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Showing papers on "Debye published in 1985"


Journal ArticleDOI
TL;DR: In this paper, a modification of Debye's distance-dependent dielectric function was proposed, which more closely approximates physical reality at small interatomic separations and yields a dielectrics function that gives reasonable agreement with experimental data in preliminary calculations.
Abstract: Electrostatic effects are believed to determine the molecular structure and function of macromolecules in many ways. In metallo-based enzymes and in metal-macromolecule interactions in solution, these effects may predominate. In order to tackle metal ion-nucleic acid interactions theoretically, a modification of Debye's distance-dependent dielectric function first proposed more than 50 years ago is proposed. This function more closely approximates physical reality at small interatomic separations. The theory proposed here yields a dielectric function that gives reasonable agreement with experimental data in preliminary calculations. 39 references, 4 figures, 6 tables.

246 citations


Journal ArticleDOI
01 May 1985
TL;DR: In this paper, the translational and rotational velocities of a colloidal particle in an applied electric field (E∞) were derived for the general case of a zeta potential (ζ) which varies with position on the particle surface.
Abstract: The translational and rotational velocities of a colloidal particle in an applied electric field (E∞) are derived for the general case of a zeta potential (ζ) which varies with position on the particle surface. Analytical results which are correct to O(∇E∞) are presented. The particle is modeled as a rigid, nonconducting sphere of radius a, and the analysis assumes ϰa → ∞ where ϰ is the Debye screening parameter of the surrounding fluid. The electrophoretic mobility in a constant field depends on the quadrupole moment of ζ and is not just related to the area-averaged zeta potential through Smoluchowski's equation, as is commonly assumed. The dipole moment of ζ contributes to rotation in a constant field, tending to align the particle. Dielectrophoretic motion results from the dipole moment interacting with ∇E∞ for unpolarized charge distributions, and from induced dipole and quadrupole moments for particles whose surface charge is mobile.

164 citations


Journal ArticleDOI
TL;DR: Close form expressions for dielectric permittivity and conductivity are suggested for use as estimators over the 10 Hz-100 GHz range.
Abstract: A computer program was developed to fit multiple-term Debye-type expressions to published data of permittivity for muscle. The number of terms in this expression was varied and tested for significance. Based on these results, closed form expressions for dielectric permittivity and conductivity are suggested for use as estimators over the 10 Hz-100 GHz range.

106 citations


Journal ArticleDOI
TL;DR: In this article, it is shown that the presence of higher frequency relaxations for components of the same dipole degrades this property by extending the memory into the timescale of relaxation, thus giving a non-debye behaviour which can be expected to occur in all practical dielectric materials.
Abstract: Debye relaxation behaviour is unique in the sense that all memory of excitation is instantaneously lost. It is shown that the presence of higher-frequency relaxations for components of the same dipole degrades this property by extending the memory into the timescale of relaxation, thus giving a nonDebye behaviour which can be expected to occur in all practical dielectric materials. In this case it is not possible, as has been suggested, that knowledge of the polarisation or of the depolarisation current at a single time is sufficient, alone, to define the relaxation behaviour of the system for all subsequent times. Furthermore the Guo and Guo experiment (1983) is shown to be incapable of discriminating between this picture of sequential relaxation and the alternative possibility of an ensemble of independent relaxations.

96 citations


Journal ArticleDOI
TL;DR: In this paper, the results of the nonperturbative theory of zero-phonon linewidths of impurities in crystals discussed by Osad’ko and us, and further developed by us in papers I and II of this series, were applied to the analysis of several absorption, photon echo, and hole burning experiments.
Abstract: We have applied the results of the nonperturbative theory of zero‐phonon linewidths of impurities in crystals discussed by Osad’ko and us, and further developed by us in papers I and II of this series, to the analysis of several absorption, photon echo, and hole burning experiments. Two (relatively) high temperature absorption experiments on 1,3‐diazaazulene in naphthalene and dilute ruby were analyzed with a model of Debye acoustic phonons. In both cases the Debye temperature was obtained from independent experiment or theory, and a one‐parameter fit was performed on the temperature‐dependent linewidth. It was found that (especially for diazaazulene) the systems are not in the weak coupling limit. For several low temperature experiments, where the dephasing is presumably due to pseudolocal phonons, the nonperturbative theory, coupled with the results of deBree and Wiersma, provides a reasonably complete understanding of the observed dephasing rates.

41 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied the Mayer series of a Coulomb gas with fixed ultraviolet cutoff in two dimensions and proved that the coefficients of order up to 2n are finite if the temperature T is
Abstract: The Mayer series of a Coulomb gas with fixed ultraviolet cutoff is studied in two dimensions. In particular, we show the existence of infinitely many thresholdsT n =(e 2/8πk)(1-1/2n)−1 k=Boltzmann's constant,e=electric charge,n=1, 2,..., which are conjectured to reflect a sequence of transitions from pure multipole phase (the Kosterlitz-Thouless region) to a plasma phase (the Debye screening region) via an infinite number of “intermediate phases.” Mathematically we prove that the Mayer series' coefficients of order up to 2n are finite if the temperatureT is

34 citations


Journal ArticleDOI
TL;DR: Variation-perturbation calculations and convergence studies on the dipole moment for HD are described, which is found to have the value 8.51 x 10/sup -4/ debye at 1.40 a.u.
Abstract: In the preceding paper we derived a new theory of the dipole moments of homopolar but isotopically asymmetric molecules (such as HD, HT, and DT) in which the electrical asymmetry appears directly in the electronic Hamiltonian (in an appropriate Born-Oppenheimer separation) and the dipole moment may be computed as a purely electronic property. In the present paper we describe variation-perturbation calculations and convergence studies on the dipole moment for HD, which is found to have the value 8.51\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$ debye at 1.40 a.u. Using the two alternative formulations of the electronic problem, we can provide a test of basis-set adequacy and convergence of the results, and such convergence studies are reported here. We have also computed vibration-rotation transition matrix elements and these are compared with experimental and other theoretical results.

32 citations


Journal ArticleDOI
TL;DR: From the temperature effect on the fluorescence bands of 4-N,N-dimethylaminobenzonitrile, the dipole moments of the two emitting species are estimated as 5 (normal fluorescence) and 15 (anomalous fluorescence), Debye above the ground-state dipole moment.

30 citations


Journal ArticleDOI
TL;DR: In this article, the total cross-section of thermal neutrons was determined as a function of temperature for neutron energies ranging from 22 × 10−4 eV to 50 eV. Precise values of σabs and σfree were given and compared to literature.
Abstract: Silicon crystals are of interest as filter material for thermal neutron beams. For this reason the total cross-section has been determined as a function of temperature for neutron energies ranging from 22 × 10−4 eV to 50 eV. Whereas cooling the filter to 77 K considerably improves the transmittance for thermal neutrons a further decrease in temperature has only a minor effect. The observed cross-section is well described by a treatment of thermal diffuse scattering based on the Debye approximation. Precise values of σabs and σfree are given and compared to literature.

21 citations


Journal ArticleDOI
TL;DR: In this article, the authors measured dielectric constants and x-ray diffraction profiles on a random mixture of ferroelectric RbH2PO4 (RDP) and antiferroelectric NH4H2P4 (ADP), and a glassy phase (dipole-glass phase) was found in the concentration range of 0·2 < × < 0·8.
Abstract: From the measurements of dielectric constants and x-ray diffraction profiles on a random mixture of ferroelectric RbH2PO4 (RDP) and antiferroelectric NH4H2PO4 (ADP), (RDP)1-x(ADP)x, a glassy phase (dipole-glass phase) was found in the concentration range of 0·2 < × < 0·8. The crystal symmetry of the glassy phase is tetragonal, although the deviations of lattice parameters from the Debye approximation are seen at low temperatures. The intensity of the x-ray diffuse scattering observed in the glassy phase increases with decreasing temperature.

21 citations


01 Jan 1985
TL;DR: In this article, the Pippard-Ziman condition on the electron-phonon interaction was used to model the electron mean free path in amorphous metals, and the results were consistent with the observed rho vs. temperature T in low resistivity glassy metals.
Abstract: : Electrical transport in amorphous metals is analyzed in the context of the Baym-Faber-Ziman theory. The theory is generalized to incorporate electron mean free path effects through the Pippard-Ziman condition on the electron-phonon interaction. A variety of model t-matrices are considered. The geometrical structure factors are modeled by Percus-Yevick hard sphere forms and a single branch Debye phonon spectrum is assumed. Detailed results for electrical resistivity rho vs. temperature T and the TCR are presented for extensive ranges of 2kF/kp and electron mean free path. The results, incorporating the Pippard-Ziman condition, are consistent with the observed rho vs. T in low resistivity glassy metals. However, although inclusion of the Pippard-Ziman condition dramatically improves agreement with the data, quantitative agreement is not obtained in high resistivity amorphous metals.

Journal ArticleDOI
TL;DR: In this paper, a thermodynamic system of equally charged, plus and minus, classical particles constrained to move in a (spherical) ball is studied in a region of parameters in which Debye screening takes place.
Abstract: A thermodynamic system of equally charged, plus and minus, classical particles constrained to move in a (spherical) ball is studied in a region of parameters in which Debye screening takes place. The activities of the two charge species are not taken as necessarily equal. We must deal with two physically interesting surface effects, the formation of a surface charge layer, and long range forces reaching around the outside of the spherical volume. This is an example in as much as 1) general charge species are not considered, 2) the volume is taken as a ball, 3) a simple choice for the short range forces (necessary for stability) is taken. We feel the present system is general enough to exhibit all the interesting physical phenomena, and that the methods used are capable of extension to much more general systems. The techniques herein involve use of the sine-Gordon transformation to get a continuum field problem which in turn is studied via a multi-phase cluster expansion. This route follows other recent rigorous treatments of Debye screening.

Journal ArticleDOI
TL;DR: In this paper, the energy dissipation per cycle due to the motion of heavy interstitials in the presence of a harmonically oscillating rigid kink is investigated analytically as well as numerically in terms of discrete Fourier k\ensuremath{\rightarrow}-space transformation technique.
Abstract: The energy dissipation per cycle due to the motion of heavy interstitials in the presence of a harmonically oscillating rigid kink is investigated analytically as well as numerically in terms of discrete Fourier k\ensuremath{\rightarrow}-space transformation technique. In the linear-response case, a discrete Debye relaxation spectrum with three distinct branches is found to represent the inelastic behavior of the system uniquely and exactly. It has been observed by extensive computer modeling experiments that the induced Snoek peak is composed of three subpeaks---one acoustic (1) and two optical (modes 2 and 3) in character---which have the following peak-maximum intensity ratios, approximately: 11:9:2 for pure screw dislocation and 13:8:3 for 71\ifmmode^\circ\else\textdegree\fi{} nonscrew dislocation, respectively. The second most intense peak which is associated with the optical mode 2, occurs exactly at the ordinary Snoek peak position, and as far as the linewidth and the skewness parameter are concerned it resembles an ideal Debye peak.

Journal ArticleDOI
TL;DR: In this paper, it was shown that self-broadening in the vibrational fundamental of HCl is inversely proportional to the temperature for transitions which lie near the Boltzmann rotational maximum and becomes monotonically less temperature-dependent as the rotational quantum number increases.

Journal ArticleDOI
Usik Lee1
TL;DR: In this article, the effects of structural and geometrical constraints on damping loss factors are investigated, and optimum conditions for the maximum damping are investigated for the stage of system design.
Abstract: The thermoelastic damping due to thermal currents and the electromagnetic damping due to electric conduction currents of vibrating solids are discussed. The effects of structural and geometrical constraints on damping loss factors are investigated. Also, optimum conditions for the maximum damping, which may be useful on the stage of system design, are investigated. It is found that damping loss factors are generally dependent upon structural and geometrical configurations. An analogy exists between thermoelastic damping and electromagnetic damping, showing Debye curves with Debye peaks. Standing transverse waves are likely to achieve larger damping than standing dilatational waves in the presence of a magnetic field. Electromagnetic damping in ferromagnetic material bodies is found to be considerable in high field. The influence of thermoelastic damping on aeroelastic stability of beam plates is investigated. This research strongly suggests that thermoelastic damping improves the aeroelastic stability of beam plates.

Journal ArticleDOI
TL;DR: An efficient numerical method for obtaining the Green's function of the Schrodinger equation was developed and used for a calculation of the dynamical polarisability in the Debye potential as discussed by the authors.
Abstract: An efficient numerical method for obtaining the Green's function of the Schrodinger equation is developed and used for a calculation of the dynamical polarisability in the Debye potential. Special emphasis is given to the static polarisability and its divergent behaviour near the 1s Mott condition.

Journal ArticleDOI
TL;DR: In this article, Pade approximations for the low-temperature Wigner region (lattice and Gell-Mann-Brueckner formulae) and Debye region (limiting law with quantum corrections) were constructed.
Abstract: By using the available knowledge about the thermodynamic functions for the low-temperature Wigner region (lattice formulae and Gell-Mann-Brueckner formulae) as well as for the high-temperature Debye region (limiting law with quantum corrections) Pade approximations are constructed. The formulae cover the whole nonrelativistic region of density and temperature except the region of ionic lattice and of bound states.

Journal ArticleDOI
TL;DR: The temperature dependence of low-energy electron diffraction intensity-energy spectra from the graphite (0001) surface has been measured from 100 to 600 K as mentioned in this paper, and the perpendicular and parallel effective surface Debye temperatures and the effective mean-square vibration amplitudes as a function of electron energy have been determined from these data.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the specific heat is dominated by another kind of excitations, which also couple to the phonons and thus determine the universal low temperature thermal conductivity of this class of solids.
Abstract: The low energy vibrational excitations of perfect crystals seen in specific heat and thermal conductivity measurements can be described in terms of Debye phonons. In amorphous solids, however, the specific heat is dominated by another kind of excitations, which also couple to the phonons and thus apparently determine the universal low temperature thermal conductivity of this class of solids. A phenomenological model of tunneling states with a uniform density of states has been very successful in describing a wide range of investigations of these excitations. Of particular importance was the discovery of a logarithmic time dependence of the specific heat, which was predicted by this model. It now appears well established that thermal equilibrium in an amorphous solid at low temperatures cannot be reached on any time scale. A physical model of the tunneling states is still lacking. The major hurdle is that of finding an entity which is common to all amorphous solids, and which leads to a thermal co...

Journal ArticleDOI
01 Jul 1985-Pramana
TL;DR: In this paper, the integrated intensities of Bragg reflections have been measured for mixed crystals in the KxRb(1−x)Br system with an x-ray powder diffractometer.
Abstract: The integrated intensities of Bragg reflections have been measured for mixed crystals in the KxRb(1−x)Br system with an x-ray powder diffractometer. From the intensities, the mean Debye-Waller factors are determined. The Debye-Waller factors are corrected for static contribution and Debye temperature values are determined for the entire composition range. The x-ray Debye temperatures follow the Kopp-Neumann equation closely.

Journal ArticleDOI
T.S. Chow1
TL;DR: In this article, the authors describe the glass relaxation in terms of the collapse of a series of free volume having different creation energies but having equal volume, and derive the equation of state and the non-equilibrium equations.
Abstract: We describe the glass relaxation in terms of the collapse of a series of free volume having different creation energies but having equal volume. The equation of state and the non-equilibrium equations are derived. The general solution of the new molecular kinetic equations is obtained and the relaxation function is found to have the form of a “Kohlrausch-Williams-Watts” function. If the relaxation time were structural independent, the relaxation function should have the classical Debye exponential form. As temperature is decreased, the width of the hole energy spectrum increases due to the increase of the shift factor.

Journal ArticleDOI
TL;DR: In this article, the Debye dispersion in the close vicinity of Tc and the resonant type dispersion of TO soft phonon mode observed in TSCC was examined through comparison of the dynamical and the static quantites by extrapolation.
Abstract: Consistency between the Debye dispersion in the close vicinity of Tc and the resonant type dispersion of TO soft phonon mode observed in TSCC was examined through comparison of the dynamical and the static quantites by extrapolation. Noticeable discrepancy was found between the two dispersions. X-ray crystal structure analysis revealed a disordered structure above Tc. The structure below Tc is well approximated with one of the two of atomic configurations above Tc. Soft mode contribution was not detected in the mean square thermal amplitude in consistent with the small extrapolated value of the static dielectric constant of the resonant type dispersion.

Journal ArticleDOI
TL;DR: In this article, the current and dipole mean square fluctuations per unit volume for a quantum mechanical jellium in thermal equilibrium at temperature beta -1 were analyzed and the authors gave a new proof of the sum rule integral dx mod x mod 2S(x)=3/4(h(cross) omega p/ pi coth( beta h(cross)/p/2) for the second moment of the charge-charge correlation function S(x), where omega p is the plasma frequency.
Abstract: By an analysis of the current and dipole mean square fluctuations per unit volume for a quantum mechanical jellium in thermal equilibrium at temperature beta -1, the authors give a new proof of the sum rule integral dx mod x mod 2S(x)=3/4(h(cross) omega p/ pi ) coth( beta h(cross) omega p/2) for the second moment of the charge-charge correlation function S(x), where omega p is the plasma frequency. No use is made of perturbation theories. The proof relies on correlation inequalities and sum rules which are valid in phases of charged systems having good screening properties. Up to second order in Planck's constant, the current-current correlations have a non-integrable spatial decay even when the corresponding classical state shows Debye screening.

Journal ArticleDOI
TL;DR: In this article, the static permittivity and high frequency limiting permittivities have been determined for n-butyl-acrylate, allyl-methacrylated, isobutyl-macrylate and isobubyl-micrylate monomers in benzene at 30°, 40°, 50° and 60°C.

Journal ArticleDOI
TL;DR: The dynamical mechanism of the ferroelectric phase transition in KH2PO4 has been confirmed as the "order-disorder dynamics" of locally distorted PO4 dipoles by Raman scattering studies.
Abstract: The dynamical mechanism of the ferroelectric phase transition in KH2PO4 has been confirmed as the "order-disorder dynamics" of locally distorted PO4 dipoles by Raman scattering studies. Through the analysis of the internal vibration modes, the local site symmetry of PO4 tetrahedrons in the paraelectric phase has been determined to be C2 which is the same site symmetry as that in the ferroelectric phase. The very low frequency central component of the x(yx)y Raman spectra has been attributed to the relaxational type polarization fluctuation of PO4 dipoles. The relaxation time of an isolated PO4 dipole has been evaluated as τ0=0.13×10-12 sec by the analysis in terms of a Debye type susceptibility.

Book ChapterDOI
01 Jan 1985
TL;DR: In this article, the Debye temperature was found to vary approximately as the first power of the temperature, which is in agreement with the experimental results in the temperature range below one percent of the debye temperature even in rather complex crystal lattices.
Abstract: In perfect, crystalline solids, the thermal motion of the atoms can be described through elastic waves, i.e. collective excitations. The Debye continuum model has been a good approximation in the long wavelength limit. It predicts, on the basis of a proper average of the measured speeds of sound, a low temperature specific heat proportional to the third power of the temperature, which is in excellent agreement with the experimental results in the temperature range below one percent of the Debye temperature even in rather complex crystal lattices. In all amorphous solids, however, i.e. solids lacking long range order, such an agreement has not been found. The discrepancy is, in fact, most pronounced in the low temperature range, where the specific heat is found to vary approximately as the first power of the temperature. The prefactor of the linear specific heat term lies typically in the range of 5 to 50 erg g-1 K-2, and appears to be independent of the microscopic structure of the glass or its bonding type.1 Figs. 1 and 2 show two examples. The covalently bonded amorphous Si02 was slowly cooled from the melt,2 while the metallically bonded amorphous Bi-Sb layer was produced by quenched condensation,3 in which process the atoms were evaporated onto a substrate which was held below 20 K. In both solids, the linear term of the specific heat anomaly has almost the same magnitude; for the amorphous Si02, it is 12 erg g-1 K-2 T, for the amorphous superconductor, it is 13 erg g-1 K-2 T.

Journal ArticleDOI
TL;DR: In this article, the Goldanskii-Karyagin effect was observed in a metallic rare earth compound at temperatures 4.1 to 600 K. This was the first observation of an anisotropic recoil free fraction in rare earth compounds and corresponded to Debye temperatures of θ|=450 K and θ⊥=180 K.
Abstract: Mossbauer studies of 151Eu2+ in EuRu2Ge2 at temperatures 4.1 to 600 K reveal the largest crystalline electric field gradient ever observed in a metallic rare earth compound, A2〈r2〉=425 K. The associated large quadropole interaction, eqQ=−440Mc/s, enabled a detailed study of the anisotropy in recoil free fraction, Goldanskii-Karyagin effect. While at 85 K the recoil free fractions along the crystallographic c-axis and perpendicular to it are 0.95 and 0.74, at 570 K they are 0.64 and 0.10, respectively. Within a Debye model this corresponds to Debye temperatures of θ|=450 K and θ⊥=180 K. This is the first observation of an anisotropic recoil free fraction in a metallic rare earth compound.

Journal ArticleDOI
Byung Chan Eu1
TL;DR: In this article, the nonlinear heat conductivity coefficients reported in a previous paper are explicitly calculated as functions of temperature and density in the case of a dilute plasma subject to a magnetic field applied in one direction.
Abstract: The nonlinear heat conductivity coefficients reported in a previous paper are explicitly calculated as functions of temperature and density in the case of a dilute plasma subject to a magnetic field applied in one direction. They are shown to deviate markedly from the linear theory prediction as the Debye length-and thus the mean free path-increases, which in turn increases with temperature and decreases with density. The deviation is thus seen to be due to a diminished collisionality of the plasma as the Debye length increases. The deviation is numerically shown for a few nonlinear thermal conductivities in order to furnish numerical insights.

Journal ArticleDOI
TL;DR: In this article, an alternative expression for the dielectric loss similar in structure to expressions appearing in the theory of diffusion is studied, and an approximate analytical evaluation and accurate numerical calculations are made from this result.
Abstract: Formal expressions for the complex electrical conductivity from linear response theory are used to obtain general formulae for the dielectric loss due to defect pairs in ionic crystals. As in the theory of Franklin and Lidiard (1984) the loss can be expressed as a sum of Debye relaxation terms in which the effective dipole moments appearing in the weights of the relaxation terms reduce to bare dipole moments when the magnitudes of the dissociation jump rates are small compared with the rates of jumps not leading to dissociation of pairs. Several literature results are obtained by well defined approximations but the Debye formula is perhaps not the most convenient framework within which to evaluate their relative merit by detailed calculation. An alternative expression for the dielectric loss similar in structure to expressions appearing in the theory of diffusion is studied. For the five-frequency model of vacancy-impurity pairs in an NaCl type crystal its evaluation can be reduced to the calculation of a frequency dependent vacancy escape factor which, at zero frequency, reduces to the Manning vacancy escape factor F of impurity diffusion theory. An approximate analytical evaluation and accurate numerical calculations are made from this result. The new formula for the loss is more accurate than earlier ones and correctly describes features missed by them which arise from jumps by a vacancy when it is more than one lattice spacing from the impurity.

Journal ArticleDOI
TL;DR: In this article, the Curie temperatures and temperature dependence of the magnetic hyperfine fields and isomer shifts were determined for Morphous FexSi90-xB10(69⩽x⩾79) alloys in the temperature range from 78 to 725 K by Mossbauer spectroscopy.