Showing papers on "Debye published in 1974"

Phonon dispersion and phonon densities of states for ZnS and ZnTe

Abstract: Neutron scattering data are reported for II–VI zincblende crystals, which are believed to be of sufficient precision to refine earlier ZnS ambiguities and to provide a basis for model fitting comparable to existing III‐V results. Valence shell models, including 9–12 parameters (VSM) and a variable shell charge extension (VCM), were fit to the data and used to generate phonon density of states and Debye temperatures. Very good fits to the neutron data were obtained, but no model was found that also predicts an accurate set of electric and mechanical constants. It is concluded that an unambiguous ionic charge Z cannot be assigned from the neutron results in either case.

Exact solution of the mean spherical model for strong electrolytes in polar solvents

Abstract: The mean spherical model (MSM) for dense fluids is solved for an arbitrary mixture of equal radii charged hard spheres with permanent embedded dipole moments. The model provides a treatment of ionic solutions that includes the feature of a molecular solvent. Thus, it gives a basis for investigating deviations from the familiar continuum dielectric model in ionic solution theory. The arbitrary polar‐ionic mixture is first reduced to an effective two component problem. One component is an effective charged species while the other is an effective polar species. This two component problem is solved in terms of three parameters closely related to the thermodynamic functions of the fluid. Nonlinear algebraic equations for these parameters are obtained. Although these equations appear to be analytically intractable for arbitrary ionic and dipolar strengths, explicit results are obtained for low ionic strength. In this limit, the ion‐ion contribution to the Helmholtz free energy is given by the classical Debye‐Hu...

Correlation of Properties of Materials to Debye and Melting Temperatures

Abstract: Many solid state properties are correlated to simple parameters like the atomic mass, the interatomic distance and some measure of the strength of the interatomic interaction, e.g. the melting temperature Tm or some Debye temperature θD. Such empirical relations are investigated for elastic properties, melting temperature, thermal expansion, vacancy formation energy, grain boundary and surface energy, cohesive energy, heat of fusion, activation energies for bulk, grain boundary, surface and dislocation pipe diffusion, viscosity, activation energy for creep, recrystallization temperature and other properties. When experimental data are available, both elements and diatomic compounds (alkali halides, oxides, carbides, III-V semiconductors) are considered. The correlations to Tm, θD(T = 0) and a high temperature effective θD are compared. It is found that for all practical purposes Tm gives the best correlation. For diatomic compounds, the average mass is not uniquely defined and various averages are discussed. The purpose of the paper is not only to present empirical relations but also to give a short account of the possibilities to calculate the considered parameters using solid state theory in its most advanced present state.

Pulse-induced critical scattering (pics) from polymer solutions

Abstract: Pulse-induced critical scattering (PICS) is a new, fast technique for determining thermodynamic and kinetic parameters of polymer solutions. Relative intensities of scattered laser light are measured over periods of seconds after a fast temperature step into the region of Debye critical opalescence. In the mode of operation using thermal pulses to progressively lower temperatures, the intensity pulse shape gives sensitive information on the fluctuation equilibrium and on the kinetics of phase separation with formation of emulsions of sub-wavelength particles, Spinodal and critical loci for the system polystyrenecyclohexane (PS–CH) are measured about 10 times faster and more accurately than in recent work based respectively on conventional light scattering equipment and on turbidimetry. The classical Debye theory of scattering near a critical point, or Scholte's extension to spinodal points, gives excellent semi-empirical extrapolations to spinodal temperatures T s . Though there are signs that the classical theory needs amendment in the sense of the generalized nonlinear theory of Fisher, Chu, and co-workers, this would generally give results on T s in close agreement with the simpler classical theory in the experimental range accessible to PICS. The effects of heterodispersity on the phase diagram are studied, comparing data by Scholte and new data by PICS on PS–CH. The evidence suggests that spinodal loci are governed mostly by M w (as suggested by recent theories). Marked secondary effects seem, however, to arise, not (as recently suggested) from M n , but from M z . Results obtained by the technique of approaching phase equilibrium from the heterogeneous side, using an emulsion carefully ‘seeded’ by a thermal step, suggest that supercooling is more serious in cloud-point determinations of dilute polymer solutions than hitherto thought. The formation of sub-wavelength droplets follows kinetics bearing more than formal resemblance to that for the nucleation and growth of spherulitic crystals in bulk.

Connection between the macroscopic electric and mechanical susceptibilities

Abstract: The following relationship is derived between the dielectric permittivity e(ω) and the complex shear viscosity η(ω): [e(ω)−e∞]/(e0−e∞) = [1−i ωη(ω)K]−1. This equation is derived from both a generalization of Debye's treatment and from the Kubo formalism. The model consists of dipoles imbedded in rigid beads that are in turn imbedded in the viscous medium. A frequency dependent η(ω) implies nonexponential decay of the electric dipoles and results in skewed-arc behavior in the Cole-Cole plots except when η(ω) is represented by a single Maxwell element or by a single Viogt element. Consistency with the requirements of causality and reality is displayed. Experimental e(ω) are predicted reasonably accurately by use of experimental η(ω) and the above equation.

Effect of satellite potential on direct ion density measurements through the plasmapause

Abstract: A simplified theory has been developed for calculating the effect of satellite potential on the ion current measured by an experiment such as an ion mass spectrometer or an ion trap. The theory is based on the use of a spherically symmetric Debye potential distribution in the sheath around the satellite and is particularly appropriate for use in regions where the Debye length is large, such as in the plasmasphere and magnetosphere. Ion data obtained from the ion trap on the Ogo 3 satellite during a pass through the plasmasphere show excellent agreement with the theory. The inferred ion densities from this analysis are as much as 1 order of magnitude different from what would be inferred from previous analyses.

Temperature and field dependence of the optical absorption edge in amorphous As2S3

Abstract: The optical absorption coefficients and the temperature dependence of the edge in amorphous As2S3 have been measured at temperatures down to 10 K. The temperature coefficients of the gap at a fixed absorption level ( delta E/ delta T)alpha , can be separated into two components. The first is attributed to electron-phonon interactions and the shift is found to be proportional to the internal energy on a Debye approximation, as predicted from the theory of zero-phonon transitions in colour centres. The second is the temperature broadening of the Urbach tail. The slope of the tail is interpreted in terms of random electric fields arising from disorder and phonons; the former is estimated to be three times larger than the contribution from zero-point motion. The electro-modulation spectrum has been measured in the region of the absorption edge and is discussed in terms of exciton and other models.

Relationship between single‐crystal and polycrystal elastic constants

Abstract: A new method is given for computing effective polycrystalline elastic constants from single‐crystal elastic coefficients. Agreement with observation is good. The method is based on the assumed equivalence of the lattice‐vibrational properties of single crystals and polycrystals of the same material; single‐crystal and polycrystal Debye temperatures are equated. Present predictions of polycrystal elastic moduli differ significantly from those of most other averaging methods by being lower than the familiar Voigt‐Reuss‐Hill results.

Neutron-scattering study of collective excitations in superfluid helium

Abstract: Extensive inelastic-neutron-scattering experiments have been performed on superfluid helium over a wide range of energy and momentum transfers. A high-resolution study has been made of the pressure dependence of the single-excitation scattering at the first maximum of the dispersion curve over the range 1-24.4 atm and at 1 atm of the wave-vector dependence of the single-excitation scattering beyond the roton minimum. The latter data, but not the former, are consistent with the idea of an instability threshold suggested by Pitaevskii and by Enz. The pressure and wave-vector dependence of the multiexcitation scattering was also studied. It is shown that the multiphonon spectrum of a simple Debye solid with the phonon dispersion and single-excitation cross section of superfluid helium qualitatively reproduces these data.

A determination of the Debye–Waller temperature factor and the X‐ray Debye temperature for Ni, Cr, Fe, Mo and W

Abstract: The integrated intensities of high-order reflexions for Ni, Cr, Fe, Mo, and W powder samples were measured at 296 and 77°K with Mo Kα radiation. The values 397 ± 6, 510 ± 6, 435 ± 6, 407 ± 6, and 333 ± 6°K respectively were obtained for the Debye temperatures after correction for thermal diffuse scattering. These values are in good agreement with those calculated from force-constant models determined by inelastic neutron scattering.

The specific heat of high purity gadolinium between 1.5 and 14K

Abstract: The specific heat of high purity gadolinium, prepared by solid electrotransport processing, has been measured in the temperature range 1.5 to 14K, and the data analysed for electronic, Debye and magnetic contributions to the total specific heat. The electronic coefficient gamma was found to be 3.7+or-0.2 mJ mol-1 K-2 and the magnetic specific heat, assumed to be of the form CM=BTn, yielded B=1.94+or-0.04 mJ mol-1 K-(n+1) with n=1.75+or-0.05. The Debye temperature between 1.5 and 5K was calculated to be 187+or-3K, while for temperatures in excess of 5K it was found to decrease with temperature to a constant value of 160+or-3K above 12K.

Low-temperature thermostatics of face-centered-cubic metallic hydrogen

Abstract: The thermostatic properties of a high-symmetry phase of metallic hydrogen with atomic sphere radius between 0.1 and 1.5 bohr are studied, with special emphasis accorded to electronic screening and quantum proton motion. The electron-proton and proton-proton interactions receive a perturbation treatment based on the Singwi dielectric function, while the proton motion is handled by self-consistent harmonic approximation. Quantum behavior is found to be less pronounced than expected, and nuclear magnetism is absent. The phonon spectrum is, however, affected by screening and large proton motion. The zero-point vibrational energy and the superconducting critical temperature are below previous estimates. The crystalline-defect formation energies are a few times the Debye energy, which implies that defects contribute significantly to melting at the lower particle densities.

Rotational relaxation of molecules in isotropic and anisotropic fluids

Abstract: A theory of rotational relaxation in isotropic and anisotropic liquids is presented. The Debye rotational diffusion model is generalized so as to include reorientations of arbitrary angle with the use of a nonlocal in orientation master equation for the orientational conditional probability. For isotropic media, we have previously demonstrated that spectral line shapes (Fourier transforms of time correlation functions) appropriate to, for example, Raman and ir line broadening spectroscopy, are always superpositions of Lorentzian lines. We present here an algebraic formulation which gives the linewidths of the Lorentzian lines in terms of the transition probability describing the reorientational motion. Several models and general trends for these linewidths are discussed in order to facilitate the comparison of experimental results and this theory. For anisotropic media, such as liquid crystals or small molecules ordered by liquid crystals, a nonlocal reorientational mechanism leads to a continuous spectru...

Elastic constants of niobium‐rich zirconium alloys between 4.2 K and room temperature

Abstract: The adiabatic elastic constants were determined for niobium and for its alloys containing 1.4, 3.6, and 6.0 at.% zirconium. The c11, c12, and c44 constants as well as the shear constant C′ = (1/2)(c11 − c12) and the bulk modulus were tabulated between 4.2 and 290 K. The unusual temperature dependence of the shear constant c44 found in niobium was also observed in the alloys. The Debye temperatures were computed from the constants at 4.2 K.

Evaluation of dielectric permittivity and conductivity by time domain spectroscopy. Mathematical analysis of Fellner‐Feldegg's thin cell method

Abstract: A mathematical analysis is presented of Fellner‐Feldegg's thin cell method from which the permittivity and conductivity of dielectric materials can be obtained in the time domain. It is proved that the thin cell response has to be interpreted as a Taylor expansion of the step response around l=0. The first term in the expansion (Fellner‐Feldegg's thin cell relation) can be found by integration over the ordinary Laplace contour (c − i ∞, c + i ∞). The other coefficients can be obtained from complex integration over a contour W enclosing all singularities of the integrand. Restrictions on the thickness of the sample are derived from the requirement that the second term in the expansion must be small relative to the first one. The step response is also calculated with asymptotic methods and with numerical methods for three currently used permittivity relations. Also, conductivity is included. For Debye materials a relation is found that tends to give a better fit to the exact response than the thin cell relation. For such materials the relaxation time found experimentally, using the thin cell relation, is always too large. An iteration procedure is suggested to obtain the correct relaxation time. For conductive materials the thin cell approximation leads to an incorrect value of the offset of the base line. The correct relation is derived.

Numerical studies of the AC conductivity of hopping systems. I. Effects of space and energy disorder

Abstract: Results are presented of exact numerical calculations of the AC conductivity of a simple, physically useful model of a hopping system. The model consists of a finite one-dimensional lattice of sites with the carrier hopping by a phonon assisted process between states localized on the lattice sites. It is shown that the frequency dependence of a finite lattice of regularly spaced sites of equal energy is of the Debye type, with a 'relaxation time' which can be related to the transit time of a carrier along the finite chain. For a lattice of equal energy sites randomly distributed in space, the conductivity saturates at high frequency and at lower frequencies can be represented by sigma ( omega )=A omega s, where s

Dielectric relaxation in water in the neighborhood of 4°C

Abstract: The complex permittivity of water has been measured at seven temperatures between 3 and 5°C over a frequency range of 0.4–4 GHz. The data are analyzed first in terms of a small but significant distribution of relaxation times of magnitude larger than that observed previously and then as two separate Debye process having relaxation times separated by a factor of ∼2. It is shown that one possible interpretation of these observations is that a bond breaking process takes place in which the rate of formation of one bonded molecules from two bonded molecules depends upon whether the latter are bonded symmetrically or unsymmetrically. The value of the high frequency permittivity (e∞) calculated from this model is shown to agree well with experiment. There is no evidence of any abrupt changes (``kinks'') greater than random experimental error in the temperature variation of the dielectric parameters of water between 3–5°C.

Vibrational dependence of the dipole moment in the A3Π1 state of ICI

Abstract: The Stark effect is measured for the A3Π1←1Σ+ band system. The dipole moment of the A state as a function of vibrational level is measured to be, in Debye, ν′μ′ν′μ′ν′μ′ν′μ′72.00(± 0.15)111.85(0.10)141.75(0.05)211.15(0.15)91.95(0.05)121.80(0.10)171.50(0.15)250.6 (0.15)101.90(0.10)131.60(0.15)181.25(0.10)270.6 (0.15) The sign of the A state moments appears to be opposite to that of the X state.

Microwave spectrum and dipole moment of 3,6‐dihydro‐2H‐pyran

Abstract: The microwave spectrum of 3,6‐dihydro‐2H‐pyran has been studied in the R‐band frequency range (26.5–40.0 GHz) with a Hewlett‐Packard Model 8400 Stark‐modulated microwave spectrometer. The spectrum is characterized by rather strong perpendicular transitions of a near oblate symmetric top. Transitions obeying a, b, and c dipole selection rules have been assigned and 24 low‐J R ‐branch transitions have been used to derive the rigid rotor constants for the ground vibrational state: (in MHz) A = 5085.152±0.012; B = 4849.365±0.013; C = 2712.487±0.013. Stark displacement measurements were made for several transitions and the dipole moment components determined by least squares fitting the displacements; (in Debye) |μa|=0.892±0.006; |μb|=0.507±0.010; |μc|=0.771±0.002 yielding a total dipole moment μtot = 1.283±0.005. Model calculations to reproduce the rotational constants and the observed dipole moment components indicate that the data are consistent with a twisted ring skeleton with the oxygen atom on one side ...

Debye potentials in Riemannian spaces

Abstract: By means of Debye potentials it is possible to get all solutions of source‐free Maxwell equations in vacuum from a single scalar equation. Sufficient conditions for the existence of Debye potentials in a given four‐dimensional Riemannian space have been found. Some examples of metrics are given, including plane gravitational waves, metrics with spherical symmetry, and cosmological models. The method is generalized to Maxwell fields with sources and Maxwell fields in dielectric media.