Showing papers on "Debye model published in 2003"

Characterisation of semiconducting V2O5–Bi2O3–TeO2 glasses through ultrasonic measurements

Abstract: Tellurite containing vanadate (50−x)V2O5–xBi2O3–50TeO2 glasses with different bismuth (x=0, 5, 10, 15, 20 and 25 wt%) contents have been prepared by rapid quenching method. Ultrasonic velocities (both longitudinal and shear) and attenuation (for longitudinal waves only) measurements have been made using a transducer operated at the fundamental frequency of 5 MHz in the temperature range from 150 to 480 K. The elastic moduli, Debye temperature, and Poisson’s ratio have been obtained both as a function of temperature and Bi2O3 content. The room temperature study on ultrasonic velocities, attenuation, elastic moduli, Poisson’s ratio, Debye temperature and glass transition temperature show the absence of any anomalies with addition of Bi2O3 content. The observed results confirm that the addition of Bi2O3 modifier changes the rigid formula character of TeO2 to a matrix of regular TeO3 and ionic behaviour bonds (NBOs). A monotonic decrease in velocities and elastic moduli, and an increase in attenuation and acoustic loss as a function of temperature in all the glass samples reveal the loose packing structure, which is attributed to the instability of TeO4 trigonal bipyramid units in the network as temperature increases. It is also inferred that the glasses with low Bi2O3 content are more stable than with high Bi2O3 content.

Lattice dynamics and correlated atomic motion from the atomic pair distribution function

Abstract: The mean-square relative displacements (MSRD) of atomic pair motions in crystals are studied as a function of pair distance and temperature using the atomic pair distribution function (PDF). The effects of the lattice vibrations on the PDF peak widths are modelled using both a multi-parameter Born--von Karman (BvK) force model and a single-parameter Debye model. These results are compared to experimentally determined PDFs. We find that the near-neighbor atomic motions are strongly correlated, and that the extent of this correlation depends both on the interatomic interactions and crystal structure. These results suggest that proper account of the lattice vibrational effects on the PDF peak width is important in extracting information on static disorder in a disordered system such as an alloy. Good agreement is obtained between the BvK model calculations of PDF peak widths and the experimentally determined peak widths. The Debye model successfully explains the average, though not detailed, natures of the MSRDs of atomic pair motion with just one parameter. Also the temperature dependence of the Debye model largely agrees with the BvK model predictions. Therefore, the Debye model provides a simple description of the effects of lattice vibrations on the PDF peak widths.

Strain and size effects on heat transport in nanostructures

Abstract: The relative role of the residual strain and dimensional scaling on heat transport in nanostructures is investigated by molecular dynamics simulations of a model Lennard-Jones solid. It is observed that tensile (compressive) strains lead to a reduction (enhancement) of the lattice thermal conductivity. A nonhydrostatic strain induces thermal conductivity anisotropy in the material. This effect is due to the variation with strain of the stiffness tensor and lattice anharmonicity, and therefore of the phonon group velocity and phonon mean free path. The effect due to the lattice anharmonicity variation appears to be dominant. The size effect was studied separately in unstrained thin films. Phonon scattering on surfaces leads to a drastic reduction of the thermal conductivity effect which is much more important than that due to strain in the bulk. It is suggested that strain may be used to tailor the phonon mean free path which offers an indirect method to control the size effect.

Heat capacity of oxide glasses at high temperature region

Abstract: Heat capacities of vitreous silica, and some binary and ternary silicate, borate and phosphate glasses were measured in the temperature range from 300 to 840 K by ac calorimetry. Our previous study has revealed that heat capacities of oxide glasses scaled with the molar heat capacity at the Debye temperature have a similar magnitude and temperature dependence from 300 K to glass transition temperatures. On the basis of this observation, the factor effecting heat capacity was investigated by use of the three-band theory which is composed of separate contributions from one- and three-dimensional Debye model and Einstein model. We revealed that the heat capacity of oxide glass in the temperature range of measurements follows the one-dimensional Debye model and the compositional variations of heat capacity are evaluated in terms of the ionic packing ratio and the dissociation energy of oxide glass.

Thermal conductivity of elemental crystalline silicon clathrate Si136

Abstract: The thermal conductivity and heat capacity of a guest-free polycrystalline silicon clathrate with the type-II hydrate crystal structure is reported. The magnitude of the thermal conductivity at room temperature is only slightly larger than that of vitreous silica, and is thirty times lower than that of diamond structured Si. The temperature dependence of the thermal conductivity of Si136 follows the well-known Debye form, and is dissimilar to that of clathrates with “guest” atoms inside their polyhedra. The Debye temperature of Si136, estimated from low temperature heat capacity measurements, is 470 K. The potential of guest-free clathrates for thermoelectric applications is discussed.

Classical and quantum transport in focused-ion-beam-deposited Pt nanointerconnects

Abstract: We study the electrical properties of Pt nanointerconnects, formed on SiO2 substrates by focused-ion-beam deposition. Studies of their temperature-dependent resistivity reveal a small residual-resistivity ratio, and a Debye temperature that differs significantly from that of pure Pt, indicative of the disordered nature of the nanowires. Their magnetoresistance shows evidence for weak antilocalization at temperatures below 10 K, with a phase-breaking length of ∼100 nm, and a temperature dependence suggestive of quasi-one-dimensional interference.

Structural behavior of Pd40Cu30Ni10P20 bulk metallic glass below and above the glass transition

Abstract: The thermal behavior of the structure of Pd40Cu30Ni10P20 bulk metallic glass has been investigated in situ through the glass transition by means of high-temperature x-ray synchrotron diffraction. The dependence of the x-ray structure factor S(q) of the Pd40Cu30Ni10P20 glass on temperature follows the Debye theory up to the glass transition with a Debye temperature θ=296 K. Above the glass transition temperature Tg, the temperature dependence of S(q) is altered, pointing to a continuous development of structural changes in the liquid with temperature. The atomic pair correlation functions g(r) indicate changes in short-range-order parameters of the first and the second neighborhood with temperature. The temperature dependence of structural parameters is different in glass and in supercooled liquid, with a continuous behavior through the glass transition. The nearest-neighbor distance decreases with temperature, changing the slope at Tg. The interatomic distances of higher coordination shells expand analogo...

Small polaron transport in V2O5–NiO–TeO2 glasses

Abstract: Semiconducting glasses of the V2O5–NiO–TeO2 system were prepared by the press-quenching method and their d.c. conductivities in the temperature range 300–450 K were measured. The d.c. conductivities at 395 K for the present glasses were determined to be 10−7 to 10−1 S m−1, indicating that the conductivity increased with increasing V2O5 concentration. A glass of composition 67.5V2O5–2.5NiO–30TeO2 (mol %) having a conductivity of 2.47×10−2 S m−1 at a temperature of 395 K was found to be the most conductive glass among the vanadium-tellurite glasses. From the conductivity–temperature relation, it was found that a small polaron hopping model was applicable at the temperature above θD/2 (θD: the Debye temperature); the electrical conduction at T>θD/2 was due to adiabatic small polaron hopping of electrons between vanadium ions. The polaron bandwidth ranged from 0.06 to 0.21 eV. The hopping carrier mobility varied from 1.1×10−7 to 5.48×10−5 cm2 V−1 s−1 at 400 K. The carrier density is evaluated to be 1.85×1019–5.50×1019 cm−3. The conductivity of the present glasses was primarily determined by hopping carrier mobility. In the low-temperature (below θD/2) regime, however, both Mott's variable-range hopping and Greaves intermediate range hopping models are found to be applicable.

Elastic wave thermal fluctuations, ultrasonic waveforms by correlation of thermal phonons

Abstract: It is widely recognized that acoustic degrees of freedom coupled to a thermal bath have amplitudes which fluctuate with a mean square proportional to temperature; this is the basis for the Debye theory of the heat capacity of insulating solids. It is shown here that these elastic wave thermal phonons have correlation functions identical to the system's ultrasonic Green's function, and furthermore that thermal noise in ultrasonic detectors should have correlation functions equivalent to conventional waveforms obtained by active transmission and reception. This suggests the possibility of doing ultrasonics without a source. Theory for the identity is presented, and several room temperature laboratory confirmations are conducted in the frequency range 0.1-1.0 MHz. The thermal nature of the origin of these correlations is established by comparing their strength with theoretical expectations. Applications are discussed.

Relationship between glass transition temperature and Debye temperature in bulk metallic glasses

Abstract: The Debye temperature and glass transition temperature of a variety of bulk metallic glasses (BMGs) were determined by acoustic measurement and differential scanning calorimetry, respectively. The relationship between the Debye temperature and glass transition temperature of these BMGs was analyzed, and their observed correlation was interpreted in terms of the characteristics of the glass transition in BMGs.

Precise measurement of the lattice parameters of α-Al2O3 in the temperature range 4.5–250 K using the Mössbauer wavelength standard

Abstract: The lattice parameters of α-Al2O3 have been measured in a temperature range from 4.5 to 250 K with a relative accuracy of better than 6 × 10−6. The experimental method uses Bragg backscattering and the recently proposed Mossbauer wavelength standard, i.e. the wavelength λM = 86.025474 (16) pm of the nuclear resonance radiation of 57Fe (Shvyd'ko et al., 2000), which has previously been applied successfully to measure the lattice parameters of α-Al2O3 at temperatures between 286 and 374 K (Shvyd'ko et al., 2002). The experimental data in the range from 4.5 to 374 K are consistent with the Debye model of thermal expansion. At 4.5 K, the thermal expansion coefficient is as low as 1.2 (9) × 10−10 K−1 in the a direction.

Molecular dynamics simulation of thermal conductivity of nanoscale thin silicon films

Abstract: Molecular dynamics simulations are performed to explore the thermal conductivity in the cross-plane direction of single-crystal thin silicon films. The silicon crystal has diamond structure, and the Stillinger-Weber potential is adopted. The inhomogeneous nonequilibrium molecular dynamics (NEMD) scheme is applied to model heat conduction in thin films. At average temperature T = 500 K, which is lower than the Debye temperature ΘD = 645 K, the results show that in a film thickness range of about 2–32 nm, the calculated thermal conductivity decreases almost linearly as the film thickness is reduced, exhibiting a remarkable reduction as compared with the bulk experimental data. The phonon mean free path is estimated and the size effect on thermal conductivity is attributed to the reduction of phonon mean free path according to the kinetic theory.

On the determination of the Debye temperature from experimental data

Abstract: It is shown that the Debye temperature as a function of temperature must satisfy certain equations in order for the thermodynamic functions calculated in terms of the Debye temperature to satisfy both the third law of thermodynamics and the law of equipartition of energy. A general expression for the Θ(T) function satisfying these thermodynamic laws is found.

Phonon, Spin-Wave, and Defect Contributions to the Low-Temperature Specific Heat of α-FeOOH

Abstract: The specific heat of α-FeOOH was measured in the temperature range 0.6 to 30 K by a combination of semi-adiabatic and isothermal techniques. A broad specific-heat anomaly was detected at approximately 1 K. The data above this anomaly were fitted to the equation C=B asw T 3 e −Δ/T +∑ B n T n, where ∑ B n T n represents the harmonic-lattice model for the lattice specific heat, and B asw T 3 e −Δ/T represents the magnetic specific heat. The e −Δ/T term that modifies the usual T 3 term for an antiferromagnetic spin-wave contribution accounts for a spin-wave gap in the spin-wave spectrum, where Δ is the width of the spin-wave gap in Kelvin. As expected, the root-mean-square deviation (RMS) of the fit decreased progressively with inclusion of additional lattice terms, but the Debye temperature, Θ D , and the spin-wave gap, Δ, remained essentially unchanged. The addition of a linear term, γT, decreased the RMS of the fit and eliminated the need for an excessive number of lattice terms. The γT contribution to the specific heat, rather than being electronic in nature, is associated either with a small number of Fe3+ vacancies, or with loosely bound particles vibrating in defect sites in the crystallite interfaces. The possibility of the existence of vacancies is implied by the excess water content in the sample (0.083 moles of H2O per mole of FeOOH) and the presence of the interfaces is indicated by the particle size (determined by BET surface area measurement) being larger than the individual crystallite size (determined by X-ray diffraction).

A high-resolution neutron powder diffraction study of ammonia dihydrate (ND3⋅2D2O) phase I

Abstract: We have measured the thermal expansivity of ammonia dihydrate (ND3.O2D(2)O) phase I from 4.2 to 174 K at ambient pressure, and the incompressibility at 174 K from 0 to 0.45 GPa, using time-of-flight neutron powder diffraction. The unit cell volume as a function of temperature, V(T), was fitted with a Gruneisen approximation to the zero-pressure equation of state (with the lattice vibrational energy calculated from a double-Debye model fitted to heat capacity data) having the following parameters at zero pressure and temperature: V-0,V-0=356.464+/-0.005 Angstrom(3), (K-0,K-0/gamma)=7.163+/-0.024 GPa, and K'(0,0)=5.41+/-0.33 (where V-P,V-T is the unit cell volume at pressure P and temperature T, K-P,K-T is the isothermal bulk modulus, K'(P,T) is its first pressure derivative, and gamma is the Gruneisen ratio). The two Debye temperatures are theta(A)(D)=165+/-3 K and theta(D)(B)=729+/-4 K. The unit cell volume at 174 K as a function of pressure, V(P), was fitted with a third-order Birch-Murnaghan equation of state having the following parameters: V-0,V-174=365.69+/-0.16 Angstrom(3), K-0,K-174=7.02+/-0.25 GPa, and K'(0,174)=9.56+/-1.28. The volume thermal expansion coefficient, alpha(V), at 174 K and atmospheric pressure is 281.3x10(-6) K-1. The proton disorder manifested at high homologous temperatures is seen to be frozen in, on the time scale of these experiments, down to 4.2 K. A high-pressure polymorph of ammonia dihydrate was observed following melting of the sample at 179 K and 0.46 GPa. (C) 2003 American Institute of Physics.

Molecular-dynamics simulation of structural properties of cubic boron nitride

Abstract: The structural and thermodynamic properties of cubic boron nitride (c-BN) have been calculated by using a molecular-dynamics simulation based on the Tersoff empirical interatomic potential. Bulk properties, elastic constants, Debye temperature, thermal expansion coefficient and specific heat have all been studied using the well-tested Tersoff potential. The calculated results are in good agreement with experimental data.

Probing dielectric relaxation properties of liquid CS2 with terahertz time-domain spectroscopy

Abstract: Terahertz time-domain spectroscopy is used to investigate the dielectric relaxation properties of liquid CS2. The frequency-dependent absorption coefficient and index of refraction were measured in the frequency range 0.2–2.0 THz. The ultrafast dielectric relaxation time of liquid CS2 was determined to be 630±30 fs by fitting the dielectric function to the Debye model which is attributed to average time for rocking and rotational response of the CS2 molecules possessing an anisotropic polarizability.

Mechanical Spectroscopy – Fundamentals

Abstract: Mechanical spectroscopy is described as a member of the fami ly of spectroscopic techniques. It is shown that mechanical spectroscopy investigates t he mechanical energy absorbed by a physical object subjected to an external time-dependent pertur bation field, that is, an impulsed, quasi-static, or harmonic mechanical field over the entire range of attainable frequencies (from 10 Hz to 10 Hz). The modulus of compliance and modulus of elasticity is discussed in t rms of generalized susceptibility within the framework of linear respons e theory. The relationship of the response and relaxation functions to generalized susceptibility is gi ven via the Fourier-Laplace transformation of the relaxation or response function. This approach des ribes linear mechanical responses to time-dependent mechanical perturbation and enables calcula tion of mechanical loss in solids. Debye and non-Debye relaxations are briefly described and illustrated. A record of discussions which took place during the Second International School on Mechani cal Spectroscopy MS-2 and author’s answers to questions raised after the lecture are included. Definition of Mechanical Spectroscopy Spectroscopy is the science which consists in the investigation of the energy absorbed or emitted by a physical object subjected to an interacting (perturbation) fie ld. Mechanical spectroscopy can be defined in the framework of an interacting system in which the ext rnal perturbing field F, used for probing the response R of the physical object, is mechanical in nature, that is, stres s σ and strain ε [1]. In general, mechanical spectroscopy consists in the investigat ion of the time-dependence of macroscopic response R(t) under the perturbation of a time-dependent m echanical field F(t); a single direct mechanical perturbation is depicted in Fig. 1.1 while coupled perturbation with mechanical probing field is illustrated in Fig. 1.2. In both cases the macroscopic response comes ultimately from the microscopic motions of relaxing entities.

Lattice dynamics and inelastic neutron scattering studies of MFX (M=Ba, Sr, Pb; X=Cl, Br, I)

Abstract: We report lattice dynamical calculation of technologically important matlockite structured compounds MFX [M(Ba, Sr, Pb); X(Cl, Br, 1)] using a transferable interatomic potential based on a shell model. Our model is validated by the inelastic neutron scattering measurement of the phonon density of states for BaFCl carried out using the triple axis spectrometer at Trombay. We have further exploited this model for the calculation of high-pressure and high-temperature thermodynamic properties of these compounds which are found to be in good agreement with various experimental data, as available in the literature. The calculations provide a theoretical understanding of the elastic constants, equation of state, phonon dispersion relations and density of states, thermal expansion, specific heat, Debye temperature, and anisotropic thermal parameters of these materials.

Extended x-ray absorption fine-structure experiments with a laser- imploded target as a radiation source

Abstract: The feasibility of using extended x-ray absorption fine structure (EXAFS) for characterizing metals shocked to megabar (1 bar = 0.1 MPa) pressures by a laser has been studied. High-contrast K-edge modulations for an unshocked Ti-foil absorber were obtained with a laser-imploded spherical target as a source. The high intensity and relative smoothness of the source spectrum enable us to work with thick Ti foils, which increases the relative modulation in the measured signal. Using a semiempirical model to describe the shock-compressed foil, we show that, because of the rise in Debye temperature with density, the compression extends the temperature range at which EXAFS modulations can be observed.

Time-dependent perturbation calculations for transition properties of two-electron atoms under Debye plasma

Abstract: Systematic investigation have been performed for the dynamic polarizabilities, energy levels, oscillator strengths and transition probabilities for the first few members of helium isoelectronic series He, Li+,Be2+,B3+ and C4+ embedded in the Debye plasma. The effect of plasma is described by introducing an exponential screening (the Debye screening) to the nuclear Coulomb potential. Systematic trend is observed for all the properties under study with respect to increased screening. The ionization potential decreases with an increased screening and the number of bound excited states supported by the Debye screened potential is finite.

Analysis of low temperature specific heat in the ferromagnetic state of the Ca-doped manganites

Abstract: The reported specific heat C (T) data of the perovskite manganites La1-x Ca x MnO3, with x = 0.1, 0.2 and 0.33, is theoretically investigated in the temperature domain $4 \le T \le 10$ K. Calculations of C (T) have been made within the two component scheme: one is the Fermionic and the other is Bosonic (phonon or magnon) contribution. Lattice specific heat is well estimated from the Debye model and Debye temperature for Ca doped lanthanum manganites is obtained following an overlap repulsive potential. Fermionic component as the electronic specific heat coefficient is deduced using the band structure calculations for ferromagnetic metallic phase. Later on, for x = 0.1, following double exchange mechanism the role of magnons is assessed towards specific heat and find that at much low temperatures (T < 10 K), specific heat increases and show almost T 3/2 dependence on the temperature. We note that, the lattice specific heat is smaller for x = 0.1 when compared to that of magnon specific heat below 10 K. For x = 0.2, i.e., in the ferromagnetic metallic phase the magnon contribution is larger with the electron contribution while the reverse is true for x = 0.33. It is further noticed that in the ferromagnetic metallic phase, electronic specific heat is small in comparison to the lattice specific heat in low temperature domain. The present investigations allow us to believe that electron correlations are essential to enhanced density of state over simple Fermi liquid approximation in the metallic phase of La1-x Ca x MnO3 (x = 0.2, 0.33). The present numerical analysis of specific heat shows similar results as those revealed from experiments.

Temperature dependence of lifetimes of Gd(0001) surface states

Abstract: Scanning tunneling spectroscopy was applied to study the temperature dependence of lifetime broadening of the Gd(0001) surface state. The observed increase of the linewidth with temperature is attributed to enhanced electron-phonon scattering, which can be described within the Debye model.