Showing papers on "Debye model published in 1989"
TL;DR: In this paper, the elastic constants of single-crystal corundum, α-Al2O3, up to 1825 K (1.75 times the Debye temperature, θD) have been measured using a new device, the rectangular parallelepiped resonance method.
Abstract: Elastic constants of single-crystal corundum, α-Al2O3, up to 1825 K (1.75 times the Debye temperature, θD) have been measured using a new device, the rectangular parallelepiped resonance method. This device uses a long, thin alumina buffer rod, which separates the transducer from the specimen and enables us to pick up the resonance vibration of the specimen at very high temperature. The elastic stiffness constants C11 and C33 show a large decrease, while C12 and C13 only slightly decrease with temperature. C44 decreases linearly with temperature, and C14 is almost constant in the measured range of temperature. The isotropic elastic parameters were calculated by means of Voigt, Reuss, and Hill averaging schemes, enabling us to analyze the high-temperature elastic properties of corundum. The present elastic data also enable us to determine the thermodynamic parameters of corundum by combining them with the existing data on thermal expansivity and heat capacity. We find that (1) the evidence for anharmonicity in the thermal pressure is quite small, and the volume dependence of the thermal pressure diminishes above 1400 K; (2) the Gruneisen parameter decreases slightly with T at constant P above the Debye temperature; (3) the isothermal Anderson-Gruneisen parameter approaches the value of the pressure derivative of the isothermal bulk modulus at high temperature; and (4) the parameter q = (∂lnγ/∂lnV)T also approaches the value 1 at high temperature.
192 citations
TL;DR: It is found that the normalized-melting--temperature versus normalized-pressure curves accurately satisfy the linear relationship for Al, Ag, Au, Cs, Cu, K, Na, Pt, and Rb and provides a sensitive tool for detecting phase transitions.
Abstract: A new method for the analysis of the experimental data for the pressure dependence of the melting temperature of metals is presented. The method combines Lindemann's law, the Debye model, and a first-order equation of state with the experimental observation that the Grueneisen parameter divided by the volume is constant. It is observed that, based on these assumptions, in the absence of phase transitions, plots of the logarithm of the normalized melting temperature versus the logarithm of the normalized pressure are straight lines. It is found that the normalized-melting--temperature versus normalized-pressure curves accurately satisfy the linear relationship for Al, Ag, Au, Cs, Cu, K, Na, Pt, and Rb. In addition, this technique provides a sensitive tool for detecting phase transitions.
51 citations
TL;DR: In this article, a linear relationship is established between the actual melting temperature of 15 fluorides and oxides with perovskite structure and the quantity M V 2 3 Θ D 2, where M, V and ΘD are respectively the mean atomic mass, the molar volume and the Debye temperature.
48 citations
TL;DR: Examining copper as a pressure calibrant for extended x-ray-absorptionfine-structure measurements of solids under pressures ranging from 0 to10 GPa shows that, for copper, only nearest-neighbor distances and second cumulants (EXAFS Debye-Waller factors) must be taken into account.
Abstract: We examine copper as a pressure calibrant for extended x-ray-absorption fine-structure (EXAFS) measurements of solids under pressures ranging from 0 to 10 GPa Great care must be exercised both in the theoretical formulation of EXAFS and in the data analysis in order to achieve the high precision required to make copper a useful pressure marker From the first-shell k-space data, phase and amplitude information is extracted both with the ratio method and from fitting parameters with the help of theoretically calculated central-atom phase shifts [B-K Teo and P A Lee, J Am Chem Soc 101, 2815 (1979)] and curved-wave backscattering phase shifts and amplitudes [A G McKale et al, J Am Chem Soc 110, 3763 (1988)] Both techniques yield practically identical results confirming the reliability of the phase and amplitude tabulations But both techniques suffer from the ambiguity that the results depend on how many EXAFS parameters are kept variable It is shown that, for copper, only nearest-neighbor distances and second cumulants (EXAFS Debye-Waller factors) have to be taken into account Then pressures can be determined with an accuracy of about 05 GPa We also present two models for the pressure dependence of the second cumulant: (1) a correlated Debye model along with simple parametrizations of the isothermal equation of state and the Gr\"uneisen parameter, and (2) a model for the calculation of the moments of the nearest-neighbor distance distribution from an expansion to third order of the potential energy Both models confirm our data analysis
46 citations
TL;DR: The electronic diffusivities in the stable i phases of Ga-Mg-Zn and Al-Cu-Li are an order of magnitude greater than those observed in previously reported icosahedral alloys, suggesting that the transport properties of some i phases resemble those of crystalline, rather than glassy, alloys.
Abstract: We report specific-heat and resistivity results on icosahedral (i) Ga-Mg-Zn, Al-Cu-Fe, and Al-Cu-V alloys. The electronic densities of states at the Fermi level obtained for the stable i phases of Ga-Mg-Zn and Al-Cu-Fe are substantially less than those found in metastable i phases (Al-Cu-V, Al-Cu-Mg, and Al-Mg-Zn), as small as one-sixth of their free-electron values. Implications for the structural stability of i phases will be discussed. Magnetic-susceptibility and specific-heat measurements on Al-Cu-Fe i phases prepared by rapid quenching and from annealing of the conventionally cast sample show an increased magnetic behavior in the melt-spun sample with respect to the annealed sample. Also, similar to earlier results on Al-Cu-Li i alloys, the Debye temperature of the melt-spun sample is found to be reduced in comparison with the annealed one. These differences in physical properties are attributed to structural differences in the samples. The electronic diffusivities in the stable i phases of Ga-Mg-Zn and Al-Cu-Li are an order of magnitude greater than those observed in previously reported icosahedral alloys, suggesting that the transport properties of some i phases resemble those of crystalline, rather than glassy, alloys.
44 citations
TL;DR: In this paper, a simple model has been considered to obtain the reversible temperature dependence of the static structure factors S(q) for liquid metals for Na, K, Mg, Zn, Al and Pb.
Abstract: A simple model has been considered to obtain the reversible temperature dependence of the static structure factors S(q) for liquid metals. The measured values of S(q) near the melting point have been utilised to obtain the same at elevated temperatures for Na, K, Mg, Zn, Al and Pb. The notion of Debye temperature in liquid metals has been discussed. The principal peak heights of S(q) computed at the melting temperature have also been discussed in the light of Verlet's freezing rule. The electrical resistivity and thermo-electric power of these metals have been computed as a function of temperature. The success and failure of the Ziman formula have been critically assessed.
34 citations
TL;DR: It is found that the shape and behavior of surface scattering rainbows observed in this system are best accounted for by a quantum mechanical treatment of the Ar-surface interaction.
Abstract: Diffraction has been observed in the scattering of Ar from a 2H-W(100) surface. Results are found to be consistent with an effective surface corrugation amplitude of about 0.05 A, which is similar to values obtained for He and Ne diffraction from this surface. The temperature dependence yields a surface Debye temperature of /similar to/400 K. We also find that the shape and behavior of surface scattering rainbows observed in this system are best accounted for by a quantum mechanical treatment of the Ar-surface interaction.
32 citations
TL;DR: In this paper, magnetic susceptibility and specific heat measurements on polycrystalline samples of the 30 K superconductor Ba0·6K0·4BiO3 were reported.
28 citations
TL;DR: Mesure de la chaleur specifique de la poudre de YBa 2 Cu 3 O 7-x frittee, de haute purete, et de la capacite calorifique sous des champs magnetiques superieures a 3 T.
Abstract: We have measured the specific heat of high-purity, sintered YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}} powder. The sample was characterized by x-ray diffraction and Raman scattering. We measured its dc magnetic susceptibility as a function of magnetic field and temperature to verify its superconducting properties and found the transition temperature {ital T}{sub {ital c}} to be 90 K. The heat capacity was determined between 2 and 10 K in magnetic fields up to 3 T. The low-temperature specific heat exhibited a linear term (with a zero-field coefficient of 4.37 mJ/mol K{sup 2}) and a cubic term (corresponding to a Debye temperature of 375 K) that varied with field. Raman-effect data obtained on our sample showed that less than one-third of the linear term could arise from the presence of BaCuO{sub 2}. Using Ginzburg-Landau theory in the London limit, we calculated the field dependence of the specific heat of a uniaxially symmetric superconductor. We were unable to account for the reduction of the cubic term, and we were able to account for only part of the enhancement of the linear term with increasing field in terms of the kinetic energy of the electrons circulating around the magnetic vortices (fluxoids). Perhaps the reasonmore » that Ginzburg-Landau theory fails to account for our data is that the superconducting order parameter does not change slowly over a length characteristic of the atomic structure of this material.« less
26 citations
TL;DR: In this paper, the Gibbs energy, the enthalpy and the entropy from 300 to 4000 K were derived from experimental phonon dispersion curves, and the elastic constants c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c33, c34, and c33 were derived.
Abstract: We use recent theoretical results on electrons and phonons in technetium and the properties of the entropy Debye temperature θS to perform a new evaluation of the thermodynamic properties of technetium. In particular, we present values for the Gibbs energy, the enthalpy and the entropy from 300 to 4000 K. We present the entropy at 298.15 K, 0S = 33.0(± 0.3) J mol−1 K−1, the entropy of fusion ΔfS = 13.7(± 1) J mol−1K−1, the melting temperature Tf = 2430(± 30) K and the liquid heat capacity CP(1) = 47(± 2) J mol−1 K−1. From experimental phonon dispersion curves we derive the elastic constants c11 = 433 GPa, c12 = c13 = 199 GPa, c44 = 117 GPa and c33 = 470 GPa with an uncertainty of about 3%. These values give the elastic limit Debye temperature (at room temperature) θE = 440K. Our derived entropy Debye temperature (at 298 K) is θs = 320(± 3) K and the electron-phonon mass enhancement parameter is λ = 0.68.
21 citations
TL;DR: In this paper, the specific heat of a single phase (Bi, Pb) 2 Sr 2 Ca 2 Cu 3 O 10+ y sample with orthorhombic structure was measured over the temperature range 90 to 135 K.
Abstract: The specific heat of a single-phase (Bi, Pb) 2 Sr 2 Ca 2 Cu 3 O 10+ y sample with orthorhombic structure has been measured over the temperature range 90 to 135 K, revealing a jump of ΔC = 5.3 J / mol · K at T c =107 K and corresponding to the value of ΔC T c = 49.5 mJ/mol·K 2 . The Sommerfeld constant γ =34.6 mJ / mol · K 2 was estimated from the weak-coupling BCS limit. The Debye temperature can be obtained by fitting to a Debye specific heat function with θ = 418 K .
TL;DR: The elastic constants of Bi2Sr2CaCu2O8+y ceramic have been determined for the first time from ultrasonic velocity measurements as mentioned in this paper, indicating a possible structural change or a phase transition.
Abstract: The elastic constants of Bi2Sr2CaCu2O8+y ceramic have been determined for the first time from ultrasonic velocity measurements. Near 200 K both longitudinal and transverse wave velocities show noticeable anomalous behaviour, indicating a possible structural change or a phase transition. The strong hysteresis and the bulk modulus softening are also remarkable. A Debye temperature theta D= 250 K is estimated. The derived elastic constants of this material are substantially smaller than those of YBa2Cu3O7-x and BaTiO3, which is attributed to the weakly interacting multilayers along the very large c axis of Bi2Sr2CaCu2O8+y. However, the Poisson ratios of these perovskite ceramics are quite close, suggesting similar interatomic bonding.
TL;DR: In this article, temperature-dependent Ag and Pd K-edge EXAFS spectra were measured for SiO2-supported small Ag and pd metal clusters, showing that the surface metal atoms of the clusters have shallower and more anharmonic interatomic potentials.
Abstract: Temperature-dependent Ag and Pd K-edge EXAFS (extended X-ray absorption fine structure) spectra were measured for SiO2-supported small Ag and Pd metal clusters. EXAFS analysis using the cumulant expansion technique has revealed that the Debye temperature is significantly lower and the themal expansion coefficient is larger for the small metal clusters compared with the corresponding bulk metal. These observations can be explained by the simple concept that the surface metal atoms of the clusters have shallower and more anharmonic interatomic potentials.
TL;DR: Etude de deux relations proposees recemment pour la temperature critique T c d'etablissement de the diffusion renforcee par le rayonnement, dans le melange ionique.
Abstract: Etude de deux relations proposees recemment pour la temperature critique T c d'etablissement de la diffusion renforcee par le rayonnement, dans le melange ionique. On montre que la relation lineaire entre T c et l'energie de cohesion Ecoh est en accord avec l'experience, tandis que la relation entre T c et la temperature de Debye ne l'est pas
TL;DR: DWF's refined from ${F}_{m}$ using calculated shell-by-shell partial structure factors yield good agreement with earlier results derived from low-order reflections but not with ab initio shell-model calculations.
Abstract: Evidence is presented for nonrigid thermal vibrations of crystal-bound silicon atoms, using an extensive set of measured structure factors ${F}_{m}$ accurate to 0.1%. A model allowing for a different Debye-Waller factor (DWF) for each electronic shell is found to fit all ${F}_{m}$ well with four such factors. DWF's refined from ${F}_{m}$ using calculated shell-by-shell partial structure factors yield good agreement with earlier results derived from low-order reflections but not with ab initio shell-model calculations. Also, no evidence is found for an anharmonic term in the atomic potential.
TL;DR: In this article, thermal expansivities from 1 to 300 K were reported for three ceramic Y-Ba-Cu-O samples and the Debye temperatures were found to be 322, 422, and 435 K for samples with a few percent excess CuO, high purity but large, elongated grains, and high purity and small grains, respectively.
Abstract: Thermal expansivities from 1 to 300 K and heat capacities from 1 to 80 K are reported for three ceramic Y-Ba-Cu-O samples. The limiting Debye temperatures, ${\mathrm{FTHETA}}_{0}$, were found to be 322, 422, and 435 K for samples with (1) a few percent excess CuO, (2) high purity but large, elongated grains, and (3) high purity and small grains, respectively. A similar range of ${\mathrm{FTHETA}}_{0}$'s for superconducting samples is found in the literature, which suggests an insensitivity of superconductivity in ceramic Y-Ba-Cu-O to lattice properties (that is, to ${\mathrm{FTHETA}}_{0}$). The expansivity data for each of these samples showed scatter and instability just below ${T}_{c}$ and between 180 and 200 K, which, in general but not in detail, may be inherent to ceramic Y-Ba-Cu-O. The expected decrease in the expansivity on warming through ${T}_{c}$ was not unambiguously observed. The expansivity data suggest lattice softening below ${T}_{c}$, with, however, normal temperature dependences for the Debye FTHETA's and the Gr\"uneisen parameters \ensuremath{\gamma}. The magnitudes and signs of the low-temperature expansivities and \ensuremath{\gamma}'s are characteristic of two sources for both the low-temperature ``electronic'' and ``anomalous'' contributions to the thermodynamic properties. The relatively small values for the lattice \ensuremath{\gamma}'s correspond to ``normal'' pressure dependences for the elastic constants of these materials, including the bulk modulus, and support the use of bulk moduli derived from x-ray measurements rather than from ultrasonic experiments.
TL;DR: In this paper, γ-ray and neutron diffractometry is used to measure the attenuation factors due to thermal and static mean atomic displacements on a large temperature range: 5 to 1464 K in a Fe-19.5 at% Al alloy.
Abstract: γ-ray and neutron diffractometry are used to measure the attenuation factors due to thermal and static mean atomic displacements on a large temperature range: 5 to 1464 K in a Fe–19.5 at% Al alloy. High-temperature measurements are made on a single crystal. A large static mean atomic displacement: 0.0032 nm is found and a Debye temperature of (476 ± 22) K at 0 K.
Nous avons mesure par diffraction de rayons γ et de neutrons les facteurs d'attenuation dus aux deplacements atomiques statiques et dynamiques, sur une large plage de temperature (5 a 1464 K) dans un alliage Fe–19,5 at% Al. Les measures a haute temperature ont ete effectuees sur un monocristal. Nous trouvons un deplacement statique moyen assez important (0,0032 nm) et une temperature de Debye a 0 K de (476 ± 22) K.
TL;DR: The low temperature specific heat of BaFCl, BaFBr and BaFI shows a behaviour typical for insulators with a T3 temperature variation in the lowest temperature range.
TL;DR: Specific heat, resistivity, and magnetic measurements on a series of glassy aluminum alloys containing up to 93 at.
Abstract: We have performed specific heat, resistivity, and magnetic measurements on a series of glassy aluminum alloys containing up to 93 at. % Al. In addition to the fact that we can extrapolate from our data the values of superconducting temperature (>5 K) and resistivity (approx.20 ..mu cap omega.. cm) for amorphous Al, our results also provide evidence that significant softening of phonon modes (in the case of glassy Al/sub 92/La/sub 8/, a drastic reduction is observed with a Debye temperature of approx.242 K as compared with approx.428 K in crystalline Al) is responsible for the enhanced superconductivity of up to 8.5 K observed in some metastable Al alloys. For glassy Al alloys containing a few at. % Gd, the maximum in specific heat is observed at more than twice the magnetic ordering temperature defined by the cusp in susceptibility, markedly different from that of canonical spin glasses. The structural differences between these glassy Al alloys and other magnetic alloys are pointed out. Ce in glassy Al shows a large valence instability, yielding an effective moment of 1.37..mu../sub B/ at room temperature to approx.0.25..mu../sub B/ at 5 K, which was not observed previously in an amorphous metal.
TL;DR: In this article, the temperature dependence of the thermal conductivity of some fluorite structured compounds, namely, CaF 2, BaF 2, SrF 2 and PbF 2 have been evaluated at and below the Debye temperature.
TL;DR: In this paper, the temperature dependence of the EXAFS spectrum was investigated on the normal and SMSI states of Rh/TiO{sub 2} and Pd/TiOsub 2} catalysts.
Abstract: The temperature dependence of EXAFS spectrum was investigated on the normal and SMSI states of Rh/TiO{sub 2} and Pd/TiO{sub 2} catalysts The mean square relative displacement (MSRD) of metal-metal bondings of supported metal was derived by the analysis of EXAFS data with the cumulant expansion technique, and the Debye temperature was estimated from the temperature dependence of MSRD The Debye temperature or Rh-Rh bond of Rh/TiO{sub 2} catalyst was found to be higher by 38 K in its SMSI state in comparison with the normal state This difference was shown to be due to the significant increase of the surface Debye temperature of Rh metal particles A similar results was obtained for Pd/TiO{sub 2} catalyst These facts were concluded to support the decoration model for the SMSI state
TL;DR: In this article, it is conjectured that the energy flow is assisted or triggered by the long wave length phonons via anharmonic coupling giving rise to the dependence on direction.
Abstract: Measurements of anisotropic thermal diffusivity and of the velocity of hypersound have been performed at room temperature on one set of stretched low density polyethylene (crystallinityv
c
=0.4). The elastic anisotropy increases with the stretching ratio λ as does the heat conduction anisotropy. It is argued that the heat conduction cannot be traced back to properties of extended crystalline and amorphous phases. The reason for the latter is the smallness of the microphases giving rise only to non-propagating modes. Phonon focussing of superstructure phonons together with the wavelength dependence of their scattering can explain the observed effects. From the parameters found and from a semiquantitative description of the temperature dependence down to 4 K it is concluded that the main transport could be due to hopping mechanisms where the localized phonons may be fractons. It is conjectured that the energy flow is assisted or triggered by the long wave length phonons via anharmonic coupling giving rise to the dependence on direction.
TL;DR: Inelastic electron scattering experiments in a transmission electron microscope provide a probe of core electron excitations that have binding energies below 2 keV, and that are localized within submicron diameter sample volumes as discussed by the authors.
Abstract: Inelastic electron scattering experiments in a transmission electron microscope provide a probe of core electron excitations that have binding energies below 2 keV, and that are localized within submicron diameter sample volumes. Extended electron energy‐loss fine‐structure measurements which show the variation with temperature of the mean squared relative displacement of aluminum yield a localized measurement of the Debye temperature which is in excellent agreement with macroscopic measurements.
Journal Article•
TL;DR: In this paper, the role of vibrational contribution to free enthalpy and interstitial distribution is discussed in accordance with the central atom model in Fe1-xNixNy austenite with 0
Abstract: Mossbauer Spectra of Fe1-xNixNy austenite with 0
TL;DR: In this paper, the atomic structure of Si(111) √3×√3-In was investigated by low energy ion scattering spectroscopy with 1 keV He+ ions.
Abstract: The atomic structure of Si(111) √3×√3-In was investigated by low energy ion scattering spectroscopy with 1 keV He+ ions. Azimuthal angular distributions of scattered ions suggest that the In atoms are located in the three-fold sites on top of the second layer Si atoms. Comparing the experimental distribution as a function of the incident angle with the calculation using the Thomas-Fermi-Moliere potential taking of the thermal vibrations, the Debye temperature of the surface In atoms and the bond length between the In atom and the first layer Si atom were estimated.
TL;DR: For two samples of the sintered superconducting oxides BiSrCaCuO with the stoichiometry 1112 the specific heat and electrical resistance were measured.
TL;DR: In this paper, the authors used the local density approximation with the augmented plane wave method to calculate the EOS and the electronic band structures of solid fcc krypton under high pressures and have estimated the metallization pressure to be 316 GPa.
TL;DR: In this article, the propagation velocities of longitudinal and transverse elastic waves in polycrystalline praseodymium have been measured by a pulsed ultrasound method at pressures up to 84 kbar at room temperature.
Abstract: The propagation velocities of longitudinal and transverse elastic waves in polycrystalline praseodymium have been measured by a pulsed ultrasound method at pressures up to 84 kbar at room temperature. The density, elastic constants, and Debye temperature are calculated as functions of pressure. The anomalies found in the pressure dependence of the sound velocities in praseodymium, as in lanthanum, which was studied previously, reflect an additional anharmonicity of longitudinal and transverse acoustic phonons at two phase transitions which occur in the intervals 12–50 and 66–80 kbar. The experimental results on lanthanum and praseodymium are discussed on the basis of a pseudopotential method and in the Friedel model with 6s-5d electronic transitions. Estimates show that the observed anomalies in the elastic characteristics of both of these metals are caused by an accelerated 6s-5d “flow” of electrons. Similar anomalies should be observed in caesium II near the first-order isomorphic electronic 6s-5d transition at 42.2 kbar.
TL;DR: In this article, the dispersion and absorption of third-order nonlinear electric susceptibilities in liquids as well as their time-transients are analyzed applying Smoluchowski's equation of rotational diffusion in the form proposed by Debye in his known dielectric relaxation theory of dipolar liquids.
Abstract: Dispersion and absorption of third-order nonlinear electric susceptibilities in liquids as well as their time-transients are analyzed applying Smoluchowski's equation of rotational diffusion in the form proposed by Debye in his known dielectric relaxation theory of dipolar liquids. On the basis of solutions derived by method of statistical perturbation calculus, the real and imaginary components of nonlinear susceptibility are plotted versus the frequency of the externally applied cosine reorienting field.