Stability of a bubble in a dielectric liquid in an external electrostatic field

Critical instability conditions are found for a gas bubble in a liquid dielectric in a uniform external electrostatic field E ₀. It is shown that they depend both on the magnitude of E ₀ and on the properties of the liquid, as well as on the gas pressure in the bubble. In a linear approximation with respect to the square of the eccentricity of an equilibrium spheroidal form, the equilibrium eccentricity of the bubble exceeds the equilibrium eccentricity of a drop in the field E ₀. The gas pressure in the bubble lowers the critical electric field E ₀ for development of an instability in the bubble. Zh. Tekh. Fiz. 69, 43–48 (August 1999)     

The pressure dependence of theE 2 reflectivity peak and of the dielectric constant in III–V semiconductors

The functional dependence on pseudopotential form factors of the Penn gap related to theE ₂ reflectivity peak is used to calculate the pressure dependence ofE ₂ and of the static electronic dielectric constant in III–V semiconductors. In a one-parameter approximation only the pressure coefficient of one Fourier coefficient of the pseudopotential is fitted to experimental values of the pressure dependence ofE ₂ in group-IV semiconductors and then taken over to III–V compounds. We find a decrease of the dielectric constant with pressure. The comparison of our results with those experimentally known supports strongly our method.This work was performed in the Arbeitsgemeinschaft A_III-B _v -Halbleiter of the Karl-Marx-Universität Leipzig.     

Local field corrections in trigonal Se

The inverse dielectric tensor ?^-1₀₀(q) in the static limit isevaluated in crystalline Se along two symmetry directions, by using a proper model Hamiltonian describing the covalent bond and modified sp³ orbitals as basis states. By comparing the results in diagonal approximation with these obtained including the off diagonal elements (ODE) of the dielectric matrix (DM) it is found that the local field corrections are very large and essential to reproduce the experimental dielectric tensor.     

Analytic theory of electric field depinning in the one-dimensional Fukuyama-Lee-Rice hamiltonian

Using Feigel'man's method in the theory of one-dimensional random systems we have evaluated analytically the depinning electric fieldE _T and the static dielectric constant ₀ for the Fukuyama-Lee-Rice hamiltonian in the weak pinning limit and for low temperatures. This is accomplished by solving a Fokker-Planck equation for finitedc electric fields in order to determine the field dependent pinning energy. The dielectric constant is found to remain independent of the electric field up to the threshold. The product ₀ E _T is also evaluated and compared with other theories.     

A comparative study of the effective dielectric constant of a medium containing randomly distributed dielectric spheres embedded in a homogeneous background medium

Abstract

The effective dielectric constant ∈_eff of a medium containing randomly distributed dielectric particles has been analysed by conventional methods: Foldy's approximation, the quasi-crystalline approximation (QCA) and the QCA with coherent potential. These conventional methods, however, have been indicated to become invalid for particles with a high dielectric constant; we have thus presented a new method that is valid for them. This paper compares ∈_eff of our method with those of the conventional methods by changing the volume fraction and the dielectric constant of spheres. As a result, our method is shown to be more powerful for the analysis of ∈_eff than the conventional methods.     

Dielectric constant and threshold electric field of charge-density-waves with strong impurity pinning

The dielectric constant ε and the threshold electric field E_T for the onset of charge-density-wave conduction are investigated within the phenomenological model proposed by Tua and Zawadowski for the strong pinning regime. The static dielectric constant ε (E) in a bias electric field E is found to be almost independent of E provided that E is not too close to E_T. For relatively small values of the pinning strength, the product ε E_T becomes independent of the parameters of the theory. Good agreement is found with the available experimental data on NbSe₃ for the case of strong pinning obtained by radiation damage.     

Nanoscale ab-initio calculations of optical and electronic properties of LaCrO3 in cubic and rhombohedral phases

We report nanoscale ab-initio calculations of the linear optical and electronic properties of LaCrO₃ in nonmagnetic cubic and rhombohedral phases using the full potential linear augmented plane wave (FP-LAPW) method. In this work the generalized gradient approximation is used for exchange-correlation potential. The dielectric tensor is derived within random-phase approximation. We present results for the band structure, density of states, imaginary and real parts of dielectric tensor, electron energy loss spectroscopy, sum rules, reflectivity, refractive index and extinction coefficient. The regions of transparent, absorption and reflection are discussed. We are not aware of any published experimental or theoretical data for these phases, so our calculations can be used to cover this lack of data for these phases.     

A dipole approximation for a dielectric mixture based on the equal field energy method

In this paper, a dipole-energy approximation for calculating the electric field distribution and saturation charge of spheres in an infinitely large dielectric mixture has been carried out. The approximation rests on the assumption that the field energy of mixture calculated using two different methods have the same value. One way is considering that the mixture in a uniform field E₀ as a uniform object of effective permittivity ?_eff from a macroscopic point of view, where ?_eff is seen as the average characteristic parameter of the object. The other way is assuming that the spheres in mixture are in the equivalent external field E₀′, and E₀′ related to the dielectric mismatch and the ratio of the sphere radius to the average distance between neighboring spheres has been obtained. Based on dipole-energy model, the approximate formulas for calculating the maximum field strength and saturation charge of spheres are derived separately.     

Density functional studies of selected metal dioxides

This study investigates the optical properties of selected metal oxides due to their high dielectric constants. The local-spin-density approximation plus Hubbard U (commonly called LDA+U) is used in a study of the structural, mechanical and optical properties of UO₂. The inclusion of a Hubbard U correction to 5f electrons of uranium changes UO₂ from a metal to an insulator and, therefore, has a dramatic effect on the localisation of the electron spin and charge density of uranium. However although the band gap can be reproduced using the effective U parameter, which is equal to 3.5 eV and optical properties were calculated in our previous work, it is difficult to calculate ionic contribution to the static dielectric constant within LDA+U formalism for this compound. It is shown in the present work that the electronic structures of both ceria and thoria exhibit similarities to urania within LDA or PBE functional implementations. Within this functional and linear response theory one can easily calculate static dielectric permittivity and it is shown that in agreement with experiment the predicted values are an order of magnitude larger than the dielectric constant of SiO₂. In this work, high accuracy, first-principles calculations are also used to compare properties of urania versus ceria and thoria and how these similarities can help in understanding these compounds. It is also shown that the B3LYP functional predicts slightly overestimated band gaps for ceria and thoria as well as smaller than experimentally observed electronic contribution to the static dielectric constant, while the index of refraction is well reproduced for thoria.     

Tensorial representation of the Dirac equation

We discuss tensor representations of the Dirac equation using a geometric approach. We find that the mass zero Dirac equations can be represented by Maxwell equations having a source which obeys the empty space wave equation. We also obtain a relation for the source in terms ofE andH. In the case of mass not equal to zero a difficulty is encountered in removing the constant spinors¯ _Aand¯ _A.We find that the arbitrary constant spinors can be eliminated in a spinor theory based on the Klein-Gordon equation.     

An approximate expression for the galvanomagnetic tensor

Using the iterative solution to the Boltzmann equation for electrons in d.c. electric and magnetic fields, an expression for the resistivity tensor can be obtained in the form of an infinite series. This series can be approximated by retaining only the first two terms. In the cases where relaxation times exist — in the sense that the collision term in the Boltzmann equation can be written asg(k)/τ(k), whereτ(k) is the relaxation time, andf (k) = f _E(ɛ k) + [∂f _E(εk)/∂ε]·g(k) the distribution function for electrons with wavevectork — this approximation is exact. For polyvalent metals in the one-OPW approximation, the complete galvanomagnetic tensor can be obtained using this approximation and the result differs from that obtained by using a time of relaxation given by an expression suggested byZiman. A calculation for a simple model Fermi surface, with screened Coulomb scattering, is carried out and the results compared with those of the relaxation time approximation.     

Vibrational and dielectric properties of magnesium aluminate spinel: A first-principles study

The vibrational and dielectric properties of MgAl₂O₄ are investigated within the framework of density functional perturbation theory. Results of phonon frequencies at the Brillouin zone center, static dielectric constant, and electronic dielectric constant are reported. In comparison with experimental results, we find that the generalized gradient approximation potential results in more accurate phonon frequencies than local density approximation potential does. Dielectric, refractive index, extinction coefficient and infrared reflectance spectra of MgAl₂O₄ are given, and the figures suggest that MgAl₂O₄ presents good transmission properties in the spectrum range above 1000 cm−1 and below 300 cm−1.     

Dielectric and anharmonic behaviour of mixed alkali halides

Summary In the present paper an analysis of the dielectric behaviour and anharmonic contribution to the dielectric constants has been made of KCl−KBr mixed ionic crystals. The temperature and volume derivatives of static (ε₀), electronic (ε_∞) dielectric constants and energy gap parameter (E _g) have been calculated using the Szigeti and Havinga and Bosman dielectric theories. The anharmonic contributions have been estimated in terms of temperature derivatives of dielectric constants at constant volumes. The modified form of Clausius-Mossotti theory of dielectric polarization has been used for the mixed crystal under study. The calculated quantities have been compared with the available experimental data. A good agreement has been obtained. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

Longitudinal dielectric constant for quantum wells

We have calculated the longitudinal dielectric constant for a GaAs-AlGaAs quantum well structure. In particular, the total contribution to the transitions is taken as a sum of separate contributions of the regions around the Λ, X, and L symmetry points of the Brillouin zone. Since the electron- and hole-state are quantized in a well formed by potential barriers of the hetrojunction, the static dielectric constant is significantly reduced. For a well width of 2 nm and barriers formed by Al_.35Ga_.65As, the reduction is almost 20%.     

Surface plasmons in small metal particles

The dielectric response of a small metal particle to a perturbing potentialv _L =r ^L Y _LM e ^iωt is considered within the random phase approximation (RPA). The static dielectric polarizability is found and the size dependence of the surface plasmon frequencies are then determined from sum rule calculations. When the particle radiusa is large compared to the Thomas-Fermi screening lengthr ₀ the RPA equation is transformed into a form appropriate for an analytical solution. The dynamic electric polarizability, the position and the width of the surface plasma resonance are found in the limita/r ₀?1.     

Experimental investigation of long-wavelength optical lattice vibrations in quaternary AlxInyGa1−x−yN alloys and comparison with results from the pseudo-unit cell model

Raman and Fourier transform infrared (FTIR) spectroscopies have been utilized to measure long-wavelength optical lattice vibrations of high-quality quaternary Al_xIn_yGa_1−x−yN thin films at room temperature. The Al_xIn_yGa_1−x−yN films were grown on c-plane (0 0 0 1) sapphire substrates with AlN as buffer layers using plasma assisted molecular beam epitaxy (PA-MBE) technique with aluminum (Al) mole fraction x ranging from 0.0 to 0.2 and constant indium (In) mole fraction y=0.1. Pseudo unit cell (PUC) model was applied to investigate the phonons frequency, mode number, static dielectric constant, and high frequency dielectric constant of the Al_xIn_yGa_1−x−yN mixed crystals. The theoretical results were compared with the experimental results obtained from the quaternary samples by using Raman and FTIR spectroscopies. The experimental results indicated that the Al_xIn_yGa_1−x−yN alloy had two-mode behavior, which includes A₁(LO), E₁(TO), and E₂(H). Thus, these results are in agreement with the theoretical results of PUC model, which also revealed a two-mode behavior for the quaternary nitride. We also obtained new values of E₁(TO) and E₂(H) for the quaternary nitride samples that have not yet been reported in the literature.     

A strictly geometric interpretation of gravitation in general relativity

A geometric interpretation of gravitation is given using general relativity. The law of gravitation is taken in the formR ₄₄=0, whereR ₄₄is the component of the contracted Riemann-Christoffel (Ricci) tensor representing the curvature of time. The remaining curvature components of the contracted Riemann-Christoffel tensor may or may not vanish. All that is required in addition toR ₄₄=0 is that the Gaussian curvatureR be nowhere infinite. The conditionR ₄₄=0 yields a nonlinear wave equation. One of the static degenerate solutions represents the gravitational field surrounding a static gravitational point singularity. It is found that for this solution, the three famous predictions of general relativity are obtained in the weak-field approximation. In addition, it is found that there is a correction to the Kepler period of revolution for an orbit.     

Nonlinear dielectric properties of amorphous Bi1.8Pb0.3Sr2Ca2Cu3−x KxOz (x = 0.2–0.3)

The dielectric constant of amorphous Bi_1.8Pb_0.3Sr₂Ca₂Cu_3?x K_xO_x (x = 0.2–0.3) is measured as a function of the static electric field strength. It is found that, as the field strength increases, the dielectric constant decreases following a quadratic law. This behavior of the dielectric constant in a static electric field indicates nonlinear dielectric properties, which can be described within the thermodynamic theory of ferroelectricity.     

Low frequency dielectric relaxation in lightly doped VO2 single crystals

The relative effects of intrinsic and extrinsic defects on the dielectric relaxation of VO₂ crystals have been investigated by measurement of the dielectric parameters of undoped crystals and crystals doped with Ti, Cr and Al. Measurements have been made in the temperature range 77–250 K and the frequency range 50–100 kHz. The dielectric data is described by a Cole-Cole distribution function with a distribution parameter α ? 0.45 which decreases with increasing temperature. However, the distribution of activation energies g(E) derived from α is almost independent of temperature. The overall dielectric relaxation behaviour is determined primarily by the intrinsic defect structure of VO₂, and the effect of impurities is observed only in changes in the low frequency limiting (static) value of the dielectric constant. The same transport mechanism is found to determine the dc conductivity and the dielectric relaxation and evidence is presented that the dielectric relaxation is of dipolar origin.