Accurate Electron Density Research Articles

Quantitative analysis of titanium alloys using one-point calibration laser-induced breakdown spectroscopy

The development of real-time and on-line quantitative composition analysis is desired for the products quality improvement in the metal producing and processing industries. Accuracy is still a challenge for classical calibration-free laser-induced breakdown spectroscopic (CF-LIBS) quantitative analysis due to the influence of the inaccurate plasma temperature calculations, uncertainties associated with Einstein coefficients and imprecise efficiency of spectral detection system. In this paper, we present an improving quantitative analysis for both major and minor elements in titanium alloys using the one-point calibration LIBS (OPC-LIBS) method. In OPC-LIBS, one matrix-matched standard sample of known composition was used to synchronously correct the essential experimental and spectroscopic parameters. A Saha–Boltzmann plot covering a large energy range was used to obtain more accurate plasma temperature and electron density values. From the comparison results, the OPC-LIBS method leads to a more accurate determination of the titanium alloy composition compared with the conventional CF-LIBS approach.

Bragg coherent diffraction imaging by simultaneous reconstruction of multiple diffraction peaks

Bragg coherent diffractive imaging (BCDI) is a noninvasive microscopy technique that can visualize the morphology and internal lattice deviations of crystals with nanoscale spatial resolution and picometer deformation sensitivity. While BCDI has been successfully applied in various studies of materials, it is less successful for highly strained crystals. Specifically, it is difficult to correctly reconstruct the electron density of a highly strained object using conventional phase retrieval algorithms. Although various algorithms have been developed to overcome this challenge, most of them require a priori knowledge that is not always available in practice. Here we report a phase retrieval workflow that can invert diffraction patterns from multiple Bragg peaks simultaneously. The workflow is explored via simulated diffraction from crystals with various strain conditions. Reconstructions from the workflow consistently demonstrate more accurate electron density maps, in comparison with the conventional method. For highly strained crystals, the workflow improves the reliability and consistency of BCDI phase retrieval significantly.

Toward a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming

Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems, and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the static correlation in DFT when frontier orbitals are degenerate by the means of using a semidefinite programming (SDP) approach to minimize the system energy as a function of the N-representable, non-idempotent 1-electron reduced density matrix. While showing greatly improved singlet-triplet gaps for local density approximation and generalized gradient approximation (GGA) functionals, the SDP procedure reveals flaws in modern meta and hybrid GGA functionals, which show no major improvements when provided with an accurate electron density.

Quantification of the Magnetic Anisotropy of a Single‐Molecule Magnet from the Experimental Electron Density

AbstractReported here is an entirely new application of experimental electron density (EED) in the study of magnetic anisotropy of single‐molecule magnets (SMMs). Among those SMMs based on one single transition metal, tetrahedral CoII‐complexes are prominent, and their large zero‐field splitting arises exclusively from coupling between the d and dxy orbitals. Using very low temperature single‐crystal synchrotron X‐ray diffraction data, an accurate electron density (ED) was obtained for a prototypical SMM, and the experimental d‐orbital populations were used to quantify the dxy‐d coupling, which simultaneously provides the composition of the ground‐state Kramers doublet wave function. Based on this experimentally determined wave function, an energy barrier for magnetic relaxation in the range 193–268 cm−1 was calculated, and is in full accordance with the previously published value of 230 cm−1 obtained from near‐infrared spectroscopy. These results provide the first clear and direct link between ED and molecular magnetic properties.

Quantification of the Magnetic Anisotropy of a Single-Molecule Magnet from the Experimental Electron Density.

Reported here is an entirely new application of experimental electron density (EED) in the study of magnetic anisotropy of single-molecule magnets (SMMs). Among those SMMs based on one single transition metal, tetrahedral CoII-complexes are prominent, and their large zero-field splitting arises exclusively from coupling between the d and dxy orbitals. Using very low temperature single-crystal synchrotron X-ray diffraction data, an accurate electron density (ED) was obtained for a prototypical SMM, and the experimental d-orbital populations were used to quantify the dxy-d coupling, which simultaneously provides the composition of the ground-state Kramers doublet wave function. Based on this experimentally determined wave function, an energy barrier for magnetic relaxation in the range 193-268 cm-1 was calculated, and is in full accordance with the previously published value of 230 cm-1 obtained from near-infrared spectroscopy. These results provide the first clear and direct link between ED and molecular magnetic properties.

Evaluation of Local Hybrid Functionals for Electric Properties: Dipole Moments and Static and Dynamic Polarizabilities

Local hybrid functionals are a class of exchange-correlation functionals that feature a real-space dependent admixture of exact (Hartree--Fock like) exchange governed by a local mixing function. Recently we reported the LH20t functional with wide chemical applicability and excellent performance for the GMTKN55 main-group energetics test suite (M.\ Haasler \emph{et al.}, \textit{J.\ Chem.\ Theory Comput.}\ \textbf{2020}, DOI: 10.1021/acs.jctc.0c00498). Here, we present a systematic evaluation of earlier and recent local hybrid functionals for large test sets of dipole moments and static polarizabilities, and for a smaller set of dynamic polarizabilities for heterocycles. Comparisons with coupled-cluster benchmark data show robust performance of all investigated local hybrids for dipole moments and polarizabilities. The two best local hybrids are the new LH20t and LH14t-calPBE. LH20t gives a percentage relative mean-square deviation of 5.87\% for the dipole-moment test set and of 4.30\% for static polarizabilities. This is only slightly inferior to the currently best performances among rung 4 functionals. Most notably, no large outliers are observed, in contrast to some other hyper-GGA functionals. This shows that the currently most highly parameterized (nine-parameter) LH20t clearly produces not only good energetics but also accurate electron densities and electric-field response. The influences of various aspects of local hybrids are examined, in order to aid in the further development of this class of functionals.

Comparison and evaluation of a bottom-up GPS-RO electron density retrieval for D and E regions using radar observations and models

The lack of reliable global E-region electron density or conductivity measurements has hampered a detailed and quantitative understanding of the E-region electrodynamic processes. The characterization of the global E-region ionospheric irregularities as a function of local time, longitude, and season remains a great challenge. In this study, we evaluate the electron densities retrieved by Wu (2018) in the D and E regions using ground-based radar data and empirical models. Unlike in the conventional top-down retrieval methodology, the new approach avoids the Abel weighting function that carries substantial sensitivity to the electron density residuals from the F-region even after they have been corrected. The new technique uses a bottom-up approach in which the F-region contributions in the excess phase are more effectively removed compared to the Abel inversion, and hence more accurate electron density retrievals in D and E regions are determined. The results are compared and evaluated with two low and mid-latitude incoherent scatter radar observations — the Arecibo Observatory’s 430 MHz radar, located in Puerto Rico (18∘N, 67∘W) and the Millstone Hill Observatory’s 440 MHz radar, located in Massachusetts (42∘N, 72∘W). In addition, the results are also compared with two models — the International Reference Ionosphere model (IRI-2016) and the Faraday International Reference Ionosphere model (FIRI-2018) at these two locations. The comparison of electron density height profiles from GPS-RO retrievals at the two locations show good agreement with radar measurements, as well as the FIRI-2018 model predictions, especially at ∼ 85–100 km. The seasonal and diurnal climatology comparisons of GPS-RO retrieved electron density show good agreement with radar observations at both locations, and also reflect the influence of the solar cycle on E-region electron density. It is noticed that the GPS-RO background electron density at Millstone Hill increases by ∼ 20% at around 105 km from solar minimum to the maximum during cycle 24 which is in agreement with radar observations and FIRI-2018 model predictions.

Post-Hartree-Fock methods for Hirshfeld atom refinement: are they necessary? Investigation of a strongly hydrogen-bonded molecular crystal

Hirshfeld atom refinement (HAR) is a method for refining X-ray crystal structures that is able to provide bond lengths involving hydrogen atoms in statistical agreement with those derived from neutron diffraction data, provided the data reach 0.8 Å resolution. Rather than using tabulated spherical atomic structure factors, HAR uses “tailor made” aspherical atomic structure factors obtained directly from quantum chemical calculations. Despite the very good results obtained so far, which make HAR an emerging refinement method of modern crystallography, until now all the Hirshfeld atom refinements were exclusively based on Hartree-Fock (HF) or density functional theory (DFT) methods, but never on the so-called post-HF techniques of quantum chemistry. Post-HF methods exploit more sophisticated multi-determinant wavefunctions and, consequently, should provide more accurate electron densities for the refinements. For this reason, for the first time we have performed HARs based on two well-known post-HF strategies (MP2 and Coupled Cluster) combined with three different basis-sets (def2-SVP, def2-TZVP and def2-TZVPP). The obtained results have been afterwards analyzed and compared to those resulting from neutron and other Hirshfeld atom refinements, the latter relying on Hartree-Fock and DFT (BLYP and B3LYP) calculations in order to evaluate if the use of more sophisticated and expensive approaches of quantum chemistry can improve the performances of the HAR technique.

Opacity of Krypton X-ray lines in high-temperature plasma implosion

For accurate electron temperature and density diagnostics in laser high-temperature plasma implosion, opacity of Krypton (Kr) helium-[Formula: see text] and Balmer-[Formula: see text] lines are discussed, and ratio of escape factor of the two X-rays are calculated, both for Gaussian and Holtzmarkian profiles. Finally, the line ratios of the two X-ray lines are analyzed for optically thin and thick plasmas. Results indicate that for the Gaussian profile, the line ratio varies greatly with the opacity of the Kr helium-[Formula: see text] line, which provides excellent source for temperature and electron density diagnostics; while for the Holtzmarkian profile, the line ratio varies less with the opacity of the Kr helium-[Formula: see text] line, which can be used for escape factor diagnostics. This method is significant in accurate plasma diagnostics using X-rays under the condition of optically thick.

One-point calibration of Saha-Boltzmann plot to improve accuracy and precision of quantitative analysis using laser-induced breakdown spectroscopy

Calibration-free laser-induced breakdown spectroscopy (CF-LIBS) has recently gained attention due to its potential to overcome matrix effects on quantitative analysis using LIBS. However, the efficiency of CF-LIBS may be compromised by uncertainties in the experimental and spectroscopic parameters. To minimize these uncertainties and improve quantitative analysis, the one-point calibration (OPC) method was recently introduced to empirically correct the emission line intensities in a Boltzmann plot. In this work, we used the OPC method on a Saha-Boltzmann plot to cover a large energy range and to obtain more precise and accurate plasma temperature and electron density (Ne) values than were obtained with a Boltzmann plot using OPC method. For the analysis, we prepared two sets of sodium chloride (NaCl) samples: one with graphite and another with calcium carbonate (CaCO3). We observed matrix effects when we evaluated the calibration curves of carbon line intensity as a function of carbon concentration. Corrections by the OPC method to the Boltzmann or Saha-Boltzmann plots minimized the matrix effects and also guaranteed that the calculated plasma temperature were the same for the primary elements of each sample, suggesting that they were in local thermodynamic equilibrium. When the OPC method was applied to the Saha-Boltzmann plot, we obtained an uncertainty of less than 0.5% for plasma temperature and Ne; an r2 value of 0.994; and a root mean square relative error (RMSRE) of 8% for C concentration. Meanwhile, the traditional OPC method resulted in an uncertainty of 2.3% for plasma temperature and Ne and a validation with r2 of 0.977 and RMSRE of 13% for C concentration. These results showed that the OPC method efficiently improved the quantitative analyses possible with the Saha-Boltzmann plot using CF-LIBS.

Atomic interdiffusion in Pt-Ni thin films at low temperatures: An in-situ X-ray reflectivity study

We have investigated the kinetic process of the atomic interdiffusion across the interface in thin platinum‑nickel (Pt-Ni) bilayer films at temperatures ranging from 230 °C to 300 °C by in-situ X-ray reflectivity (XRR). The Pt-Ni interface width obtained by analyzing the XRR curve provides the time evolution of the diffusion length in nanometer scale and the diffusivity of atoms across the interface. We find that the interdiffusion is dominated by Ni atoms with an associated activation energy Q of 0.87 ± 0.05 eV. The analysis of the anomalous XRR measured with various X-ray energies across the K absorption edge of Ni provides more accurate electron density profile near the interface.

Improved Frequency Monitoring System for Sky-Wave Over-the-Horizon Radar in Canada

Sky-wave over-the-horizon radar (OTHR) systems are of particular interest to the Canadian Department of National Defence (DND) since they provide the potential for surveillance of Canada. Because of dynamic ionospheric conditions in polar regions, any OTHR would necessitate a system where the operating frequencies and elevation angles change periodically to maintain constant detection of targets downrange. In this regard, an accurate electron density model is necessary for the purpose of improving operational OTHR and OTHR planning/design. Recently, the first phase of the Empirical Canadian High Arctic Ionospheric Model (E-CHAIM) was released, which was funded under the Defence Research and Development Canada’s (DRDC) All Domain Situational Awareness (ADSA) program. In this letter, the E-CHAIM is used to determine the feasible radar parameters such as operating frequencies and elevation angles by a 3-D ray-tracing technique. The results will help to form the basis of the frequency monitoring systems (FMS) that will control these polar OTHR systems.

Calculation of averaged collision strength of magnesium for non-Maxwellian distributions in plasma

In this paper, kappa and Druyvesteyn distributions of electronic velocity are discussed for non-Maxwellian distribution. For accurate temperature and electron density diagnostics of Magnesium plasma, for the Magnesium VIII [Formula: see text] to [Formula: see text] transitions, we calculate kappa averaged collision strengths for [Formula: see text] = 2, 3 and 5 and the Druyvesteyn averaged collision strengths for [Formula: see text] = 1.5, 2 and 3, for temperature between [Formula: see text] and [Formula: see text]. Results indicate that the kappa averaged collision strengths are slightly larger than those for the Maxwellian distribution, and the Druyvesteyn averaged collision strengths are slightly smaller than those for the Maxwellian distribution, furthermore, the averaged collision strengths will be close to those for Maxwellian distribution with increasing [Formula: see text] for the kappa distribution and with decreasing [Formula: see text] for the Druyvesteyn distribution. The excitation rate coefficients are also calculated for Maxwellian and non-Maxwellian distributions. This discussion will be significant in study of plasma for the non-Maxwellian distribution.

Density functional orbitals in quantum Monte Carlo: The importance of accurate densities.

There has been significant recent attention surrounding the accuracy of electronic densities produced by modern parameterized density functional approximations (DFAs). Here, we investigate the impact of using orbitals from density functional calculations in fixed-node Diffusion Monte Carlo (DMC) methods, which is common practice in the calculation of large systems. We find that the accuracy of the density is a strong indicator of the quality of the many-body nodal surface produced by a determinant of the corresponding Kohn-Sham orbitals. Functionals which produce the most accurate electronic densities also produce the lowest variational DMC energies, while functionals that produce poor densities lead to significantly higher energies. This result simplifies the process of choosing orbitals for DMC calculations of large systems and suggests that prioritizing accurate densities in the future development of DFAs would also contribute to the continued improvement of DMC.

Efficient Calculation of Non-local Thermodynamic Equilibrium Effects in Multithreaded Hydrodynamic Simulations of Solar Flares

Abstract Understanding the dynamics of the chromosphere is crucial to understanding energy transport across the solar atmosphere. The chromosphere is optically thick at many wavelengths and described by non-local thermodynamic equilibrium (NLTE), making it difficult to interpret observations. Furthermore, there is considerable evidence that the atmosphere is filamented, and that current instruments do not resolve small-scale features. In flares, it is likely that multithreaded models are required to describe the heating. The combination of NLTE effects and multithreaded modeling requires computationally demanding calculations, which has motivated the development of a model that can efficiently treat both. We describe the implementation of a solver in a hydrodynamic code for the hydrogen level populations that approximates the NLTE solutions. We derive an accurate electron density across the atmosphere that includes the effects of nonequilibrium ionization for helium and metals. We show the effects on hydrodynamic simulations, which are used to synthesize light curves using a postprocessing radiative transfer code. We demonstrate the utility of this model on IRIS observations of a small flare. We show that the Doppler shifts in Mg ii, C ii, and O i can be explained with a multithreaded model of loops subjected to electron beam heating, so long as NLTE effects are treated. The intensities, however, do not match the observed values very well, which is due to assumptions about the initial atmosphere. We briefly show how altering the initial atmosphere can drastically alter line profiles and derived quantities and suggest that it should be tuned to preflare observations.

The effect of surface contamination of tiny satellite on DC probe ionosphere measurement

The DC Langmuir probe is a widely-used instrument for the plasma measurement in the space missions. But to apply DC Langmuir probe to a tiny satellite, such as a cubesat, for ionosphere study is difficult to get accurate electron density (ne) and electron temperature (Te) for two reasons: the contamination on both satellite surface and the electrode to be used, and a lack of conductive surface area of the tiny satellite. Under the charging effect of the satellite with an insufficient area ratio between the surface of the probe and the spacecraft, the contaminations on the surface of both probe and the satellite, acting as equivalent capacitances and resistances, modify both the potentials on the satellite and the probe, and an elevated Te and a suppressed ne are derived incorrectly. In this paper, the effect of the surface contamination on the DC Langmuir probe measurements onboard a tiny satellite is investigated in detail. The effects of the accumulated charge and the impedances on the contamination layers have been identified in the experiments done in a ground chamber with similar plasma conditions in the Earth’s ionosphere, and the characteristic dependences of the probe sweeping frequency and the plasma density are presented. The experiment result suggests that a contamination-free instrument TeNeP, operated at 0.2∼10 MHz probe sweeping frequency and sweeping potentials below 500 mV, is a better solution to obtain accurate Te and ne, onboard a satellite with a surface area ratio below 100.

On the electron density diagnostics of silicon viii ion in solar transition region

The conditions for accurate electron density diagnostics in the solar transition region are discussed, and result shows that lines from Si viii can provide an excellent tool for electron density diagnostics of the emitting plasma. For the Si viii 1440.50 A and 1445.75 A lines, the principle of the electron density diagnostics is discussed for any intensity ratio. By the observed intensity ratio, the diagnostic results of the electron density for the quiet sun and the active region are calculated, and results indicate that in the quiet sun, the averaged electron density is $\log (N_{e}) = 8.63$ ; while in the active region, the averaged density gets the maximum $\log (N_{e}) = 8.86$ in the active region (B), and gets the minimum $\log (N_{e}) = 8.38$ in the active region (E), where the electron density is in the unit of cm−3. Finally, the relationship of intensity ratio and electron density is discussed, in the case of lower and higher electron density limits. This discussion is significant in the electron density diagnostics, which will be important for study on coronal heating and acceleration of solar wind.

Comparison of approximate methods for computation of the concerted adiabatic electronic and nuclear fluxes in aligned [formula omitted

Approximate methods of computing the concerted electronic and nuclear fluxes associated with electronically adiabatic processes are developed and applied to the prototypal system, namely aligned H2+ vibrating in its electronic ground state (2Σg+), the only realistic system for which highly accurate (exact) electronic (EPD) and nuclear (NPD) probability densities, electronic (EFD) and nuclear (NFD) flux densities, as well as corresponding fluxes, are available. Alternative formulas for the electronic flux, Fe,EPD and Fe,EFD, based on either the EPD or the EFD, are derived from the continuity equation. The results of Born-Oppenheimer approximation (BOA) and of an ordered sequence of Born-Huang expansions (BHE) are presented. The BOA and first-order BHE are in excellent agreement with the exact for both the NPD and NFD, as well as for the EPD and Fe,EPD up to about 1ps. Higher-order BHE are necessary to achieve similar accuracy at longer times. In contrast, the BOA and first-order BHE yield zero EFD and therefore also zero Fe,EFD. Although the higher-order BHE give non-zero values for these properties, they disagree flagrantly with their exact correlates. The error is traceable to numerical ill-conditioning of the working expression for the EFD. In summary, the BOA is adequate to compute accurate NPD, NFD, EPD and Fe,EPD for times corresponding to several dozens of vibrational periods; the higher-order BHE is required for longer times. But neither the BOA nor the BHE can provide reliable estimates of the EFD and Fe,EFD.

Nonlocal kinetic energy functionals by functional integration.

Since the seminal studies of Thomas and Fermi, researchers in the Density-Functional Theory (DFT) community are searching for accurate electron density functionals. Arguably, the toughest functional to approximate is the noninteracting kinetic energy, Ts[ρ], the subject of this work. The typical paradigm is to first approximate the energy functional and then take its functional derivative, δTs[ρ]δρ(r), yielding a potential that can be used in orbital-free DFT or subsystem DFT simulations. Here, this paradigm is challenged by constructing the potential from the second-functional derivative via functional integration. A new nonlocal functional for Ts[ρ] is prescribed [which we dub Mi-Genova-Pavanello (MGP)] having a density independent kernel. MGP is constructed to satisfy three exact conditions: (1) a nonzero "Kinetic electron" arising from a nonzero exchange hole; (2) the second functional derivative must reduce to the inverse Lindhard function in the limit of homogenous densities; (3) the potential is derived from functional integration of the second functional derivative. Pilot calculations show that MGP is capable of reproducing accurate equilibrium volumes, bulk moduli, total energy, and electron densities for metallic (body-centered cubic, face-centered cubic) and semiconducting (crystal diamond) phases of silicon as well as of III-V semiconductors. The MGP functional is found to be numerically stable typically reaching self-consistency within 12 iterations of a truncated Newton minimization algorithm. MGP's computational cost and memory requirements are low and comparable to the Wang-Teter nonlocal functional or any generalized gradient approximation functional.

Density profile evolution on EAST tokamak by the polarimeter/interferometer system

An 11-channel POlarimeter/INTerferometer (POINT) system with high time resolution (1 μs) was built in 2015 to measure the accurate line-integrated electron density and Faraday rotation angle on the EAST tokamak. An improved density profile reconstruction method was developed based on the POINT measurements to provide accurate density profiles. Furthermore, the pedestal factor from reflectometry data statistics was also introduced. The accuracy of this method is discussed thoroughly. Based on this method, the evolution of the density profile with much higher time resolution than Thomson scattering system can be obtained. These will make for a better understanding of the formation of the internal transport barrier (ITB) on the EAST tokamak.