipolar character of resonant modes. In particular, we correlate magnetoelectric and dipole–quadrupole polarizabilities with different light-matter orientation-dependence in both near- and far-field localized surface plasmon activity. Additionally, the attribution of far-field optical response to higher-order multipoles highlights the sensitivity offered by these orientation-dependent characterization techniques to probe the influence of localized electromagnetic field gradients on a plasmonic response. The sensitivity afforded by orientation-dependent optical characterization is further observed by the manifestation in both plasmon and chiral plasmon responses of unpredicted structural nanocrescent variance (e.g., left- and right-tip asymmetry) not physically resolved through topographical imaging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Electrical Control of the Nuclear Spin States of Rare-Earth Adatoms

Rare-earth adatoms on surfaces have been studied for potential atomic-scale magnetic storage, quantum sensing, and quantum computing applications. Despite accumulating experimental efforts, a comprehensive description of the electronic configurations of the adatoms remains elusive. Here, we investigate two charge states and several electronic configurations, including 5d and 6s valence shells, for a Sm adatom on a MgO substrate using multiconfigurational ab initio methods, for the possibility of using the Sm nuclear spin levels as qubits. For the configurations in a neutral charge state, we find that the electronic ground state is a singlet, and thus the hyperfine interaction associated with the 147 Sm nucleus is absent, which may greatly enhance nuclear spin coherence time. The degeneracy of the nuclear levels is lifted by the nuclear quadrupole interaction. We show that the splitting of the nuclear levels can be controlled by a static electric field, and that Rabi oscillations between the nuclear levels can be induced by a time-dependent electric field. For the configurations in a singly charged state, electronic Kramers doublets are formed. The electronic configurations including an unpaired 6s orbital exhibit a strong hyperfine Stark effect due to a large Fermi contact contribution to the hyperfine interaction. In these configurations, electric-field-induced Rabi oscillations between the electronic-nuclear levels can occur at frequencies up to 3 orders of magnitude higher than those for the neutral charge state. The proposed system may be experimentally observed within scanning tunneling microscopy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Time-Evolving Chirality Loss in Molecular Photodissociation Monitored by X-ray Circular Dichroism Spectroscopy

In this work, the ultrafast photoinduced chirality loss of 2-iodobutane is studied theoretically by time- and frequency-resolved X-ray circular dichroism (TRXCD) spectroscopy. Following an optical excitation, the iodine atom dissociates from the chiral center, which we capture by quantum non-adiabatic molecular dynamics simulations. At variable time delays after the pump, the resonant X-ray pulse selectively probes the iodine and carbon atom involved in the chiral dissociation through a selected core-to-valence transition. The TRXCD signal at the iodine L 1 edge accurately captures the timing of C–I photodissociation and thereby chirality loss, c.a 70 fs. The strong electric dipole–electric quadrupole (ED–EQ) response makes this signal particularly sensitive to vibronic coherence at the high X-ray regime. At the carbon K-edges, the signals monitor the molecular chirality of the 2-butyl radical photoproduct and the spin state of the iodine atom. The ED–EQ response is masked under the strong electric dipole-magnetic dipole response, making this signal intuitive for the electronic population. The evolution of the core electronic states and its chiral sensitivity is discussed. Overall, the element-specific TRXCD signal provides a detailed picture of molecular dynamics and offers a unique sensitive window into the time-dependent chirality of molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The Energetic Origins of Pi–Pi Contacts in Proteins

Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein’s stability and structure. Pi–pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi–pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi–pi contact motifs. We find that neutral pi–pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter–Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi–pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi–pi contacts in polar media and like typical ion–pi interactions in nonpolar environments. Like-charged pairs such as arginine–arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi–pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Mg-Ion Conduction in Antiperovskite Solid Electrolytes Revealed by 25 Mg Ultrahigh Field NMR and First-Principles Calculations

Magnesium-ion batteries hold the potential to outperform the energy density of lithium-ion batteries, given the divalent charge carried by each Mg 2+ cation, but remain in an early stage of development. Here, in this study, 25 Mg solid-state nuclear magnetic resonance (ssNMR) is used to gain insight into the local structure and Mg-ion dynamics of candidate Mg-ion solid electrolytes, the antiperovskites Mg 3 SbN and Mg 3 AsN. Using the highest available magnetic field (35.2 T) for high-resolution solid-state NMR, the largest 25 Mg quadrupole coupling constants (C Q ) yet measured of up to 22 MHz are reported and corroborated by first-principles calculations. Predicted C Q values are shown to correlate with the antiperovskite’s tolerance factor; thus, 25 Mg NMR linewidths can report on lattice distortions and phase stability of these antiperovskites. Variable-temperature 25 Mg NMR spectra demonstrate changes at elevated temperatures, ascribed to Mg-ion motional effects. 25 Mg T 1 relaxometry measurements at ultrahigh field reveal a lower activation energy for the more distorted Mg 3 AsN phase, matching computational predictions of a lower energy barrier for Mg 2+ ion migration and suggesting that additional scrutiny of antiperovskites as Mg-ion conductors is warranted. Given the inherent challenges of 25 Mg NMR, this work demonstrates the benefits of combining ultrahigh field NMR spectroscopy, advanced pulse sequences, modern signal processing, and first-principles calculations to facilitate NMR of quadrupolar nuclei as a tool to probe the local structure and ion dynamics in beyond-Li battery materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

High Mass Analysis with a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer: From Inorganic Salt Clusters to Antibody Conjugates and Beyond

Analysis of proteins and complexes under native mass spectrometric (MS) and solution conditions was typically performed using time-of-flight (ToF) analyzers, due to their routine high m/z transmission and detection capabilities. However, over recent years, the ability of Orbitrap-based mass spectrometers to transmit and detect a range of high molecular weight species is well documented. Herein, we describe how a 15 Tesla Fourier transform ion cyclotron resonance mass spectrometer (15 T FT-ICR MS) is more than capable of analyzing a wide range of ions in the high m/z scale (>5000), in both positive and negative instrument polarities, ranging from the inorganic cesium iodide salt clusters; a humanized IgG1k monoclonal antibody (mAb; 148.2 kDa); an IgG1-mertansine drug conjugate (148.5 kDa, drug-to-antibody ratio; DAR 2.26); an IgG1-siRNA conjugate (159.1 kDa; ribonucleic acid to antibody ratio; RAR 1); the membrane protein aquaporin-Z (97.2 kDa) liberated from a C8E4 detergent micelle; the empty MSP1D1-nanodisc (142.5 kDa) and the tetradecameric chaperone protein complex GroEL (806.2 kDa; GroEL dimer at 1.6 MDa). We also investigate different regions of the FT-ICR MS that impact ion transmission and desolvation. Finally, we demonstrate how the transmission of these species and resultant spectra are highly consistent with those previously generated on both quadrupole-ToF (Q-ToF) and Orbitrap instrumentation. This article serves as an impactful example of how FT-ICR mass analyzers are competitive to Q-ToFs and Orbitraps for high mass detection at high m/z.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

193 nm Ultraviolet Photodissociation for the Characterization of Singly Charged Proteoforms Generated by MALDI

MALDI imaging allows for the near-cellular profiling of proteoforms directly from microbial, plant, and mammalian samples. Despite detecting hundreds of proteoforms, identification of unknowns with only intact mass information remains a distinct challenge, even with high mass resolving power and mass accuracy. To this end, many supplementary methods have been used to create experimental databases for accurate mass matching, including bulk or spatially resolved bottom-up and/or top-down proteomics. Herein, we describe the application of 193 nm ultraviolet photodissociation (UVPD) for fragmentation of quadrupole isolated singly charged ubiquitin (m/z 8565) by MALDI-UVPD on a UHMR HF Orbitrap. This platform permitted the high-resolution accurate mass measurement of not just terminal fragments but also large internal fragments. Finally, the outlined workflow demonstrates the feasibility of top-down analyses of isolated MALDI protein ions and the potential toward more comprehensive characterization of proteoforms in MALDI imaging applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

Abstract Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s – d -hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- ( α ) and intermediate-temperature ( α ″ ) phases of Cd 3 As 2 , KMgBi, and rutile-structure ( $$ \beta ^{\prime} $$ β ′ -) PtO 2 .

Science & Technology - Other Topics↗
DOE OSTI2021

Measurement of the neutron charge radius and the role of its constituents

The neutron is a cornerstone in our depiction of the visible universe. Despite the neutron zero-net electric charge, the asymmetric distribution of the positively- (up) and negatively-charged (down) quarks, a result of the complex quark-gluon dynamics, lead to a negative value for its squared charge radius, $\langle r^2_n\rangle$. The precise measurement of the neutron’s charge radius thus emerges as an essential part of unraveling its structure. Here we report on a $\langle r^2_n\rangle$ measurement, based on the extraction of the neutron electric form factor, $G^n_E$, at low four-momentum transfer squared (Q 2 ) by exploiting the long known connection between the N → Δ quadrupole transitions and the neutron electric form factor. Our result, $\langle r^2_n\rangle$=-0.110±0.008(fm 2 ), addresses long standing unresolved discrepancies in the $\langle r^2_n\rangle$ determination. The dynamics of the strong nuclear force can be viewed through the precise picture of the neutron’s constituent distributions that result into the non-zero $\langle r^2_n\rangle$ value.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Chiral structures of electric polarization vectors quantified by X-ray resonant scattering

Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO 3 /SrTiO 3 superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.

36 MATERIALS SCIENCE↗