Showing papers on "Charge density published in 1968"
TL;DR: In this article, the self-consistent perturbation theory developed in earlier papers is extended to the open-shell case and density matrices for both shells are calculated iteratively until first-order selfconsistency is achieved.
Abstract: The self‐consistent perturbation theory developed in earlier papers is extended to the open‐shell case. Density matrices for both shells are calculated iteratively until first‐order self‐consistency is achieved. A numerical application indicates the importance of considering both shells separately when discussing the effects of polarization on the charge density and the spin density.
402 citations
TL;DR: In this paper, the specific surface charge density on a silica sample of known surface area was measured in the presence of LiCl, NaCl, KCl, CsCl and (C2H5)4NCl.
371 citations
TL;DR: In this paper, a unified semi-empirical formulae for the mean charge and width of fast ion beams after their passing through solids have been obtained for all particles with atomic number Z ⪆ 20.
236 citations
TL;DR: In this paper, a collisionless Boltzmann equation with the approximation that the scale length of the equilibrium is long compared to the ion gyro radius is used to determine the stability of an experimental configuration such as the multipole.
Abstract: A method is described for the detailed investigation of electrostatic instabilities in real experimental geometries. These have frequently been discussed in the plane slab model, and modifications of it, but the present work includes all geometrical effects from the outset. The starting point is the collisionless Boltzmann equation with the approximation that the scale length of the equilibrium is long compared to the ion gyro radius. The main interest is in perturbations of low frequency but of arbitrary wavelength, which may be comparable to the ion Larmor radius. Thus several instabilities such as drift wave, flute or trapped particle, come within the scope of the theory. Expressions are first obtained for the contribution to the charge density produced by an arbitrary electrostatic perturbation affecting particles whose unperturbed orbits are (i) trapped between magnetic mirrors; (ii) circulating around closed field lines; (iii) tracing out a magnetic surface. Together with Poisson's equation these expressions lead, via the appropriate Nyquist contours, to stability criteria valid for arbitrary equilibria. Finally it is shown how this method leads to a differential equation whose solution will determine the stability of an experimental configuration such as the multipole.
197 citations
TL;DR: In this paper, a simple method based on the characteristic property of the electric free energy was proposed to calculate the repulsive force between parallel rod-like macroions in a solution as a function of the charge density on rods.
Abstract: This paper gives a very simple method based on the characteristic property of the electric free energy to calculate the repulsive force between parallel rodlike macroions in a solution as a function of the charge density on rods. The total extensive force (∂f/∂X) of an assembly of m rods of length l and charge number n (charge density − neo /l) at small extension X in the absence of low molecular sals is given by
where z is the valency of counterions and Q (= neO2/ekTl) is a dimensionless quantity representing the charge density. The repulsion between two parallel rods is given by putting m = 2. At large charge densities the repulsion is very much smaller than the direct coulomb force between charged rods, even at small distances. The addition of low molecular salts does not depress the repulsion appreciably, as long as the average concentration of salt ions is much smaller than the concentration of counterions accumulated in the space between rods. The effect of fluctuation of the coumerion distribution is also analyzed, and it is found that the attractive force due to the ion fluctuation may predominate over the above repulsive force in the case of polyvalent counterions and rods of high charge densities at small distances.
177 citations
TL;DR: In this paper, experimental results on the scattering of 250-MeV electrons were presented in terms of a phenomenological three-parameter shape, and a new, more accurate charge distribution was obtained for ${\mathrm{Ca}}^{40}$.
Abstract: Experimental results are presented on the scattering of 250-MeV electrons by ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{42}$, ${\mathrm{Ca}}^{44}$, ${\mathrm{Ca}}^{48}$, and ${\mathrm{Ti}}^{48}$, and of 500-MeV electrons by ${\mathrm{Ca}}^{40}$ and ${\mathrm{Ca}}^{48}$. An analysis is made in terms of a phenomenological three-parameter shape, and a new, more accurate charge distribution is obtained for ${\mathrm{Ca}}^{40}$. The experiments also lead to a detailed exploration of the radial dependence of the differences in charge distributions of the various isotopes. Implications for nuclear theory are discussed. Comparison is made with the results of other electron scattering and of muonic x-ray experiments. The latter comparison permits an independent determination of an upper limit on the muon electromagnetic radius ${{〈{r}^{2}〉}_{\ensuremath{\mu}}}^{\frac{1}{2}}\ensuremath{\lesssim}0.35$ F.
172 citations
TL;DR: In this paper, a self-consistent model was proposed to represent the Ohmic conduction process in the bulk of the fluids, with surface shears induced by the free interfacial charges placed in dynamic equilibrium by viscous stresses.
Abstract: It is well known that electromechanical polarization surface waves propagate along the lines of electric field intensity imposed tangential to the interface between perfectly insulating fluids. These waves have a stiffening effect on electrohydrodynamic equilibria that is analogous to that of the Alfven surface waves on hydromagnetic equilibria. An investigation is presented of the dynamical effects of charge relaxation on these waves. A self‐consistent model represents the relaxation in terms of an Ohmic conduction process in the bulk of the fluids, with surface shears induced by the free interfacial charges placed in dynamic equilibrium by viscous stresses. The dominant effect of the charge relaxation is to produce overstability. Experiments are described where this instability appears as a spontaneous oscillation of the interface with wavenumbers directed along the lines of electric field intensity. Detailed analytical results are given for liquid‐gas and liquid‐liquid interfaces. The field required to produce incipient instability and the propagation direction of the observed instability are satisfactorily predicted. It is found that in this liquid‐vapor case, relatively simple explicit expressions can be given for the incipient instability conditions. A discussion is given of the significance of this work for the dielectrophoretic orientation of liquids in the zero‐gravity environments of space.
154 citations
TL;DR: The Hartree-Fock wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater-type atomic orbitals as basis sets as mentioned in this paper.
Abstract: Several approximate Hartree–Fock SCF wavefunctions for the ground electronic state of the water molecule have been obtained using an increasing number of multicenter s, p, and d Slater‐type atomic orbitals as basis sets. The predicted charge distribution has been extensively tested at each stage by calculating the electric dipole moment, molecular quadrupole moment, diamagnetic shielding, Hellmann–Feynman forces, and electric field gradients at both the hydrogen and the oxygen nuclei. It was found that a carefully optimized minimal basis set suffices to describe the electronic charge distribution adequately except in the vicinity of the oxygen nucleus. Our calculations indicate, for example, that the correct prediction of the field gradient at this nucleus requires a more flexible linear combination of p orbitals centered on this nucleus than that in the minimal basis set. Theoretical values for the molecular octopole moment components are also reported.
147 citations
TL;DR: In this article, the Hartree-Fock wave functions were used to compare the formation of stable and unstable molecular species in terms of their respective charge distributions for H2 and Li2.
Abstract: The process of bond formation as a function of internuclear separation for H2 and Li2 is interpreted in terms of the changes in the charge distributions and the forces which they exert on the nuclei. The charge distributions are calculated from extended Hartree–Fock wave functions which reduce to the Hartree–Fock atomic functions for infinite nuclear separation. The results for H2 indicate that at separations greater than 5 a.u. the net attractive force exerted on the approaching nuclei arises from a simultaneous inwards polarization of the atomic charge distributions. For separations less than 5 a.u. the nuclei are bound by the force exerted by the delocalized component of the charge distribution. The density distributions and forces for He2 over a range of internuclear separations are compared with those for H2 to contrast the formation of stable and unstable molecular species in terms of their respective charge distributions.The final section of the paper examines in detail the changes in the Hartree–F...
113 citations
TL;DR: In this article, a bias is applied across the vibrating and fixed electrodes sufficient to produce zero output signal, and the value of this bias and a simple calculation yields the surface charge and its polarity.
Abstract: A new method of measuring the charge density on a dielectric surface has been developed. An electrode is vibrated in the surface field to produce a signal that is displayed on an oscilloscope, or measured with a VTVM. A bias is then applied across the vibrating and fixed electrodes sufficient to produce zero output signal. The value of this bias and a simple calculation yields the surface charge and its polarity. The method is simple, nondestructive, gives reliable results when compared with other techniques, and has few disadvantages. Measurements may be made at atmospheric pressure without fear of discharges at a wide range of surface‐to‐electrode gaps. The measurement of the surface charge is independent of circuit parameters.
108 citations
TL;DR: Comparison of log K' for magnesium, calcium, strontium, and barium as a function of surface chargedensity suggests that the larger cations are able to form ion triplets at high surface charge density while the smaller cations will be unable to do so.
TL;DR: In this paper, the Hartree-Fock wavefunctions for the molecules N2, CO, BF (isoelectronic with 14 e−), and BeO, LiF (Isoelectric with 12 e−) were calculated by a polynomial fit of the forces exerted on the nuclei as a function of the internuclear separation.
Abstract: The force constants are calculated from Hartree–Fock wavefunctions for the molecules N2, CO, BF (isoelectronic with 14 e−), and BeO, LiF (isoelectronic with 12 e−) by a polynomial fit of the forces exerted on the nuclei as a function of the internuclear separation. The magnitude of the force constant and its variation through the two series of molecules are interpreted in terms of the relaxation of the molecular charge distribution which accompanies a displacement of the nuclei. It is found that the charge distribution of a covalently bound molecule relaxes in such a way as to facilitate the motion of the displaced nuclei. In a molecule with the characteristics of ionic binding, the relaxation of the charge density localized on the cation opposes the nuclear displacement while the charge density on the anion facilitates its nuclear displacement. The relaxations are illustrated in the form of density difference maps between the extended and equilibrium molecular charge distributions. Such relaxation diagra...
TL;DR: In this article, the bias dependence of the photoelectric barrier energy of n-GaAs-Al diodes has been measured by extrapolation of the photoresponse vs. photon energy plots.
Abstract: The bias dependence of the photoelectric barrier energy of n-GaAs-Al diodes has been measured. The devices were fabricated by cleavage of the GaAs in an evaporating stream of metal in a vacuum of 10^(−8) torr. The barrier energies at various bias levels were determined by extrapolation of the photoresponse vs. photon energy plots. The electric field dependence of the photoresponse was also measured at constant photon energy. The calculated change in barrier energy from the latter method was then compared with the changes in extrapolated values of barrier energy. A small systematic disagreement was observed and attributed to the effects of collection efficiency in the GaAs. The field dependence of Schottky barriers on 5×10^(16) GaAs was found to be in good agreement with that expected from the exponential charge distribution associated with the surface states which determine the barrier energy.
TL;DR: In this article, the wavelength-dependent dielectric response function for the primitive model electrolyte, e(k), is evaluated by means of a self-consistent torque calculation for ion pairs in an external field.
Abstract: The theoretical program initiated in the preceding paper is continued. The wavelength‐dependent dielectric response function for the “primitive‐model” electrolyte, e(k), is evaluated by means of a self‐consistent torque calculation for ion pairs in an external field. The result is used to obtain the longestranged component of the ion‐atmosphere charge density. The rigorous second‐moment condition on the ion atmosphere then is used to compute crudely the short‐ranged components. Besides the usual lowconcentration terms, the implied free energy [Eq. (76)] and activity coefficient [Eq. (77)] contain negative terms varying with the four‐thirds power of concentration.
TL;DR: The detailed dependence of surface state density on crystallographic orientation was determined by measuring the ac metaloxide-semiconductor conductance on the surface of a thermally oxidized singlecrystal silicon hemisphere as discussed by the authors.
Abstract: The detailed dependence of surface state density on crystallographic orientation was determined by measuring the ac metal‐oxide‐semiconductor conductance on the surface of a thermally oxidized single‐crystal silicon hemisphere. It was found that the 〈111〉 poles are located at maxima, the 〈100〉 poles at minima, and the 〈110〉 poles at saddle points in the surface state density distribution. The symmetry of the surface state density distribution is generally similar to that of the ``fixed'' interface charge density, but differences are noted in the vicinity of the 〈100〉 directions.
TL;DR: In this paper, the authors considered charged dust distributions in equilibrium and showed that the whole system of field equations can be reduced to a single Laplace equation in the empty space outside and to a nonlinear modified Poisson equation within the charged dust distribution.
Abstract: The paper considers charged dust distributions in equilibrium. If the dust be uniformly charged (i. e. if the ratio of the charge density to the matter density be constant) or if the surfaces of the dust distributions be equipotential surfaces and inside these surfaces there is no hole or pocket of alien matter, then there exists a simple relation between and g 00 and ϕ , the electrostatic potential and the charge density must be equal to the matter density. Further in this case, the whole system of field equations can be reduced to a single Laplace equation in the empty space outside and to a nonlinear modified Poisson equation within the charged dust distributions.
TL;DR: In this paper, the Hartree-Fock approximation of the four alkaline-earth oxides BeO, MgO, CaO, and SrO in the 1 Σ ground state is presented.
Abstract: Molecular properties of the four alkaline-earth oxides BeO, MgO, CaO and SrO in the 1 Σ ground state, computed in close to the Hartree-Fock approximation, are presented Computed properties are total energies, dissociation energies, electric dipole and quadrupole moments, forces on the nucleus, field gradients at the nucleus and other mean values Potential curves, spectroscopic constants, dipole moment function, µ( R ), and variation of field gradients with internuclear separation are also presented and discussed Although the computed sign of the dipole derivative d µ/ d R at the equilibrium internuclear separation is negative only for MgO and positive for others, the fact that the computed sign for MgO and also the observed sign for SrO are negative suggests that d µ/ d R for CaO may also have the negative sign This indicates that the charge distribution in the alkaline-earth oxide can not be described by a simple polarizable ion-pair model Crude estimates of magnetic properties of the molecules are
TL;DR: In this article, the screening of the 7s electron charge density at the nucleus by 6d, 7s, and 7p electrons was discussed, and it turns out that the same screening factors as for the 6s electron in lighter elements can be used.
Abstract: The isotope shifts of unperturbed electron configurations have been determined from isotope shift measurements in the spectra of Th, U, Pu, and Am. The screening of the 7s electron charge density at the nucleus by 6d, 7s, and 7p electrons is discussed. It turns out that the same screening factors as for the 6s electron in lighter elements can be used. The screening of the 7s electron charge density at the nucleus by one 5f electron amounts to about 25%: [δT(fns)−δT(fn)]/[δT(fn}s)−δ(fn})]=0.75. The charge density at the nucleus due to the filleds (andp1/2) shells is considerabely screened by anf electron. The isotope shiftδT(fn}-1dm+2)−δT(fndm) produced by this effect is of the same order of magnitude as the isotope shiftδT(fndms)-δT(fndm) due to ans electron. The experimental isotope shift constants are found to be:Β Cexp(Th230–Th232)=880±120;Β Cexp(U233–U235)=1000±180;Β Cexp(U234–U236)=1070±200;Β Cexp(U236–U238)=1080±180;Β Cexp(Pu238–Pu240)=1200±120;Β Cexp(Pu239–Pu241)=1060±100;Β Cexp(Pu240–Pu242)=900 ±90;Β Cexp(Am241–Am243)=890±50 [10−3cm−1]. The ratiosΒ Cexp/Cth are discussed.
TL;DR: In this article, the nuclear quadrupole resonance frequencies of the halogen atoms in the trihalide ions 13 and Ibr2 in some of their crystalline salts have been measured.
Abstract: The nuclear quadrupole resonance frequencies of the halogen atoms in the trihalide ions 13 and Ibr2 in some of their crystalline salts have been measured. The results have been correlated with a simple LOAD-MO bonding description and the charge distributions in the ions have been calculated. These ions can be regarded as charge-transfer complexes as described by Mulliken. The effect of the crystal field on the charge distribution in the I3 ion has been investigated.
TL;DR: In this paper, it was shown that a simple square well solute potential can be obtained semi-empirically which leads to quantitative agreement in terms of the existing free electron expressions of the partialwave analysis with the available experimental values of the residual resistivity (by definition), the solvent Knight shift and the solute characteristic thermopower.
TL;DR: In this paper, an electrostatic fluxmeter for the examination of electric fields and charge densities present in the corona has been developed and used, which can measure electric fields down to 10 V/cm with a time resolution of 0.5 ms.
Abstract: Measurements have been made of corona discharges in positive rod/earthed plane systems subjected to impulse voltages up to 200 kV. For this an electrostatic fluxmeter for the examination of electric fields and charge densities present in the corona has been developed and used. Measurements of electric fields and current densities so obtained during the discharge are compared with conventional measurements of total current densities. These show that the transient at the centre of the plane is a double pulse of time separation 0.1 to 1.0 μs. The first pulse is shown by the fluxmeter to be due to induced charge on the plane surface and the second to electron emission from the surface. At the plane electrode the space charge electric field can be as great as 8 kV/cm, and the conduction current density in the corona 45 A/m2. The duration of the decaying space-charge field is several seconds. The construction, calibration and synchronization of the fluxmeter, which can measure electric fields down to 10 V/cm with a time resolution of 0.5 ms, are described. The principles of the device in separating the displacement and conduction current components in the discharge process are discussed.
IBM1
TL;DR: In this article, a selfconsistent scheme of subpicocoulomb charge measurement and two-dimensional transport analysis has been used to calculate the distribution of charge in high speed (3-7 GHz) Ge and Si transistors.
Abstract: A self-consistent scheme of subpicocoulomb charge measurement and two-dimensional, transport analysis has been used to calculate the distribution of charge in high speed (3-7 GHz) Ge and Si transistors. This scheme carefully measures total stored charge and calculates the mobile charge stored in the two-dimensional base and collector space charge regions. Storage in the emitter space charge layer is obtained by subtraction of calculated charge from measured charge. The conclusions of this study are" (1) The majority (as much as 80%) of the mobile charge is stored in the emitter; (2) 30-50% of the remaining charge is injected through the emitter side-wall and stored in the remote base region; (3) overall transit time is dominated by low field mobility regions -- thus Johnson's fundamental limitations do not apply, and the transit time of state-of-the-art devices continues to reflect the low-field mobility of the material ( \micro Ge ∼ 3 × \micro Si).
TL;DR: In this paper, a perturbation calculation is made of the energy levels of muons in the field of a nucleus, starting from a nucleus of uniform charge distribution, and the effect of a change of the nuclear charge distribution ϱ ( r ) on the energy of the 1s and 2p states is expressed as a simple integral over ϱ( r ).
TL;DR: Replication of ice crystals with vapor of methyl 2-cyanoacrylate has produced evidence of whiskers on them and confirms crystal clustering in the atmosphere and appears to confirm the distribution of electrical charge on ice crystals.
Abstract: Replication of ice crystals with vapor of methyl 2-cyanoacrylate has produced evidence of whiskers on them; an additional mechanism for the necessary multiplication of ice crystals in the atmosphere is suggested. This replication technique also confirms crystal clustering in the atmosphere and appears to confirm the distribution of electrical charge on ice crystals.
TL;DR: In this paper, the authors examined the relationship between the electrical force between a pair of parallel uncharged plates of infinite thickness and low dielectric constant, immersed in an aqueous 1-1 electrolyte, and showed that the force is caused by the ion image self-atmosphere potentials associated with the electrolyte ions in the neighborhood of the two plates.
Abstract: The nature of the electrical force between a pair of parallel uncharged plates of infinite thickness and low dielectric constant, immersed in an aqueous 1–1 electrolyte, is examined. The force is caused by the ion‐image self‐atmosphere potentials associated with the electrolyte ions in the neighborhood of the two plates. For anions and cations of the same size and polarizability in the electrolyte, these potentials of the two ion species are equal and consequently with uncharged plates there is no mean volume charge density. We have only considered point ions and neglected corrections due to ion size, except for introducing a distance of nearest approach of an ion to the plane of dielectric discontinuity. There are a number of contributions to the ion‐image force between the two plates. The simplest is the ideal osmotic pressure term which is attractive because the repulsive image forces cause a depletion of ions in the region between the plates. Another term is the Debye–Huckel self‐atmosphere contribution to the osmotic pressure, which is responsible for attraction. In addition, there are two direct image effects on the ions. One already occurs explicitly in the work of Buff and Stillinger and gives an attractive force which at large plate separations decays as the inverse cube of this separation. The second, which is new, may be described as a “cross effect” representing the direct image force of each plate on the diffuse layer of the second plate. It is repulsive and likewise decays as the inverse cube law at large separations, where it exceeds the first direct‐image force. The net result is that the force between the two dielectric plates is an attraction at small separations but a repulsion at large separations. Except for sign this repulsion takes the same form as the Hamaker attraction, with an equivalent Hamaker constant equal to about 3 × 10−14 erg at room temperature. In Appendix C it is shown that the local free energy density and local pressure formalisms used in this paper yield the surface tension relations which Buff and Stillinger obtained by using molecular distribution functions in grand ensemble theory. It is also shown that the three different forms for the surface tension considered by these authors give the same values when the dependence of local ion density on distance from the interface is introduced consistently, even though superposition and linearization approximations are implicit in the expression for the potential of the mean force between two ions.
TL;DR: The surface conductivity of salt free montmoriUonite clay gels saturated with lithium, sodium, potassium and cesium has been studied in this article, where it was shown that the depolarization factor may be extra-polated to 1 in the direction of the small axis of the platelet, meaning that the field action is zero in this direction.
Abstract: The surface conductivity of salt free montmoriUonite clay gels saturated with lithium, sodium, potassium and cesium has been studied. The theory of the behavior of heterogeneous dielec- trics adapted to systems having a surface charge density has been applied to the clay gels. From numerical calculations it became evident that the value of the depolarization factor may be extra- polated to 1 in the direction of the small axis of the platelet, meaning that the field action is zero in this direction. Along the long axis, however, the action is complete and the motion of the charge carriers is essentially tangential to the platelet. The values of the surface conductance are of an order of magnitude of l 0 -9 Mho. The investigation of the behavior of the water molecules has been carried out over a wide tem- perature range (145-320~ At temperatures below 273~ the conduction appears to be predomin- antly protonic; the counterions are considered to be disturbing elements in the water layer structures, thus creating a number of lattice defects able to transport the current. Above 273~ the conduction is essentially due to the adsorbed cations, their contribution starts during the phase change.
TL;DR: It is shown that the effects of near neighbors on a reference ion become far more significant than those of more distant ions; interionic electrostatic energies no longer are small compared to kT and thereby the necessary condition for the existence of a smoothed charge density disappears.
Abstract: the other hand, the effects of near neighbors on a reference ion become far more significant than those of more distant ions; interionic electrostatic energies no longer are small compared to kT and thereby the necessary condition for the existence of a smoothed charge density disappears. Clearly, then, a different model must be chosen as the basis of theory. The upper limit of the concentration scale corresponds to the randomized' fused salt; as solvent molecules are added, to make concentrated solutions, average interionic distances will vary as the cube root of concentration. This naturally suggests a cell model for the higher concentrations. As the solution is diluted, we know that the c'"/ behavior must give way to c /2 properties. There is, of course, no critical concentration at which a solution suddenly stops acting like a diluted and randomized crystal lattice and rearranges its ions to the distribution characteristic of the ion atmosphere. Rather, a smooth transition from one model to the other must occur. A stochastic description can be formulated2 as