Showing papers on "Debye published in 1980"

Outer-sphere electron transfer in polar solvents

Abstract: The theory of outer-sphere electron transfer reactions in polar solvents is developed. It is based on a description of the solvent by complex dielectric permittivity in the Debye approach. It was shown that the pre-exponential factor of the electron transfer probability in the case of a strong interaction differs from all known pre-exponential factors of earlier works. An activation energy for electron transfer is obtained larger than the well-known expression first obtained by Marcus [1]. A new criterion distinguishing between non-adiabatic and adiabatic reactions is developed. Outer-sphere electron transfer was treated by generalizing and solving the Landau-Zener problem for the case where the system passes the intersection point of electronic terms without velocity and motion in the crossing region is diffusive.

Dynamics of gas–surface interactions: 3D generalized Langevin model applied to fcc and bcc surfaces

Abstract: A three dimensional generalized Langevin formalism is presented and applied to Ar and Xe interactions with Pt (111). Approximations for the random force and friction terms are proposed which permit realistic description of the motion and response of the surface atoms, including proper correlations among neighboring atoms. A ’’ghost atom’’ technique is developed which provides convenient numerical solution of the generalized Langevin equations in such a way that the fluctuation–dissipation theorem relating the random force and friction is satisfied rigorously. A simple prescription for determining parameters in the random force and friction is outlined. The prescription is applied to a four‐atom active zone to obtain explicit relationships for all parameters, depending only on the bulk and surface Debye frequencies, for fcc (100), (110), and (111), and bcc (100) and (110) surfaces. Calculations of energy accommodation, sticking probabilities, and thermal desorption rates are reported for Ar and Xe on Pt(111). The sensitivity of these properties on the parameters of the random force and friction, i.e., on the phonon spectrum, is examined. The dependence is found to be sufficiently weak to demonstrate convincingly that the generalized Langevin approach with relatively simple parameterization is capable of describing gas–surface dynamics with high accuracy.

Thermal expansion in insulating materials

Abstract: A model of thermal expansion in terms of the Morse potential which was developed earlier for low temperatures is extended to high temperatures and applied to a semiempirical calculation of thermal expansion in insulating materials. In this model, the localized quantum mechanical solutions of the Morse potential are combined with the Debye model to give a localized-continuum description of thermal expansion. A set of empirical rules is developed for characterizing the interatomic potential in terms of the Morse potential. These are then applied to the quantitative calculation of thermal expansion in the alkali halide crystals and a group of binary high temperature materials with the aid of the known crystal structures, compressibilities, and Debye temperatures of these materials. Good agreement between calculated and experimental values is obtained for temperatures ranging between 0 K to values near the melting points. A discussion of the underlying basis of the empirical rules is given as well as their likely applicability to a wide range of insulating materials.

Sound velocities and elastic-constant averaging for polycrystalline copper

Abstract: This study deals with the tensor-averaging problem, with the relationship between single-crystal and polycrystalline elastic constants. For polycrystalline copper, sound velocities were measured within a 0.1% inaccuracy at T=295K. Comparison with average values from twelve previous studies shows agreement within 0.2% in vt, 0.1% in ve, and 0.1% in v1. Among eight elastic-constant averaging methods, the Hershey-Kroner-Eshelby method works best for copper's polycrystalline and single-crystalline Debye temperatures differ by about 9K.

The temperature dependence of rotational tunneling

Abstract: In the last few years tunneling transitions have been observed for the highly symmetric groups CH4, CD4, NH4+, and CH3 rotating in various environments. Typically the tunneling lines shift to lower energies with increasing temperatures. In this paper the shift of the tunneling energy is calculated in a microscopic approach to the problem. The coupling of the rotating groups to the lattice modes is studied in two stages. First the rotating group is coupled to a single oscillator, then to the modes of a Debye crystal. The first calculation leads to a set of discrete tunneling lines with an energy that diminishes as the oscillator is excited into higher levels. The second approach yields a single tunneling line shifted down-wards with increasing phonon population. The shiftΔ ω is proportional toT4. The calculation explains the energy shift of the tunneling lines with reasonable values for the coupling parameters. In some cases also a broadening has been observed which does not follow from our calculations.

Debye-Waller factors for incommensurate structures

Abstract: Overhauser has predicted that thermal fluctuations in the phase of the modulation wave will give rise to large Q-independent Debye-Waller factors for incommensurate diffraction satellites. We show that a key to understanding this surprising result is a spatial modulation of the fluctuation of atomic positions in an incommensurate solid. The range of validity of Overhauser's assumptions is discussed and an alternate calculation which should be valid over a larger range of relative fluctuation amplitude is presented. This new calculation predicts the existence of fluctuation- and displacement-dominated regimes, in which higher-order diffraction satellites display qualitatively different behavior.

Dynamical structure factor and frequency distribution of the metallic glass Cu46Zr54 at room temperature

Abstract: The dynamical structure factor of glassy Cu46Zr54 has been measured at room temperature, for momentum transfers between 1 and 8 AA-1 and energies (h(cross) omega =E0-E) between -45 and 45 meV, using neutron inelastic scattering. From the measured time-of-flight spectra a generalised frequency distribution has been determined. The experiment was repeated after crystallisation of the sample. The results show a strong increase of low-frequency modes in the amorphous sample compared with the polycrystal, and the frequency distribution of the metallic glass shows a slope approximately omega 4/3 between 4.7 and 7 meV, where the frequency distribution of the polycrystalline sample still shows a Debye type of spectrum.

The vibrational states in a realistic model of amorphous iron

Abstract: The vibrational density of states (DOS) of a realistic model structure of amorphous iron was calculated in two ways, using the equation of motion method and the recursion method, in which the quantitative disorder due to variations of interatomic force constants was found using the empirical potential of Pak and Doyama for alpha -Fe. It is shown that the vibrational DOS of amorphous iron has two peaks, an enhanced broad one on the low-frequency side and a fairly reduced one in the high-frequency side. The Debye parameters which characterise the whole spectrum and can be obtained by Mossbauer spectroscopy, were calculated. They are about 6% smaller than those values for the crystalline state ( alpha -Fe). The 'phonon' dispersion curves in amorphous iron were also computed from the wavenumber-dependent spectra both for longitudinal and transverse excitations. The authors observed a considerable softening of phonons associated with the metallic amorphous state.

Displacement correlations in covalent semiconductors

Abstract: Displacement-displacement correlation functions as well as vibrational amplitudes and Debye temperatures were calculated for covalent semiconductors using the adiabatic bond charge model. The results were compared with the shell model and heat capacity as well as X-ray and Mossbauer data. Radial and transverse correlation were computed. Good agreement was found with recent EXAFS results. Values for the mean square dynamic deformations of the bond length and bond angles are presented and the dynamical disorder of crystalline germanium is compared with the static disorder of amorphous germanium.

Computer simulation of the structure and atomic vibration of the Σ=5 tilt boundary in aluminium

Abstract: The structure of the Sigma =5 tilt grain boundary in aluminium was simulated by molecular dynamics using the Morse potential. Two types of structure were obtained. The local density of states (LDS) of phonons was calculated by the recursion method developed by Haydock and colleagues. The Debye parameters ( theta D(n)) were found to be very small near the boundary plane and there were large mean atomic displacements in the direction perpendicular to the boundary plane.

Near-Debye dielectric responses

Abstract: It is shown on the example of the dielectric data for Er-doped CaF2 that very slight departures from the true Debye response can be assessed very accurately using the analysis of the real part of the susceptibility. Given adequate precision of measurements, this method is far more sensitive than the plotting of the complex plane Cole-Cole circle or the examination of the loss as a function of frequency. It is shown that a concentration of 1 part Er in 104 gives a noticeable departure from the Debye behaviour, while at a concentration of 1 part in 105 the susceptibility is so small that insufficient sensitivity remains to enable a meaningful fitting to be obtained. This shows that one cannot move away from many-body interactions by successive dilution of the interacting species, before losing the signal strength in the measuring process.

Dynamic deformation and the Debye–Waller factors for silicon-like crystals

Abstract: Calculations are presented of the Debye-Waller factors for silicon, diamond and germanium in the temperature range 1 to 1000 K and for grey tin in the range 1 to 280 K. Values were obtained from the shell model, the adiabatic bond-charge model and the valence force potential model for all four materials. Further values are listed from the fitted Born-von Karman model for silicon and germanium and from two additional parametrizations of the valence force potential model for silicon. The effect of dynamic deformation on the Debye-Waller factor of silicon and, to a slightly lesser extent, the other three elements, is investigated. The Debye-Waller factor for the shells only in the shell models is calculated. The effect introduced by dynamic deformation whereby the Debye-Waller B value varies with scattering vector K is evaluated. Finally, the anisotropic Debye-Waller factor components for the bond charges are calculated for all four elements. It is found that the bond charges in the bond-charge model and the shells in the shell model vibrate substantially less than the main atomic cores. It is concluded that if the models are at all realistic then the effects of dynamic deformation on the Debye-Waller factors of these elements should be seriously considered.

The D‐C MOSFET Dopant Profile Method

Abstract: Dopant profiles can be determined from d‐c measurements on a four‐terminal surface‐channel MOSFET The region from about three Debye lengths from the oxide‐silicon interface to a maximum depth, limited by the avalanche breakdown in silicon, can be profiled by this method Within three Debye lengths of the surface, the depletion approximation fails, and in this region the profile has a characteristic dip which is easily recognized Other limitations include effects due to the field dependence of the channel mobility, short channel enects, and the lack of parallelism of the depletion edge with the interface The method is illustrated by dopant profiles of bulk wafers, implanted layers, and a diffused layer The dopant densities covered by these profiles vary from to

Doppler-free optical double resonance spectroscopy using a single-frequency laser and modulation sidebands

Abstract: Principles and applications are described for a form of Doppler-free optical double resonance spectroscopy which uses amplitude modulation sidebands (v L ±v) imposed on a single laser frequency (v L ). The sidebands are generated by passing the carrier radiationv L through an electro-optic modulator, driven at a radiofrequency ν, which enables the intensity and polarization characteristics of the emerging radiation to be varied for enhancement of selected double-resonance processes. The technique has been applied to infrared-infrared double-resonance studies of the Stark effects of a variety of molecules—13CH3F,12CH3F, PH3,15NH3, GeH4, SiH4, and CH3D—for which physical results are presented and discussed. These results include determination of extremely small electric dipole moments (10−3–10−5 debye) for GeH4 and CH3D and, for the dipole moment of PH3, a vibrational state dependence which is extremely small (Δμ=0.0028(5) debye for ∣Δv 2∣=1) and a rotational state dependence which is of an unexpected sign. The spectra recorded in some cases display unusual polarization and optical saturation effects which deviate markedly from the predictions of a simple three-wave polarization theory.

Theory of the low-temperature Seebeck coefficient in dilute alloys

Abstract: The Seebeck coefficient in dilute alloys at low temperatures is investigated in a simple model in which free electrons are scattered by a random array of fixed impurities and interact with longitudinal Debye phonons through a Fr\"ohlich Hamiltonian. As has been shown by Vilenkin, the wave-number dependence of the Fourier-transformed impurity potential removes the near cancellation of several contributions due to the electron-phonon renormalizations discussed by Vilenkin and Taylor. The net electron-phonon enhancement of the Seebeck coefficient is found to be close to the usual mass-enhancement ratio in the case of a screened Coulomb potential.

Low-temperature specific heats of some uranium ternary compounds UAsY (Y = S, Se, Te)

Abstract: The specific heats of the UAsY (Y = S, Se, Te) ternary compounds have been studied in the temperature range 1–300K. λ-type anomalies are reported at 125.8, 108.8, and 62.8 K, respectively, corresponding to ferromagnetic ordering. The experimental results are analyzed in terms of the Debye model and electronic contributions. Debye temperatures, electronic specific heat coefficients, and magnetic entropies are derived. A comparison is made with the isostructural binary compounds UX2 (X = P, As, Sb, Bi).

Dynamic Susceptibility of a Spin Glass Compound (Ti 0.9 V 0.1 ) 2 O 3

Abstract: The imaginary part of the susceptibility of (Ti 0.9 V 0.1 ) 2 O 3 was measured and the temperature dependence of the characteristic relaxation time, which showed a sharp peak at a spin freezing temperature T g , was obtained using a modified Debye formula proposed by Matsubara and Yoshimitsu.

Specific heat of the superconducting high pressure phase Ga II

Abstract: The high pressure modification gallium II, which becomes superconducting near 6.4 K, has for the first time been investigated calorimetrically at about 35 kbar in the temperature range of liquid helium. From the data a Debye temperatureΘ D = 178K and an electronic specific-heat coefficient γ=1.75 mJ/mole K2 are obtained. These values are in good qualitative accord with the increased superconductingT c with respect to that of Ga I.

Specific heats of the pyrochlore compounds Eu2Ir2O7 and Lu2Ir2O7

Abstract: The specific heats of the pyrochlore compounds Eu2Ir2O7 and Lu2Ir2O7 were measured below 20 K. The data was found to be described by the expression C=γT+αT3 below 6 K for both compounds. The Debye temperatures were calculated from the T3‐term coefficients. The values for γ were found to be 13.0 mJ/mole K2 for Eu2Ir2O7 and 12.5 mJ/mole K2 for Lu2Ir2O7. The ΘD values were 304 and 352 K, respectively.

Calculation of the free carrier density profile in a semiconductor near an ohmic contact

Abstract: : In this note, a quantitative attempt is made to answer the question: 'To what depth does the equilibrium free carrier density penetrate into a low doped semiconductor from a heavily doped region interfacing it.' The simple answer 'A few Debye lengths' can sometimes prove to be inadequate.

Debye shielding and the thermal emission of hydrogen

Abstract: In thermal plasmas transitions, emissions of photons occur in the presence of perturbing particles, mostly electrons. Their effect on the spectral intensity distribution, especially of recombination radiation, is estimated by use of the Debye-Huckel potential.

Temperature dependence of the exciton—phonon coupling in the strong coupling limit: Results for solid nitrogen

Abstract: High resolution (Δ E = 0.75 meV) absorption profiles of the vibronic bands in the range of the w 1 Δ u ← X 1 Σ + g and a 1 II g ← X 1 Σ + g exciton progressions at hv ≈ 8.9 eV in solid N 2 have been measured in the temperature range between 6 K and 30 K. These excitations are strongly localized so that the observed temperature dependence of the fine structure, consisting of a zero phonon line and a phonon side band, can be described very well in the model of strong exciton—phonon coupling at point defects. The experimental results for the w 1 Δ u transition are found to be consistent with the assumption of a Debye spectrum for the phonon density of states and we derive a value for the Debye temperature of θ = 78 K, which is in very good agreement with that derived from other measurements.