Lattice Parameters Research Articles

Hadronic physics from a Wilson fermion mixed-action approach: charm quark mass and D(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{(s)}$$\\end{document} meson decay constants

We present our first set of results for charm physics, using the mixed-action setup introduced in a companion paper [1]. Maximally twisted Wilson valence fermions are used on a sea of non-perturbatively O(a)-improved Wilson fermions, made up by CLS Nf=2+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_\\mathrm {\\scriptstyle f}=2+1$$\\end{document} ensembles. Our charm-sector observables are free from O(amc)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(am_c)$$\\end{document} discretisation effects, without need of tuning any improvement coefficient, and show continuum-limit scaling properties consistent with leading cutoff effects of O(a2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(a^2)$$\\end{document}. We consider a subset of CLS ensembles – including four values of the lattice spacing and pion masses down to 200 MeV – allowing to take the continuum limit and extrapolate to the physical pion mass. A number of techniques are incorporated in the analysis in order to estimate the systematic uncertainties of our results for the charm quark mass and the D(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{(s)}$$\\end{document}-meson decay constants. This first study of observables in the charm sector, where the emphasis has been on the control of the methodology, demonstrates the potential of our setup to achieve high-precision results.

Observation of Hydrostatic‐Pressure‐Modulated Giant Caloric Effect and Electronic Topological Transition

AbstractPhase transition is a fundamental phenomenon in condensed matter physics, in which states of matter transform to each other with various critical behaviors under different conditions. The magnetic martensitic transformation features significant multi‐caloric effects that benefit the solid‐state cooling or heat pumping. Meanwhile, the electronic topological transition (ETT) driven by pressure has been rarely reported in martensitic systems. Here, the modulation effects of hydrostatic pressure on phase transitions in a magnetic martensitic alloy are reported. Owing to the huge volume expansion during the transition, the martensitic transition temperature is driven from 339 to 273 K by pressure within 1 GPa, resulting in highly tunable giant baro‐ and magneto‐caloric effects (BCE and MCE) in a wide working temperature range. Interestingly, an ETT is further induced by pressure in the martensite phase, with a sudden drop of the measured saturation magnetization around 0.6 GPa. First‐principles calculations reveal a sharp change in the density of states (DOS) due to the orbit shift around the Fermi level at the same pressure and reproduce the experimental observation of magnetization. Besides, the ETT is accompanied by remarkable changes in the lattice parameters and the unit‐cell orthorhombicity. The study provides insight into pressure‐modulated exotic phase‐transition phenomena in magnetic martensitic systems.

Hybrid-DFT study of halide perovskites, an energy-efficient material under compressive pressure for piezoelectric applications

Recent studies have reported that lead-halide perovskites are the most efficient energy-harvesting materials. Regardless of their high-output energy and structural stability, lead-based products have risk factors due to their toxicity. Therefore, lead-free perovskites that offer green energy are the expected alternatives. We have taken CsGeX3 (X = Cl, Br, and I) as lead-free halide perovskites despite knowing the low power conversion rate. Herein, we have tried to study the mechanisms of enhancement of energy-harvesting capabilities involving an interplay between structure and electronic properties. A density functional theory simulation of these materials shows a decrease in the band gaps, lattice parameters, and volumes with increasing applied pressure. We report the high piezoelectric responses and high electro-mechanical conversion rates, which are intriguing for generating electricity through mechanical stress.

Anisotropic optical property of ferroelectric Bi2O2X (X=S,Se,Te) monolayer and strain engineering.

Based on the first-principles calculations, ferroelectric Bi2O2X (X=S, Se, Te) monolayers with unequivalent in-plane lattice constants are confirmed to be the ground state, which is consistent with the experiment result (Nano Lett. 19, 5703(2019)), and the anisotropic optical property is firstly investigated. We find that the polarizations of Bi2O2X monolayers points along the direction of a-axis, and Bi2O2T e monolayer process the largest polarization. Furthermore, both the biaxial and uniaxial strains are favor for the enhancement of polarization of Bi2O2X monolayers. It should be mentioned that the type of band gap will convert from indirect to direct for Bi2O2T e monolayer when the a-axial tensile strain is larger than 2%. At last, the optical absorption coefficient for Bi2O2X monolayers are calculated, and we obtain that Bi2O2Te monolayer has the strongest optical absorption within the range of visible light, the anisotropy and possible strain engineering to improve the optical absorption are discussed in detail. Our findings are significant in fields of optoelectronics and photovoltaics.&#xD.

Investigation of the magnetic and structural properties in the non‐stoichiometric Heusler alloy Ni50Mn25+xSn25‐x; x = 13, 14

AbstractMemory shape magnetic alloys, especially Heusler alloys, are important materials in replacing conventional cooling with magnetic systems. In the present study off stoichiometric Heusler alloys with nominal composition Χ50Υ25+xΖ25‐x (X = Ni; Y = Mn; Z = Sn; x = 13, 14) were prepared by arc melting followed by thermal treatment. Structural properties were analyzed with X‐ray diffraction at room temperature (RT) and at elevated temperatures, above the martensite—austenite transition area, to determine the relevant crystallographic parameters and observe the transition. Martensite stabilization at RT appears to be a challenge, coexistence of martensite—austenite phases were observed and calculated for both 38–12 and 39–11 (16% and 12% austenite, respectively). Magnetization measurements versus temperature and field were recorded in the areas of interest where 1st order transitions were expected (355 K for x = 13 and 408 K for x = 14), and the magnetic entropy's changes (ΔSm) were determined [0.4 (J/kgK) for x = 13 and 0.3 J/(kgK) for x = 14; Hmax = 1 T]. The complex character of the magnetic properties and their dependence on Mn‐Sn ratio and on the distance between Mn atoms is discussed. The structure and the lattice parameters were determined using an anisotropic strain broadening model; stress and strain were detected in the structure due to crystal phase coexistence.

High‐pressure studies of Mn2(C2H6N6)4(NO3)4·2H2O by Raman scattering, infrared absorption, and synchrotron X‐ray diffraction

AbstractMn2(C2H6N6)4(NO3)4·2H2O (Mn) as one of the energetic coordination complexes was chosen for high‐pressure research. In this work, Mn was analyzed by in situ Raman scattering, infrared absorption, and synchrotron angle‐dispersive X‐ray diffraction (ADXRD) technologies up to ~20 GPa at room temperature. The vibrational modes of Mn at ambient pressure were comprehensively resolved based on the experimental results. Detailed spectral analyses revealed that Mn underwent three pressure‐induced phase transitions at 0.5, 2.5, and 5.7 GPa, respectively. ADXRD experiments confirmed the existence of these three phase transitions in Raman and infrared spectra analyses. Based on the analysis of the vibrational spectra and the changes of lattice parameters under pressure, it can be considered that the deformation of the 3‐hydrazino‐4‐amino‐1, 2, 4‐triazole (HATr) ligand led to the first phase transition, and the distortion of the triazole ring induced the second phase transition, and the rearrangement of the hydrogen bonds resulted in the third phase transition. In addition, it can be inferred from Raman spectra and ADXRD data that Mn may have experienced the abnormal expansion during the first phase transition. This work may lay the foundation for further investigating the structure and properties of energetic coordination complexes under pressure.

AlN and Nb(C,N) Composite Precipitation Behaviors and Their Effects on Austenite Grain Growth in SCr420H High‐Temperature Carburized Gear Steel

The effects of nitrogen (N) and niobium (Nb) contents on the precipitation behaviors of AlN, Nb(C,N), and AlN‐Nb(C,N) precipitates and austenite grain growth during the pseudo‐carburizing process are investigated for the carburized steel SCr420H. The results indicate that an increase of N content from 0.011% to 0.019% leads to the emergence of fine and uniform austenite grain structure in the sample while being held at 930 °C for 6 h, which is attributed to a notable rise in the number density of AlN and a decrease in the coarsening rate of AlN. In the steel containing 0.023% Nb, the composite precipitates AlN‐Nb(C,N) play a primary role in the pinning effect on austenite grains growth. The isolated Nb(C,N) and AlN precipitates have minor pinning effects due to their very low volume fractions. Nb(C,N) cap forming on AlN substrate obeys the Shoji–Nishiyama orientation relationship. The favorable lattice matching between AlN and Nb(C,N) and accelerated coarsening rate of Nb(C,N) cap decrease hindrances to the nucleation, growth, and coarsening of Nb(C,N) on AlN substrate. Meanwhile, these simultaneous effects also suppress the same processes for the isolated Nb(C,N) in the matrix.

Microstructure Evolution and Homogenization Kinetics of 15Cr–30Ni–Fe Heat‐Resistant Alloy

The as‐cast microstructure, microsegregation of alloying elements, and microstructure evolution during homogenization of the newly designed 15Cr–30Ni–Fe heat‐resistant alloy are studied. Ti, Nb, Si, and Mo segregate at the interdendritic region. The brittle eutectic Laves phase contains Fe, Ti, Ni, Nb, Si, and Mo, which is identified as the Fe2Ti Laves phase. The activation energy for the Fe2Ti Laves phase dissolution is close to the activation energy for Ti diffusion in the γ matrix based on the Johnson–Mehl–Avrami–Kolmogorov analysis. The back‐diffusion of Ti to the γ matrix is the limiting step for the dissolution of Fe2Ti Laves phase. The kinetic equation of homogenization considering lattice parameters and pre‐exponential factor correction is established. After the double‐stage homogenization at 980 °C/10 h + 1140 °C/4 h, the volume fraction of the Laves phase decreases from 5.11% to 0.26%, and the large eutectic Laves phase is completely dissolved. The reduction in the standard deviation of microhardness at different soaking times effectively reflects the gradual decrease in the degree of microsegregation of alloying elements. The average grain size of the alloy after homogenization is 410 ± 63.1 μm, which is beneficial to control the further refinement of grain during the subsequent hot working.

Nucleon form factors in Nf=2+1 lattice QCD at the physical point: Finite lattice spacing effect on the root-mean-square radii

We present results for the nucleon form factors: electric (GE), magnetic (GM), axial (FA), induced pseudoscalar (FP), and pseudoscalar (GP) form factors, using the second PACS10 ensemble that is one of three sets of 2+1 flavor lattice QCD configurations at physical quark masses in large spatial volumes [exceeding (10 fm)3]. The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared O(a) improved Wilson quark action and Iwasaki gauge action at the second gauge coupling β=2.00 corresponding to the lattice spacing of a=0.063 fm. We determine the isovector electric, magnetic and axial radii, and magnetic moment from the corresponding form factors, as well as the axial-vector coupling gA. Combining our previous results for the coarser lattice spacing [E. Shintani , ; ], the finite lattice spacing effects on the isovector radii, magnetic moment, and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on gA is kept smaller than the statistical error of 2% while the effect on the isovector radii was observed as a possible discretization error of about 10%, regardless of the channel. We also report the partially conserved axial-vector current relation using a set of nucleon three-point correlation functions in order to verify the effect by O(a) improvement of the axial-vector current. Published by the American Physical Society 2024

Synthesis, crystal structure and properties of YB2C2

ABSTRACT YB2C2 is a novel ultra-high temperature ceramic material with high damage tolerance. In this work, the synthesis mechanism, crystal structure, electronic structure, elastic properties and thermal shock resistance of YB2C2 were systematically investigated through experiments and calculations. It was determined by differential scanning calorimetry with the heating rate of 10°C/min that YB2C2 was formed by the reaction of YB2C and C at about 1202°C, and became the main phase at 1450°C. The space group of YB2C2 was determined to be P4/mbm by X-ray diffraction, transmission electron microscopy, Rietveld refinement and first-principles calculations for the first time. The lattice constants are a = b = 0.5351 nm and c = 0.3561 nm. The atom positions are as follows: Y is located at 2a (0, 0, 0), B is located 4 h (0.133, 0.633, 0.5) and C is located at 4 h (0.662, 0.162, 0.5). The chemical bonding of YB2C2 displayed sharp anisotropy, with strong B-C bond within the B2C2 nets, and weak Y-B/Y-C bond between Y atom layers and B2C2 nets. Additionally, YB2C2 exhibited abnormal thermal shock resistance when the thermal shock temperature exceeded 800°C, with the residual flexural strength at 1300°C being more than 70% of the strength at room temperature.

Constructing Robust Interfacial Chemical Bond Enhanced Charge Transfer in S‐Scheme 3D/2D Heterojunction for CO2 Photoreduction

AbstractA stable ZnTe@Cs3Sb2I9 catalyst with 3D/2D‐hollow‐composite structure is constructed for CO2 photocatalytic reduction via the in situ growth of Cs3Sb2I9 nanosheets on hollow ZnTe microspheres using lattice matching. The formed Tellurium‐Antimony (Te─Sb) bonds improved the poor contact at the heterojunction interface, effectively promoted charge separation, and successfully suppressed photocorrosion. The unique core‐shell structure not only strengthens light absorption but also improves CO2 adsorption capacity. Consequently, the S‐scheme heterojunction with the synergistic effect of chemical bonds and 3D/2D‐hollow‐composite structure significantly enhances photocatalytic performance. The ZnTe@Cs3Sb2I9 photocatalyst offers a CO selectivity of 90.5%, which is higher than that of pure ZnTe (22.9%) and Cs3Sb2I9 (56.9%). This structure holds great promise for practical applications in CO2 photocatalytic reduction.

The tin content of lead inclusions in ancient tin-bronze artifacts: a time-dependent process?

In antiquity, Pb was a common element added in the production of large bronze artifacts, especially large statues, to impart fluidity to the casting process. As Pb does not form a solid solution with pure Cu or with the Sn–Cu alloy phases, it is normally observed in the metal matrix as globular droplets embedded within or in interstitial positions among the crystals of Sn-bronze (normally the α phase) as the last crystallizing phase during the cooling process of the Cu–Sn–Pb ternary melt. The disequilibrium Sn content of the Pb droplets has recently been suggested as a viable parameter to detect modern materials [Shilstein, Berner, Feldman, Shalev & Rosenberg (2019). STAR Sci. Tech. Archaeol. Res. 5, 29–35]. The application assumes a time-dependent process, with a timescale of hundreds of years, estimated on the basis of the diffusion coefficient of Sn in Pb over a length of a few micrometres [Oberschmidt, Kim & Gupta (1982). J. Appl. Phys. 53, 5672–5677]. Therefore, Pb inclusions in recent Sn-bronze artifacts are actually a metastable solid solution of Pb–Sn containing ∼3% atomic Sn. In contrast, in ancient artifacts, unmixing processes and diffusion of Sn from the micro- and nano-inclusions of Pb to the matrix occur, resulting in the Pb inclusions containing a substantially lower or negligible amount of Sn. The Sn content in the Pb inclusions relies on accurate measurement of the lattice parameter of the phase in the Pb–Sn solid solution, since for low Sn values it closely follows Vegard's law. Here, several new measurements on modern and ancient samples are presented and discussed in order to verify the applicability of the method to the detection of modern artwork pretending to be ancient.

Insight into the Physical Properties of the Chalcogenide XZrS3 (X = Ca, Ba) Perovskites: A First-Principles Computation

AbstractThis study investigates the structural, mechanical, optical, thermal, and electronic properties of the ionic semiconducting materials XZrS3 (X = Ca, Ba) within the framework of density functional theory (DFT). Here, the elastic constants, modulus (bulk, shear, Young's), ratios (Pugh, Poisson) and elastic anisotropy for XZrS3 (X = Ca, Ba) are studied. Furthermore, the electronic, optical, and thermal properties for XZrS3 (X = Ca, Ba) are regenerated and designed using the values obtained with Cambridge Serial Total Energy Package (CASTEP) software. The calculated lattice parameters show excellent agreement with theoretical and experimental values. The elastic stiffness constants confirm the mechanical stability of both compounds. Although XZrS3 (X = Ca, Ba) is elastically anisotropic, it has little optical anisotropy. The electronic band structures of the material exhibit direct-bandgap semiconducting behavior, with values of 1.3 eV (CaZrS3) and 1.1 eV (BaZrS3) using the generalized gradient approximation (GGA), respectively, which is ideal for solar cell (0.9–1.56 eV) and optoelectronic device applications. Bandgap values of 1.9 eV and 1.6 eV are found for CaZrS3 and BaZrS3, respectively, using the Heyd–Scuseria–Ernzerhof HSE06 functional, which is consistent with previous theoretical and experimental bandgap results. The optical properties including dielectric function, refractive index, absorption coefficient, reflectivity, and loss function are characterized using the GGA of Perdew–Burke–Ernzerhof (GGA-PBE) and HSE06 methods and are discussed in detail. Because of the relatively low Debye temperature (D), thermal conductivity of the lattice (kph), and minimum thermal conductivity (Kmin), the studied materials can be used as thermal barrier coating (TBC) materials. The capacity of heat, Debye temperature, and thermal coefficient of expansion are all computed.

Properties of spray pyrolysis deposited Zr-doped ZnO thin films and their UV sensing properties

This study investigated the characteristics of Zr-doped ZnO thin films with varying Zr doping concentrations. X-ray diffraction (XRD) analysis confirmed the presence of the ZnO hexagonal phase without any additional phases detected. The crystallite size was determined using Scherrer’s equation and Halder-Wagner equation, revealing distinct trends as the Zr content increased. The impact of Zr doping concentration on structural properties such as lattice parameters was also explored. Field emission scanning electron microscopy (FE-SEM) images indicated agglomeration, with a peak value observed at Zr-5 wt% of 175 nm that decreased at higher Zr contents. Optical properties exhibited minor variations with increasing Zr content, with the maximum band gap recorded at 3.28 eV for Zr-7 wt% and Zr-10 wt% films. Utilizing the Spitzer-Fan model, the high-frequency dielectric constant peaked at 14.26 for Zr-7 wt% films. Optical mobility displayed fluctuations with rising Zr content. Direct current (DC) conductivity results unveiled two donor levels in the deposited films, showcasing minimum activation energies of 0.23 and 0.165 eV for high and low-temperature ranges in the Zr-3 wt% film. Furthermore, the response to UV light illumination at a wavelength of 365 nm was examined, revealing notable changes in rise and decay times with varying Zr content.

Investigation of Structural, Optical, and Antifungal Characteristics of Al‐Doped MnFe2O4 Ferrite Nanoparticles

In present study, a series of MnAlxFe2−xO4 (x = 0.1, 0.2, 0.3) ferrite nanoparticles are synthesized via auto‐combustion method and investigated for the structural, optical, and antifungal characteristics. X‐ray diffraction and transmission electron microscopy are employed to analyze the structure and morphology, revealing alterations in the lattice parameters and crystallite size (24.83–17.95 nm) due to Al doping. The optical properties of the synthesized nanoparticles are examined through UV–visible spectroscopy, indicating a decrease in the bandgap energy (1.44–1.33 eV) with the incorporation of Al3+ ions. Additionally, the antifungal activity of the Al‐doped MnFe2O4 nanoparticles is assessed against two selected fungal strains, i.e., Aspergillus niger (MTCC 282) and Candida albicans (MTCC 227). The findings contribute to the understanding of the multifaceted properties of Al‐doped MnFe2O4, highlighting its potential applications in diverse fields such as sensors, and biomedical research.

Stabilization of Na‐Ion Cathode Surfaces: Combinatorial Experiments with Insights from Machine Learning Models

Na–Fe–Mn–O cathodes hold promise for environmentally benign high‐energy sodium‐ion batteries, addressing material scarcity concerns in Li‐ion batteries. To date, these materials show poor stability in the air and suffer significant Fe/Mn dissolution during use. These two detrimental surface effects have so far prevented the commercialization of these materials. Herein, high‐throughput experiments to make hundreds of substitutions into a previously optimized Na–Fe–Mn–O material are utilized. Numerous single‐phase materials are made with good electrochemical performance that shows moderate improvements over the unsubstituted. By contrast, dramatic improvements are made in suppressing decomposition in air and Fe/Mn dissolution. Machine learning algorithms are utilized to further understand the changes in air stability and to decouple the effects of various structural parameters such as lattice parameters and crystallite size. The comprehensive dataset and methodology established here lay the groundwork for future exploration and optimization of cathode materials, driving the advancement of next‐generation sodium‐ion batteries.

Regulation of monolayer MgGeN2 thin film with uniaxial and biaxial strain

Abstract The regulation of electronic and optical properties with uniaxial and biaxial strains are computationally investigated for the monolayer thin film of a newly discovered quasi-layered MgGeN$_2$ phase. It was found that, under uniaxial compression in both [100] and [010] directions with the perpendicular lattice parameter relaxable, the band gap will first increase and then decrease, while with uniaxial tensile strain the band gap monotonically decreases and the light absorption in visible range is greatly enhanced. When uniaxial compression was applied with perpendicular lattice constant fixed, the band gap behaves as the first kind of uniaxial compression and the light absorption is enhanced in visible range by compression. When biaxial strain was presented, the band gap shows a monotonic decrease from the largest compression down to the largest tensile strain, while the light absorption behaves in an opposite way. Therefore, the band structure and light absorption of monolayer MgGeN$_2$ can be efficiently tuned with strain and stress, which may be potentially used for MgGeN$_2$ film fabrication in device design and hence boost its applications in optoelectronics and photocatalysis.

Step height measurement of monoatomic silicon crystal lattice steps with a commercial atomic force microscope

Abstract Precise control of advanced materials relies on accurate dimensional metrology at the sub-nanometre scale. At this scale, the accuracy of scanning probe microscopy (SPM) has been limited by the lack of traceable transfer standard artefacts with calibration structures of suitable dimensions. With the adoption in 2019 of the silicon crystal lattice spacing as a secondary realization of the metre in the International System of Units (SI), SPM users have direct access to a realization of the SI metre at the sub-nanometre level by means of the step height of self-assembled monatomic lattice steps that can form on the surface of silicon crystals. A key challenge of successfully adopting this pathway is establishing the need for established protocols to minimize measurement errors and artifacts in routine laboratory use.
In this study, step height measurements of monoatomic lattice steps in an ordinal/staircase structure on a Si(111) crystal surface have been derived from images acquired with a commercially available, research-level atomic force microscope (AFM). Measurement results derived from AFM images using three different SPM image processing and analysis software packages are compared. Significant sources of measurement uncertainty are identified; principally the contribution from the dependence on scan direction. The calibration of the
AFM derived from this measurment was used to traceably measure the sub-nanometre lattice steps on a silicon carbide crystal surface to demonstrate the viability of this calibration pathway.

Bi2S3 for aqueous copper ion battery based intercalation chemistry

Aqueous multivalent ion batteries have attracted increasing attention due to their high capacity, long cycle life, and impressive output energy. Considering that intercalation electrodes are more suitable for long cycle battery compared to the conversion ones, Cu2+ with appropriate ion radii has been chosen as intercalation carriers and bismuth sulfide with the matched lattice spacing as cathode to achieve long cycle life aqueous battery. We have synthesized the micrometer-scale flower-like Bi2S3 by regulating temperature and it is proved to be a perennial phase during Cu2+ intercalation/deintercalation of the Bi2S3 host when charge/discharge with a capacity of 104.5 mAh g–1 retention at 0.5 A g–1 after 1000 cycles. Lastly, build a hybrid ion battery with Zn and ZnSO4 electrolyte, the Bi2S3 cathode for Cu2+ intercalation can reach a maximum energy of 427.5 Wh Kg–1. The study provides a new intercalation cathode for aqueous multivalent ion batteries and will broaden the energy storage system.

Current density functional framework for spin-orbit coupling: Extension to periodic systems.

Spin-orbit coupling induces a current density in the ground state, which consequently requires a generalization for meta-generalized gradient approximations. That is, the exchange-correlation energy has to be constructed as an explicit functional of the current density, and a generalized kinetic energy density has to be formed to satisfy theoretical constraints. Herein, we generalize our previously presented formalism of spin-orbit current density functional theory [Holzer et al., J. Chem. Phys. 157, 204102 (2022)] to non-magnetic and magnetic periodic systems of arbitrary dimension. In addition to the ground-state exchange-correlation potential, analytical derivatives such as geometry gradients and stress tensors are implemented. The importance of the current density is assessed for band gaps, lattice constants, magnetic transitions, and Rashba splittings. In the latter, the impact of the current density may be larger than the deviation between different density functional approximations.