Debye Characteristic Temperature Research Articles

Lattice dynamical calculations for HgTe, CdTe and their ternary alloy CdxHg1−xTe

We present the results of the lattice dynamical calculations for CdTe, HgTe and their ternary alloy CdxHg1−xTe in the framework of three-body shell model. This model incorporates the effect of the short-range repulsive interactions up to and including the second nearest neighbors, in addition to the long-range Coulombic interactions in the framework of the rigid-shell model with both the ions are polarizable. The application of the present model has been made to calculate the phonon dispersion relations, phonon density of states and Debye characteristic temperatures for CdTe, HgTe and its ternary alloy CdxHg1−xTe are plotted along with their available experimental results. We find an overall good agreement with the experimental results. The comparison of the theoretical results with the available experimental results has been made and good agreement is observed.

Correlation between the thermal expansion, isothermal compressibility, and photoconductivity of the (TlGaSe2)1 − x (TlInS2) x (x = 0.1, 0.2) solid solutions

The thermal expansion coefficient, isothermal compressibility, and photoconductivity of the (TlGaSe2)0.9(TlInS2)0.1 and (TlGaSe2)0.8(TlInS2)0.2 solid solutions have been measured as a function of temperature. The measurement results have been used to evaluate the Debye characteristic temperature and band gap temperature coefficient of the solid solutions. It is shown that an increase in their thermal expansion coefficient is accompanied by a decrease in their band gap temperature coefficient.

Heat capacity and thermodynamic properties of crystalline SrB4O7

The heat capacity of a strontium tetraborate (SrB4O7) single crystal has been determined in the temperature range 55–300 K by adiabatic calorimetry, and its Debye characteristic temperature, entropy change, enthalpy increment, and phonon mean free path have been calculated as functions of temperature.

Modification in electrical transport with a change in geometry from a nanowire to a nanotube of copper: effect of the extra surface

We have studied the temperature-dependent (3–300 K) electrical resistance of metal nanowires and nanotubes of the same diameter with the specific aim to understand the changes in electrical transport brought about by a change in the geometry of a nanowire to a nanotube. Single crystalline nanowires and nanotubes of copper were synthesized by electrodeposition in nanoporous alumina templates. The temperature-dependent resistivity data have been analysed using the Bloch–Grüneisen function for the lattice contribution to resistivity, and the characteristic Debye temperature θR was determined along with the residual resistivity ρ0. Substantial size effects were observed in both the parameters ρ0 and θR, where the former is enhanced and the latter is suppressed from bulk to nanowires and further to nanotubes. It has been observed that the transport parameters in the nanotubes with wall thickness t are similar to those of a nanowire with diameter d, where d ≈ 2t in the specific size range used in this work. It is suggested that appreciable size effects in the electrical transport parameters occur due to the extra surface in the nanotube. In both nanotubes and nanowires, the single parameter that determines the size effect is the surface area to volume ratio.

Low-temperature structure and lattice dynamics of the thermoelectric clathrate Sn24P19.3I8

The crystal structure of the thermoelectric clathrate Sn24P19.3I8 was determined down to 10K showing no variations with the temperature. Even at 10K Sn24P19.3I8 crystallizes in the type-I clathrate structure, space group Pm3-n, with the cubic unit cell parameter ranging from 10.9173Å at 10K to 10.9554Å at room temperature. In its crystal structure, tin and phosphorus atoms form the framework that traps the guest iodine atoms in the polyhedral cavities of two different shapes. The temperature-dependent crystal structure data and the results of the heat capacity measurements revealed the localized vibrations of the guest atoms inside the oversized cavities with the characteristic Einstein temperatures of θE1=60K and θE2=78K, whereas the characteristic Debye temperature for Sn24P19.3I8 is 265K. The room temperature lattice thermal conductivity was calculated using the Debye model to be κL=0.85Wm−1K−1, which is in excellent agreement with the experimentally measured data and demonstrates that the thermal conductivity is almost entirely phononic.

A study of the structure and thermal parameters of Ni88.6Cr11.4 alloy

The structure and thermal parameters of the alloy Ni88.6Cr11.4 have been studied by an in-situ x-ray diffraction technique. The experiments show that the alloy has a single phase with fcc (A1) structure, the phase boundary of which extends beyond 1050 K. No evidence of the formation of ordered structures was found. The temperature factor was found to be independent of the static displacements. The mean linear thermal expansion does not follow the classical Gruneisen relationship. Further, the addition of Cr into Ni leads to an increase in the value of the characteristic Debye temperature ΘD, whereas a minor effect is observed in the coefficient of linear thermal expansion α(T) of the alloy. The results are in good agreement with those in the literature for other compositions of Ni–Cr alloys.

Many Body Interactions and Lattice Dynamics of Gold

Lattice dynamics of gold is studied theoretically using phenomenological model. This model considers (i ion-ion and (ii) ionelectron interactions to evaluate the potential energy. Contribution to ion-ion interaction is the sum of two body central interactions between ions and many body interactions among ions. Contribution to potential energy due to ion-electron interactions is evaluated using screened coulomb potential. Using this model phonon frequencies of gold are computed at 48 non-equivalent points of Brillouin zones of crystal and compared with experimental points. Lattice specific heats at different temperatures are evaluated by dividing the frequency spectrum in interval of 0.1 tiga hertz. Using the computed values of lattice specific heats, Debye characteristic temperatures of gold are computed. The model is used to calculate compressibility and Poission's ratio. Agreement of theoretical calculations with experimental results is satisfactory.Key words: Ion-ion interaction; Ion-electron interaction; Phonon frequency; Lattice specific heat; Debye characteristic temperatureThe Himalayan Physics Vol.1, No.1, May, 2010Page: 44-47Uploaded Date: 28 July, 2011

Electrical properties and reduced Debye temperature of polycrystalline thin gold films

The temperature-dependent electrical properties of four suspended polycrystalline thin gold films with thicknesses of 20.0, 23.0, 36.0 and 54.0 nm have been measured in the temperature range 100–310 K. The measured results show that the electrical resistivity of the films significantly increases while the corresponding temperature dependence decreases compared with bulk gold. The significantly increased electrical resistivity indicates that grain boundary scattering dominates over surface scattering in the studied films. However, fixing the Debye temperature to the bulk value will lead to an erroneous temperature dependence of resistivity. Taking into account the reduced characteristic Debye temperature along with the surface and grain boundary scattering, the electrical properties of the films can be well described in the whole temperature range. The extracted grain boundary reflection coefficient is 0.3 ± 0.03, within the range of the previous reported values, 0.1–0.45. The films' characteristic Debye temperatures decrease from the bulk value of 165 K to between 83 and 121 K and tend to increase with increasing film thickness. This tendency coincides with the previous studies on thin gold, copper, platinum, silver films or wires, and cobalt/nickel superlattices. The possible mechanism responsible for the reduced Debye temperature is phonon softening at the surfaces, grain boundaries, disorder, defects and impurities, part of which has been demonstrated in other studies.

GENERALIZED BOSE-EINSTEIN CONDENSATION IN SUPERCONDUCTIVITY

Unification of the BCS and the Bose-Einstein condensation (BEC) theories is surveyed in detail via a generalized BEC (GBEC) finite-temperature statistical formalism. Its major difference with BCS theory is that it can be diagonalized exactly. Under specified conditions it yields the precise BCS gap equation for all temperatures as well as the precise BCS zero-temperature condensation energy for all couplings, thereby suggesting that a BCS condensate is a BE condensate in a ternary mixture of kinematically independent unpaired electrons coexisting with equally proportioned weakly-bound two-electron and two-hole Cooper pairs. Without abandoning the electron-phonon mechanism in moderately weak coupling it suffices, in principle, to reproduce the unusually high values of Tc (in units of the Fermi temperature TF) of 0.01-0.05 empirically reported in the so-called "exotic" superconductors of the Uemura plot, including cuprates, in contrast to the low values of Tc/TF ≤ 10-3 roughly reproduced by BCS theory for conventional (mostly elemental) superconductors. Replacing the characteristic phonon-exchange Debye temperature by a characteristic magnon-exchange one more than twice in size can lead to a simple interaction model associated with spin-fluctuation-mediated pairing.

Temperature dependence of middle infrared absorption lines in silver halide crystals doped with Pr3+, Dy3+, and Nd3+ ions

The electron-phonon coupling was investigated for mid-infrared transitions in silver halide crystals doped with Pr, Dy, or Nd. The temperature dependence of the absorption spectral line widths and the line shifts were measured in mid-infrared absorption lines in these crystals. It was shown that in each case the temperature dependence is consistent with the two-phonon Raman process model having a single characteristic Debye temperature. This Debye temperature was found to be in the range of 142–155.5 K. It was also found that below 50 K the line widths are caused by inhomogeneous crystal strains.

Thermal conductivity, heat capacity, and thermodynamic functions of the Bi4Ge3O12 single crystal

The thermal conductivity and the heat capacity of a single crystal of bismuth orthogermanate Bi4Ge3O12 have been experimentally investigated in the temperature ranges 50–300 and 56–300 K, respectively. The temperature dependences of the phonon mean free path, the characteristic Debye temperature, and the changes in the entropy and enthalpy have been calculated.

Heat capacity and thermodynamic functions of LaVO4 and LuVO4 from 7 to 345 K

The heat capacities of lanthanum and lutetium orthovanadates have been measured at temperatures from 7 to 345 K using an adiabatic calorimeter. No anomalies have been detected in the heat capacity data. The thermodynamic functions (Cp0(T), S0(T), and H0(T) − H0(0)) of the two compounds have been calculated in the temperature range studied, and their Debye characteristic temperatures have been estimated.

ELASTIC MODULI AND SOUND VELOCITY IN La1-xSrxMnO3 (x = 0 to 0.3)

The longitudinal and shear sound velocity in colossal magnetoresistive La 1-x Sr x MnO 3 (x = 0.0, 0.05, 0.15 and 0.3) were measured using the pulse-echo-overlap technique in the temperature range of 80 to 300 K. An abrupt increase in the longitudinal velocity was observed immediately below the insulator-metal transition (T im ) in the x = 0.05 and 0.15 samples. This anomaly shifted towards higher temperature with an increase in Sr content. The absolute velocities (measured at 80 K) increased with Sr content. Hystereses in the longitudinal and shear velocity were observed in the x = 0.05 and 0.15 samples. A step-like longitudinal sound velocity anomaly between 150 K and 220 K during warming and cooling was observed in the x = 0.05 sample. A sudden hardening was observed for longitudinal and shear sound velocity coinciding with second broad resistance peak at temperature below T im in x = 0.15 sample. The characteristic Debye temperature increases as Sr content was increased, indicating a hardening trend. These results indicate the importance of phonons in the transport mechanism of these colossal magnetoresistive materials.

Phonon spectrum and thermal properties of semiconducting compounds ZnS and ZnSe

Phonon spectrum and thermal properties of semiconducting compounds ZnS and ZnSe have been calculated by using a proposed three-body shell model (TBSM).This model incorporates the effect of three-body and short-range repulsive forces, in addition to long-range Coulombic interactions in the frame work of rigid-shell model with both the ions polarizable. Using the above proposed model the phonon dispersion relations, phonon density of states and the Debye characteristic temperature have been calculated and plotted for the compounds ZnS and ZnSe. We find an overall good agreement between theoretical and experimental results.

Elastic-Stiffness Coefficients of Titanium Diboride.

Using resonance ultrasound spectroscopy, we measured the monocrystal elastic-stiffness coefficients, the Voigt Cij, of TiB2. With hexagonal symmetry, TiB2 exhibits five independent Cij: C11, C33, C44, C12, C13. Using Voigt-Reuss-Hill averaging, we converted these monocrystal values to quasiisotropic (polycrystal) elastic stiffnesses. Briefly, we comment on effects of voids. From the Cij, we calculated the Debye characteristic temperature, the Grüneisen parameter, and various sound velocities. Our study resolves the enormous differences between two previous reports of TiB2’s Cij.

Thermodynamic properties of V3Te4

The heat capacity of V3Te4 has been measured as a function of temperature using an adiabatic calorimeter, and its thermodynamic properties were evaluated. We have determined the Debye characteristic temperature and fracton dimension of crystalline V3Te4.

Application of Neumann–Kopp rule for the estimation of heat capacity of mixed oxides

The empirical Neumann–Kopp rule (NKR) for the estimation of temperature dependence of heat capacity of mixed oxide is analyzed. NKR gives a reasonable estimate of C pm for most mixed oxides around room temperature, but at both low and high temperatures the accuracy of the estimate is substantially lowered. At very low temperatures, the validity of NKR is shown to be predominantly determined by the relation between the characteristic Debye and Einstein temperatures of a mixed oxide and its constituents. At high temperatures, the correlation between their molar volumes, volume expansion coefficients and compressibilities takes the dominance. In cases where the formation of a mixed oxide is not accompanied by any volume change, the difference between dilatation contributions to heat capacity of a mixed oxide and its constituents is exclusively negative. It turns out that in the high-temperature range, where the contribution of harmonic lattice vibrations approached the 3 NR limit, Δ ox C p assumes negative values. For more complex oxides whose heat capacity has contributions from terms such as magnetic ordering, electronic excitations, the applicability of NKR is only restricted to lattice and dilatation terms.

Thermodynamic properties of VTe2

The methods of adiabatic and differential scanning calorimetry are used to measure the temperature dependence of the heat capacity. Thermodynamic functions are calculated for VTe2. The Debye characteristic temperature is determined and the fractal dimension of crystalline vanadium ditelluride is calculated.

Thermal properties of the pyrochlore, Y 2Ti 2O 7

The thermal conductivity and heat capacity of high-purity single crystals of yttrium titanate, Y 2Ti 2O 7, have been determined over the temperature range 2 K⩽ T⩽300 K. The experimental heat capacity is in very good agreement with an analysis based on three acoustic modes per unit cell (with the Debye characteristic temperature, θ D, of ca. 970 K) and an assignment of the remaining 63 optic modes, as well as a correction for C p − C v . From the integrated heat capacity data, the enthalpy and entropy relative to absolute zero, are, respectively, H( T=298.15 K)− H 0=34.69 kJ mol −1 and S( T=298.15 K)− S 0=211.2 J K −1 mol −1. The thermal conductivity shows a peak at ca. θ D/50, characteristic of a highly purified crystal in which the phonon mean free path is about 10 μm in the defect/boundary low-temperature limit. The room-temperature thermal conductivity of Y 2Ti 2O 7 is 2.8 W m −1 K −1, close to the calculated theoretical thermal conductivity, κ min, for fully coupled phonons at high temperatures.

The phonon heat capacity of diborides: The approximation of interacting sublattices

The temperature dependence of the heat capacity of structures formed by alternating layers with different atomic compositions is described using the model of interacting three- and two-dimensional Debye sublattices. The parameters of the model are the characteristic temperatures Θ1 and Θ3 of the sublattices and the characteristic temperature Θ2 corresponding to vibrations between the sublattices. (In the accepted approximation, Θ2 equals the characteristic Debye temperature of the substance at absolute zero.) The model was used to analyze the temperature dependences of the lattice (phonon) heat capacities of transition and rare-earth metal diborides MB2. This allowed the characteristic temperatures Θi and trends of their variations depending on metal atomic numbers to be determined.