Showing papers on "Debye published in 1981"
TL;DR: In this article, a wide ranging critical analysis of the existing wealth of data shows that the dielectric loss obeys power-law dependences on frequencies, both below and above any loss peaks that may be present.
Abstract: The frequency dependence of the dielectric response of solids shows an apparently bewildering variety of patterns, virtually none of which corresponds to the classical Debye behaviour. However, a wide ranging critical analysis of the existing wealth of data shows that the dielectric loss obeys power-law dependences on frequencies, both below and above any loss peaks that may be present. This corresponds to power-law dependences on time under step-function excitation and it applies completely generally regardless of the detailed physical and chemical nature of the materials in question and also applies equally to dipoles, ions and hopping electrons as the polarizing species. Moreover, the power-law responses persist down to the lowest temperatures in the milliKelvin range, thus proving the importance of non-thermal transitions. The power laws are characterized by exponents in the range ± 1 and they cover as special cases the complete range of the observed types of response, from virtually frequency-independent “flat” losses often seen in low-loss materials, through various forms of asymmetric loss peaks to strongly dispersive behaviour in which both the real and the imaginary components of the susceptibility vary almost inversely with frequency. The “universality” of the power law strongly suggests the dominance in all materials of a common mechanism of dielectric relaxation and this is found in many-body interactions which provide a model capable of explaining the totality of the observed responses of solids, including both the frequency- and the temperature-dependence. In this interpretation, the classical one-particle Debye law represents but a singularity in a more general behaviour and is usually overshadowed by the new many-body mechanisms.
487 citations
TL;DR: In this paper, the magnetic entropy of a typical 3-dimensional ferromagnetic substance near the Curie temperature as a function of temperature and magnetic field strength was calculated and compared with the experimental results.
250 citations
TL;DR: In this article, a simple sufficiency condition is obtained, under which the Debye diffraction integral may be expected to give a good approximation to the solution of a boundary value problem that is generally taken to represent a field in the region of focus.
164 citations
TL;DR: In this article, the work function decreases to a minimum and the initial dipole moments were determined to μ 0 = 7.0 Debye for Fe(110), μ 0 ≥ 4.4 Debye and μ 0 ≤ 3.9 Debye, respectively, for K/Fe(100), K ≥ 3.5 × 1014 K-atoms/cm2 in all three cases.
102 citations
TL;DR: In this article, the authors discuss the nature of the Debye averaging that takes place in the C-V profiling of highly non-uniform electron distributions in semiconductors and show that the averaging process preserves the moment of the electron distribution.
Abstract: We discuss the nature of the Debye averaging that takes place in the C-V profiling of highly non-uniform electron distributions in semiconductors. It is shown that the averaging process preserves the moment of the electron distribution. This property can be used to extract certain quantitative details about the electron distribution that appear to have been obliterated by the averaging, without a need to reconstruct the entire true electron distribution. As an example, the extraction of the steepness of a diffusion gradient is discussed. In the limit of a weak electron concentration gradient, the width of the Debye averaging is shown to be such that the RMS averaging distance is (2)L D , where L D is the Debye length.
72 citations
TL;DR: In this paper, the dipole moment of an adsorbed CO molecule was determined to be 0.28 Debye with a negative end of the molecule projecting outward from the surface.
60 citations
TL;DR: In this article, the Debye temperatures of hexagonal crystals of 42 elements and compounds have been calculated from the elastic constants, by numerical integration and by Pynn's method.
Abstract: The Debye temperatures of hexagonal crystals of 42 elements and compounds have been calculated from the elastic constants, by numerical integration and by Pynn's method. It is found that Pynn's method is inapplicable in certain cases; the cause of this is analyzed, and a modification of Pynn's method is suggested for these cases. The calculated Debye temperatures are compared with the calorimetric Debye temperatures, wherever data are available. Large discrepancies are pointed out for Pr, Dy, Ho, and Er, and small ones for Be, Mg, Y, Ti, Zr, Hf, and Tb.
40 citations
TL;DR: In this article, the authors measured the heat capacities of SnSe and SnSe2 in the temperature range 230-580 K using a computer interfaced differential scanning calorimeter.
34 citations
TL;DR: The theory of dislocation damping for movable pinning points is developed by using results found earlier by the authors for the relaxation strength and relaxation time for the damped vibrating string model.
Abstract: The theory of dislocation damping for movable pinning points is developed by using results found earlier by the authors for the relaxation strength and relaxation time for the damped vibrating-string model. In this way new formulas are not needed but only a reinterpretation of the constants of the old theory. This is justified by exact calculations for the case of $n$ equidistant movable pinners. It is shown that the results can be represented in good approximation in the form of Debye relaxations. Four different such approximations are considered and compared. It is found that the main dependence of the effects on the parameters for any number of movable pinning points is the same as that for a continuously dragged string with only small changes of the order of 30% or less in numerical factors for the relaxation time and strength. These changes are of the same order as those introduced by a Debye approximation. The relation of the results to earlier work is discussed. In addition, the theory is placed within the framework of an even more general theory formulated in terms of a rigid-rod approximation.
33 citations
TL;DR: In this paper, the numerical contours for a moving test charge in isotropic Maxwellian plasma are determined numerically for a wide range of test charge speeds for a test charge.
Abstract: Equipotential contours for a moving test charge in isotropic Maxwellian plasma are determined numerically for a wide range of test charge speeds.
32 citations
TL;DR: In this article, the specific heat Cv of the ternary semiconducting compounds ZnSiP2, CdGeAs2 and CdNiP2 was determined experimentally in a temperature region within 2 and 30 K.
Abstract: The specific heat Cv of the ternary semiconducting compounds ZnSiP2, ZnSiAs2, ZnSnAs2, and CdGeAs2 is determined experimentally in a temperature region within 2 and 30 K. From the results the Debye temperatures, frequency moments, and standard entropies are calculated. By dividing Cv into a Debye and an Einstein contribution the approximate shape of the low frequency phonon mode is estimated.
TL;DR: In this paper, the temperature dependence of dc conductivity of V2O5, layers ≈ 500 nm thick, was studied from room temperature down to 28 K. The following vaiues were deduced: activation energy for hopping, WH ≈ 0.09 eV, Anderson disorder energy, WD = 0.13 eV and the Debye temperature, θD ≈ 325 K.
Abstract: The temperature dependence of the dc conductivity of V2O5, layers ≈ 500 nm thick is studied from room temperature down to 28 K. The following vaiues are deduced: activation energy for hopping, WH ≈ 0.09 eV, Anderson disorder energy, WD = 0.13 eV, and the Debye temperature, θD ≈ 325 K.
Nous avons etudie la variation de la conductivite de films de V2O5, (epaisseur 500 nm) entre 300 et 28 K. A partir de ces mesures nous deduisons les valeurs suivantes: energie de saut WH ≈ 0.09 eV, energie de desordre d'Anderson WD = 0,13 eV et temperature de Debye θD ≈ 325 K.
TL;DR: In this article, a deformation dipole model with 13 adjustable parameters gave the best fit to the phonon dispersion of LiD known from neutron and Raman experiments, which was used to compute elastic and dielectric constants, Szigeti effective charges, phonon densities of states, Debye temperatures and second-order Raman spectra of LiH and LiD.
Abstract: The deformation dipole model, the shell model, and also extended versions of these models have been investigated for the lattice dynamics of LiH and LiD. A deformation dipole model with 13 adjustable parameters gave the best fit to the phonon dispersion of LiD known from neutron and Raman experiments. The model has been used to compute elastic and dielectric constants, Szigeti effective charges, phonon densities of states, Debye temperatures and second-order Raman spectra of LiD and LiH. Good agreement with the experimental data was obtained. The contributions of short-range three- and four-body forces to the model force constants are discussed. First calculations of the phonon dispersion curves of the hydrides and deuterides of Na, K, Rb and Cs, which are based on shell models, are presented.
TL;DR: In this article, the phase transition of a superionic Cu 2 Se conductor was investigated by X-ray diffraction methods, and it was found that the transition was of the first order.
TL;DR: In this article, a formalism based on linear response theory is used to obtain an expression for the free energy of a non-uniform charged fluid in terms of the local ion number density and the bulk direct correlation functions.
Abstract: A formalism based on linear response theory is used to obtain an expression for the free energy of a non-uniform charged fluid in terms of the local ion number density and the bulk direct correlation functions. When the fluid is a restricted primitive model electrolyte the free energy splits into two independent parts, the minimization of which leads to expressions for the equilibrium charge and density distributions. From the free energy an expression for the force between two thick plates immersed in an electrolyte is obtained. In the limit of point ions, the expressions we obtain reduce to those of the Debye-Huckel theory of electrolytes. The equations are solved numerically and at low bulk electrolyte concentrations the monotonically decaying repulsive force of the classic Verwey and Overbeek results is found. But at higher concentrations and larger inverse Debye screening lengths the force displays pronounced oscillations. Correspondingly, the electric potential displays oscillations which have conse...
TL;DR: In this paper, light scattering spectra of mixed crystals KDP 1- x DKDP x with x = 0.08, 0.04 and 0.15 were measured by a Fabry-Perot interferometer with a free spectral range of 8 cm -1.
Abstract: Light scattering spectra of mixed crystals KDP 1- x DKDP x with x =0.08, 0.04 and 0.0 (KDP) are measured by a Fabry-Perot interferometer with a free spectral range of 8 cm -1 . Spectra are analyzed with the Debye type susceptibility of a polarization fluctuation coupled to an acoustic phonon. The relaxation times of an isolated dipole for x =0.08, 0.04 and 0.0 are found to be 0.27, 0.21 and 0.15 in the unit of 10 -12 sec, respectively.
TL;DR: In this article, the authors generalized the extended rotational diffusion models to treat liquids composed of asymmetric top molecules and determined the correlation functions and their Fourier transforms by both an analytical mechanics approach and a memory function approach.
Abstract: The extended rotational diffusion models are generalized to treat liquids composed of asymmetric top molecules. The correlation functions and their Fourier transforms are determined by both an analytical mechanics approach and a memory function approach. The limit of very short angular momentum correlation time is examined and is compared with the Debye anisotropic rotational diffusion model. The results are applied to infrared and Raman spectroscopy. A series of representative band profiles is presented. For asymmetric top molecules, the J-model is shown to be more realistic than the M-model.
TL;DR: In this paper, the low temperature heat capacities of 13 group IV chalcogenides were examined and it was shown that the heat capacity of groups with largely isotropic structure (GeTe, SnSe, GeSe, SnTe, GeS2 and SnS2) can be represented by pairs of two-dimensional Debye functions for the longitudinal and transverse lattice vibrations.
Abstract: The low temperature heat capacities of 13 group IV chalcogenides are examined. The heat capacity of crystals with largely isotropic structure (GeTe, SnSe, SnTe, PbS, PbSe, PbTe) can be represented within ±3% by a three-dimensional Debye function (θ3=205, 230, 175, 225, 150 and 130, respectively). The heat capacity of crystals with anisotropic structures (GeS, GeSe, SnS, GeS2 and SnS2) could only be represented by pairs of two-dimensional Debye functions for the longitudinal and transverse lattice vibrations (error ±0.5 to 3%;θ2(l)=505, 345, 400, 705, 480 and 570, respectively, andθ2(t)=200, 185, 160, 175, 100 and 265, respectively).
TL;DR: In this paper, an approximate analytic calculation of the functional derivative δT c δα 2 (Ω)F(Ω), where Tc is the superconducting critical temperature and α 2 is the electron-phonon spectral function, within the square-well model for the phonon mediated electron-electron interaction and weak coupling limit ω D (2πT c )⪢ 1 (ω D is the Debye energy).
TL;DR: In this paper, thermal and dielectric measurements at low temperatures on ceramic samples of ferroelectric Cd2Nb2O7 and non-ferroelectric cdNb 2O6 are reported.
Abstract: Thermal and dielectric measurements at low temperatures on ceramic samples of ferroelectric Cd2Nb2O7 and non-ferroelectric CdNb2O6 are reported. The data indicate ordinary Debye behavior for CdNb2O6, but the data for Cd2Nb2O7 suggest glasslike behavior.
TL;DR: In this paper, the specific heat at constant volume was calculated and the thermal dependence of the Debye's parameter θ D was obtained for the LaSn 3 compound, and the magnetic properties confirm that there is no evidence of the existence of a magnetic moment localized on La atoms.
TL;DR: In this paper, a universal empirical relationship connecting the Debye temperatures of a metal and its hydride, θ H, with the heat of formation, Δ H f, is derived from experimental data.
TL;DR: The known Debye temperatures of isostructural covalent substances, and especially those of diamond, silicon, germanium and grey tin, fall on a straight line versus 1/√r04 through the origin this paper.
Abstract: A survey of the literature demonstrated that the known Debye temperatures of alkali halides form a linear function of 1/√r03 through the origin, where r0 is the nearest-neighbor distance and is the averaged mass. The known Debye temperatures of isostructural covalent substances, and especially those of diamond, silicon, germanium and grey tin, fall on a straight line versus 1/√r04 through the origin. The Debye temperatures of the alkali halides and alkaline-earth oxides with the rock salt structure are appropriately evaluated on a simple model from their elastic stiffness constants.
01 Jan 1981
TL;DR: In this paper, the Debye Huckel theory is used to describe Coulomb systems in equilibrium classical statistical mechanics (at low density or high temperature) at low temperature, where the background charge distribution arranges itself in a spherically symmetric way about the fixed charge.
Abstract: The standard approach to Coulomb systems in equilibrium classical statistical mechanics (at low density or high temperature) was invented by Debye and Huckel It may be found under their names in most text books on physical chemistry Typically one considers a charge fixed in a background sea of other charges which are approxmated by a continuous charge distribution density The Debye Huckel theory shows that this background charge distribution arranges itself in a spherically symmetric way about the fixed charge so that by Newton’s theorem the view from distance r is equivalent to a single charge at r = 0 whose magnitude equals the total charge of the fixed charge plus that of the “cloud” of radius r about it Furthermore this total charge behaves as exp(-const × r) so that the charge is “shielded” and its “effective potential” is a Yukawa, exp(−cr)/r
TL;DR: In this article, it was shown that certain linear combinations of the associated radial coefficients are the solutions of the Ornstein-Zernike equation for hard discs in the Percus-Yevick approximation at densities θ, Kθ and -Kθ with θ the number density and K a self-determined parameter of the solution.
Abstract: The mean spherical approximation is solved exactly for a two dimensional fluid of dipolar hard discs. Using the basis functions 1, Δ = Ŝ 1 · Ŝ 2 and D = Ŝ 1 · (2[rcirc][rcirc]-U) · Ŝ 2, it is shown that certain linear combinations of the associated radial coefficients are the solutions of the Ornstein-Zernike equation for hard discs in the Percus-Yevick approximation at densities θ, Kθ and -Kθ with θ the number density and K a self-determined parameter of the solution. A numerical investigation of the thermodynamic properties of this exact result culminates in the finding of a liquid-gas critical point identified by θR 2=0·114 and K B TR 2/m 2=0·200 with R the disc diameter, k B Boltzmann's constant, m the dipole moment strength and T the absolute temperature. In addition, the dielectric constant of such a fluid within the mean spherical approximation is calculated and the resulting closed-form expression is compared with the values of the Debye and Onsager theories over a wide range of θm 2/(k B T) values.
TL;DR: In this article, it was shown that the common logarithms of the ration of the calculated intensities to observed intensities log (I calc /I obs ) of all diffraction lines are plotted against sin 2 θ, and a straight line should be obtained, the slope of which gives 2Bloge/λ 2, where B is a physical quantity to be determined contained in the Debye factor e (-2Bsin 2 ǫ/γ 2 ) in the intensity expression.
Abstract: The methods of determining Debye characteristic temperatures from X-ray diffraction intensities for the case of homogeneous and isotropic crystals have been fully discussed.It is proposed that if the common logarithms of the ration of the calculated intensities to observed intensities log (I calc /I obs ) of all diffraction lines are plotted against sin 2 θ, a straight line should be obtained, the slope of which gives 2Bloge/λ 2 , where B is a physical quantity to be determined contained in the Debye factor e (-2Bsin 2 θ/λ 2 ) in the intensity expression, λ being the wave length of the radiation used. In the Debye theory of specific heats, B may be expressed as (6h 2 T/MkΘ D 2 ){Φ(x) + x/4}, where h and k represent Planck constant and Boltzmann constant respectively, M is the mass of the atom or of the group of atoms situated at the lattice points, T is the absolute temperature at the time of taking Debye-Scherrer photographs, and Θ D is the Debye characteristic temperature. X = Θ D /T, and φ(x) is a function of x, given in the original Debye theory. It is seen that if we let G=BMkT/6h 2 , then φ(x)+x/4=Gx 2 Having obtained B, G in this equation is a measurable number, and solution of the equation may be performed graphically. By making Y 1 =Gx 2 and Y 2 =φ(x)+x/4, the plotting of these two equations should give two curves, the intersection of which should give x which determines the characteristic temperature at that temperature.It is pointed out that owing to the fact that Θ D itself is a function of temperature, the method proposed affords a possibility of determining Debye temperatures at required temperatures.