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Showing papers on "Debye published in 1995"


Journal ArticleDOI
TL;DR: Neutron time-of-flight data of polybutadiene and polyisoprene in a wide temperature range around the glass transition are reported and two different interpretations of the short time behavior are considered, namely a fast Debye regime of the \ensuremath{\alpha} relaxation and a vibrational softening of the boson peak.
Abstract: Neutron time-of-flight data of polybutadiene and polyisoprene in a wide temperature range around the glass transition are reported. The anharmonic part of the spectra is evaluated using a recently developed time domain Fourier transform technique. The results corroborate the recent finding of two different time domains in the dynamics, one above a crossover time of about 2 ps and the other below it. Two different interpretations of the short time behavior are considered, namely a fast Debye regime of the \ensuremath{\alpha} relaxation and a vibrational softening of the boson peak.

167 citations


Journal ArticleDOI
TL;DR: This work shows how the Debye mass can be defined nonperturbatively in a manifestly gauge-invariant manner (in vectorlike gauge theories with zero chemical potential) and how the {ital O}({ital e}{sup 2}{ital T}) correction could be determined by a fairly simple, three-dimensional, numerical lattice calculation of the perimeter-law behavior of large, adjoint-charge Wilson loops.
Abstract: In quantum electrodynamics, static electric fields are screened at nonzero temperatures by charges in the plasma. The inverse screening length, or Debye mass, may be analyzed in perturbation theory and is of order eT at relativistic temperatures. An analogous situation occurs when non-Abelian gauge theories are studied perturbatively, but the perturbative analysis breaks down when corrections of order ${\mathit{e}}^{2}$T are considered. At this order, the Debye mass depends on the nonperturbative physics of confinement, and a perturbative ``definition'' of the Debye mass as the pole of a gluon propagator does not even make sense. In this work, we show how the Debye mass can be defined nonperturbatively in a manifestly gauge-invariant manner (in vectorlike gauge theories with zero chemical potential). In addition, we show how the O(${\mathit{e}}^{2}$T) correction could be determined by a fairly simple, three-dimensional, numerical lattice calculation of the perimeter-law behavior of large, adjoint-charge Wilson loops. \textcopyright{} 1995 The American Physical Society.

163 citations


Journal ArticleDOI
TL;DR: In this article, a finite difference time-domain (FDTD) method for electromagnetic wave propagation in two different kinds of linear dispersive media: an Nth order Lorentz and an Mth order Debye medium is presented.
Abstract: Finite difference time-domain (FDTD) methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media: an Nth order Lorentz and an Mth order Debye medium. The temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first-order differential equations. From this, the final equations are temporally advanced using the classical leapfrog method. One-dimensional scattering from a dielectric slab is chosen for a test case. Provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space, as shown in the error analysis, the agreement between the computed and exact solutions will be excellent. The attached data, which are associated with the four pole Lorentz dielectric and the five pole Debye medium, verify this assertion. >

149 citations


Journal ArticleDOI
TL;DR: In this paper, a detailed and unified account of the theory of the generalized Bloch equations for weakly coupled two-level systems with a heat bath and subject to a monochromatic rotating field of arbitrary intensity is presented.
Abstract: A detailed and unified account of the theory of the generalized Bloch equations is presented. The equations apply to a two‐level system weakly coupled to a heat bath and subject to a monochromatic rotating field of arbitrary intensity. The relaxation tensor obtained is explicitly field‐dependent. The derivation is valid for general coupling to a quantum heat bath. The generalized Bloch equations are shown to be thermodynamically consistent, as opposed to the standard Bloch equations. Different limits of the generalized Bloch equations are examined and related to previous studies. The potential use of the generalized Bloch equations as a probe of the bath spectral density is demonstrated for the case of a two‐level system embedded in a Debye solid.

123 citations


Journal ArticleDOI
TL;DR: In this article, the relation between the nanometer-scale structure and scattering and EXAFS experimental data is discussed on the basis of the atomic density distribution function, with an emphasis on the model substance Pd.

69 citations


Journal ArticleDOI
TL;DR: In this article, complex permittivity spectra in the frequency range 0.95-v (GHz)≤89 for acetonitrile and its solutions of LiBr, NaI, NaClO4, and Bu4NBr at 25°C show one Debye equation for the neat solvent whereas the superposition of a Debye process for the solute and a Cole-Cole distribution for the solvent is necessary to account for the dielectric relaxation behavior of the solutions.
Abstract: Complex permittivity spectra in the frequency range 0.95≤v (GHz)≤89 for acetonitrile and its solutions of LiBr, NaI, NaClO4, and Bu4NBr at 25°C show one Debye equation for the neat solvent whereas the superposition of a Debye process for the solute and a Cole-Cole distribution for the solvent is necessary to account for the dielectric relaxation behavior of the solutions. The reorientation of bulk acetonitrile is diffusive and only weakly coupled to viscosity. The number of solvent molecules irrotationally bound to the electrolyte is in good agreement with conventional solvation numbers for all electrolytes, when kinetic depolarization is assumed to be negligible. The solute relaxation process is dominated by the formation kinetics and reorientation of contact ion pairs. There is evidence for solvent-shared ion pairs in dilute NaClO4 solutions.

63 citations


Journal ArticleDOI
TL;DR: A reorientation/solvatochromic mechanism, whereby the electrical field reorients the dye molecules so that they experience a change in polarity of their lipid environment is likely to make a significant contribution to both the spectral changes and to the field effect on the acid-base properties of the dye.

58 citations


Journal ArticleDOI
TL;DR: In this article, it is shown that, with exception of the alkali metals, such a law is only poorly fulfilled for other cubic elements and compounds, and a relation is often used that correlates Debye temperature and bulk modulus (c 11 + 2c 12 )/3 by a square-root law.
Abstract: Sophisticated methods have been put forward in the literature to calculate Debye temperatures from the elastic constants C ik . As a simple alternative method for cubic crystals, a relation is often used that correlates Debye temperature and bulk modulus (c 11 + 2c 12 )/3 by a square-root law. It is shown that, with exception of the alkali metals, such a law is only poorly fulfilled for other cubic elements and compounds. If one takes, however, elastic moduli such as [c 44 (c 11 - c 12 ) (c 11 + c 12 + 2c 44 )] 1/3 or {c 44 [(c 11 - c 12 ) c 44 /2] 1/2 (c 11 - c 12 + c 44 )/3} 1/3 instead of the bulk modulus the square-root law is established for various cubic material classes. This procedure eventually allows to easily evaluate hitherto unknown Debye temperatures from the elastic constants with high precision.

51 citations


Journal ArticleDOI
TL;DR: In this paper, the one-loop effective action for a slowly varying electromagnetic field is computed at finite temperature and density using a real-time formalism, and the gauge invariance of the result is discussed.

48 citations


Journal ArticleDOI
01 Jun 1995
TL;DR: In this article, the authors measured the van der Waals component of the hopping site energies in tri-p-tolylamine (TTA) doped polymers with polymer dipole moments that range from near zero to 1.7 debye.
Abstract: Hole mobilities have been measured in tri-p-tolylamine (TTA) doped polymers with polymer dipole moments that range from near-zero to 1.7 debye. The results are described within the framework of a formalism based on disorder, due to Bassler and coworkers. The formalism is based on the assumption that charge transport occurs by hopping through a manifold of localized states with superimposed energetic and positional disorder. The key parameter of the formalism is σ, the variance of the hopping site energies. The principal observations of this work are: (1) σ increases with increasing intersite distance for all polymers studied, and (2) σ increases with increasing dipole moment of the polymer. The interpretation of the results leads to the conclusion that for weakly polar dopant molecules, a major contribution to the width of the distribution of hopping site energies is the component due to van der Waals forces. For TTA doped poly(styrene)s, the van der Waals component is estimated as between 0.074 and 0.116 eV, increasing with incresing intersite distance or decreasing TTA concentration.

44 citations




Journal ArticleDOI
TL;DR: The pair-function formalism has been extended to the calculation of atomic and ionic properties in plasma environments that are modeled in terms of analytic screening potentials of the usual Debye form and the more general Debye-Laughton type.
Abstract: The pair-function formalism has been extended to the calculation of atomic and ionic properties in plasma environments that are modeled in terms of analytic screening potentials of the usual Debye form and the more general Debye-Laughton type. The theory has been applied to two-electron systems. As particular applications, the stability of ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ and the energy splitting of several 1sns and 1snp states of the He atom have been studied in model plasma environments as well as the energies of allowed and forbidden transitions.

Journal ArticleDOI
10 Mar 1995-EPL
TL;DR: In this paper, an upward shift of the critical temperature proportional to the square of the electric field was derived and an induced dipolar interaction among the critical fluctuations, which suppresses the fluctuations and yields another upward shift.
Abstract: Electric-field effects are investigated in non-ionic fluids near the critical point. We first derive an upward shift of the critical temperature proportional to the square of the field. Its sign is opposite to that predicted by Debye and Kleboth. Second, we derive an induced dipolar interaction among the critical fluctuations, which suppresses the fluctuations and yields another upward shift. The fluctuation contribution to the macroscopic dielectric constant is also examined.

Journal ArticleDOI
TL;DR: In this paper, the electrokinetic lift on a sphere, freely rotating and translating in linear shear flow along a plane wall, was calculated numericaly assuming that the zeta potentials of the sphere and the plate are equal and that the Debye length is sufficiently small that the space charge density is not perturbed by flow.

Journal ArticleDOI
TL;DR: In this paper, the exact solution for the transverse (i.e., in the direction perpendicular to the director axis) component of a nematic liquid crystal and the corresponding correlation time T⊥ is presented for the uniaxial potential of Martin et al.
Abstract: The exact solution for the transverse (i.e. in the direction perpendicular to the director axis) component α⊥(ω) of a nematic liquid crystal and the corresponding correlation time T⊥ is presented for the uniaxial potential of Martin et al. [Symp. Faraday Soc. 5 (1971) 119]. The corresponding longitudinal (i.e. parallel to the director axis) quantities α⊥(ω), T⊥ may be determined by simply replacing magnetic quantities by the corresponding electric ones in our previous study of the magnetic relaxation of single domain ferromagnetic particles Coffey et al. [Phys. Rev. E 49 (1994) 1869]. The calculation of α⊥(ω) is accomplished by expanding the spatial part of the distribution function of permanent dipole moment orientations on the unit sphere in the Fokker-Planck equation in normalised spherical harmonics. This leads to a three term recurrence relation for the Laplace transform of the transverse decay functions. The recurrence relation is solved exactly in terms of continued fractions. The zero frequency limit of the solution yields an analytic formula for the transverse correlation time T⊥ which is easily tabulated for all nematic potential barrier heights σ. A simple analytic expression for T∥ which consists of the well known Meier-Saupe formula [Mol. Cryst. 1 (1966) 515] with a substantial correction term which yields a close approximation to the exact solution for all σ, and the correct asymptotic behaviour, is also given. The effective eigenvalue method is shown to yield a simple formula for T⊥ which is valid for all σ. It appears that the low frequency relaxation process for both orientations of the applied field is accurately described in each case by a single Debye type mechanism with corresponding relaxation times (T∥, T⊥).

Journal ArticleDOI
TL;DR: In this article, a model of the crystal polarization of polyvinylidene fluoride using an atomic potential energy function based on the shell model of electronic polarization was developed, and the lattice constants, crystal polarization, and dielectric constants at finite temperatures were determined through minimization of the Gibbs free energy calculated using consistent quasi-harmonic lattice dynamics.
Abstract: A model of the crystal polarization of β‐poly(vinylidene fluoride) utilizing an atomic potential energy function based on the shell model of electronic polarization is developed. Lattice constants, crystal polarization, and dielectric constants at finite temperatures are determined through minimization of the Gibbs free energy calculated using consistent quasi‐harmonic lattice dynamics. Molecular dynamics is used to include the effects of thermal oscillations of the dipoles. We find that in going from a single chain in vacuum to a chain packed in the crystal the repeat unit dipole increases by approximately 50% or 0.9 debye. Increasing temperature results in a decrease in polarization due to: (i) an increase in the unit cell volume, (ii) a decrease in the local electric field, and (iii) an increase in the magnitude of dipole oscillations. It is found that the dipole oscillation is consistent with the excitation of a single rotational lattice mode.

Journal ArticleDOI
TL;DR: In this article, the orientation and alignment phenomena for direct s−p excitation in electron-hydrogenic ion collisions were investigated using a first-order semiclassical straight-line path approximation.
Abstract: In dense plasmas the orientation and alignment phenomena for direct s‐p excitation in electron–hydrogenic ion collisions are investigated using a first‐order semiclassical straight‐line path approximation. The interaction potential between the projectile and bound electrons is obtained by a nonspherical Debye–Huckel model. Angular momentum orientation parameter L⊥ for direct s‐p excitation is determined for various Debye lengths and projectile energies. The plasma‐screening effect appreciably reduces a favoring of the s→p−1 transition, especially, for high‐energy projectiles.

Journal ArticleDOI
TL;DR: In this article, a Debye spectrum was used to describe the dynamics of a nonpolymeric glass-forming liquid at a critical temperature, and the coupling model data, when analyzed in the manner used for mode...
Abstract: Calculations have been presented for the intermediate scattering function, dynamic structure factor, and dynamic susceptibility of a complex correlated system undergoing relaxation with independent vibrations. The vibrational contribution was approximated by a Debye spectrum, smoothed at high frequency, while the coupling model was used to describe the relaxation. This model asserts for nonpolymeric glass‐forming liquids a crossover at a microscopic time from intermolecularly uncorrelated relaxation at a constant rate to intermolecularly coupled relaxation with a time‐dependent, slowed‐down rate. Although the model has previously been employed to successfully predict and otherwise account for a number of macroscopic relaxation phenomena, critical phenomena are not included in, and cannot be addressed by, the coupling model. Notwithstanding an absence of any change in transport mechanism for the supercooled liquid at a critical temperature, the coupling model data, when analyzed in the manner used for mode...

Journal ArticleDOI
TL;DR: In this paper, it has been demonstrated that the dielectric loss due to the main relaxation in 1-propanol exhibits the Debye width up to timescales of 1000 s.
Abstract: By combining time- and frequency-domain techniques, the dielectric response of 1-propanol has been measured in a spectral range covering eleven decades. In particular it has been demonstrated that the dielectric loss due to the main relaxation in 1-propanol exhibits the Debye width up to timescales of 1000 s. In order to extend the range in which the dynamics of propanol can be exploited to high temperatures, conductivity relaxation due to ionic impurities has been used. The occurrence of high-frequency relaxation processes has been studied in both isomers of propanol. It is shown that the 1-propanol data yield a master curve in a previously suggested scaling representation. However, owing to the presence of the high-frequency excitations, no agreement with the universal scaling form is obtained.

Journal ArticleDOI
TL;DR: In this article, the Brownian relaxation of three ferrofluids with Fe 2 CoO 4 particles dispersed in water, dibutyl phthalate and diethylene glycol is presented and compared with the theoretical model of Debye adapted to the magnetism.

Journal ArticleDOI
TL;DR: The calculations demonstrate that the dichroism decay time constants are not simply determined by the size/shape of the proteins, but are strongly influenced by the orientation of the dipole vector with respect to the axis of maximal absorbance.

Journal ArticleDOI
TL;DR: In this article, a power series expansion of the radial distance from the source with frequency-dependent coefficients is proposed to calculate the electrostatic potential distributed around a point source in isotropic Maxwellian plasma.
Abstract: A new algebraic approach is proposed to calculate the electrostatic potential distributed around a point source in isotropic Maxwellian plasma. The method derives a power series expansion of the radial distance from the source with frequency-dependent coefficients. Distance and frequency are normalized to the Debye length and to the plasma frequency, respectively, so that the expression keeps its entire generality whatever the experimental conditions might be. The proposed method is based upon the Mittag-Lefler expansion of the inverse of the plasma dispersion function for the infinite series of Landau poles. After mathematical clarification of the validity of this expansion, a significant correction of the previous works leads to a self-consistent interpretation of the true contribution of the higher-order poles at large distance from the source. The power series expansion is compared to the classical so-called “Landau wave approximation” which is proved to include in reality the contribution of higher-order poles independently from the plasma temperature. For practical use the power expansion is needed to obtain a precise result at distances from the source shorter than about 15 Debye lengths, while the Landau wave approximation gives correct results at larger distances. This work provides all necessary baselines for precise three-dimensional modeling of mutual impedance devices to be used in space plasma experiments where the Debye length is comparable to the spacecraft size.

Journal ArticleDOI
TL;DR: In this article, a generalization of the usual BCS-Eliashberg scheme to include non-adiabatic effects beyond Migdal's Theorem is proposed. But the main results, the possible lines of development and the main open problems are discussed.
Abstract: A common characteristic of all the high Tc materials, oxides and Fullerene compounds, is that the Fermi energy is much smaller than in usual metals and it is of the order of the Debye phonon frequencies. This requires a generalization of the usual BCS-Eliashberg scheme to include non adiabatic effects beyond Migdal's Theorem. We have developed the first steps of this generalization and here we discuss the main results, the possible lines of development and the main open problems. The key point is that the first order non adiabatic effects (vertex corrections and similar processes) depend crucially on the momentum (q) of the exchanged phonons. If small q scattering is predominant, one obtains a strong enhancement of Tc and various other effecs also for the normal state that should lead to precise experimental predictions. The predominance of small q scattering can be naturally obtained from electronic correlations but it could arise also from different properties like peaks in the density of states.

Journal ArticleDOI
TL;DR: The new theory of dynamic shielding, developed herein, is in good agreement with experiments in pure electron plasmas and results solely from electrons dynamically trapped in the neighborhood of the test charge.
Abstract: While shielding in collisional, strongly magnetized (one-dimensional) plasmas obeys the standard Debye result, shielding in collisionless, immobile ion plasmas is far more complex than commonly believed. In some circumstances, the plasma will antishield a positive test charge; i.e., the plasma becomes more positive in the neighborhood of a positive test charge. When shielding does occur, it results solely from electrons dynamically trapped in the neighborhood of the test charge. The new theory of dynamic shielding, developed herein, is in good agreement with experiments in pure electron plasmas.

Journal ArticleDOI
TL;DR: In this paper, a theoretical model for description of dielectric relaxation in highly polarizable dielectrics with dipole impurities like K1−x Li x TaO3 (KTL) is suggested.
Abstract: The theoretical model for description of dielectric relaxation in highly polarizable dielectrics with dipole impurities like K1–x Li x TaO3 (KTL) is suggested. In this model the distribution function of relaxation times is expressed through distribution function of random electric fields of impurity dipoles, which in turn calculated on the base of dipole-dipole interaction law only. The derived expressions for dynamic dielectric permittivity together with equation for long-range order parameter determine completely the relaxational properties of the system under consideration in whole range of temperatures and impurity content: in dipole glass state, in mixed ferroglass phase, in paraelectric and ferroelectric phases. It is shown that in dipole glass state relaxation has long-time logarithmic character, while in mixed phase the crossover between glassy and purely Debye dynamics, peculiar to paraelectric and ferroelectric phases occurs. It is shown also that Cole-Cole diagram in mixed phase has tw...

Journal ArticleDOI
TL;DR: In this paper, a Monte Carlo simulation of enhanced backscatterings from the disordered dense media is investigated by means of the Rayleigh-Debye scattering theory, and numerical simulations demonstrate the dependences of the peak, width and spatial anisotropy of enhanced intensity distributions on the size of scattering particles.
Abstract: Enhanced backscatterings from the disordered dense media are investigated by means of the Monte Carlo simulation. On the basis of the Rayleigh-Debye scattering theory, numerical simulations demonstrate the dependences of the peak, width and spatial anisotropy of enhanced intensity distributions on the size of scattering particles. Discussions are made by decomposing the backscattering intensity to the contributions with different scattering orders. As a result, it is shown that the particle-size dependence of the peak and width is described by the probability density function of the scattering order and the mean free pathlength. It is also shown that the spatial anisotropy of the intensity peak is described by the depolarization at each scattering event and the extinction in propagation within the random media.

Journal ArticleDOI
TL;DR: In this paper, the Debye-Scherrer diffraction pattern profiles were obtained by combining a series of multislice calculations performed on model particles over a range of orientations.
Abstract: Dynamic diffraction pattern profiles are calculated for randomly oriented aggregates of gold and silver in the size range from 147 to 5083 atoms and at incident electron energies of 40 kV and 100 kV. The Debye–Scherrer diffraction patterns were obtained by combining a series of multislice calculations performed on model particles over a range of orientations. Calculations are performed for both fcc and icosahedral structures. The results show that corrections to the kinematical theory (Debye equation) are more important than predicted by the two‐beam theory of Blackman. One calculation, a fcc 923‐atom silver aggregate at 100 kV, showed a distortion to the (111) Bragg peak causing it to to shift its center to a higher scattering angle. Scattering corrections to the icosahedral results are less important than for an equivalent sized fcc aggregate and preserve the general diffraction features seen in kinematic calculations.

Journal ArticleDOI
01 Mar 1995
TL;DR: In this paper, a permanent, vibrationally induced electric dipole moment |μ 0 | = (8.6 ± 1.4).10 −3 Debye for CH 2 D 2.
Abstract: The pure rotational spectrum in the far-infrared and its absolute intensity in the vibrational ground state of CH 2 D 2 and CHD 3 were measured by high-resolution interferometric Fourier transform techniques. The analysis of the integrated absorption cross sections results in a permanent, vibrationally induced electric dipole moment |μ 0 | = (8.6 ± 1.4).10 −3 Debye for CH 2 D 2 . This value is much more reliable than the older value existing in the literature and is also in much better agreement with our previously published theoretical estimate (μ z 0 = −(7.60±0.50).10 −3 Debye, the z-axis being the C 2 axis with sign chosen such that the H-atoms have positive H-coordinates)

Journal ArticleDOI
TL;DR: In this article, the lattice dynamics of ReO3 were studied for the first time by X-ray absorption spectroscopy (XAS) in the temperature range from 77 to 350 K at the rhenium L3 edge.
Abstract: The lattice dynamics of ReO3 is studied for the first time by X-ray absorption spectroscopy (XAS) in the temperature range from 77 to 350 K at the rhenium L3 edge, The Debye-Waller factors are extracted for the first, fourth and sixth coordination shells of rhenium, and their temperature dependences are discussed on the basis of the Debye and Einstein vibrational models. The obtained characteristic temperatures Theta D and Theta E are compared with the ones found by other experimental techniques. The application of the Debye and Einstein models to the analysis of the XAS and X-ray diffraction data for compounds with different degrees of correlation in atomic motion is also discussed.