Showing papers on "Debye model published in 2004"

Role of electron–phonon coupling in thermal conductance of metal–nonmetal interfaces

Abstract: We theoretically show that the thermal conductance associated with electron–phonon coupling in a metal near a metal–nonmetal interface can be estimated as hep=Gkp, where G is the volumetric electron–phonon coupling constant and kp is the phonon or lattice thermal conductivity of the metal. The expression suggests hep≈1/T at temperatures comparable to the Debye temperature of the metal. The predicted values of hep fall within the range of conductance values experimentally observed (0.3–1 GW/m2 K), suggesting that it cannot be ignored, and could even play a dominant role at high temperatures. Predictions of the total thermal conductance, that include both electron–phonon and phonon–phonon interfacial conductances, show reasonable agreement in its temperature dependence with experimental data for TiN/MgO interfaces.

Temperature dependence of the force sensitivity of silicon cantilevers

Abstract: The resonance frequency $\ensuremath{\omega}$ and internal friction ${Q}^{\ensuremath{-}1}$ of the first eigenmode of microfabricated silicon cantilevers are measured in the temperature range of 15--300 K. The analysis shows that variation of Young's modulus is responsible for the temperature dependence of the resonance frequency, whereas the dependence of the geometrical dimensions can be neglected. Accordingly, the data can be fitted by the Wachtman equation, yielding a Debye temperature ${\ensuremath{\Theta}}_{D}=634\mathrm{K}.$ The temperature variation of internal friction ${Q}^{\ensuremath{-}1}$ is analyzed in terms of Zener's theory of thermoelastic damping. Due to the temperature dependence of the thermal expansion coefficient $\ensuremath{\alpha},$ thermoelastic damping is expected to vanish at 20 K and 125 K. A minimum of internal friction is observed at 20 K, whereas the minimum at 125 K appears to be hidden by other dissipation effects. A maximum of internal friction at 160 K is observed, which is an activation peak due to phonon scattering by atomic-scale defects. The best force sensitivity is achieved at 20 K, where a factor of 10 is gained compared to room temperature.

Properties of Ce-based bulk metallic glass-forming alloys

Abstract: We find that a family of $\mathrm{CeAlNiCu}$ alloy system can be readily cast into bulk glassy rods with up to $3\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ diameter. The $\mathrm{Ce}$-based bulk metallic glasses (BMG's) exhibit a wide supercooled region up to $78\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, very low glass transition temperature $({T}_{g}=359\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, and Debye temperature $({\ensuremath{\theta}}_{D}=144\phantom{\rule{0.3em}{0ex}}\mathrm{K})$. The glass formation, crystallization, glass transition, liquid behavior, and elastic and acoustic properties of the $\mathrm{CeAlNiCu}$ alloys are investigated. Ultrasonic measurements demonstrate that the $\mathrm{Ce}$-based BMG's are the softest in elastic moduli in known BMG's due to their very low glass transition temperature. The fragility parameter $(m)$ is determined to be 21, indicating the strong liquid behavior of the alloy concerning the temperature dependence of viscosity. A remarkable large softening of long-wavelength acoustic phonons in the BMG relative to its crystalline state is observed, and the phonon softening is attributed to its intrinsic microstructural features and strong liquid behavior.

Effect of TeO2 on the elastic moduli of sodium borate glasses

Abstract: Sodium borate glass containing tellurite as TexNa2−2xB4−4xO7−5x with x=0, 0.05, 0.15, 0.25 and 0.35 have been prepared by rapid quenching. Ultrasonic velocity (both longitudinal and shear) measurements have been made using a transducer operated at the fundamental frequency of 4 MHz at room temperature. The density was measured by the conventional Archimedes method. The elastic moduli, the Debye temperature, Poisson's ratio, and the parameters derived from the Makishima–Mackenzie model and the bond compression model have been obtained as a function of TeO2 content. The monotonic decrease in the velocities and the elastic moduli, and the increase in the ring diameter and the ratio Kbc/Ke as a function of TeO2 modifier content reveals the loose packing structure, which is attributed to the increase in the molar volume and the reduction in the vibrations of the borate lattice. The observed results confirm that the addition of TeO2 changes the rigid character of Na2B4O7 to a matrix of ionic behaviour bonds (NBOs). This is due to the creation of more and more discontinuities and defects in the glasses, thus breaking down the borax structure.

Soft bulk metallic glasses based on cerium

Abstract: CeAlNiCu alloys can be readily cast into glassy rods with up to 5mm in diameter. The Ce-based bulk metallic glasses (BMGs) exhibit a wide supercooled region up to 78K, very low glass transition temperature (Tg=359K), melting temperature (Tm=637K), and Debye temperature (θD=144K). Ultrasonic measurements demonstrate that these Ce-based BMGs are very soft, having the lowest elastic moduli in known BMGs. These features suggest that the “soft” BMGs are an ideal model system for investigating physical problems in glass transition, supercooled liquid and melt states, and have potential applications as a functional material as well.

Size effect of the resistivity of thin epitaxial gold films

Abstract: The temperature dependence of the electrical resistivity of thin, epitaxial, and flat (111)-oriented gold films with thickness between 2 and $50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ is investigated. The quality of these Au films is superior to epitaxial Au films grown on mica, therefore the investigation of well-defined thin films was possible. The experiments are analyzed within the frame of classical size-effect theories of the resistivity. It turns out that for thin films, the characteristic Debye temperature is strongly decreased as compared to the bulk value. In contrast to the more physically motivated approach of Soffer, the original model of Fuchs-Sondheimer describes the experimental data in a physically consistent way.

Extended x-ray-absorption fine-structure measurements of copper: Local dynamics, anharmonicity, and thermal expansion

Abstract: Extended x-ray-absorption fine-structure (EXAFS) of copper has been measured from 4 to 500 K and analyzed by the cumulant method, to check the effectiveness of EXAFS as a probe of local dynamics and thermal expansion. The comparison between parallel mean square relative displacements (MSRD) of the first four coordination shells has allowed detecting a significant deviation from a pure Debye behavior. The first-shell EXAFS thermal expansion is larger than the crystallographic one: the difference has allowed evaluating the perpendicular MSRD, whose Debye temperature is slightly larger than the one of the parallel MSRD, due to anisotropy effects. High-order first-shell cumulants are in good agreement with quantum perturbative models. The anharmonic contribution to the first-shell parallel MSRD amounts to less than 1.5 percent. The third cumulant cannot be neglected in the analysis, if accurate values of the first cumulant are sought; it cannot however be used to directly estimate the thermal expansion. The shape of the effective pair potential is independent of temperature; a rigid shift, partially due to the relative motion perpendicular to the bond direction, is however observed.

Existence of Temperature on the Nanoscale

Abstract: We consider a regular chain of quantum particles with nearest neighbor interactions in a canonical state with temperature T. We analyze the conditions under which the state factors into a product of canonical density matrices with respect to groups of n particles each and under which these groups have the same temperature T. In quantum mechanics the minimum group size n(min) depends on the temperature T, contrary to the classical case. We apply our analysis to a harmonic chain and find that n(min)=const for temperatures above the Debye temperature and n(min)proportional toT(-3) below.

Ultrasonic studies on network structure of ternary TeO2–WO3–K2O glass system

Abstract: Longitudinal and shear ultrasonic velocities were measured in different compositions of the glass system (TeO 2 ) 80 –(WO 3 ) (20− x ) –(K 2 O) x using pulse echo technique. Measurements were carried out at 6 MHz frequency and at room temperature. Elastic moduli and some other physical parameters such as, glass transition temperature, Debye temperature, softening temperature, and fugacity have been calculated. Results indicated that these parameters depend upon the alkali oxide modifier (K 2 O) content i.e., glass composition. Quantitative analysis has been carried out, in order to obtain more informations about the structure of these glasses, based on bond compression model, and ring deformation model, i.e., the cation-anion bond of each oxide.

Single-crystal elastic constants of Fe-15Ni-15Cr alloy

Abstract: Resonant ultrasound spectroscopy (RUS) and pulse-echo (PE) superposition techniques have been used to determine the three independent elastic-stiffness constants C11, C12, and C44 as a function of temperature for single crystals of 70Fe-15Ni-15Cr alloy. The values of the elastic moduli determined using RUS and PE are in very good agreement within the range of uncertainties. This particular ternary composition of Fe, Ni, and Cr undergoes an fcc-bcc structural phase transformation near 190 K resulting in a low-temperature ferromagnetic phase. The Debye characteristic temperature was determined to be 447 K from PE and 451 K from RUS measurements. The Zener elastic anisotropy A=2C44/(C11−C12) is nearly constant: A=3.53±0.16 in Fe-Ni-Cr alloys with similar compositions. For these alloys, only small variations are observed in the Gruneisen parameter, γ≈2.08, and in the Poisson ratio, v[hkl]=0.293±0.013.

Analysis of the intermolecular interaction of nanocomposites by THz spectroscopy

Abstract: Transmission and reflection measurements on polyamide nanocomposite films were performed in the THz frequency region, and the dielectric function was calculated using the Debye model to interpret the data. The relaxation time from the signal of orientation polarization due to the permanent dipole moments exhibits intermolecular interaction. In nanocomposites, the extreme increase of the interaction from polymer clay was first observed by THz spectroscopy. The essential interaction was thought to occur between the amide functional (−NH) group in polyamide-6 and the surface of the clay by considering the correlation with the results of infrared spectroscopy.

Structural analysis of alkali borate glasses

Abstract: This paper reports on the elastic properties of alkali borate glass systems (R 2 O–B 2 O 3 , R=K, Rb, Cs). The elastic moduli were calculated in terms of Makishima–Mackenzie model and a model by Bridge et al. The average cross-link density, number of network bonds per unit volume, average stretching force constant, atomic ring size, and the ratio K bc / K e , have been calculated and discussed according to bond compression model to analyze the borate anomaly. Young's modulus, packing density and Poisson's ratio have been calculated and analyzed according to Makishima–Mackenzie model. Debye temperature has been calculated and discussed in terms of the cross-link density of these glasses. The borate anomaly was discussed in terms of experimentally derived Debye temperature and theoretically calculated elastic moduli. The results showed good agreement between experimental and theoretical data for the borate anomaly representation.

Possibility of a superfluid phase in a Bose condensed excitonic state

Abstract: In the condensed excitonic phase of intermediate valent ${\mathrm{TmSe}}_{0.45}{\mathrm{Te}}_{0.55}$ the thermodynamic properties have been measured. The heat conductivity and the thermal diffusivity have been obtained between 300 K and 1.5 K and between ambient pressure and 17 kbar (1.7 GPa), as a first experiment of its kind. Pressure and temperature are used to navigate in three different phases of the material, the intermediate valent semiconducting phase, the condensed excitonic phase, and the intermediate valent metallic phase. In the condensed excitonic phase the heat conductivity \ensuremath{\lambda} increases strongly below about 20 K, suggesting a superfluid phase for the lowest temperatures. In a solid under equilibrium conditions this has never been seen before. Also the thermal diffusivity $a$ strongly increases below 20 K, giving evidence for second sound. The quotient $\ensuremath{\lambda}/\ensuremath{\rho}a$ represents the specific heat, which thus can be calculated, for the first time as a function of pressure. When entering the condensed excitonic phase under pressure and from high temperatures (100 K--250 K), the Dulong-Petit value of the specific heat drops precipitously to about half its value. Also this phenomenon is unprecedented. The entropy has been calculated from the heat capacity and the Debye temperature has been obtained as a function of pressure. In addition the longitudinal sound velocity has been measured under pressure and as a function of temperature. Entering the excitonic phase the sound velocity drastically increases by about a factor 2.

Beryllium's monocrystal and polycrystal elastic constants

Abstract: Using resonant-ultrasound spectroscopy, we measured beryllium’s elastic constants for both a monocrystal and a polycrystal Thus, we consider the monocrystal–polycrystal elastic-constant relationship for hexagonal symmetry Beside the Cij, we report the Debye characteristic temperature Θ and the Gruneisen parameter γ We comment on beryllium’s chemical bonding and its remarkably low Poisson ratio

Thermal expansion of Mg2SiO4 ringwoodite at high pressures

Abstract: [1] Unit cell volumes of Mg2SiO4 ringwoodite were measured at temperatures from 300 to 2000 K and pressure from 15 to 24 GPa and at a temperature of 300 K and pressure from 0 to 21 GPa. The measurements were conducted using a Kawai-type multianvil apparatus that is equipped with an oscillation system to obtain high-quality diffraction pattern against grain growth. We obtained the following relations and parameters describing the pressure-volume-temperature relations of Mg2SiO4 ringwoodite. The unit cell volume of Mg2SiO4 ringwoodite at 0 GPa and 300 K is 524.8(1) A3 (values in parentheses are errors). Fixing the isothermal bulk modulus to 182 GPa, its pressure derivative is 4.6(2). The thermal expansion coefficient at 0 GPa is α0 = 2.57(9) × 10−5 + 1.42(8) × 10−8 (T − 300) K−1, where T is absolute temperature in K, and its logarithmic volume dependence, Anderson-Gruneisen parameter, is 6.9(4). The temperature derivative of the isothermal bulk modulus is (∂KT/∂T) = −0.029(1) GPa K−1. The Debye temperature, Θ, is 846(26) K. The Gruneisen parameter and its logarithmic volume dependence are 1.93(3) and 3.5(3), respectively. The adiabatic temperature gradient in the mantle largely depends on temperature. That in the model Mg2SiO4 mantle increases from 0.29 to 0.40 K km−1 when temperature increases from 1600 to 2000 K.

Phonon density of states in iron at high pressures and high temperatures

Abstract: The phonon density of states (DOS) in iron has been measured in situ by nuclear resonance inelastic X-ray scattering (NRIXS) at high pressures and high temperatures in a resistively heated diamond anvil cell. The DOS data provide a variety of thermodynamic and elastic parameters essential for characterizing iron at depth in the Earth interior, such as average sound velocity, Debye temperature, atomic mean square displacement, average kinetic energy, vibrational entropy and specific heat. The NRIXS data were collected at 6, 20, and 29 GPa and at temperatures up to 920 K. Temperatures were directly determined from the measured spectra by the ratio of intensities of the phonon creation/annihilation side bands that are determined only by the Boltzmann factor. The change of the DOS caused by the structural transition from α-Fe to ɛ-Fe is small and not resolvable within the experimental precision. However, the phonon energies in γ-Fe are clearly shifted to lower values with respect to α- and ɛ-Fe. The temperature dependence of derived thermodynamic parameters is presented and compared with those obtained by Debye’s model. The Debye temperatures that best describe the data decrease slightly with increasing temperature.

Mean-field potential approach to the quasiharmonic theory of solids

Abstract: Adopting the quasiharmonic approximation, a newly developed classical mean-field potential (MFP) approach is extended to the quantum case. Two new Debye temperature expressions, which are in accordance with the thermodynamic theory of Dugdale and MacDonald and with the free volume theory, respectively, are derived in addition to the well-known expression of Slater. The Gruneisen law is now implied explicitly in the Debye temperature expression, and therefore no additional conditions for the Gruneisen constant are needed for realistic thermodynamic calculations. The thermal expansion and specific heat of Na, Cu, Mo, Ta, and Th have been calculated from 10 K up to the melting point.

Thermophysical Properties of α-Tungsten Carbide

Abstract: Upper and lower bounds for the thermal expansion of polycrystalline tungsten carbide (α-WC) are predicted at ultrahigh temperatures from low-temperature experimental data. The lower bound is obtained from an α V K T V model, where α V is the volume thermal expansion, K T the isothermal bulk modulus for a randomly oriented polycrystalline sample, and V the molar volume. For many materials, the α V K T V product approaches a constant value that is similar to the specific heat at the highest temperatures. The upper bound uses Griineisen's rule with a constant Gruneisen parameter γ at temperatures >1.3θ D (where θ D is the Debye temperature) and experimental data below that temperature. Literature data for the thermophysical properties of α-WC have been reviewed and used in our α V K T V model to calculate a lower bound for the thermal expansion at temperatures >2θ D and to calculate the temperature dependence of the bulk modulus. The ultrahigh-pressure thermal expansion has been calculated from the lower bound. Model predictions of the thermophysical properties of WC are given for an extended temperature range.

Are the calorimetric and elastic Debye temperatures of glasses really different

Abstract: Below 1 K, the specific heat C p of glasses depends approximately linearly on temperature T, in contrast with the cubic dependence observed in crystals, and which is well understood in terms of the Debye theory. That linear contribution has been ascribed to the existence of two-level systems as postulated by the tunnelling model. Therefore, a least-squares linear fit C p = C 1 T +C 3 T 3 has been traditionally used to determine the specific-heat coefficients, although systematically providing calorimetric cubic coefficients exceeding the elastic coefficients obtained from sound-velocity measurements, that is C 3 > C Debye. Nevertheless, C p still deviates from the expected CDebye (T) ∝ T 3 dependence above 1 K, presenting a broad maximum in C p / T 3 which originates from the so-called boson peak, a maximum in the vibrational density of states g(ν)/ν2 at frequencies ν ≈ 1 THz. In this work, it is shown that the apparent contradiction between calorimetric and elastic Debye temperatures long observed in gla...

Local versus global thermal states: correlations and the existence of local temperatures.

Abstract: We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature T. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of n subsystems each, and when these groups have the same temperature T. While in classical mechanics the validity of this procedure only depends on the size of the groups n, in quantum mechanics the minimum group size n(min) also depends on the temperature T! As examples, we apply our analysis to a harmonic chain and different types of Ising spin chains. We discuss various features that show up due to the characteristics of the models considered. For the harmonic chain, which successfully describes thermal properties of insulating solids, our approach gives a quantitative estimate of the minimal length scale on which temperature can exist: This length scale is found to be constant for temperatures above the Debye temperature and proportional to T-3 below.

Thermal behavior and glass transition of Zr-based bulk metallic glasses

Abstract: The thermal behaviour of Zr-based bulk metallic glasses has been investigated in situ through the glass transition by means of differential scanning calorimetry, high temperature X-ray synchrotron diffraction, electrical resistivity, and dilatometry. The temperature dependence of the X-ray structure factor can be well described by the Debye theory. The Debye temperature of the glassy and the supercooled liquid state of Zr 52 Ti 5 Cu 18 Ni 15 Al 10 is θ =412 and θ =162 K, respectively. The temperature coefficient of the electrical resistivity and the thermal expansion coefficient change also at the calorimetric glass transition temperature. The results point to a significant changes in the dynamics of molecular motion at T g .