Showing papers on "Charge density published in 1982"
TL;DR: In this paper, a new method for generating and using pseudopotentials is developed to treat explicitly the nonlinear exchange and correlation interaction between the core and the valence charge densities.
Abstract: A new method for generating and using first-principles pseudopotentials is developed to treat explicitly the nonlinear exchange and correlation interaction between the core and the valence charge densities. Compared to existing potentials, the new scheme leads to significant improvement in the transferability of the potential. In particular, the spin-polarized configurations are well described with a single potential. The need for separate spin-up and spin-down ionic pesudopotentials is, thus, eliminated. The method can easily be implemented with minimal increase in computational effort. Results for both atoms and solids are demonstrated.
1,632 citations
TL;DR: This paper presents a meta-analysis of 9-Amino Acridine technique and its applications in particle electrophoresis and concludes that the technique can be applied to surface charge determination as well as other determinants of surface attraction.
Abstract: INTRODUCTION . DETERMINATION OF SURFACE CHARGE DENSITy . Particle Electrophoresis . 9-Amino Acridine Technique and Similar Approaches .... . . .. . .. . Reaction Rates Involving Charged Electron Donors and Acceptors . Conclusions from Various Approaches .. ORIGIN AND DISTRIBUTION OF SURFACE CHARGE .
501 citations
TL;DR: In this paper, an analytic expression of the surface charge density/surface potential relationship and double-layer potential distribution for a spherical colloidal particle in 1-1 and 2-1 electrolyte solutions and a mixed 1 1 and 2 1 electrolyte solution was derived.
370 citations
TL;DR: In this paper, the amplitude of the superconducting gap propagates as an undamped collective mode with a finite frequency and the dispersion and damping of this mode are calculated.
Abstract: At low temperature the long-wavelength perturbations of the amplitude of the superconducting gap propagate as an undamped collective mode with a finite frequency. The dispersion and damping of this mode are calculated. The phase or the Bogoliubov modes of a superconductor are strongly affected by Coulomb interactions and rendered indistinguishable from plasmons. By contrast, the amplitude modes are shown not to perturb the charge density thus remaining unaffected by the Coulomb interactions. Under certain conditions long-wavelength phonons couple to this mode. This coupling is derived and the observation of the amplitude mode through Raman scattering experiments in the charge-density-wave compound Nb${\mathrm{Se}}_{2}$ are quantitatively explained.
217 citations
TL;DR: In this article, a laser-induced pressure-pulse method for measuring the charge distribution in (10 to 100 µm) dielectric samples with a resolution of about 4 µm was described.
Abstract: A laser-induced pressure-pulse method for measuring the charge distribution in (10 to 100 \ensuremath{\mu}m thick) dielectric samples with a resolution of about 4 \ensuremath{\mu} m is described. A short ( ns) energetic light pulse from a neodymium-doped yttrium aluminum garnet laser is applied to a specially coated surface of the sample. The recoil due to ablation of material from the coating generates a pressure pulse (\ensuremath{\sim}2 ns) which propagates through the sample. The charge distribution is evaluated by measuring the electrode currents from 25- and 75-\ensuremath{\mu}m polymers charged with corona and electron-beam methods.
208 citations
TL;DR: In this article, the charge density in α-Al2O3 has been refined with respect to X-ray structure factors [complete spheres for both Mo Kα and Ag Kα radiations with (sin θ/λ)max = 1.19 and 1.495 A-1 respectively] and electric-field gradient tensors at both atomic sites.
Abstract: The charge density in α-Al2O3 has been refined with respect to X-ray structure factors [complete spheres for both Mo Kα and Ag Kα radiations with (sin θ/λ)max = 1.19 and 1.495 A-1 respectively] and electric-field gradient tensors at both atomic sites, using Hirshfeld- type deformation functions. Atomic charges from a κ refinement are + 1.32 (5) for Al and -0.88 (8) e for O. The charge distribution of O is polarized towards the four Al neighbours, and metal-metal bonds are clearly absent. Quadrupole coupling constants and asymmetry parameters of the field-gradient tensors cannot be determined from the structure factors. They define the quadrupolar deformations near the atomic centers, and the X-ray data define the charge density between the atoms. The orientational parameters of the tensors and the signs of their largest eigenvalues can be qualitatively retrieved from the X-ray data. The refinement of anisotropic secondary-extinction parameters may, however, destroy this information. Refinement with respect to the field gradients affects mainly the quadrupolar deformation terms, and has little influence on the X-ray scale factor (i.e. monopolar terms) and computed electrostatic fields (i.e. dipolar terms). Properties of the charge density with different angular symmetries are thus only weakly correlated.
189 citations
TL;DR: In this article, the authors compared experimental basal spacings with dL/n-plots to determine the average charge density of 25 vermiculites and found that the high-charged vermicules (≥ 0.8 eq/(Si,Al)4O10) with paraffin-type interlayers follow a straight line in the dL /n plots.
Abstract: The broad charge heterogeneity typical of nearly all smectites is not necessarily characteristic of vermiculites. In addition to vermiculites with pronounced heterogeneity, minerals with no or only limited charge heterogeneities are known. Layer charge and charge heterogeneity of 25 vermiculites were determined by alkylammonium ion exchange. The comparison of experimental basal spacings with dL/n-plots provided a simple determination of the average charge density. The spacings of high-charged vermiculites (≥0.8 eq/(Si,Al)4O10) with paraffin-type interlayers follow a straight line in the dL/n-plots. Lower-charged vermiculites were recognized by stepwise increasing spacings due to mono-, two-, or three-layer chain packings. Charge heterogeneity produced a superposition of the dL/n-curves for different charges, and the basal reflections of some of the alkylammonium derivatives became nonintegral.
183 citations
TL;DR: In this article, the hypernetted chain integral equations (HNC/MSA version) for the reduced density profiles of a model electrolyte near a charged electrode are solved and the resulting density and potential profiles are compared with recent Monte Carlo calculations.
Abstract: The hypernetted chain integral equations (HNC/MSA version) for the reduced density profiles of a model electrolyte near a charged electrode (the so‐called electrical double layer problem) are solved and the resulting density and potential profiles are compared with recent Monte Carlo calculations. Good agreement is found when the bulk electrolyte direct correlation functions are calculated from the mean spherical approximation. In particular, the HNC/MSA correctly predicts that for divalent salts, the potential profile is nonmonotonic and changes sign. As a result, there is charge oscillation or a layering of charge. That is, near the electrode the ions predominately have the opposite charge as the electrode but in some situations the ions at a greater distance generally have the same charge as the electrode. In contrast, the Gouy–Chapman theory gives poor results. The Gouy–Chapman density and potential profiles are always monotonic. Thus, the widely used practice of estimating the effects of solvent or n...
179 citations
TL;DR: In this paper, the effect of surface polarization on the properties of electrical double layers is studied by means of Monte Carlo calculations on a primitive model electrolyte next to a planar charged surface bounding a semi-infinite dielectric.
Abstract: The effect of surface polarization (i.e., image forces) on the properties of electrical double layers is studied by means of Monte Carlo calculations on a primitive model electrolyte next to a planar charged surface bounding a semi‐infinite dielectric. Two cases are considered, that of a conducting material for which an ion is attracted by its own image and that of an insulator for which the self‐image force is repulsive. At low surface charge densities the image forces cause quite dramatic changes in the ionic densities near the wall; the effect on the electrostatic potential is small but increases with surface charge density. The modified Poisson–Boltzmann theory of Outhwaite is quite successful in describing the Monte Carlo results for the range of parameters studied. A screened self‐image model of image effects is also considered for which both Monte Carlo calculations and numerical solution of the HNC equation have been obtained.
166 citations
TL;DR: In this article, it was shown that the Si(111)-(2 x 1) surface can be formed easily in the cleavage process without increasing the total energy by more than 0.03 eV/(surface atom).
Abstract: Pseudopotential total-energy calculations show that the ..pi..-bonded chain reconstruction of the Si(111)-(2 x 1) surface can be reached from the ideally bonded surface without increasing the total energy by more than 0.03 eV/(surface atom). Hence, the chain surface can be formed easily in the cleavage process. The minimum-energy chain geometry is determined, and the corresponding surface-state dispersion is in remarkable agreement with recent angle-resolved photoemission experiments.
164 citations
01 Aug 1982
TL;DR: In this article, the electrophoretic mobility of a particle whose gross radius of curvature greatly exceeds the Debye length is calculated without assuming that the particle has a smooth surface.
Abstract: The electrophoretic mobility of a particle whose gross radius of curvature greatly exceeds the Debye length is calculated without assuming that the particle has a smooth surface The particle's surface is modeled as a layer of appendages which exert frictional forces on the solvent The functional dependence of the electrophoretic mobility on the surface geometry, surface charge density, and ionic strength is determined using the Debye—Bueche theory of polymer hydrodynamics It is found that the surface structure can result in an augmented or a diminished electrophoretic velocity relative to that of a smooth body The Debye—Bueche theory fails at high ionic strengths, and a second model is introduced to consider that regime A Pade approximant is constructed from the two models, yielding an expression for the electrophoretic mobility which should be valid over a greater range of ionic strengths Mobilities calculated from the Pade approximant agree reasonably well with the measured mobilities of human erythrocytes as a function of ionic strength
TL;DR: In this paper, a model of charge-density wave motion at large velocities is used to describe the nonlinear response of the charge density wave in fields well above the threshold.
Abstract: A classical model of charge-density wave motion at large velocities is used to describe the nonlinear response of the charge-density wave in fields well above the threshold. The charge-density wave is regarded as a charged, deformable medium and its interaction with pinning centers is treated in perturbation theory. The results fit the available high-field data on NbSe3 well. The observed interference effects between a large dc field and an ac field are also explained.
TL;DR: In this paper, a balloon carried a particle charge instrument, an electric field meter, and a standard meteorological radiosonde upward into thunderclouds over Langmuir Laboratory in central New Mexico, and the instruments encountered two regions of positive charge below the main negative charge center.
Abstract: We designed an instrument to measure the charge and vertical velocity of individual precipitation particles inside thunderclouds. A balloon carried the particle charge instrument, an electric field meter, and a standard meteorological radiosonde upward into thunderclouds over Langmuir Laboratory in central New Mexico. During one balloon flight the instruments encountered two regions of positive charge below the main negative charge center. We identify these positive regions with the lower positive charge centers that have been described in the literature for many years. We find the following points: (1) One region had an estimated total charge of 0.4 C. The other had 2 C. (2) The charge resided on precipitation particles. The particles' charges typically ranged between 10 and 200 pC, but a few particles had charges up to 400 pC. Their diameters lay between an estimated 1–3 mm. The charges were too large to be explained by the polarization induction mechanism. We favor the hypothesis that lightning provided the positive charge in the lower positive charge centers. (3) The motion of the lower positive charge centers enhanced the electrical energy of the storm, but their contribution to the overall electrical budget was small. (4) The field excursions (at the ground) associated with precipitation (FEAWPs) described by C. B. Moore and B. Vonnegut are probably caused by lower positive charge centers descending on precipitation. The larger (2 C) lower positive charge center caused a FEAWP. Negatively charged precipitation particles passed through our instrument near the top of its trajectory just before the balloon was struck by lightning. The charge density on precipitation particles was substantial, but we do not have enough information to comment on the role the particles may have had in generating the main region of negative charge.
TL;DR: In this paper, the charge density of the 4f-shells of all trivalent rare earth ions is calculated for the eigenstates of a component of total angular momentum.
Abstract: The charge density of the 4f-shells of all trivalent rare earth ions is calculated for the eigenstates of a component of total angular momentum. The angular dependence of the charge distribution is plotted for all these states in order to visualize the asphericity of the 4f-shells.
TL;DR: The sputtering of condensed gas films by ions with energies > 10 keV / amu is controlled by the electronic energy loss of the ions as discussed by the authors, and the sputtering yields are large, from 0.1 to 103 or more molecules lost per incident ion.
TL;DR: In this paper, a systematic study of the correlation between the core and valence level X-ray photo-emission spectra has been conducted, where the nature of chemical bonding and charge redistribution for bulk transition metal silicides has been examined.
Abstract: Via a systematic study of the correlation between the core and valence level X-ray photoemission spectra, the nature of the chemical bonding and charge redistribution for bulk transition metal silicides has been examined. Particular emphasis is placed on Pt2Si and PtSi. It is observed that the strength of the metal (d)-silicon (p) interaction increases in the order Ni2Si, Pd2Si, Pt2Si. It is also observed that both the metal and silicon core lines shift to higher binding energy as the silicides are formed. The notion of charge redistribution for metallic bonds is invoked to explain these data.
TL;DR: In this paper, all available information on charge distributions of even-even nuclei is analyzed systematically, including the extension of the nuclei, surface thickness, and the average slope in the inner part of the nucleus.
TL;DR: In this article, high-angle X-ray diffraction data (Ag Ka and Mo Net radiation) have been collected at 74 K on dimanganese decacarbonyl Mn2(CO)I 0, and the crystal structure was refined.
Abstract: X-ray diffraction data (Ag Ka and Mo Net radiation) have been collected at 74 K on dimanganese decacarbonyl Mn2(CO)I 0, and the crystal structure was refined. The atomic positional and thermal parameters were determined from high-angle AgKa data to avoid systematic errors due to bonding effects. The molecular geometry is discussed. The distortions are larger than at room temperature: for example, the torsion angle of the two Mn(CO) 5 fragments is 50.2 °, compared to 47.4 ° at room temperature, and 45 ° for an ideal D4a symmetry. 'X-X' deformation-density maps were computed and averaged over chemically equivalent sites. No significant charge-density accumulation is observed on the Mn-Mn bond. The configuration around the Mn atoms is essentially octahedral, with about 75% of the 3d electrons in the diagonal orbitals (dxy,d~z,dy ~) and the remaining 25% in d: and dx2_/. Atomic charges were determined both by direct integration and by least-squares refinement. Directly integrated charges are very small. Mn seems slightly negative. Both methods of charge integration show a clear difference between axial and equatorial carbonyls, which is confirmed by comparing their electron density with that of free carbon monoxide: the differences are characteristic of a a-bonding n-backbonding mechanism, and are larger for the axial carbonyls than for the equatorial carbonyls. This confirms the stronger bonding of the axial carbonyls, also responsible for the longer C-O bond and the shorter Mn-C bond.
TL;DR: In this paper, a contour integral in the complex energy plane was proposed to calculate the charge density of a single-electron Green's function, which can be used for band structure calculations.
TL;DR: This paper presents calculations of the image potential for an ion in an aqueous pore through lipid membrane and the electric field produced in such a pore when a transmembrane potential is applied and develops a projection method that explicitly accounts for this behavior.
TL;DR: In this paper, the authors determined quantitatively the charge density in different parts of the double layer (Stem model) at the TiO2-electrolyte interface using three complementary techniques (potentiometry, electrophoresis, radiotracer technique).
TL;DR: In this article, an improved surface charge method for computation of three-dimensional electric field distribution and its application to optimum insulator design is described, where each curved surface on which the charge is distributed is divided into many curved surface elements instead of planar elements.
Abstract: This paper describes an improved surface charge method for computation of three-dimensional electric field distribution and its application to optimum insulator design. In this method, each curved surface on which the charge is distributed is divided into many curved surface elements instead of planar elements. After computing numerically the charge distribution, the distributions of both potential and electric field are obtained. Because the use of many curved surface elements provides a good approximation of the insulator contour, the correction of insulator contour to achieve optimum insulator design can be performed smoothly.
TL;DR: In this paper, a self-consistent field model of atoms in dense plasmas has been devised and incorporated in a computer program, where a uniform positive charge distribution with a hole in it and at the center of the hole an atomic nucleus is used.
Abstract: A self-consistent field model of atoms in dense plasmas has been devised and incorporated in a computer program. In the model there is a uniform positive charge distribution with a hole in it and at the center of the hole an atomic nucleus. There are electrons, in both bound and continuum states, in sufficient number to form an electrically neutral system. The Dirac equation is used so that high Z atoms can be dealt with. A finite temperature is assumed, and a mean field (average atom) approximation is used in statistical averages. Applications have been made to equations of states and to photoabsorption.
TL;DR: In this paper, a model-independent way with a Fourier-Bessel parametrization of the charge distribution was analyzed in a model independent way, and the behavior of the form factor in the diffraction minimum was investigated.
Abstract: Elastic electron scattering cross sections for the nucleus $^{12}\mathrm{C}$ have been measured in a momentum transfer range from 0.25 to 2.75 ${\mathrm{fm}}^{\ensuremath{-}1}$. The data were analyzed in a model independent way with a Fourier-Bessel parametrization of the charge distribution. For the rms radius, the value ${〈{r}^{2}〉}^{\frac{1}{2}}=(2.464\ifmmode\pm\else\textpm\fi{}0.012)$ fm (no dispersion corrections applied) has been obtained, and agrees with those of other electron scattering experiments and with muonic atom experiments, but disagrees with data obtained from measurements of muonic x-ray transitions with a crystal spectrometer which show a larger rms radius. The extracted distribution disagrees with Hartree-Fock calculations in both the radial dependence and the rms radius. The behavior of the form factor in the diffraction minimum was investigated in detail. The experimentally determined cross sections in the minimum are always larger than those obtained from the Fourier-Bessel analysis. These deviations amounted to 5% for a primary energy of 320 MeV and to 2% for 240 MeV and may be interpreted as an indication of dispersion effects.NUCLEAR REACTIONS $^{12}\mathrm{C}$; absolute ($e, e$) cross sections measured. Charge distribution and rms radius deduced. Discussion of dispersion effects, comparison with HF calculations.
TL;DR: In this paper, the singularities and approximations that occur in the charge-density method of solving electrostatic problems in which space-charge is absent (Laplace's equation) or present (Poisson's equation).
Abstract: Discusses the singularities and approximations that occur in the charge-density method of solving electrostatic problems in which space-charge is absent (Laplace's equation) or present (Poisson's equation). Describes the application of the method to electrostatic lenses in general and to the particular case of a high-current triode gun.
TL;DR: In this paper, a numerical model taking into account ion capture by the neutral aerosol particles leads to theoretical charge density profiles which display features close to those of the experimental profiles, which reveals the existence of important space charge layers near the ground.
Abstract: High electric fields created by thunderclouds at ground level are enhanced by the irregularities of the surface. This causes corona discharges to occur. The generated ions, when they are not blown away, form a space charge layer which reduces the magnitude of the electric field at ground level. During the LANDES 79 experiment (south western France), electric field soundings have been performed. The sensor is a balloon-borne double field-mill device designed for measuring the vertical and horizontal components of the external electric field. At several occasions, a strong vertical field increase with height was detected in the lower part of the sounding. This reveals the existence of important space charge layers near the ground. Space charge density profiles are deduced from electric field soundings. They display density values running from 2 to 7 nC m−3, distributed over shallow layers. A numerical model taking into account ion capture by the neutral aerosol particles leads to theoretical charge density profiles which display features close to those of the experimental profiles. Computation shows that the initial number of neutral aerosol particles has a drastic effect on both density maximum values and layer depths. According to aerosol density, charge density values run from 0.6 nC m−3 (in clean air) up to 3.1 nC m−3 (high aerosol density).
TL;DR: In this paper, the statistical mechanics of a polyion in a dilute ionic solution were studied, and it was shown that if the length of the polyion is much larger than the distance of closest approach, counterion condensation occurs.
Abstract: Starting from the BBGKY hierarchy and using the method described in paper I, the statistical mechanics of a polyion in a dilute ionic solution is studied. It is shown that if the length of the polyion is much larger than the distance of closest approach, ’’counterion condensation’’ occurs. If the length of the polyion is comparable to the Debye length or larger, then the critical charge density is shown to be independent of the ionic strength. If the length is much smaller than the Debye length, the critical value is shown to depend logarithmically on the ionic strength and the length of the polyion. Expressions are derived for the critical charge density and the distribution of the counterions around the polyion.
TL;DR: In this article, a model of a strong, time-independent, and relativistic double layer is studied, where double layers having the electric field parallel to the current are described.
Abstract: A model of a strong, time-independent, and relativistic double layer is studied. Besides double layers having the electric field parallel to the current the model also describes a certain type of oblique double layers. The ‘Langmuir condition’ (ratio of ion current density to electron current density) as well as an expression for the potential drop of the double layer are derived. Furthermore, the distributions of charged particles, electric field, and potential within the double layer are clarified and discussed. It is found that the properties of relativistic double layers differ substantially from the properties of corresponding non-relativistic double layers.