Showing papers on "Debye model published in 1970"
TL;DR: In this article, the elastic constants of poly crystalline and single-crystal MgO were measured in a gas high-pressure system over a temperature range from 300°K to the Debye temperature of the material.
Abstract: MgO has been measured again. Most measurements of the elastic properties of materials, interesting to geophysics, have been made as a function of pressure at room temperature or as a function of temperature at atmospheric pressure. A lapped seal between a buffer rod and sample has made it possible to use ultrasonic interferometry to 1000°K and 10 kb. The elastic constants of poly crystalline and single-crystal MgO were measured in a gas high-pressure system over a temperature range from 300°K to the Debye temperature of MgO. Data from the polycrystalline specimen indicated large effects of temperature on the pressure derivatives. These data did not agree with the results obtained from single-crystal measurements. Upon remeasuring the ceramic sample it becomes apparent that the data are not reproducible after the sample has been cycled to high temperature and pressure. Additional sintering, deformation of the individual grains, and recrystallization take place, which change the properties of the sample. These problems and the problems of sintering isotropic aggregates of theoretical density limit the usefulness of this widely used procedure.
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280 citations
TL;DR: In this paper, the elastic constants of single crystals of ZnTe and ZnSe (zincblende type) have been determined over the temperature range 77°-300°K by means of the ultrasonic pulse-echo method.
Abstract: The elastic constants of single crystals of ZnTe and ZnSe (zinc‐blende type) have been determined over the temperature range 77°–300°K by means of the ultrasonic pulse‐echo method. The velocity of the longitudinal and two transverse waves propagated in the [110] direction showed 1%–1.4% increase at 77°K from the room‐temperature values and as a result, the elastic constants of both crystals showed 2%–3.5% increase at 77°K from the room‐temperature values. From the low‐temperature elastic constants, the Debye temperature was calculated to be 225.3°K for ZnTe and 278.5°K for ZnSe, respectively.
113 citations
TL;DR: In this article, the phonon frequencies in 512000 equally spaced points in an octant of the Brillouin zone were calculated using the extended shell model with both ions polarizable and including next-nearest-neighbor interactions.
Abstract: In a series of earlier papers, experimental results on phonon dispersion relations at 80 \ifmmode^\circ\else\textdegree\fi{}K in NaCl, KCl, RbCl, and RbF have been reported. We now present calculations on these halides using the extended-shell-model approach with both ions polarizable and including next-nearest-neighbor interactions. The parameters obtained in a least-squares fit to the experimental points in the symmetry directions have been used to calculate the phonon frequencies in 512000 equally spaced points in an octant of the Brillouin zone, whereby, after sorting these into intervals of width $\ensuremath{\Delta}\ensuremath{\omega}=2\ifmmode\times\else\texttimes\fi{}{10}^{11}$ rad ${\mathrm{sec}}^{\ensuremath{-}1}$, the frequency spectrum was obtained. From these spectra the variation of the Debye temperature with temperature was also calculated. The agreement with results from specific-heat measurements for NaCl and KCl is quite satisfactory at low temperatures.
78 citations
TL;DR: In this article, a Debye model is used to describe the phonon spectrum of the solid. But, it appears almost impossible to extract from a kinematical model reliable quantitative information about the average thermal displacements of the surface and bulk ion cores.
Abstract: The evaluation of the elastic scattering differential cross section of electron scattering from a planar surface of a vibrating lattice is reduced to the solution of a set of coupled algebraic equations for the associated scattering amplitude. This reduction is valid both for overlapping potentials (thus removing the restriction of previous analyses to muffin-tin potentials) and for the nonspherical potentials associated with ion cores at solid surfaces. The algebraic equations are solved using a double-diffraction analysis of the inelastic-collision model. Surface scatterers are taken to be geometrically equivalent but electronically and vibronically inequivalent to those in the bulk. A Debye model is used to describe the phonon spectrum of the solid. Numerical results are presented for a hypothetical fcc metal with the lattice parameters of aluminum. Thermal expansion alters the energies of peaks in the elastic intensity profiles ($I\ensuremath{-}V$ curves), whereas the thermal vibration of the ion cores alters the intensities of the peaks. The temperature dependence of the peak heights can be described by the kinematic model in which it is attributed to the Debye-Waller factor associated with an "effective" Debye temperature. However, the multiple scattering of the electron from the lattice causes these "effective" Debye temperatures to be related to the parameters of the model (e.g., bulk and surface electron---ion-core scattering phase shifts, the inelastic-collision mean free path, bulk- and surface-model Debye temperatures) in a complicated fashion. Although the trends evident in the dependence of the effective Debye temperature on the model parameters can be rendered plausible, it appears almost impossible to extract from a kinematical model reliable quantitative information about the average thermal displacements of the surface and bulk ion cores.
67 citations
TL;DR: In this article, the degree of long range order in the γ′-phase of the nickel-aluminum system was determined as a function of temperature by means of X-rays.
Abstract: The degree of long range order in the γ′-phase of the nickel–aluminum system was determined as a function of temperature by means of X-rays. The measurements were carried out on {h00} single crystals, using a high-temperature vacuum X-ray diffractometer. Two compositions were investigated: stoichiometric Ni3Al and an off-stoichiometric nickel-rich alloy. Complete long-range order was present to within 65°C of the melting point, the highest temperature measured. Line breadth measurements indicated a large, temperature independent anti-phase domain size. From the intensity variation of the 400 reflection with temperature, a Debye temperature of 360°K was deduced. The linear coefficient of thermal expansion between 25 and 800°C was found to be 15 x 10−6 per °C.
61 citations
TL;DR: In this article, the specific heat of polymethyl methacrylate and polystyrene has been measured using the heat pulse method between 0.5 and 4.3°K.
Abstract: Measurements of the specific heat of polymethyl methacrylate and polystyrene have been performed using the heat pulse method between 0.5 and 4.3°K. Above 2°K the specific heat is about double that expected on the basis of the Debye theory and acoustic measurements. Below 2°K the experimental data approach the Debye value. The excess specific heat can be fit by two Einstein modes. For polymethyl methacrylate the Einstein temperatures are 4.9 and 17.5°K containing 0.014% and 1.0% of all modes, respectively. For polystyrene the corresponding modes are 5.5 and 16°K with strengths of 0.038% and 1.8% respectively. The data support a model of pendant side groups near voids capable of independent low frequency torsional oscillations. The barrier to internal rotation of the pendant group is estimated.
57 citations
TL;DR: In this article, the frequency-wave-vector dispersion relation for the normal modes of vibration of terbium at room temperature has been measured by means of slow-neutron inelastic scattering techniques.
Abstract: The frequency-wave-vector dispersion relation for the normal modes of vibration of terbium at room temperature has been measured by means of slow-neutron inelastic scattering techniques. The triple-axis spectrometer at the Oak Ridge high flux isotope reactor was used, mostly in the constant-$Q$ mode of operation. Phonon frequencies for wave vectors along the principal symmetry directions have been determined and, in addition, measurements of phonon frequencies along the boundaries of the Brillouin zone and along a more general direction are reported. The data have been fitted with a Born-von K\'arm\'an force model which includes interactions out to the eighth nearest neighbor. The interactions have been assumed to be general (tensor) out to the fourth neighbor and axially symmetric beyond. The model has been used to calculate a frequency distribution function $g(\ensuremath{
u})$ and related quantities such as the lattice specific heat and Debye temperature.
48 citations
TL;DR: In this article, a simplified version of the generalized shell model, involving a variable number of parameters was fitted to the experimental dispersion curves, from an eleven parameter model the frequency spectrum, the Debye temperature and other physical quantities have been calculated.
Abstract: Phonon dispersion relations in RbI have been obtained by inelastic scattering of thermal neutrons. Measurements were performed in the crystallographic symmetry directions Δ, Σ, A, and Z at 80 °K and some selected zone boundary phonons were also measured at 300 °K. A simplified version of the generalized shell model, involving a variable number of parameters was fitted to the experimental dispersion curves. From an eleven parameter model the frequency spectrum, the Debye temperature and other physical quantities have been calculated.
41 citations
TL;DR: The band motion (tunneling) of small polarons in thermally activated energy levels of molecules is postulated to be the conduction mechanism is some organic and biological semiconductors and the compensation law is derived from this model.
Abstract: The band motion (tunneling) of small polarons in thermally activated energy levels of molecules is postulated to be the conduction mechanism is some organic and biological semiconductors. The compensation law is derived from this model. The characteristic temperature is shown to be related to the Debye temperature.
41 citations
TL;DR: In this paper, the static magnetic susceptibilities of simplified model vibronic systems where non-Kramers paramagnetic ions in triplet ground state interact either with localized tetragonal modes of vibration with sharp frequency spectrum at ω (localized model), or with TRSs composed of the superposition of phonons with continuous frequency spectrum (Debye model) are calculated in a rigorous way.
Abstract: Static magnetic susceptibilities of simplified model vibronic systems where non-Kramers paramagnetic ions in triplet ground state interact either with localized tetragonal modes of vibration with sharp frequency spectrum at ω (localized model), or with tetragonal modes composed of the superposition of phonons with continuous frequency spectrum (Debye model) are calculated in a rigorous way. The susceptibility is simply expressed in terms of a temperature dependent reduction factor γ L ( T ) for the localized model, or γ D ( T ) for the Debye model, which diminishes the effective Curie constant and makes the susceptibility deviate from the Curie-Weiss law. The theory explains the characteristic features of the susceptibilities of dilute solid solutions of UO 2 in ThO 2 measured by Slowinski and Elliott and by Comly, for example, the convex curvature of reciprocal susceptibility vs. temperature plot. The values of parameters determined to fit the observed susceptibilities are reasonable in orders of magnitude.
40 citations
TL;DR: The thermal shift of the Mossbauer ray in rhombohedral Fe${\mathrm{F}}_{3} gives a weak indication of a magnetization-dependent Debye temperature.
Abstract: The thermal shift of the $^{57}\mathrm{Fe}$ M\"ossbauer $\ensuremath{\gamma}$ ray in rhombohedral Fe${\mathrm{F}}_{3}$ gives a weak indication of a magnetization-dependent Debye temperature. A small isomer-shift discontinuity exists at the transition to cubic structure at high temperature.
TL;DR: In this article, the effects of compositional changes on parameters used in the theory of superconductivity to describe the transition temperature have been investigated and it has been shown that changes in transition temperature with changes in composition cannot be explained simply on the basis of an alteration of the density of states except in the case of binary Nb-Ta alloys.
Abstract: The electronic specific heat coefficient, γ, the Debye temperature, θD, and the superconducting transition temperature, Tc, have been measured for binary b.c.c. alloys of V, Nb, and Ta. These results have been used to investigate the effects of compositional changes on parameters used in the theory of superconductivity to describe the transition temperature. It has been shown that changes in transition temperature with changes in composition cannot be explained simply on the basis of an alteration of the density of states except in the case of binary Nb-Ta alloys. It is concluded that, for V-Nb and V-Ta alloys, changes in the interaction responsible for superconductivity also govern changes in the transition temperature.
TL;DR: Silicates thermal conductivity-Debye temperature relationship from thermal conductivities and acoustic data, applying to earth conductivity measurements, is discussed in this article, where the authors apply this relationship to Earth conductivity measurement.
Abstract: Silicates thermal conductivity-Debye temperature relationship from thermal conductivity and acoustic data, applying to earth conductivity measurements
TL;DR: In this paper, the Debye-Waller B k factors for the alkali halides NaF, NaCl, NaBr, NaI, KCl, KBr in the temperature range 5 to 295°K were calculated by sampling eigendata given by fitted shell models at 64,000 points in the Brillouin zone.
TL;DR: In this paper, the temperature dependence of the intensities of the Bragg peaks in the intensity plots gives values for the Debye temperature as a function of primary electron energy, in order to deduce the thermal expansion coefficient for the surface layers normal to the surface.
Abstract: Measurements of the temperature dependences of the intensities and energies of LEED peaks in the intensity plots for the specular beam from a (111) copper surface are reported. An analysis is made, for the peak shifts as a function of temperature, in order to attempt to deduce the thermal expansion coefficient for the surface layers normal to the surface. Several additional effects are accounted for but the shifts appear to be dominated by an unknown process and no deductions are drawn concerning the expansion coefficient. The temperature dependence of the intensities of the Bragg peaks in the intensity plots give values for the Debye temperature as a function of primary electron energy. The results indicate that this is not strongly dependent on diffraction condition. From the Debye temperature, the ratio of the mean square vibrational amplitude of the surface atoms perpendicular to the surface to that for the bulk is found to be 1.9 ± 0.1, in agreement with theoretical predictions.
TL;DR: In this article, the normal state specific heat coefficient of pure lead and four dilute PbTl and PbBi alloys has been measured in the temperature range 1.0-2.3 K.
Abstract: The normal-state specific heats of pure lead and four dilute PbTl and PbBi alloys have been measured in the temperature range 1.0-2.3 K. The fractional rate of change of the electronic specific-heat coefficient $\ensuremath{\gamma}$ with respect to the number of conduction electrons per atom was found to be 0.25\ifmmode\pm\else\textpm\fi{}0.06 for PbTl alloys and 0.51\ifmmode\pm\else\textpm\fi{}0.04 for PbBi alloys. When changes in the electron-phonon enhancement factor as determined from tunneling measurements are included, good agreement is found between the measured changes in $\ensuremath{\gamma}$ and those expected from the rigid-band model. Semiquantitative calculations indicate that changes in the electron-phonon enhancement factor may also account for the apparent discrepancy between previous experimental results and the rigid-band model in noble-metal alloys. The Debye temperature was found to decrease for both lead alloy series.
TL;DR: The phenomenon of splitting of states by the electron-phonon interaction studied in an electron spin resonance experiment is used to determine the Debye temperature of cubic ZnS.
TL;DR: In this paper, measurements of the lattice parameter, electronic specific heat, magnetic susceptibility, and Debye temperature are presented in the Ni-Ir alloy system from 0 to 100 at.% Ir.
Abstract: Measurements of the lattice parameter, electronic specific heat, magnetic susceptibility, and Debye temperature are presented in the Ni-Ir alloy system from 0 to 100 at.% Ir. This system forms an uninterrupted series of solid solutions over the entire concentration range. No ordering nor decomposition could be observed after annealing for several days at temperatures between 500 and 1100\ifmmode^\circ\else\textdegree\fi{}C. The system develops a sharp peak in the electronic specific heat versus concentration at 85 at.% Ni, a concentration slightly higher than the critical concentration determined magnetically (81 at.% Ni). A weak anomaly was found also in the ${T}^{3}$ term of the low-temperature specific heat around the same concentration. Generally, no lowtemperature anomaly, such as was predicted by the early paramagnon theories, was detected down to 1.5\ifmmode^\circ\else\textdegree\fi{}K. The susceptibility was measured on the paramagnetic side only up to 79 at.% Ni, where a spontaneous moment develops at low temperature.
TL;DR: In this article, a sonic resonance technique was used to investigate the room-temperature elastic and anelastic properties of physically mixed U0.8PU0.2O2 as a function of density, stoichiometry, and cation homogeneity.
Abstract: A sonic resonance technique was used to investigate the room-temperature elastic and anelastic properties of physically mixed U0.8PU0.2O2 as a function of density, stoichiometry, and cation homogeneity. The effect of porosity on the elastic moduli was linear and is described by E=2102.7 (1–2.03P)± 13.5 Kbars for the Young's modulus, G=823.5(1–2.05P)± 9.1 kbars for the shear modulus, and B= 1584.8(1–1.89P)± 59.1 kbars for the bulk modulus, where P is the volume fraction porosity. Poisson's ratio was 0.28 and was not a function of porosity. The Debye temperature of U0.8Pu0.2O2 computed from the Young's and shear moduli for theoretically dense specimens was 379°K. Variation of the O/M ratio from 1.968 to 2.006 produced no significant change in either the damping capacity or the elastic moduli of single-phase 80%UO2-20% PuO2 solid solutions. An approximate 24% decrease of the room-temperature Young's and shear moduli and an approximate increase by a factor of 14 in the internal friction were observed with gross modifications of plutonium cation homogeneity. Preliminary results suggest that internal friction measurements might be used to assay the homogeneity of UO2-PuO2 solid solutions.
01 Jan 1970
TL;DR: In this paper, the effects of these lattice modifications on various aspects of the Mossbauer spectra, together with a summary of the relevant literature, are examined and discussed.
Abstract: Major modifications of the crystal lattice occur in microcrystals. This paper presents an examination of the effects of these lattice modifications on various aspects of Mossbauer spectra, together with a summary of the relevant literature. Examples discussed include the following: Surface vibrational modes and partial decoupling from the supporting medium can modify the Debye-Waller factor. The Debye temperature is affected by the “internal pressures” (which can be as much as ±200 kbar) corresponding to the changes in the lattice spacing created by surface effects. These internal pressures can result in isomer shifts. Various chemical valence states may be preferentially stabilized in microcrystals. The finite crystallite size leads to superparamagnetism. Transition temperatures, such as those of the Neel and Morin transitions, may be shifted through the internal pressures. Surface and core distortions through unsaturated chemical bonds and internal pressures can lead to changes in the electric-quadrupole interaction.
TL;DR: In this article, the oxide structures on niobium and the effective Debye temperature at the Nb surface were reported, as well as some observations of oxide structures and their properties.
TL;DR: In this article, the Debye temperature was compared with an exact numerical integration by computer to complement a paper by Konti and Varshni, and the results showed that the latter was more accurate than the former.
Abstract: Approximation methods for calculating the Debye temperature are compared with an exact numerical integration by computer to complement a paper by Konti and Varshni. Except for the alkali metals the...
TL;DR: In this article, a model for the band structure of TIBr and T1C1 has been outlined, based on an analysis of the optical spectra, pressure shifts and band structures of isoelectronic compounds.
Abstract: Measurements have been made on the optical absorption of freely mounted thin crystals of TIBr, and evaporated films of T1C1, TIBr and TlI, from room temperature down to 4°K. The shift with pressure to 6 kbars of the sharp excitonic features has been followed at 80°K and 274°K. All the exciton peaks move to lower energies with pressure, but the spin-orbit doublet moves at a slower rate than the other peaks. The pressure coefficient of the energy of the first exciton peak (minimum gap) rises sharply with temperature above the Debye temperature (ca. 130°K). From these measurements information on the electron lattice interactions and deformation potentials has been obtained. A model for the band structure of TIBr and T1C1 has been outlined, based on an analysis of the optical spectra, pressure shifts and band structures of isoelectronic compounds. We thank Trinity College for the award of a studentship to A. J. G.; Gonville and Caius College for a Research Fellowship to W. Y. L.; and the Science Rese...
TL;DR: In this paper, the influence of temperature and pressure on the recoilless fraction and the Mossbauer energy shift for the 9.3 keV transition of Kr 83m was evaluated using the Debye frequency distribution of the lattice vibrations of the Kr solid.
Abstract: The influence of temperature and pressure on the recoilless fraction and the Mossbauer energy shift for the 9.3 keV transition of Kr 83m is evaluated using the Debye frequency distribution of the lattice vibrations of the Kr solid. The contribution to the recoilless fraction due to the lattice anharmonicity is incorporated and the results are compared with the experiment. “Mossbauer characteristic temperature” \(\varTheta_{\text{M}}\) of 42°K is suggested for the Krypton solid. A strong correlation between the recoilless fraction and the density of the solid is exhibited.
TL;DR: In this article, the temperature dependence of the specular electron reflectivity of low-energy electrons from a Ni (001) surface has been investigated for two regions of different electron penetration, and a Debye temperature θ D = (415 ± 20)°K for Ni was determined.
TL;DR: In this paper, the shielding potential for a test charge in a plasma is derived for the case in which the velocity of the charge is much less than the thermal velocity, and it is shown that, although the inverse third-power term dominates at very large distances, the Debye term dominates over the very important region out to at least several Debye lengths.
Abstract: The shielding potential for a test charge in a plasma is derived for the case in which the velocity of the charge is much less than the thermal velocity. This potential is an analytical expression valid for any angle in space. The potential contains the Debye term and also a term which is due to the particle's motion. At large distances from the test charge the latter term asymptotically becomes proportional to the inverse third power of the distance. On the other hand, as the distance to the test charge approaches zero, this term vanishes and the potential becomes the Coulomb potential. It is shown that, although the inverse third-power term dominates at very large distances, the Debye term dominates over the very important region out to at least several Debye lengths.
TL;DR: In this article, an approximate fit to the data can be obtained on a Debye model, although it is not possible to conclude whether longitudinal or transverse modes dominate, and it is suggested this is also the case for all previous work on semiconductor alloys.
Abstract: Measurements have been made of the thermal conductivity of GaSb-InSb alloys at 300 K and over the whole range of concentration. The data are generally in good agreement with those of Woolley and Briggs and Kudman, Ekstrom and Seidel (1964, 1967). It is shown that an approximate fit to the data can be obtained on a Debye model, although it is not possible to conclude whether longitudinal or transverse modes dominate, and it is suggested this is also the case for all previous work on semiconductor alloys. The additional thermal resistance in the alloys is approximately proportional to the reciprocal relaxation time for defect scattering up to much higher defect concentrations than would be the case for a Debye model.
TL;DR: In this article, the dielectric constant of a binary system of t-butyl chloride and carbon tetrachloride was made in the entire composition range and in three different phases, the liquid, the fee solid, and the rhombohedral phases.
Abstract: Careful measurements of the dielectric constant of a binary system of t-butyl chloride and carbon tetrachloride were made in the entire composition range and in three different phases, the liquid, the fee solid, and the rhombohedral phases. The simple Debye theory applies to the liquid and the fee solid, giving an effective dipole moment of t-butyl chloride of 2.11±0.01 D whereas in the rhombohedral phase, it was 2.00±0.03 D. Molecular polarization shows no discontinuity between the vapor, the liquid, and the fee solid but there is a jump between the fee and the rhombohedral solids. The molecular rotation in the plastic rhombohedral phase is more hindered by 450 cal/mol than in the liquid or the fee phase. The 1:1 solid solution data were examined on the basis of the Onsager theory.