Showing papers on "Debye model published in 1984"

Influence of grain boundaries and surface Debye temperature on the electrical resistance of thin gold films

Abstract: The electrical resistivity of thin gold films deposited on amorphous substrates is found to increase with decreasing film thickness. The temperature-dependent part of the resistivity, however, is independent of the film thickness. This observation cannot be reconciled with existing theories that deal with surface scattering effects. We show that electron scattering at grain boundaries explains our measurements. Moreover, the main effect of the surface appears to be a change in the effective Debye temperature.

Nonperturbative theory of temperature‐dependent optical dephasing in crystals. I. Acoustic or optical phonons

Abstract: We continue the discussion of the nonperturbative theory of zero‐phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In that paper, a diagrammatic analysis was undertaken which led to analytic results for the thermal width and shift of the zero‐phonon line. Here we evaluate these results for two model phonon densities of states: the Debye model for acoustic phonons, and a sharply peaked density of states appropriate for optical phonons. For Debye phonons we find that at low temperatures the standard (perturbative) theory of optical dephasing is qualitatively correct, but at high temperatures it becomes very inaccurate. Moreover, if one of the excited state phonon frequencies tends to zero (a soft mode), then perturbation theory breaks down completely. For optical phonons our results give an Arrhenius temperature dependence for the linewidth and place an upper bound on the value of the preexponential. In paper II of this series we will discuss dephasing by pseudo‐local phonons,...

Specific Heat and Superconductivity in BaPb1-xBixO3

Abstract: Specific heat coefficient of BaPb 1- x Bi x O 3 at low temperatures was measured by the thermal relaxation method. Although the discontinuity in the specific heat C at the superconducting transition temperature T c could not be detected, it was clearly observed in the lowest experimental temperature region that C in the superconducting state at zero magnetic field was smaller than in the normal state at H =59 kOe. The electronic specific heat coefficient γ increased with x until x =0.25 and then decreased above, corresponding to the composition dependence of T c . However, the γ value, e.g. 1.6 mJ mole -1 K -2 at x =0.25, was one to two orders of magnitude smaller than those of the other typical high T c superconducting metals. The Debye temperature was in the range 166 K to 196 K for 0 ≤ x ≤0.3.

Glasslike thermal properties of antiferroelectric PbZr O 3 at low temperatures

Abstract: Specific-heat and thermal-conductivity data (1.7---40 K) are reported for the first time on ceramic samples of the antiferroelectric PbZr${\mathrm{O}}_{3}$. A linear term in the specific heat is resolved below 3 K, and the thermal conductivity displays a quadratic temperature dependence below 4 K. The coefficients of these glasslike properties agree with those for amorphous solids, and the data suggest a plateau in the thermal conductivity above 40 K of \ensuremath{\sim}10 mW ${\mathrm{cm}}^{\ensuremath{-}1}$${\mathrm{K}}^{\ensuremath{-}1}$. A large maximum in $\frac{C}{{T}^{3}}$ at 14 K can be represented by two Einstein terms (44.1 and 25.0 ${\mathrm{cm}}^{\ensuremath{-}1}$), and the fitted Debye temperature (391 K) agrees well with the elastic value (396 K). A review of the glasslike properties observed in ferroelectric-type materials is given, and it is concluded that glasslike behavior is intimately associated with a spontaneous polarization (on one or two sublattices), irrespective of domain walls or ceramic grain boundaries.

Effect of temperature-dependent energy-level shifts on a semiconductor's Peltier heat

Abstract: The Peltier heat of a charge carrier in a semiconductor is calculated for the situation in which the electronic energy levels are temperature dependent. The temperature dependences of the electronic energy levels, generally observed optically, arise from their dependences on the vibrational energy of the lattice (e.g., as caused by thermal expansion). It has been suggested that these temperature dependences will typically have a major effect on the Peltier heat. The Peltier heat associated with a given energy level is a thermodynamic quantity; it is the product of the temperature and the change of the entropy of the system when a carrier is added in that level. As such, the energy levels cannot be treated as explicitly temperature dependent. The electron-lattice interaction causing the temperature dependence must be expressly considered. It is found that the carrier's interaction with the atomic vibrations lowers its electronic energy. However, the interaction of the carrier with the atomic vibrations also causes an infinitesimal lowering (approx.1/N) of each of the N vibrational frequencies. As a result, there is a finite carrier-induced increase in the average vibrational energy. Above the Debye temperature, this cancels the lowering of the carrier's electronic energy. Thus, the standard Peltier-heat formula,more » whose derivation generally ignores the temperature dependence of the electronic energy levels, is regained. This explains the apparent success of the standard formula in numerous analyses of electronic transport experiments.« less

Elastic constants of Se1−xTex solid amorphous alloys — the role of tellerium

Abstract: From the 15 MHz ultrasound velocity (shear and longitudinal) the elastic parameters ( E , G , K ) have been calculated, other than the Debye temperature θ m in solid Se 1− x Te x amorphous alloys in the temperature region containing the T g range. Assisted by results of optical spectroscopy and by shear viscosity tests an analysis has been carried out to explain the role of tellurium in these alloys. We find a double action played through the covalent bonds in the inside of the copolymeric chains and between them by means of the Van der Waals forces. Other results, from the literature, have been taken into account to support our hypothesis.

Contribution of optical phonons to the thermal expansion of α'-PdHx and α'-PdDx

Abstract: From thermal expansion measurements between 10 and 250K on alpha '-PdHx and alpha '-PdDx with 0.63

Phonon anomalies in ZrRuP

Abstract: The specific heat of a new orthorhombic structure modification of ZrRuP has been measured. The superconducting transition temperatureT c of this new phase, 3.76 K, is concluded to be much lower than that of the hexagonal modification (T c =13.0 K) due to the 30% stiffer lattice of the orthorhombic phase as determined by the Debye temperature. The high- and low-T c phases of ZrRuP are found to have nearly identical densities of states at the Fermi energy.

Indirect transitions in angle-resolved photoemission

Abstract: Until now almost all the angle-resolved photoemission experiments have been interpreted in a direct-transition model. We show for the first time that in the case of metals with low Debye temperature indirect transitions dominate the photoemission spectra, and to obtain $E(\stackrel{\ensuremath{\rightarrow}}{\mathrm{K}})$ it is necessary to work at low temperature.

Temperature and volume dependence of the thermal conductivity of solid neon

Abstract: The thermal conductivity $\ensuremath{\kappa}$ of solid natural neon has been measured by the linear-flow method for specimens isobarically frozen from the dense-fluid phase within a high-strength steel cell. By crossing the fusion curve at several different pressures to as high as 7 \ifmmode\times\else\texttimes\fi{} ${10}^{3}$ bars, crystalline samples with molar volumes between 11.16 and 13.35 ${\mathrm{cm}}^{3}$/mole were grown, and for each the isochoric variation of $\ensuremath{\kappa}$ vs $T$ was determined at a set of temperatures in the experimentally accessible range between 5 and 40 K. The large magnitude of $\ensuremath{\kappa}$ and reproducibility of the results demonstrate that the present method of preparation and manipulation of solid neon consistently yields good-quality specimens. An analysis utilizing the zero-degree limit of the Debye temperature ${\ensuremath{\Theta}}_{0}$ to account for all volume dependence indicates that the array of data, when expressed in terms of the resistive mean free path, may be rendered into a single function of the inverse reduced temperature $\frac{{\ensuremath{\Theta}}_{0}}{T}$. The exponential variation of this common curve over more than 2 orders of magnitude is characteristic of three-phonon umklapp scattering and thereby gives support to Peierls's model of heat transport in dielectric crystals. More recent first-principles theoretical calculations are in qualitative agreement with experiment but yield conductivities somewhat below the observed values.

Study of the Kondo effect and intrinsic electrical conduction in titanium diboride

Abstract: Electrical resistivity data for seven dense polycrystalline TiB2 samples are reported. The data, which extend from 4.2 to 300 K, all show resistivity minima in the 34 – 47 K range and this is attributed to the Kondo effect. Although the residual resistivity values varied by only a factor of about 2, the strength of the Kondo effect changed by a factor of 15. These differences are related to the effects of processing variables. The ideal resistivity of TiB2 was calculated from the measurements and was found to vary about as T5 at low temperatures. These values can be adequately described by the Bloch–Gruneisen equation, and the characteristic temperature obtained from resistivity, 720 K, is in reasonably good agreement with the Debye temperature from specific heat measurements. A comparison of the electronic scattering part of the Bloch–Gruneisen constant shows that TiB2 is a somewhat better conductor than Ti and the electronic band structures of ZrB2 and Zr help to explain this difference.

Pressure Dependence of the Melting Point of Al

Abstract: The temperature dependence of the mean-square displacement for Al is quantitatively calculated from first principles. The Debye temperature at higher and lower temperatures is also estimated using Debye's model. Then, using the volume dependence of the mean-square displacement, the pressure effect on the melting temperature of Al is studied by Lindeman's melting law, and the melting curve obtained increases as function of the compressed volume.

Quantum theory of light-interstitial hopping

Abstract: The light-interstitial hopping process is reviewed by taking a statistical viewpoint of the latticetrap integral. The validity of applying the central-limit theorem to the integral is tested by the Lindeberg-Feller and Liapounov conditions. Both are satisfied in the high-temperature limit. At low temperatures, the factor $\frac{\ensuremath{\hbar}{\ensuremath{\omega}}_{D}}{{E}_{a}}$ becomes decisive for the effectiveness of the closed-form Gaussian solution which shows a ${T}^{6}$ rate law below 0.1 of the Debye temperature. The conditions are used to investigate several systems.

Temperature dependence of the thermal expansivity of polymer crystals: Linear chain model

Abstract: A linear chain model is used to calculate the thermal expansivities of polymer crystals from room temperature down to liquid-helium temperature. Because of restraint by strong covalent forces, vibrations along the chains give a negligible contribution. Vibrations transverse to the chains cause the length projected along the chain direction to decrease. The expansivity along the chain direction, αc∥ is therefore negative, and has temperature dependence characterized by the low Debye temperature of transverse vibrations. These vibrations, through a cubic term in the interchain van der Waals potential, also cause a positive expansivity, αc⟂ perpendicular to the chain direction. The theoretical predictions for αc∥ and αc⟂ agree quite well with experimental data over the wide temperature range under consideration.

Variable temperature 57 Fe Mössbauer studies on polymers of vinylferrocene and 1, 1′-divinylferrocene

Abstract: Variable temperature57Fe Mossbauer spectra have been recorded in the range 80–300 K for a number of low molecular weight amorphous polymers containing ferrocene units. These include samples of polyvinylferrocene, polydivinylferrocene by anionic initiation and polydivinylferrocene by cationic initiation. A similar non-linear temperature dependence of InA was observed for all the polymers, although they contain ferrocene units in different structural arrangements. A Debye model was extended to include intramolecular vibrations, and a fit to the experimental data was obtained. However, the model did not yield satisfactory fitting parameters. The observed behaviour of the experimental data could be accounted for by assuming that each macromolecule vibrates within an anharmonic potential.

Contributions to the heat capacity of solid molybdenum in the range 300-2890 K

Abstract: An analysis has been made of contributions to the heat capacity of Mo, with a special examination of the effect of the formation of vacancies near the melting point. Literature values of the heat capacity at constant pressure CPwere fitted to a polynomial. Using recent measurements of the velocity of sound at high temperature and literature data of the coefficient of expansion, the dilation correction was made to CPto obtain the heat capacity at constant volume CV. This heat capacity was taken to consist only of independent contributions from electron excitations (CVE), harmonic lattice vibrations (CVH), anharmonic lattice vibrations (CVA), and the formation of vacancies (CVV). Three models of CVE(free electron, band theory, and electron-photon) have been used to calculate the electronic contribution, and an examination of the results indicates that the electron-phonon model is the best. CVHis assumed to be given by the Debye model, with a single Debye temperature. Thus, the excess heat capacity CVEX= CV-CVE-CVHis taken as equal to (CVA+CVV), where CVAis linear with temperature (CVA=A T), and we have fitted the values of CVEXto determine the values of A and the energy and entropy of formation of vacancies which give the best fit. The anharmonic contribution is positive. The energy of vacancy formation is 100,000 J · mol−1, in agreement with estimates by Kraftmakher from CPdata. The entropy of formation is 11.6 J · mol−1 · K−1. The concentration of vacancies at the melting point (2890 K) is calculated to be 6.3%.

Mossbauer study of the lattice dynamics of pyrite

Abstract: The Mossbauer-effect spectra of a polycrystalline sample of natural pyrite (FeS2) have been measured in the temperature range 290-430K. On the basis of the centre shift and f' as a function of temperature the plus and minus second moments of frequency of the thermal vibrations of Fe atoms have been established: omega (2)=(5.68+or-0.18)*1013 and omega (-2)=(4.35+or-0.18)*1013 s-1. The ratio of these moments (1.3+or-0.1) corresponds to the Debye model with theta D=568+or-20K. The anisotropy of the Fe atom thermal vibrations at room temperature is represented by the mean-square amplitudes (z2)=(0.14+or-0.08)*10-22 m2, where the z axis is identified with the (111) crystallographic direction and (x2)=(y2)=(0.30+or-0.05)*10-22 m2. The detection of this anisotropy by the Mossbauer methods is difficult owing to the small value of the asymmetry of the lines.

Phonon frequencies and Debye temperature of copper

Abstract: The phonon frequencies at low temperature and the temperature variation of the Debye temperature of copper have been calculated using a two-parameter model. The model satisfies the Cauchy relation and the symmetry requirements of the lattice, and the lattice is in equilibrium without recourse to external forces. The theoretical phonon frequencies along the principal symmetry directions and the Debye temperature of copper exhibit good agreement with the available neutron scattering and calorimetric measurements.

Vibrational and configurational contributions to the thermodynamics of metallic solutions

Abstract: We have developed a solution model for the thermo-dynamics of metallic systems that is composed of three contributions beyond the regular solution model. The contribution due to the nonrandomness is based upon a two-term expansion of the Guggenheim statistical mechanical model. There is a vibrational contribution that is treated as being an alloying effect on the Debye temperature. In fitting this model to the data in Hultgren et al. it was necessary to include a third term that represented a bias, the precise nature of which could not be determined. It was possible to select fixed values for the three parameters that represent these effects, along with an individual interaction energy for each system, that provided a satisfactory fit of the majority of the solution data in Hultgren et al.

A Semiquantum Liquid and a New Ordered Phase of 4He Adsorbed in Y Zeolite

Abstract: A fluidity and a quantum effect of a new helium 4 system, unsaturated 4 He adsorbed in a narrow void channel of Y-zeolite crystal, have been studied by measuring the heat capacity. In the case of the quantity adsorbed n =0.445 ×10 -3 mol/g, the heat capacity C is proportional to the temperature, i.e. C = n α T , in the condition T c (=3.25 K)\( \leqq T \lesssim 9\) K, and it reduces suddenly below T c . The coefficient α is 2.2 J/K 2 /mol. The experimental result shows that the state above T c is a semiquantum liquid such as bulk 4 He which remains liquid to much lower temperatures than the Debye temperature. Below T c , the result indicates the presence of an ordered state.

Dynamics of the dielectric relaxation process in some dichlorotoluenes

Abstract: The molecular dynamics of 2,6-, 2,4- and 3,4-dichlorotoluenes has been studied by measurements in the GHz region and in the temperature range 293–323 K of the real and imaginary parts of the complex dielectric permittivity in the pure liquid and in benzene solution. For all three isomers a single absorption band and a similar relaxation mechanism have been found both in the pure liquid and in solution. The results obtained have been interpreted according to the Debye model.

X-Ray investigations of BaLaGa3O7 single crystals

Abstract: X-ray investigations have been carried out on single crystals of BaLaGa3O7. Debye temperature as well as thermal expansion coefficients were determined, and values of which are respectively Es wird uber Rontgenuntersuchungen an BaLaGa3O7 berichtet. Gemessene Debye-Temperatur und thermische Ausdehnung sind

Debye characteristic temperatures of Nb3Os, Nb3Pt and Nb3Au

Abstract: Determination des temperatures de Debye et des facteurs de Debye-Waller a partir de resultats experimentaux et de donnees de la litterature

Physical basis of temperature dependence of strength in polymers

Abstract: The Zhurkov equation for long-term strength, σ(T, τ), is presented in the form σ(T, τ) = E(T, τ)e∗E0l/(κE0), where E(T, τ) is Young's modulus as a function of temperature and time, E0 is the modulus averaged over the sample volume, E0l is the value of the modulus at the crack tip (both at 0 K), e∗ is that value of deformation for which the interatomic bonds loose their stability and begin to break, and κ is the stress concentration factor. Reasons for the deviations from linearity in the temperature dependence of strength have been investigated (at a fixed value of time-to-break, τ=const.), which are observed in the temperature region T⩽≡D/3 and T≌Tg (≡D is the Debye temperature and Tg the glass transition temperature). It has been established that the stress concentration factor does not vary in these regions (κ=const.); the deviations from linearity are explained by changes in the thermal expansion coefficient in these temperature intervals.