Electron Density
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2022 ◽  
Sergey A. Shteingolts ◽  
Adam I. Stash ◽  
Vladimir G. Tsirelson ◽  
Robert R. Fayzullin

Intricate behavior of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Bosonic and fermionic quantum potentials were utilized in bonding analysis as descriptors of the localization of electrons and electron pairs. Channels of locally enhanced kinetic potential and the corresponding saddle Lagrange points were found between chemically bonded atoms linked by the bond paths. Superposition of electrostatic φ_es (r) and kinetic φ_k (r) potentials and electron density ρ(r) allowed partitioning any molecules and crystals into atomic ρ- and potential-based φ-basins; the φ_k-basins explicitly account for electron exchange effect, which is missed for φ_es-ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between ρ- and φ-zero-flux surfaces. The gap between φ_es- and ρ-basins represents the charge transfer, while the gap between φ_k- and ρ-basins is proposed to be a real-space manifestation of sharing the transferred electrons. The position of φ_k-boundary between φ_es- and ρ-ones within an electron occupier atom determines the extent of electron sharing. The stronger an H‧‧‧O hydrogen bond is, the deeper hydrogen atom’s φ_k-basin penetrates oxygen atom’s ρ-basin. For covalent bonds, a φ_k-boundary closely approaches a φ_es-one indicating almost complete sharing the transferred electrons, while for ionic bonds, the same region corresponds to electron pairing within the ρ-basin of an electron occupier atom.

Tim Jacobus Adrianus Staps ◽  
Tim Jacobus Maria Donders ◽  
Bart Platier ◽  
J Beckers

Abstract Negative ions are an important constituent of the spatial afterglow of atmospheric pressure plasmas, where the fundamental plasma-substrate interactions take place that are vital for applications such as biomedicine, material synthesis, and ambient air treatment. In this work, we use laser-induced photodetachment to liberate electrons from negative ions in the afterglow region of an atmospheric pressure plasma jet interacting with an argon-oxygen mixture, and microwave cavity resonance spectroscopy (MCRS) to detect the photodetached electrons. This diagnostic technique allows for the determination of the electron density and the effective collision frequency before, during and after the laser pulse was shot through the measurement volume with nanosecond time resolution. From a laser saturation study, it is concluded that O− is the dominant negative ion in the afterglow. Moreover, the decay of the photodetached electron density is found to be dominantly driven by the (re)formation of O− by dissociative attachment of electrons with O2. As a consequence, we identified the species and process responsible for the formation of negative ions in the spatial afterglow in our experiment.

Maria Pia Valdivia Leiva ◽  
Gilbert W Collins IV ◽  
Fabio Conti ◽  
Farhat Beg

Abstract Talbot-Lau X-ray Deflectometry (TXD) enables refraction-based imaging for high-energy-density physics (HEDP) experiments, and thus, it has been studied and developed with the goal of diagnosing plasmas relevant to Inertial Confinement and Magnetic Liner Inertial Fusion. X-pinches, known for reliably generating fast (~1 ns), small (~1 µm) x-ray sources, were driven on the compact current driver GenASIS (~200 kA, 150 ns) as a potential backlighter source for TXD. Considering that different X-pinch configurations have characteristic advantages and drawbacks as x-ray generating loads, three distinct copper X-pinch configurations were studied: the wire X-pinch, the hybrid X-pinch, and the laser-cut X-pinch. The Cu K-shell emission from each configuration was characterized and analyzed regarding the specific backlighter requirements for an 8 keV TXD system: spatial and temporal resolution, number of sources, time of emission, spectrum, and reproducibility. Recommendations for future experimental improvements and applications are presented. The electron density of static objects was retrieved from Moiré images obtained through TXD. This allowed to calculate the mass density of static samples within 4% of the expected value for laser-cut X-pinches, which were found to be the optimal X-pinch configuration for TXD due to their high reproducibility, small source size (≤5 µm), short duration (~1 ns FWHM), and up to 10^6 W peak power near 8 keV photon energy. Plasma loads were imaged through TXD for the first-time using laser-cut X-pinch backlighting. Experimental images were compared with simulations from the X-ray Wave-Front Propagation code, demonstrating that TXD can be a powerful x-ray refraction-based diagnostic for dense Z-pinch loads. Future plans for Talbot-Lau Interferometry diagnostics in the pulsed-power environment are described.

2022 ◽  
Vol 0 (0) ◽  
Peter Luger ◽  
Birger Dittrich

Abstract The electron density distribution (EDD) of a tetrasaccharide composed of four benzoylated fructopyranosyl units was obtained by refinement with scattering factors from the invariom library. X-ray diffraction data was downloaded from the Cambridge Structural Database (CSD). Bond topological and atomic properties were obtained by application of Bader’s QTAIM formalism. From a large number of 105 C–C bonds in the molecule average bond orders for 33 single and 72 aromatic bonds were calculated yielding values of 1.33 and 1.61. Molecular Hirshfeld and electrostatic potential (ESP) surfaces show that only weak non-covalent interactions exist. The phenyl rings of the benzoyl fragments in the outer regions of the molecule generate a positive ESP shell with repulsive properties between adjacent molecules. Weak surface interactions result in a rather unusual low density around 1.3 g cm−3, which is understandable when compared to other carbohydrates where strong O–H⋯O hydrogen bonds allow a 20% more dense packing with densities >1.5 g cm−3 as determined by single crystal X-ray diffraction.

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 145
Paweł A. Wieczorkiewicz ◽  
Halina Szatylowicz ◽  
Tadeusz M. Krygowski

Substituted heterocyclic arenes play important roles in biochemistry, catalysis, and in the design of functional materials. Exemplary six-membered heteroaromatic molecules, that differ from benzene by inclusion of one heteroatom, are pyridine, phosphorine, arsabenzene, and borabenzene. This theoretical study concerns the influence of the heteroatom present in these molecules on the properties of substituents of two types: electron-donating (ED) NH2 group and electron-accepting (EA) NO2 group, attached at the 2-, 3-, or 4-position. The effect is evaluated by the energy of interaction (Erel) between the substituent and the substituted system and electronic properties of the substituents described by the charge of the substituent active region (cSAR) index. In addition, several geometric descriptors of the substituent and heteroaromatic ring, as well as changes in the aromaticity, are considered. The latter are assessed using the Electron Density of Delocalized Bonds (EDDBs) property of delocalized π electrons. The obtained results show that the electronegativity (EN) of the heteroatom has a profound effect on the EA/ED properties of the substituents. This effect is also reflected in the geometry of studied molecules. The Erel parameter indicates that the relative stability of the molecules is highly related to the electronic interactions between the substituent and the heteroarene. This especially applies to the enhancement or weakening of π-resonance due to the EN of the heteroatom. Additionally, in the 2-heteroarene derivatives, specific through-space ortho interactions contribute to the heteroatom effects.

2022 ◽  
Vol 11 (2) ◽  
pp. 364
Jonathan Pham ◽  
Minsong Cao ◽  
Stephanie M. Yoon ◽  
Yu Gao ◽  
Amar U. Kishan ◽  

Purpose: To evaluate dosimetric impact of air cavities and their corresponding electron density correction for 0.35 tesla (T) Magnetic Resonance-guided Online Adaptive Radiation Therapy (MRgART) of prostate bed patients. Methods: Three 0.35 T MRgRT plans (anterior–posterior (AP) beam, AP–PA beams, and clinical intensity modulated radiation therapy (IMRT)) were generated on a prostate bed patient’s (Patient A) planning computed tomography (CT) with artificial rectal air cavities of various sizes (0–3 cm, 0.5 cm increments). Furthermore, two 0.35 T MRgART plans (‘Deformed’ and ‘Override’) were generated on a prostate bed patient’s (Patient B) daily magnetic resonance image (MRI) with artificial rectal air cavities of various sizes (0–3 cm, 0.5 cm increments) and on five prostate bed patient’s (Patient 1–5) daily MRIs (2 MRIs: Fraction A and B) with real air cavities. For each MRgART plan, daily MRI electron density map was obtained by deformable registration with simulation CT. In the ‘Deformed’ plan, a clinical IMRT plan is calculated on the daily MRI with electron density map obtained from deformable registration only. In the ‘Override’ plan, daily MRI and simulation CT air cavities are manually corrected and bulk assigned air and water density on the registered electron density map, respectively. Afterwards, the clinical IMRT plan is calculated. Results: For the MRgRT plans, AP and AP–PA plans’ rectum/rectal wall max dose increased with increasing air cavity size, where the 3 cm air cavity resulted in a 20%/17% and 13%/13% increase, relative to no air cavity, respectively. Clinical IMRT plan was robust to air cavity size, where dose change remained less than 1%. For the MRgART plans, daily MRI electron density maps, obtained from deformable registration with simulation CT, was unable to accurately produce electron densities reflecting the air cavities. However, for the artificial daily MRI air cavities, dosimetric change between ‘Deformed’ and ‘Override’ plan was small (<4%). Similarly, for the real daily MRI air cavities, clinical constraint changes between ‘Deformed’ and ‘Override’ plan was negligible and did not lead to change in clinical decision for adaptive planning except for two fractions. In these fractions, the ‘Override’ plan indicated that the bladder max dose and rectum V35.7 exceeded the constraint, while the ‘Deformed’ plan showed acceptable dose, although the absolute difference was only 0.3 Gy and 0.03 cc, respectively. Conclusion: Clinical 0.35 T IMRT prostate bed plans are dosimetrically robust to air cavities. MRgART air cavity electron density correction shows clinically insignificant change and is not warranted on low-field systems.

Jiamao Gao ◽  
Shimin Yu ◽  
Hao Wu ◽  
Yu Wang ◽  
Zhijiang Wang ◽  

Abstract Matching networks are of vital importance for capacitively coupled plasmas to maximize the power transferred to the plasma discharge. The nonlinear interaction between the external circuit and plasma has to be considered to design suitable matching networks. To study the effect of the matching circuit, we coupled PIC/MC model and nonlinear circuit equations based on Kirchhoff’s laws, in a fully nonlinear and self-consistent way. The single-frequency capacitively coupled discharge with ”L”-Type matching networks are simulated. Fully self-consistently results of circuit and plasma parameters are presented and then power absorbed by the plasma and efficiency are calculated. With the tune of the matching network, the efficiency can reach 28.7 %, leading to higher potential as well as higher electron density at fixed source voltage. Besides, only very small components of the third harmonics are found in the plasma voltage and current while surface charge densities have multiple harmonics on account of the strong plasma nonlinearity. Finally, the effects of matching capacitors on discharge are analyzed, results show that smaller Cm1 and Cm2 of 500 pF to 1000 pF may be a proper choice for better matching, resulting in higher voltage across the CCP, and thus higher electron density and power absorption efficiency are obtained.

Wan Dong ◽  
Yi Fan Zhang ◽  
ZhongLing Dai ◽  
Julian Schulze ◽  
Yuan-Hong Song ◽  

Abstract Radio frequency capacitively coupled plasmas (RF CCPs) sustained in fluorocarbon gases or their mixtures with argon are widely used in plasma-enhanced etching. In this work, we conduct studies on instabilities in a capacitive CF4/Ar (1:9) plasma driven at 13.56 MHz at a pressure of 150 mTorr, by using a one-dimensional fluid/Monte-Carlo (MC) hybrid model. Fluctuations are observed in densities and fluxes of charged particles, electric field, as well as electron impact reaction rates, especially in the bulk. As the gap distance between the electrodes increases from 2.8 cm to 3.8 cm, the fluctuation amplitudes become smaller gradually and the instability period gets longer, as the driving power density ranges from 250 to 300 W/m2. The instabilities are on a time scale of 16-20 RF periods, much shorter than those millisecond periodic instabilities observed experimentally owing to attachment/detachment in electronegative plasmas. At smaller electrode gap, a positive feedback to the instability generation is induced by the enhanced bulk electric field in the highly electronegative mode, by which the electron temperature keeps strongly oscillating. Electrons at high energy are mostly consumed by ionization rather than attachment process, making the electron density increase and overshoot to a much higher value. And then, the discharge becomes weakly electronegative and the bulk electric field becomes weak gradually, resulting in the continuous decrease of the electron density as the electron temperature keeps at a much lower mean value. Until the electron density attains its minimum value again, the instability cycle is formed. The ionization of Ar metastables and dissociative attachment of CF4 are noticed to play minor roles compared with the Ar ionization and excitation at this stage in this mixture discharge. The variations of electron outflow from and negative ion inflow to the discharge center need to be taken into account in the electron density fluctuations, apart from the corresponding electron impact reaction rates. We also notice more than 20% change of the Ar+ ion flux to the powered electrode and about 16% difference in the etching rate due to the instabilities in the case of 2.8 cm gap distance, which is worthy of more attention for improvement of etching technology.

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