Showing papers on "Debye published in 1976"

Lattice dynamics with three-body forces: solid Xe and Kr

Abstract: Phonon dispersion curves, elastic constants. and the pV isotherms are calculated for solid Xe and Kr at 0 K using quasiharmonic lattice dynamics derived from multiparameter pair potentials. The computations account for the Axilrod-Teller-Muto three-body triple-dipole forces that arise in third-order perturbation theory. Approximate allowance is also made for anharmonic effects and, in the case of Xe, for three-body, third-order, dipole-quadrupole interactions and the three-body dipole interactions that arise in fourth-order perturbation theory. The over-all agreement with experimental phonon data is good except in the case of xenon, for the lowest-energy phonons in the [110] direction. This has the consequence that the sheaer lastic constant (C11 - C12)/2 and the zero temperature Debye theta are somewhat lower than current experimental values.

Ionic interactions in solutions. I. The association concepts and the McMillan-Mayer theory

Abstract: A review is given of the most common models of ionic-pair association used by Bjerrum, Fuoss, and Eigen to supplement the breakdown of the Debye-Huckel law for the mean activity coefficient of symmetrical electrolytes in lower-dielectric-constant solvents. The compressibility and pressure equations of Rasaiah and Friedman and the virial equation are used to rederive the activity coefficients from the distribution functions of Meeron and of Debye and Huckel. The results are compared to the well-known results of Debye and Huckel and that of Bjerrum. In each case the anion-cation pair association concept of Bjerrum is verified. Finally, a discussion is included on the best evaluation of the critical distance which distinguishes between free and associated ions. The activity equation is easily generalized to any short-range Hamiltonian model.

Role of polar optical phonon scattering in electrical resistivities of LaB6 and ReO3 (metallic conduction)

Abstract: The electrical resistivities of single crystals of LaB6 and ReO3 were measured in the temperature ranges of 4.2-360K and 4.2-300K, respectively. The residual resistance ratio of LaB6 was 450 and that of ReO3 was 90. The resistivity value of LaB6 at 300K is 8.90*10-6 Omega cm and for ReO3, 10.5*10-6 Omega cm. The experimental data were analysed from the scattering of electrons by polar optical phonons in addition to the scattering by acoustic phonons and impurities. The temperature dependences of the resistivities were explained well by this model for the temperature range measured, taking the Debye and the Einstein temperatures as 245 and 920K for LaB6 and 330 and 800K for ReO3, respectively.

Specific Heat Study of Magnetic Ordering and Band Structure of 3d Transition Metal Disulfides Having the Pyrite Structure

Abstract: Specific heats of FeS 2 -CoS 2 -NiS 2 Solid solutions and of Ni 0.95 Cu 0.05 S 2 have been measured from 10 K to 350 K. Debye temperatures, coefficients of electronic contribution γ, magnetic ordering temperatures, and magnetic entropies have been determined. The magnetic entropy of ferromagnetic Fe 1- x Co x S 2 is proportional to cobalt concentration and is 40% of that expected for a localized spin 1/2 per Co atom, suggesting an itinerant character of e g electrons. The magnetic entropy of NiS 2 is smaller than that of a localized spin 1 and is in good agreement with that expected for the magnetic moment observed by neutron diffraction. The magnetic entropy of antiferromagnetic Co 1- x Ni x S 2 Suggests that only Ni atoms have magnetic moment in Ni-rich phase. The density-of-states curve of e g band for NiS 2 has been constructed from γ values assuming a rigid band. The band width of lower half of e g band is 0.6 eV. The Debye temperature decreases monotonously from 605 K of FeS 2 to 455 K of NiS 2 .

A treatment of solvent effects in the potential theory of electrolyte solutions

Abstract: The potential theory of electrolyte solutions is extended to non-ideal solvents using the Kirkwood hierarchy of integral equations. Two closures are considered in the statistical mechanical analysis. The first closure, which is equivalent to that of Debye and Huckel, implies a dielectric constant of 1 + x (x = 4π∑σμσ 2ρσ kT, μσ dipole moment, ρσ dipole number density) and Debye shielding in the ion-dipole, dipole-dipole potentials of mean force. The second closure leads to the Onsager expression for the dielectric constant and predicts that the primitive model potential of mean force at infinite solute dilution is modified by a damped oscillatory term. Within this closure the analysis given here is restricted to those values of x such that Onsager's dielectric constant is less than 5·603.

Theoretical study of gas-solid energy transfer: An isotropic Debye model

Abstract: We present a model calculation for gas–solid energy transfer in which the solid is approximated as an isotropic Debye solid. For a given initial state of the solid (described by phonon occupation numbers), only states differing from this arbitrary initial state by one phonon (created or destroyed in an arbitrary state) are included in the basis set describing the solid. Using this basis set, a close‐coupling calculation is carried out describing energy transfer during a gas–solid collision. Since the scattering calculation does not employ perturbation, all states in the basis set are coupled. Averages over phonon momenta and directions are carried out before the calculation, which results in considerable simplification. Comparisons are made with He+Ag(111) experimental results. Qualitative agreement is good, and quantitative agreement is within a factor of 2. Our model tends to underestimate inelastic effects. The importance of kinematic and geometric considerations is stressed.

Determination of polymer chain conformation in amorphous polymers

Abstract: We present the results of a careful examination of neutron scattering from polymer chains in bulk; we have arrived at the following conclusions: 1) Macromolecular chains (in bulk) have the same dimensions as in a θ solvent; 2) They obey the Debye formula q−1 as low as 5 A. In order to show this clearly, we compare the theoretical Debye curve and the experimental result for deuterated polystyrene (Mw = 21,000) in a matrix of ordinary polystyrene. The fit is remarkably good and leaves very little room for other interpretations.

Self-Consistent Einstein Model and Surface Debye Temperature

Abstract: On the basis of a self-consistent Einstein model, which has been applied to a theory of melting of metallic fine particles in a previous publication, we discuss the problem of the surface Debye temperature. A semi-infinite metal crystal with a plane surface is considered and the vibrational frequency of each atom is self-consistly determined as function of atomic position. By making use of a simplified interatomic potential, an expression for the difference between square of the bulk and surface Debye temperatures is derived.

Dipole moments of KI, RbBr, RbI, CsBr, and CsI by the electric deflection method

Abstract: Electric deflection experiments using a velocity selected molecular beam apparatus have given the following electric dipole moments [measured in μe (Debye)]: KI, 10.82 (10); RbBr, 10.86 (10); RbI, 11.48 (10); CsBr, 10.82 (10); CsI, 11.69 (10).

Use of the memory function to simulate the Debye and Poley absorptions in liquids

Abstract: A single, simple equation is derived to describe the molecular rotational processes giving rise to the microwave and far infrared absorption bands of dipolar molecules in the liquid phase. The absorption spectrum over ∼3 decades of frequency is deduced by approximating the associated orientational correlation function with a hierarchy of response functions (or memory functions). These and the correlation function form a set of integro-differential equations called the Mori series. By truncating this at a certain level, with an empirical function such as a single exponential of correlation time 1/γ, a spectrum can be calculated which contains equilibrium averages proportional to the intermolecular mean square torque, 〈o(v)2〉, its derivative 〈o(v)2〉, etc., depending on the level at which the Mori series is truncated. The formalism is tested with the liquids CHF3, CClF3, CBrF3 HCCCH3 and the nematogen MBBA, a series chosen to cover the extremes of molecular isotropy and anisotropy.

Coriolis coupling and the Raman spectra of SF6 and CF4 in the liquid and plastic phases

Abstract: It is shown how to correct the J model to take account of first order Coriolis coupling on triply degenerate lines of spherical tops. The Debye limit of the J model is examined. Corrected J spectra are then compared to the experimental Raman lines of SF6 and CF4 in their condensed phases.

Can positrons self-trap in metals?

Abstract: The recent proposal that positrons are self-trapped by lattice dilations in metals is investigated The metal lattice is represented by an elastic continuum with a cut-off on the minimum wavelength of the dilations corresponding to the Debye wavevector The positron ground state energy is calculated by a strong-coupling variational method It is found that positron self-trapping does not occur unless the strength of the deformation potential coupling is stronger than is found in simple metals Furthermore the large and rapidly varying dilations that would accompany self-trapping were it to occur are inconsistent with the harmonic elastic continuum model Thus any further study demands an anharmonic model

The low-temperature heat capacities of Tb, Lu and Y

Abstract: The heat capacities of Tb, Lu and Y, refined by solid state electro-transport processing have been measured between 1.5 and 16K. Below 4K the results were fitted to the expression C= gamma T+AT3 where for Tb the nuclear and magnetic contributions were first calculated and subtracted from the total heat capacity. The resultant values of gamma (mJ mol-1K-2) and limiting Debye temperatures theta D(T to 0) were as follows. Tb: gamma =4.4+or-0.1, theta D=178+or-2K; Lu: gamma =6.8+or-0.1, theta D=205+or-3K; Y: gamma =8.2+or-0.1, theta D=248+or-3K. The Debye temperature was found in all instances to decrease by about 10% between 4 and 16K.

Computation on collisionless steady-state plasma flow past a charged disk

Abstract: A computer method is presented using the 'inside-out' approach, for predicting the structure of the disturbed zone near a moving body in space. The approach uses fewer simplifying assumptions than other available methods, and is applicable to large ranges of the values of body and plasma parameters. Two major advances concerning 3-dimensional bodies are that thermal motions of ions as well as of electrons are treated realistically by following their trajectories in the electric field, and the technique for achieving self-consistency is promising for very large bodies. Three sample solutions were obtained for a disk-shaped body, charged negatively to a potential 4kT/e. With ion Mach number 4, and equal ion and electron temperatures, the wakes of a relatively small body (radius 5 Debye lengths) and a relatively large body (radius 100 Debye lengths) both begin to fill up between 2 and 3 body radii downstream. For the large body there is in addition a potential well (about 6kT/e deep) behind the body. Increasing the ion Mach number to 8 for the large body causes the potential well to become wider and longer but not deeper. For the large body, the quasineutrality assumption is validated outside of a cone-shaped region in the very near wake. For the large as well as the small body, the disturbed zone behind the body extends transversely no more than 2 or 3 body radii, a result of significance for the design of spacecraft boom instrumentation.

Elastic constants of solid hexagonal close-packed hydrogen and deuterium

Abstract: Zero-pressure elastic constants for hcpp-H2 ando-D2 atT=0 K are calculated within the framework of the self-consistent phonon approximation with cubic anharmonicities. A pairwise additive model potential of the Barker-Pompe form, which reproduces the equation of state in the solid over a wide range of pressures, is used for the calculations. Debye temperatures and Gruneisen constants are also presented and the results are compared with recent experiments on the velocity of sound, inelastic neutron scattering, and specific heat.

Asymptotic behavior of equilibrium pair correlations in a dense electron gas

Abstract: The nodal expansion of the potential of average force is worked out systematically by iterating all the nonconvolution compact graphs from the order at which they appear first to infinity. For this purpose, we perform an exhaustive study of the asymptotic behavior of the bridge (without articulation points) graphs, and show that they decrease as ..beta..e/sup -//sup alpha//subr/r, with ..cap alpha.. > 1 and r in units of the Debye length lambda/subD/. We demonstrate that the asymptotic w/sub 2/(r) expansion is obtained from the resummation of the longest convolution chains l > or = 2(n-1) with n-1 two-bubbles and 0 < or = c < or = n Debye lines, which allow for a systematic improvement of the usual hypernetted-chain (HNC) approximation with the replacement of one, two, or more two-bubbles by bridge graphs. Substantial simplification of the final expression is achieved with the aid of the n-bubble sum which decreases asymptotically faster than the Debye line. The onset of short-range order is shown to arise at the critical value ..lambda../subc/ = 4.247 of the plasma parameter ..lambda.. = e/sup 2//k/subB/Tlambda/subD/ in excellent agreement with the Del Rio--DeWitt calculations. (AIP)

Anharmonic Debye-Waller factors using quantum statistics

Abstract: Anharmonic Debye-Waller factors and thermal smearing functions are derived for all temperatures in the one-particle-potential (OPP) model of vibrations by applying a perturbed density-matrix expansion about the harmonic case. Where possible, general results appropriate to sites of arbitrary symmetry are described, while the important case of sites possessing cubic point-group symmetry is investigated in detail. A useful finding is that the OPP model appears capable of describing the temperature dependence of anharmonic Debye-Waller factors at least down to Theta M/4, while the previous classical approaches begin to fail, as expected, at about Theta M, where Theta M is the Debye characteristic temperature.

Laboratory microwave spectrum of ClONO 2 and evidence for the existence of ClONO

Abstract: The microwave spectrum of ClONO 2 has been analyzed in the laboratory under high resolution. Rotational constants are reported for the ground and lowest vibrational states of the 35Cl and 37Cl isotopic forms. From Stark effect measurements the electric dipole moment was found to have components along two principal axes, μ a = 0.72 ± 0.10 Debye and μ b = 0.28 ± .04 Debye. Difficulties encountered in handling gas phase samples of ClONO 2 are discussed in some detail and evidence is presented for the existence of a closely related chlorine containing compounds which is believed to be ClONO. This second compound may also prove to be important in detailed atmospheric modeling. The rotational constants for ClONO are also given.

The earth‐ionosphere cavity

Abstract: To analyze ELF wave propagation in the earth-ionosphere cavity, a flat earth approximation may be derived from the exact equations, which are applicable to the spherical cavity, by introducing a second-order or Debye approximation for the spherical Hankel functions. In the frequency range 3 to 30 Hz, however, the assumed conditions for the Debye approximation are not satisfied. For this reason an exact evaluation of the spherical Hankel functions is used to study the effects of the flat earth approximation on various propagation and resonance parameters. By comparing the resonance equation for a spherical cavity with its flat earth counterpart and by assuming that the surface impedance Z/sub i/ at the upper cavity boundary is known, the relation between the eigenvalue ..nu.. and S/sub v/, the sine of the complex angle of incidence at the lower ionosphere boundary, is established as ..nu..(..nu.. + 1) = (kaS/sub v/)/sup 2/. It is also shown that the approximation ..nu..(..nu.. + 1) approximately equals (..nu.. + 1/2)/sup 2/ which was used by some authors is not adequate below 30 Hz. Numerical results for both spherical and planar stratification show that (1) planar stratification is adequate for the computation of the lowest three ELF resonancemore » frequencies to within 0.1 Hz; (2) planar stratification will lead to errors in cavity Q and wave attenuation which increase with frequency; (3) computation of resonance frequencies to within 0.1 Hz requires the extension of the lower boundary of the ionosphere to a height where the ratio of conduction current to displacement current, (sigma/..omega..epsilon/sub 0/), is less than 0.3; (4) atmospheric conductivity should be considered down to ground level in computing cavity Q and wave attenuation.« less

Measurement of the temperature dependence of Debye Waller factors by energy-dispersive methods: application to NbC0.98

Abstract: A new method is reported for evaluating the temperature dependence of Debye-Waller factors, or equivalently the mean-square atomic displacements (MSD), from X-ray spectroscopic data. By irradiating a properly oriented single crystal with polychromatic radiation, several orders of a given Bragg reflection can be simultaneously excited at a fixed scattering angle. These multi-order peaks can then be recorded in a single measurement with an energy dispersive detector. For experiments requiring only relative intensity data, this method offers a number of improvements over conventional techniques, e.g., (i) a substantial reduction in data acquisition time, (ii) a possible reduction in angular flexibility requirements and (iii) access to regions of reciprocal space which might otherwise be inaccessible. This procedure has been employed to determine the temperature dependence of the mean-square displacements of NbC0.98 over the temperature range from 296 to 600 K. These results are compared with published values computed from a double-shell lattice-dynamical force model; the agreement is found to be satisfactory. The data have also been used to evaluate the thermal expansivity of NbC0.98 over the temperature range of measurement; excellent agreement is found upon comparison with published thermal expansion data.

Ion dynamical corrections to the holtsmark theory of spectral line broadening

Abstract: Summary A method is described whereby earlier work by Kogan and Griem on ion dynamical corrections to the Holtsmark theory of spectral line shapes may be generalized to include the effects of Debye shielding and ion-ion correlations. Expressions for the dynamical corrections to the Holtsmark profile of a single Stark component are obtained to second order in the inverse Debye length. The correction terms are evaluated in the case of a high-density plasma (Ne ∼ 1017 cm−3), and the results used to discuss the central structure of the hydrogen Balmer β line profile. On the basis of our model, it is concluded that allowance for ion motion, with or without shielding, cannot account for outstanding discrepancies between the calculated and measured central structure of this line, under these conditions.

One‐component plasma in 2+ε dimensions

Abstract: The one‐component plasma (ocp) model with neutralizing background is extended to real dimensionality ν=2+e with −2⩽e⩽2. The equilibrium properties (pair correlation and thermodynamic functions) investigated within the Debye approximation, up to the second‐order in the plasma parameter e2/kBTλeD, with the aid of the Wilson quadratures, interpolate between two‐ and three‐dimensional results for 0

Geometrical-optics phenomena in the elastic scattering of fictitious heavy neutral nuclei by absorbing potentials

Abstract: A fictitious scattering phenomenon between neutral heavy particles is analysed by using both the square-well and trapezoidal complex potentials. After a preliminary phenomenological discussion based on the behaviour of the exact scattering matrix and the trajectories of Regge poles and zeros as continuous functions of the imaginary part of the potential, the contributions to the scattering amplitude from the external and multiple internal reflections and from the « surface waves » are separated by using the Debye expansion of theS(λ)-matrix. The most important first two terms of this expansion are then compared with the exact behaviour of both the partial-wave scattering amplitude and cross-section, and the results are discussed. In particular, for potentials with large imaginary parts, the first term of the Debye expansion, which is associated with the rays directly reflected by the surface, well approximates the exact scattering matrix for all angular momenta. In these cases, by applying to this first term the Watson transformation, one is able to separate the contributions from the reflected rays (saddlepoint contribution in the background integral) from that of the surface waves (surface pole contribution) which are responsible for the diffraction phenomenon. Studies are in progress in order to extend this approach to the Saxon-Wood potential with Coulomb interaction.