Showing papers on "Charge density published in 1971"

RMS Envelope Equations with Space Charge

Abstract: Envelope equations for a continuous beam with uniform charge density and elliptical cross-section were first derived by Kapchinsky and Vladimirsky (K-V). In fact, the K-V equations are not restricted to uniformly charged beams, but are equally valid for any charge distribution with elliptical symmetry, provided the beam boundary and emittance are defined by rms (root-meansquare) values. This results because (i) the second moments of any particle distribution depend only on the linear part of the force (determined by least squares method), while (ii) this linear part of the force in turn depends only on the second moments of the distribution. This is also true in practice for three-dimensional bunched beams with ellipsoidal symmetry, and allows the formulation of envelope equations that include the effect of space charge on bunch length and energy spread. The utility of this rms approach was first demonstrated by Lapostolle for stationary distributions. Subsequently, Gluckstern proved that the rms version of the K-V equations remain valid for all continuous beams with axial symmetry. In this report these results are extended to continuous beams with elliptical symmetry as well as to bunched beams with ellipsoidal form, and also to one-dimensional motion.

Hydrodynamic instabilities of nematic liquid crystals under A. C. electric fields

Abstract: We present an extension of the Helfrich theory of hydrodynamic instabilities to the case of alternating electric fields. The electrohydrodynamic effects are described by two coupled equations for the charge density (q) and the local curvature of the molecular alignment (ψ). The relaxation time for q is the dielectric relaxation time τ (∼ 10-2 s in typical samples). The relaxation time T for ψ is strongly dependent on the field magnitude. Provided that the sample thickness d is above a certain limit dc, the nature of the instability is very different, depending on the ratio of the field frequency ω to a critical frequency ω c. For ω ωc the situation at threshold corresponds to a constant q and an oscillating ψ. These predictions, together with the calculated curves of threshold voltage vs ω and d, are in reasonable agreement with a number of recent experiments.

Dielectric Screening in a Layered Electron Gas

Abstract: A model anisotropic system, suggestive of the graphite structure, is investigated: It consists of a series of equally spaced parallel planes. A finite two-dimensional density of electrons in each plane is allowed to move freely in the plane, but tunneling between planes does not take place. The dielectric screening of a point charge is evaluated exactly in the random-phase approximation. For realistic electron densities and interlayer separations the screened potential drops off very rapidly both in the plane of the charge and perpendicular to it. The induced charge density is determined, and validity of the Thomas-Fermi approximation is discussed.

Pseudopotential Calculations of Electronic Charge Densities in Seven Semiconductors

Abstract: Electronic charge densities are calculated as a function of position in the unit cell for seven diamond and zinc-blende semiconductors using wave functions derived from pseudopotential band-structure calculations. Detailed plots of the charge density are presented in the (110) plane for each valence band of Ge, GaAs, and ZnSe and for the sum of the valence bands of Ge, GaAs, ZnSe, $\ensuremath{\alpha}\ensuremath{-}\mathrm{S}\mathrm{n}$, InSb, CdTe, and Si. Trends in bonding and ionicity are discussed in detail. The covalent-bonding charge is also calculated for these crystals and is plotted against the ionicity scales of Phillips and Van Vechten and of Pauling. It is shown that an extrapolation to zero covalent-bonding charge yields a critical value of the ionicity which separates fourfold-coordinated and sixfold-coordinated diatomic crystals. This value is in agreement with the empirical value obtained by Phillips and Van Vechten.

SCF-MO-LCGO studies on hydrogen bonding. The water dimer

Abstract: The hydrogen bond in the water dimer is studied within the SCF-MO-LCAO framework, using a large Gaussian basis set to approximate the wavefunction. A geometry search restricted to structures with linear and bifurcated hydrogen bonds is performed and the associated potential energy curves are displayed. The minimum energy geometry of the water dimer is found to form a linear hydrogen bond with a hydrogen bond distance of 2.04 A and a binding energy of 4.84 kcal/mole relative to the monomer (exp. 5.0 kcal/mole). No semistable structures are found. The charge density and charge density difference maps are discussed for the structure with a linear hydrogen bond for different subsystem (water) separations, including the minimum energy geometry. The dipole moment of the dimer is computed to be 1.69 a.u. The shift of the IR bands on hydrogen bond formation is explained qualitatively by comparing the potential energy curves of the hydrogen in the OH-bonds of the monomer and the dimer, and the intensity increase of the fundamental OH-stretching band is computed. The shift of the proton magnetic resonance signal is discussed qualitatively by inspecting the charge density change on hydrogen bond formation, and the average diamagnetic shielding is calculated.

Molecular Orbital Approach to Chemisorption. II. Atomic H, C, N, O, and F on Graphite

Abstract: The calculation of the chemisorption behavior of atomic H, C, N, O, and F on a graphite basal (0001) surface is examined with the CNDO (complete neglect of differential overlap) molecular-orbital scheme. This approach is a semiempirical approximation to the Hartree-Fock self-consistent field procedure, in which the Hamiltonian explicitly depends upon both atomic and orbital charge distribution. The location of binding sites and changes in relative binding energies and net charges with the identity of the adsorbed species are explored with an extended carbon (0001) surface, simulated by an 18-carbon lattice with appropriate boundary connections. The strength of binding to the simulated graphite substrate increases in the order H, F, O, N, and C. The atoms C and N are most stable when positioned above the center of a hexagonal sixcarbon ring, whereas H, F, and O are most stable above the center of a bond connecting nearest-neighbor carbons. Calculated charge distributions are used to predict a work-function decrease with the adsorption of atomic H or N on graphite, but an increase with the adsorption of C, O, or F. The commonly used electronegativity reasoning is shown to be inadequate for the prediction of adsorbate-charge transfer.

Charge conservation and chemical potentials in time-dependent Ginzburg--Landau theory

Abstract: A phenomenological, charge-conserving, time-dependent Ginzburg-Landau theory is found to lead to a charge density and a difference between the quasiparticle electrochemical potential and the pair electrochemical potential when there is a divergence of the supercurrent. Experimental consequences are discussed.

Decay of Excess Charge in Dielectrics Having Shorted Electrodes

Abstract: The flow equations are derived for the discharge of dielectrics having an arbitrary initial charge and shorted electrodes, for the case of rapid shallow trapping. The case of an initial charge distribution which is uniform down to a depth y is considered in detail. Nonisothermal conditions are readily handled. It is shown that only a small fraction f of the initial charge can be observed in the external circuit, and that a significant fraction g ≠ 1‐f is retained in the specimen when the external current flow ceases. The calculation is applied to the ionic thermo‐current observed in Mylar and is shown to accord well with the experimental measurements.

Wave-particle interactions in electrostatic waves in an inhomogeneous medium

Abstract: The system studied is that of a narrow-band electrostatic wave packet in a collision-free plasma. Inhomogeneous effects are represented by a wave-number, which varies linearly with distance. The system is excited by a weak resonant beam, and, to first order in a smallness parameter associated with the weakness of the beam, the resonant-particle distribution function and charge densities are calculated. It is found that second-order resonant particles become stably trapped in the wave, and, after a few trapping periods, make a dominant contribution to the resonant particle charge density. The growth rate due to the resonant beam was found to increase linearly with trapping time, and typically a pulse which traps particles for n trapping periods exhibits a growth rate ˜ n times the linear Landau value. Furthermore, a reactive component of charge density was found that was able to cause a steady change in wave frequency and wave-number. These features of large growth rates and changing frequency should appear in parallel problems involving other wave types. An obvious application is that of VLF emissions in the whistler mode.

Charge Transport by Self‐Generated Turbulence in Insulating Liquids Submitted to Unipolar Injection

Abstract: During unipolar (or ambipolar) injection of charge carriers into an insulating liquid, a liquid motion is generally observed. This motion, generated by the charge carriers, is thought to be responsible for the high carrier mobility which is about 2×10−3 cm3 V−1 sec−1 in nitrobenzene, i.e., an order of magnitude higher than the true mobility value (1.9×10−4 cm2 V−1 sec−1). Recent schlieren photographs strongly support the assumption that when the applied voltage is high enough, for nitrobenzene of the order 103‐104 V, the “self‐generated” motion is turbulent shortly after the voltage is applied. This turbulence invades the undisturbed fluid at practically constant velocity. Neglecting the true carrier mobility and making certain assumptions concerning the turbulent structure, the charge transport and consequently the entrainment can be described to a good approximation by a Lagrangian diffusion process and the charge distribution is governed by a diffusion equation. The latter remains valid during the stea...

Ultraviolet‐Enhanced Oxidation of Silicon

Abstract: This paper describes the results of dry thermal oxidation of silicon under uv‐irradiation conditions. A model is proposed to explain the enhanced oxidation and reduced surface‐state charge density that occur under these conditions.

Ion Transport to Cloud Droplets by Diffusion and Conduction, and the Resulting Droplet Charge Distribution

Abstract: The influence of an electric field on the diffusion of ions to cloud droplets is calculated by the method of matched asymptotic expansions. The model assumes the droplet suspension is disperse and stationary in the ionic gas, ignores space charge and selective adsorption of ions, and regards each droplet as a perfectly conducting sphere. The resulting mean charge and dispersion of an assumed normal distribution of charge among a set of equal-sized droplets are determined. It is found that the dispersion increases with electric field strength, as does the mean charge for a fixed ratio of polar conductivities.

Method for Measurement of Surface Charge Densities on Electrets

Abstract: An accurate method for determining the surface charge density on foil electrets is described. The method is based on the measurement of an induction charge on a capacitive probe parallel to, and at a certain distance from, one of the charged surfaces of the electret. The method does not interfere electrically or mechanically with the electret charges. It is simple to implement and capable of measuring surface charge densities from 5×10−11 to some 10−6 C/cm2. For a surface charge density of 10−8 C/cm2, the reproducibility error is less than 1% and the systematic errors are estimated to be of the same order.

13C‐, 14N‐ und 1H‐kernresonanzspektroskopische Untersuchungen an m‐/p‐substuierten N‐Methylpyridiniumjodiden

Abstract: In a series of 21 m-/p-substituted N-methylpyridinium salts, N-methyl proton, carbon-13 and pyridinium nitrogen-14 chemical shifts were determined by heteronuclear double resonance, and partly in the case of the 14N nucleus and the methyl protons by direct measurement. In a few compounds the quadrupole relaxation times proved to be too short for the 14N coupling to be detected. This problem was overcome by adequately rising the sample temperature. For all three nuclei a marked dependence of the chemical shifts on the nature of the substituent could be established. Increased nitrogen π-electron density shifts the resonances towards higher fields. In the case of the 14N shieldings, this tendency is attributed to changes in the paramagnetic screening term, whereas for 13C and 1H an interpretation is given in terms of a neighbour anisotropy contribution. The latter explanation is based on the observation that the calculated carbon and hydrogen charge densities show no significant variations throughout the series. Excellent shift correlations were obtained with Hammett substituent constants when σ+-values were used for donor substituents. A similar substituents, dependence could be observed for the direct 13CH methyl coupling constants, whose magnitude increases with decreasing nitrogen charge density.

Covalency Effects on the 3 d -Charge-Density Distribution in Solid Ferrous Compounds

Abstract: A phenomenological description of the $3d$-charge-density distribution in solids, based on M\"ossbauer hyperfine interaction data, studies of crystal structures, EPR, neutron scattering and optical spectroscopy, has been developed for divalent iron ions in solids. From this work, it appears that one can obtain an internally consistent picture of the $3d$-charge-density distribution in solids by allowing for large, but distinctly different, modifications of the radial $3d({e}_{g})$ and $3d({t}_{2g})$ electronic wave functions. These modifications vary continuously with covalency on going from the completely ionic to the completely covalent ferrous compounds. They account for the large changes (in order of magnitude) in the mean $3d$ charge (or spin) densities, indicated by the experimental data. These results cannot be explained by theoretical models of bonding based on crystal field and molecular-orbital theories, using free-ion wave functions. The present model emphasizes the importance of the radial modifications of the $3d$ wave functions, thus supporting the point of view that, in self-consistent-field-type theoretical computations, the radial wave functions should be described by variational rather than fixed parameters.

Charge density and NMR parameters. Aliphatic derivatives

Abstract: The charge distribution in several substituted aliphatic derivatives was determined by a parametric MOLCAO method. The charges were successfully employed to interpret NMR parameters, namely proton and carbon chemical shift and vicinal proton-proton coupling constants in ethyl derivatives and carbon-proton coupling constants. The linear correlations found between NMR parameters and charge densities are restricted to substituents of the same row of the periodic system. The decay along the aliphatic chain of the perturbation induced by substituents on proton chemical shift is also reproduced by charge distribution. Some results also seem to indicate that the substituents affect the hybridization of the attached carbon atom.

Calculation and Plotting of the Charge Density of Ionic Crystals

Abstract: Using SCF wavefunctions for the free ions obtained by the Roothaan method the electron density of some ionic crystals has been studied. A comparison with experimental results for NaCl shows a good agreement. Computer-produced density plots are given showing the total density as well as the contributions from single ions.

Elastische Elektronenstreuung am 40 Ar zur Bestimmung des quadratisch gemittelten Kernradius

Abstract: The elastic electron scattering cross section of40Ar has been measured relative to that of the proton using gas targets. The momentum transfer ranged between 0.28 and 0.50 fm−1 (40–60 MeV, 90–120 °). From partial wave calculations, anrms charge radius of (3.41±0.04) fm was evaluated. The error includes uncertainties due to the choice of the charge distribution.

Pulsar radio emission from expanding charge sheets.

Abstract: We semi-quantitatively calculate the distribution of energy in frequency and angle emitted from a sheet of charges that are moving out relativistically along dipolar magnetic field lines originating near the magnetic polar caps of a rotating neutron star. The angular distribution is conical with the angle of maximum intensity varying with frequency ω as ω−1/4 for ω≲ω c ≈2 c /(Rθ M 2), whereRθM is the initial angular radius of the charge sheet at the surface of the star of radiusR. At higher frequencies the width of the angular cone remains constant. The radiation is linearly polarized with the polarization vector in the plane of the line of sight and the magnetic axis. A sheet of uniform charge density and finite thickness has a frequency spectrum that varies from ω−3/2 to ω−4 for ω≲ω c and ω≲ω c , respectively. These features are in good general agreement with the observed characteristics of the intensity, pulse shape, and frequency spectrum of the radio pulses from pulsars.