Showing papers on "Debye model published in 1979"
TL;DR: In this article, the authors studied the thermal conductivity of non-metallic crystals at temperatures comparable to or higher than the Debye temperature, where the dominant carriers of thermal energy are phonons and the dominant scattering mechanism is the intrinsic phonon-phonon scattering.
Abstract: Publisher Summary This chapter reviews the thermal conductivity of nonmetallic crystals at temperatures comparable to or higher than the Debye temperature. It deals with the intrinsic behavior of such pure crystals at high temperatures. In such crystals, the dominant carriers of thermal energy are phonons and the dominant scattering mechanism to be considered is the intrinsic phonon–phonon scattering. This is a small section of the much larger problem of the thermal conductivity of nonmetallic solids and clearly it neglects possible heat transport by photons, charge carriers, polarons, and magnons. It also neglects other possible phonon scattering mechanisms such as isotopes, impurities, vacancies, charge carriers, dislocations, grain boundaries, and crystal boundaries. It presents the absolute value of the thermal conductivity, K, as determined by phonon–phonon scattering, the temperature dependence of K, the volume dependence of K, the change in K upon melting, and the minimum value of K. The chapter discusses a composite curve for the thermal conductivity versus temperature of pure KCl measured at a constant pressure of, say, one atmosphere.
734 citations
TL;DR: In this paper, the Debye theory of lattice vibrations has been examined in terms of the lattice vibrational spectra, and it is demonstrated that heat capacities of silicates show large deviations from the behavior expected from Debye theories, and that the observed thermodynamic deviations in minerals probably arise from four effects not included in Debye model: anisotropy of elastic parameters, dispersion of acoustic waves toward Brillouin zone boundaries, optic vibrations in excess of Debye spectrum at low frequencies, and optic vibrations at frequencies much greater than the debye cutoff frequency predicted
Abstract: This is the first of a series of five papers in which the thermodynamic properties of minerals are interpreted in terms of lattice vibrational spectra. In this paper, measured heat capacities for minerals are examined in terms of the Debye theory of lattice vibrations, and it is demonstrated that heat capacities of silicates show large deviations from the behavior expected from Debye theory. The underlying assumptions of Debye theory are critically reviewed, and it is shown that the observed thermodynamic deviations in minerals probably arise from four effects not included in the Debye model: anisotropy of elastic parameters, dispersion of acoustic waves toward Brillouin zone boundaries, optic vibrations in excess of the Debye spectrum at low frequencies, and optic vibrations at frequencies much greater than the Debye cutoff frequency predicted by acoustic measurements. Each of the four effects influences the heat capacity in a particular temperature range: anisotropy, dispersion and low-frequency optic vibrations are important at low temperatures (0°K to ∼100°K); high-frequency vibrations are important at higher temperatures. It is necessary to include all four effects in a generalized lattice vibrational model for minerals; such a model is developed in papers 2-5 of this series. The minerals included in this study are halite, periclase, brucite, corundum, spinel, quartz, cristobalite, silica glass, coesite, stishovite, rutile, albite, microcline, jadeite, diopside, enstatite, tremolite, talc, muscovite, forsterite, zircon, kyanite, andalusite, sillimanite, pyrope, grossular, andradite, spessartine, almandine and calcite.
249 citations
TL;DR: In this paper, the theory of thermal expansion by Gruneisen is improved and the acquired data are analyzed to derive the harmonic and anharmonic parameters of manganosite MnO.
Abstract: Thermal expansion of manganosite MnO at temperatures between 20°C and 850°C has been carefully determined by a dilatometric technique. The theory of thermal expansion by Gruneisen is improved and the acquired data are analyzed to derive the harmonic and anharmonic parameters of MnO. Gruneisen's parameter γ is 1.56, Debye temperature is 441 K, and pressure derivative of bulk modulus is 7. The volume expansion coefficient is 34.3×10-6/K at 20°C and 47.1×10-6/K at 850°C; almost the same in magnitude to those of MgO and FeO.
129 citations
TL;DR: In this paper, the authors used the extended x-ray absorption fine structure (EXAFS) of Cu at temperatures from 10 to 683K to evaluate the disorder term and compare it with theory.
Abstract: The extended x-ray absorption fine structure (EXAFS) of Cu at temperatures from 10 to 683K has been used to evaluate the EXAFS disorder term and compare it with theory. The change in disorder for different temperatures was extracted from the slopes of $\mathrm{ln}(\frac{{\ensuremath{\chi}}_{1}}{{\ensuremath{\chi}}_{2}})$ plots and by using a least-squares curve-fitting program. The values of the disorder parameter vs temperature are compared to a pure Debye model without correlation, a Debye model with correlation, and a model incorporating the measured phonon spectrum of Cu. The pure Debye model predicts too large an effect, whereas there is good agreement between the experimental data and either of the other two theories. This indicates that models which account for the correlated motion of the absorbing and scattering atom can give $\ensuremath{\sigma}$ values which are in good agreement with those determined experimentally.
105 citations
TL;DR: In this paper, a matrix-inversion method was used to calculate the intensities of normally incident low-energy electrons diffracted from GaAs(110) and compared with measured intensities.
Abstract: Dynamical calculations of the intensities of normally incident low-energy electrons diffracted from GaAs(110), performed using a matrix-inversion method, are compared both with earlier kinematical calculations and with measured intensities. The insensitivity of the calculated intensities to the choice of exchange potential and vacuum-solid boundary conditions is displayed. Surface lattice vibrations are found to be adequately described by the bulk Debye temperature. We consider second- and third-layer structural distortions as well as top-layer reconstructions. This analysis leads to the selection of the most probable surface structure for GaAs(110) as one in which the top layer undergoes both a rigid rotation of 27.4\ifmmode^\circ\else\textdegree\fi{} and a 0.05-\AA{} contraction with the As atoms moving outward and the Ga atoms inward, giving a relative vertical shear of 0.65 \AA{}. In the second layer the Ga moves outward 0.06 \AA{} and the second-layer As moves inward 0.06 \AA{}. The dynamical analysis reported herein shows no evidence for third-layer distortions.
81 citations
TL;DR: In this article, a very fast television method with automatic thermal diffuse background subtraction for both the (1 × 1) and c(2 × 2) surface structure phases was used to evaluate the surface Debye temperature.
58 citations
TL;DR: In this paper, the size dependence of the melting temperature of fine particles is discussed, on the basis of the Debye model and the Lindemann law, by phenomenologically taking into account surface phonon softening.
Abstract: The size dependence of the melting temperature of fine particles is discussed, on the basis of the Debye model and the Lindemann law, by phenomenologically taking into account surface phonon softening.
53 citations
TL;DR: In this paper, the elastic constants of tourmaline crystals of known chemical composition have been measured by the ultrasonic phase-comparison method and the Debye temperature of the tourmalines derived from these constants is 785°K.
Abstract: Elastic constants of tourmaline crystals of known chemical composition have been measured by the ultrasonic phase‐comparison method. The values in 1012 dyn/cm2 are C11=3.050, C33=1.764, C44=0.648, C66=0.984, C14=−0.06, and C13=0.51. The Debye temperature of the tourmaline derived from the elastic constants is 785 °K.
50 citations
TL;DR: In this paper, an investigation of the dependence on temperature of the extended X-ray absorption fine structure (EXAFS) above the K-edges of Cu and Co in the metals and above the k-edge of Rb and Sr in the compounds RbCl, SrS, SrF2 and SrCl2 has been performed, and the values of the correlated mean square relative displacements of nearest-neighbour atoms derived from EXAFS spectra show a good agreement with those calculated from a Debye model.
Abstract: An investigation of the dependence on temperature of the extended X-ray absorption fine structure (EXAFS) above the K-edges of Cu and Co in the metals and above the K-edges of Rb and Sr in the compounds RbCl, SrS, SrF2 and SrCl2 has been performed. For Cu, Co, RbCl and SrS, the values of the correlated mean square relative displacements of nearest-neighbour atoms derived from EXAFS spectra show a good agreement with those calculated from a Debye model. The experimental data obtained are also compared with available data for mean square displacements of the individual atoms calculated from more-refined lattice vibrational models and with Debye-Waller factors used in X-ray diffraction experiments.
50 citations
TL;DR: In this paper, the two-dimensional solid compressibility obtained from an adsorption isotherm near 42 K agrees reasonably well with a simple calculation using empirical ArAr potentials.
41 citations
TL;DR: In this article, the 4.2 K isotherm of H2 has been determined and compared to the extrapolated low-pressure isochore of Anderson and Swenson (AS).
Abstract: Isochores of solid hydrogen and deuterium have been measured for melting line pressures up to 2000 bar. These are corrected to correspond to para-H2 and ortho-D2. The 4.2 K isotherm of H2 has been determined and compared to the extrapolated low-pressure isochore of Anderson and Swenson (AS). Deviations have led us to reanalyze the AS data. The 4.2 K isotherm and the isochores are used, with the aid of a Mie-Gruneisen analysis, to determine P-V-T data for these solids up to 25 kbar. An analysis is presented which enables a determination of P-V-T-C
1 for all values of C
1, the ortho-para concentration. Results, including the Debye temperature, Gruneisen constant, and bulk modulus, are presented both in tabulated and graphical form. We also present what we feel to be the best of the 4.2 K, zero-pressure molar volumes of disordered H2 and D2 as a function of C
1. Our measurements show no indication of the premelting phase transition reported in recent Russian literature and a possible explanation is presented.
TL;DR: In this article, the internal and free energies of a two-dimensional one-component plasma model, in the high-temperature Debye approximation, are investigated, and a domain of validity for this model is discussed.
Abstract: The internal and free energies of a two-dimensional one-component plasma model, in the high-temperature Debye approximation, are reinvestigated, and a domain of validity for this model is discussed.
TL;DR: The low temperature specific heats of two isomorphous Laves compounds, TiBe2 and ThMg2, have been measured in this article, and the results for both compounds are discussed in regards to the theory of Enz and Matthias.
TL;DR: The singlecrystal elastic constants of vanadium and vanadium with 1.07, 1.85, and 3.46% oxygen have been measured ultrasonically over the temperature range 4.2-300 K as mentioned in this paper.
Abstract: The single‐crystal elastic constants of vanadium and of vanadium with 1.07, 1.85, and 3.46 at.% oxygen have been measured ultrasonically over the temperature range 4.2–300 K. These compositions cover virtually the complete composition range of the terminal solubility at the temperatures of the experiments. Monotonic but nonlinear increases with increasing oxygen content were observed for all three of the directly measured constants, and the compositional trends were found to be relatively insensitive to temperature so the same trends should persist at elevated temperatures. A Debye temperature of 401.2 K was evaluated for 0 K. The monotonic hardening of vanadium by oxygen addition contrasts with previously published results for niobium, where oxygen additions produced a slight initial softening followed by a hardening.
TL;DR: In this article, a new expression for the DW factor corrected for a stationary part of the gas-surface interaction potential is derived kinematically and semi-classically by the use of a Morse potential.
TL;DR: The generalized Langevin method for gas-solid scattering is combined with a London-Eyring-Polanyi-Sato type potential function in order to allow calculation of collisions and simple reactions at the gas solid interface.
TL;DR: In this paper, the systematics of elementary atom-solid energy exchange processes are studied based on the generalized Langevin equation (GLE) classical trajectory method, where the solid dynamics is parameterized by two bulk properties, a Debye frequency ωD and a transverse to longitudinal sound velocity ratio Rs.
Abstract: Model studies of the systematics of elementary atom–solid energy exchange processes are presented. The studies are based on the generalized Langevin equation (GLE) classical trajectory method [S. A. Adelman and J. D. Doll, J. Chem. Phys. 64, 2375 (1976)] and on a full isotropic continuum elastic treatment of both bulk and surface solid atom velocity response functions ? (t). Within both bulk (BEM) and surface (SEM) elastic models, the solid dynamics is parameterized by two bulk properties, a Debye frequency ωD and a transverse to longitudinal sound velocity ratio Rs. The Debye model used in earlier GLE simulations is a specialization of the BEM, Rs=1.0, and thus does not include surface effects, e. g., Rayleigh waves, accounted for in the SEM. The main results of the trajectory studies are as follows: Gas–solid energy transfer efficiency within the BEM depends very sensitively on Rs (for fixed ωD). For physical Rs values ∼0.2–0.6, BEM energy transfer is often much larger than Debye energy transfer. SEM en...
TL;DR: In this paper, the electrical resistivity ρ, thermal conductivity κ, and thermoelectric power S have been measured for two bare K specimens between 80 and 330 K. The data fully support the main conclusions of an earlier preliminary study by Cook and Laubitz.
Abstract: The electrical resistivity ρ, thermal conductivity κ, and thermoelectric power S have been measured for two bare K specimens between 80 and 330 K. The data fully support the main conclusions of an earlier, preliminary study by Cook and Laubitz. The Lorenz function L = κρ/T does not approach the Sommerfeld value L0 with increasing temperature. Both the magnitude and temperature dependence of L–L0 indicate the presence of an added term Wee in the thermal resistivity, due to electron–electron scattering. Such scattering also affects S. It is shown that the data for K, together with published values of B = Wee/T for Na, Rb, and the noble metals, form a consistent picture of electron–electron scattering in the monovalent metals above the Debye temperature.
TL;DR: A new perovskite material has been found, Pb (Mn12 Ta12)O3 which has the smallest thermal diffusivity of any known, densified solid at low temperatures (9 × 10 −3 < k < 5 × 10−2 cm2 sec−1 between 4-10 K) as discussed by the authors.
TL;DR: In this article, measurements of the specific heat at low temperatures were reported for single-crystal samples of K2ReCl6, K2IrCl6 and K2PtCl6.
Abstract: Measurements of the specific heat at low temperatures are reported for single-crystal samples of K2ReCl6, K2IrCl6, and K2PtCl6 The data for K2IrCl6 give strong evidence that in addition to the well-established antiferromagnetic phase transition occurring at a temperature T
N = 301 ± 001 K, a displacive phase transition occurs at T
c= 283 ± 002 K Although the compounds are structurally similar, the background specific heats at low temperatures are significantly different A careful analysis of these data plus previous data for K2OsCl6 shows that the reason for the large differences in the lattice specific heats is the presence of low-lying rotary modes A Debye temperature of 911 ± 05 K is deduced and effective rotary mode frequencies of 286, 291, 300, and 379 cm−1 are found for K2ReCl6, K2OsCl6, K2IrCl6, and K2PtCl6, respectively
TL;DR: In this paper, the Mossbauer spectrum of FePS3 in powder form between 125 K and 450 K was analyzed and attributed to the Goldanskii-Karyagin effect and lattice anisotropy was found to be ∼ 1.4.
Abstract: Mossbauer studies have been performed on FePS3 in powder form between 125 K and 450 K. The Mossbauer spectrum consists of an asymmetric doublet, ratio∼0.93 at room temperature. The asymmetry is attributed to the Goldanskii-Karyagin effect and the lattice anisotropy is found to be ∼1.4, with the largest vibrations parallel to thec⋆ axis of the monoclinic unit cell. The Debye temperature is ∼200 K.
TL;DR: The model proposed by the present author (this journal 28, 309 (1978) as discussed by the authors, which explained successfully the temperature independent mobilities above about the Debye temperature θ, predicts that the drift velocity becomes saturated in the high-electric-field region when T≲θ, and that it makes a peak in the low-field one with an intermediate minimum when T « θ.
TL;DR: In this article, the dependence of specific heat of ( La 0.8 Ca 0.2 ) MnO 3+ y on oxygen deficiency was measured between 110 and 300 K and it was found that the oxygen deficiency tends to increase the Debye temperature in these substances at temperatures around room temperature.
TL;DR: The Debye temperature of Fe-Ni alloys was obtained from measurements of the X-ray integrated intensity and the electrical resistivity at low temperatures from 4 to 300 K as discussed by the authors.
TL;DR: In this article, a model for the lattice dynamics of covalent crystals was developed, which is used to calculate the phonon dispersion relations of diamond, silicon, and germanium at all the irreducible points of the first Brillouin zone and to calculate phonon density of states, lattice specific heats, and Debye characteristic temperatures.
Abstract: To study the lattice dynamics of covalent crystals, a model which, in addition to central (two‐body) forces, involves unpaired forces of the type of D.C. Gazis, F. Herman, and R.F. Wallis [Phys. Rev. 119, 533 (1960)] has been developed. The model is used to calculate the phonon dispersion relations of diamond, silicon, and germanium at all the irreducible points of the first Brillouin zone and to calculate phonon density of states, lattice specific heats, and Debye characteristic temperatures. The R. Brout [Phys. Rev. 113, 43 (1954)] sum rule for ionic crystals as extended by H.B. Rosenstock [Phys. Rev. 129, 1959 (1963)]; H.B. Rosenstock and G. Blanken [Phys. Rev. 145, 546 (1966)] for diamond and zincblende crystals has also been verified by calculating the compressibilities of the above crystals. The model satisfies all the symmetry requirements of the perfect crystals. Results show reasonably good agreement with available experimental data.
TL;DR: In this article, it was shown that thermoelectric refrigeration might become an effective technique at or below a temperature of several mK. This is because the heat conduction due to the lattice vibrations becomes very small at these low temperatures.
TL;DR: In this paper, the contribution of bare electrons and harmonic phonons to the heat capacity of platinum was evaluated from the available data on the band structure and the phonon spectrum of platinum.
TL;DR: The specific heat of ThC0,75, ThC 0,6N0,4 and ThP samples has been measured in the range 2-15 K as mentioned in this paper.
Abstract: The specific heat of ThC0,75, ThC0,6N0,4 and ThP samples has been measured in the range 2-15 K. From the results, the Debye temperature θD and the density of states at the Fermi level NF of the three compounds have been calculated. NF increases with vacancy content in ThC1-x and is minimal for ThC0,6N0,4 compared to ThC and ThN.