Showing papers on "Debye model published in 1977"

Phonon-assisted hopping due to interaction with both acoustical and optical phonons

Abstract: Previous calculations of the nonadiabatic phonon-assisted jump rate have included electron coupling to either optical or acoustical phonons. Such calculations have yielded expressions for the jump rate which are essentially identical in the high-temperature ($T\ensuremath{\gtrsim}{T}_{\mathrm{Debye}}$) regime, in which the lattice motion can be treated classically, but which differ qualitatively from one another in the complementary low-temperature ($T\ensuremath{\ll}{T}_{\mathrm{Debye}}$) regime. In this article we have extended the calculations to include coupling of the electron to both phonon modes. The theory is not limited by temperature or by the strength of the electron-phonon coupling. Results are obtained which exhibit the essential characteristics of the jump rate for numerous values of the relative coupling of the electron to the optical and acoustical modes. It is found that when the electron's coupling to acoustical modes is comparable to or stronger than its coupling to optical phonon modes and when the difference in energy between the final and initial electronic state, $\ensuremath{\Delta}$, is of the same order as $\ensuremath{\hbar}{\ensuremath{\omega}}_{\mathrm{Debye}}$, the jump rate is qualitatively similar to that obtained when only the coupling to acoustic phonons is included. For instance, in the strong-coupling (small-polaron) situation the jump rate exhibits a high-temperature activated form above some fraction of the Debye temperature (typically $\frac{{T}_{\mathrm{Debye}}}{2}$). However, below this temperature its temperature dependence decreases sharply, exhibiting a nonactivated behavior. Finally in the limit of sufficiently low temperatures the jump rate is found to be simply the product of the acoustic-phonon jump rate (electrons coupling to acoustical modes only) and an additional factor related to the extra binding of the electron due to its coupling with optical phonons. Only when the coupling of the electron to optical modes is much stronger than its coupling to acoustical modes does the jump rate exhibit deviations from the temperature-dependent behavior described above. Additionally, the dependence of the jump rate on $\ensuremath{\Delta}$ is discussed in detail. For instance, in the high-temperature case, it is found that only when $\ensuremath{\Delta}$ is small compared with the polaronic binding energy the jump rate varies with $\ensuremath{\Delta}$ as $\mathrm{exp}(\ensuremath{-}\frac{\ensuremath{\Delta}}{2kT})$. For sufficiently large positive or negative values of $\ensuremath{\Delta}$ the jump rate will decrease with increasing $|\ensuremath{\Delta}|$. Thus even in the case for $\ensuremath{\Delta}l0$ (a hop downward in energy) the jump rate will ultimately decrease to zero as $|\ensuremath{\Delta}|$ increases.

Debye temperature and standard entropies and enthalpies of compound semiconductors of the type I-III-VI 2

Abstract: The heat capacities at constant pressure have been measured for CuInSe2, CuInTe2 and AgGaTe2 in the temperature range 1K ≤T≤40K and for CuInS2 and AgInTe2 between 1 K and room temperature. From the low temperature data we derive the following Debye temperatures θD in the limit T → O K: θD(CuInS2) = 273 K, θD(CuInSe2) = 222 K, θD(CuInTe2) = 191 K, θD(AgGaTe2) = 182 K and θD(AgInTe2) = 156 K. A plot of the average atomic heat capacity at constant volume Cv shows that the data scale to one general curve for all 5 compounds considered in this paper. This is, also, true for a plot Cv, i.e., all I-III-VI2 compounds measured thus far deviate similarly from the Debye approximation. By integration of the general curves Cv(T/θD) and θD x Cv(T/θD) we derive tne standard entropies S 0 298 and energies E 0 298 -E 0 0 of 11 compounds of the type I-III-VI2, for which the Debye temperatures are known. The difference between the energies E 0 298 -E 0 0 and enthalpies H 0 298 -H 0 0 is within the error limits of the experimental data (< 1%). The molar S 0 298 and H 0 298 -H 0 0 values for the I-III-VI2 compounds are approximately twice the corresponding molar values for their II-VI isoelectronic analogs. The thermodynamic functions at standard state obtained by integration of the experimental data are all < 10% smaller than the corresponding values estimated on the basis of the Debye approximation.

Elastic Properties of Monoclinic Hafnium Oxide at Room Temperature

Abstract: The Young's and shear moduli of polycrystalline monoclinic hafnium oxide were determined by the sonic resonance method at room temperature as a function of volume fraction porosity. The Spriggs equation empirically described the data and the zero porosity moduli as 283.6 GN/m/sup 2/ and 109.2 GN/m/sup 2/ for Young's and shear moduli, respectively. The Debye temperature calculated from the elastic constants was 484/sup 0/K. Several specimens had anomalously low moduli values, attributed to microcracking. Grain size and internal friction measurements showed that the microcracking occurred in specimens with grain sizes >2 to 3 ..mu..m and was characterized by high internal friction.

Elastic constants of the bcc phase in niobium-zirconium alloys between 4.2 and 300 K

Abstract: The adiabatic elastic constants have been determined for quenched single crystals of niobium‐zirconium alloys of the following nominal compositions: 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 70 at.% Zr. The c11, c12, and c44 constants as well as the shear constant C′= (1/2) (c11−c12) and the bulk modulus are given between 4.2 and 300 K. We observe for the whole range of compositions an anomalous temperature behavior for c44 similar to that found in pure Nb, but here the amplitude of the effect disappears progressively with increasing Zr concentration. The Debye temperatures were computed from the constants at 4.2 K.

Size and temperature dependence of the mössbauer debye waller factor of iron microcrystals

Abstract: Iron microcrystal ranging in size from 70 to 450 A have been investigated by the Mossbauer effect. There is, compared to the bulk value, a small enhancement of the magnetic field at the site of the nucleus of about 1% which can be interpreted as due to the demagnetisation field of the microcrystals and their geometric arrangement. The observed drastic size and temperature dependent lowering of the Debye Waller factor cannot be explained by a change of the Debye temperature of the microcrystals. Two different models are proposed to explain the effect.

The temperature dependence of the Raman spectra of some alkaline earth crystals with the fluorite structure

Abstract: The temperature dependence of the one-phonon Raman bands in single crystals of CaF2, BaF2, SrF2 and SrCl2 has been investigated over the temperature range 15-1300K The frequency shifts and linewidths are calculated according to quasi-harmonic theory Agreement is satisfactory for T< Theta , the Debye temperature, indicating a two-phonon decay process A small contribution due to anharmonic effects becomes evident above the Debye temperature for all crystals The temperature dependence of the Raman-active frequencies is found to increase in the order CaF2

Temperature dependence of the elastic shear moduli of the cubic metals

Abstract: A theoretical model for the temperature dependence of the elastic shear moduli of the cubic metals is presented which accounts for the quantitative relationship of these elastic properties to the thermal expansion. The particular phenomenon which the model is concerned with is the extremely rapid temperature variation of the shear moduli, which typically is about 25 times as great as the rate of thermal expansion. The model has the following salient features: (i) The interatomic pair pseudopotential is approximated over the important thermal range by means of a Morse potential; (ii) the thermal expansion is assumed to arise from anharmonic Morse oscillators which are further assumed not to be significantly coupled to each other; (iii) the exact quantum-mechanical solutions for the Morse oscillators are then combined with the Debye model to give an analytic formula for the thermal expansion; (iv) the elastic shear moduli are calculated from this, assuming nearest-neighbor interactions only. The calculated thermal expansions are found to agree quite well with the experimental values, particularly at low temperatures. The rapid temperature variation of the shear moduli is explained by the model in terms of the thermal movement of the nearest neighbors with respect to the interatomic-potential minima. Complete agreement between calculated and experimental shear moduli has been limited, however, by the contributions beyond the nearest neighbors which are not zero, and which have not been included in the formulas.

Anisotropic phonon dispersion in GaS

Abstract: The group theoretical analysis of lattice vibrations in GaS and neutron inelastic scattering measurements of acoustic phonons propagating along the Delta , Sigma and T directions are presented. The elastic constants C11, C33, and C44 are derived and the results for the Delta direction are analysed to determine interlayer force constants. The frequencies of the B1 modes along Sigma and T show a weak quadratic dependence on wavevector. A simple interatomic force model is fitted to the phonon frequencies, and the frequency distribution function is calculated. The temperature dependence of the lattice specific heat and of the corresponding Debye temperature is calculated; over a small temperature range the variation of the specific heat is characteristic of a pseudo-two-dimensional solid.

Phonon spectrum of CuCl at 4.2K and its temperature dependence

Abstract: The phonon dispersion curves of cuprous chloride have been determined at 4.2K by inelastic neutron scattering. The curves are very similar to those for the isomorphous CuBr and CuI. They are analysed within the shell model formalism, which permits the calculation of derived quantities such as one- and two-phonon densities of states, Debye temperature and amplitudes in the Debye-Waller factor for the individual ion. The frequencies of the phonons are not very temperature dependent: 6% renormalisation for some optic modes between 4.2K and 300K, but the peak intensity or the visibility is rapidly decreasing with increasing temperature, indicating the strong anharmonicity of CuCl.

High-Precision, Ultralow-Temperature Resistivity Measurements on Bismuth

Abstract: We report the first ultralow-temperature resistivity measurements on Bi with a precision better than 0.01% using a superconducting quantum interference device null detector. The results are inconsistent with simple carrier-carrier scattering. A Bloch-Gr\"uneisen formula for electron-phonon scattering gives an approximate fit to the lowest-temperature data with an effective reduced Debye temperature of the order of 2 K.

Comparison of the single‐crystal elastic constants of Th and a ThC0.063 alloy

Abstract: The elastic constants of a single crystal of pure thorium have been measured over the temperature range 4.2–300 K. Measurements were repeated on the same crystal after sufficient carbon had been added to bring the composition to ThC0.063. The results show that carbon addition strengthens thorium with respect to dilational deformation and with respect to torsional deformation along 〈110〉 directions, but weakens thorium with respect to torsional deformation along 〈100〉 directions. The changes with respect to torsional resistance result in a reduced anisotropy ratio, 2C44/(C11−C12). Carbon addition raises the Debye temperature by only ∼3%. Magnetic susceptibility measurements were made on the crystal both before and after carbon addition. The overall results are in qualitative accord with a directional covalent character for the Th‐C bonding interactions.

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

Abstract: The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 A (TmSe), 155 ± 7°K, 0·244 ± 0·012 A (SmS), 153 ± 14°K, 0·221 ± 0·020 A (SmSe) and 151 ± 20°K, 0·204 ± 0·027 A (SmTe).

Properties of 2:2 Chalcogenide Crystals with Sodium Chloride Structure

Abstract: Values of the compressibility, cohesive energy, atomization energy, force constant, i.r. absorption frequency, Debye temperature, Griineisen parameter, Anderson-Griineisen parameter and MoelwynHughes parameter for 45 chalcogenide crystals with sodium chloride structure are reported here. These have been obtained using a logarithmic interaction potential energy function. A new method of calculation, derived on the basis of the Moelwyn-Hughes parameter, has been employed for the computation of the potential parameters, since previous methods cannot be applied to these crystals in the absence of compressibility data. The results obtained are encouraging.

Melting of the Phase Locking of Linear Charge Density Waves in TTF–TCNQ

Abstract: The method of self-consistent phonons is applied to the melting of the interchain phase locking of linear CDWs. The melting point is obtained as T c =0.11( m * / m ) 1/2 θ t , where m * is the effective mass of the phase mode phonon and θ t is its transverse Debye temperature essentially equal to the phase locking energy of Lee, Rice and Anderson.

Electrical Conductivity in the Hubbard Model Including Electron‐Phonon Interaction

Abstract: Using the Hubbard model including weak electron-phonon coupling the electrical conductivity σ is calculated for U ≫ t (U intra-atomic Coulomb energy, —t nearest-neighbour hopping integral) and low frequencies. Especially the dc conductivity is investigated for the half-filled band and T ≫ TD (TD Debye temperature). It is compared with the dc conductivity in the phononless Hubbard model calculated in the approximation lim (σ/t2). The inclusion of phonons results in t 0 a finite transport relaxation time the temperature dependence of which leads to a shift of the conductivity maximum temperature to a lower value, the sharpening of the maximum, and to the decrease of the conductivity for high temperatures according to T−2. [Russian Text Ignored].

Empirical T3/2 law for atomic thermal vibration parameters

Abstract: The Debye‐Waller factor, as measured by x‐ray and neutron diffraction and Mossbauer techniques, is shown to be of the form a+bT3/2 over an extensive temperature range in a diverse set of crystalline solids. This two‐parameter empirical relationship may be interpreted within the framework of the Debye theory, modified to include quasiharmonic effects.

Mössbauer spectrum of 57Fe associated with a vacancy in aluminium

Abstract: The Mossbauer spectrum of a rapidly quenched Al-0·02 at. %−57Fe alloy hag been measured. The spectrum consists of two peaks. One corresponds to that of a solid solution of 57Fe in Al and appears at S T = 0·57 mm/s, while the other, at S T = 0·24 mm/a, is inferred to be that of 57Fe atoms associated with a vacancy. The s-electron density at the 57Fe nucleus associated with the vacancy is larger than that at the nucleus in solid solution. From the change in the recoilless fraction with temperature, the Debye temperature is estimated to be 240 K. for 57Fe in solid solution and 210 K for 57Fe atoms associated with a vacancy.

Specific Heat of CoSe2 and Mössbauer Effect of 57Fe Doped in CoSe2

Abstract: The specific heat and Mossbauer effect were measured of the metallic compound CoSe 2 , which has been reported to be antiferromagnet. It is concluded that CoSe 2 is not an antiferromagnetic but a paramagnetic metal down to 4.2 K. The Debye temperature is 345 K and the coefficient of electronic contribution to specific heat γ is 11 mJ/K 2 -mole.

Vacancy motion in solid helium

Abstract: A model calculation of the vacancy tunneling frequency in bcc 3 He, hcp 3 He, and hcp 4 He is presented. Only the Debye temperature (and its volume dependence) and vacancy activation energies (from NMR data) are used; comparison with experiment is made. The relative tunneling rates in the three systems along with NMR and specific heat data provide evidence for the nature of vacancy motion in each of these systems.

Adsorption and specific heat studies of4He in 0.2-µm Nuclepore filters

Abstract: We have made adsorption studies and specific heat measurements for helium adsorbed on Nuclepore filters with a pore size of 0.2 µm. We have been able to identify the first and second layer completion on this substrate by a Langmuir and BET analysis of the data. For coverages near the second layer completion the data obey a Frenkel-Halsey-Hill isotherm, and we have obtained the van der Waals constant α=(2.4±0.4)×10−37 erg-cm3. We find this result in excellent agreement with a theoretical estimate of 2.17 × 10−37 erg-cm3. The interpretation of the isotherm data is confirmed by measurements of the specific heat. Data near a monolayer completion is found proportional toT2 with a characteristic two-dimensional Debye temperature of ΘD=23±1 K. Measurements of specific heat with helium samples equivalent to about 17 layers and higher show two λ transitions shifted in temperature, as is characteristic of helium confined to two different small dimensions. These data are in agreement with the thermodynamic instability for capillary condensation in a cylindrical geometry as calculated by Saam and Cole.

Soft mode behavior of the high-superconducting transition temperature Sn-and pb-ternary molybdenum sulfides

Abstract: The heat capacities and magnetic susceptibilities of SnMo5S6 and PbMo5.1S6 were measured between 2 and 400 K. Superconducting transitions occur at Tc-values of ∼11.4 K and ∼12.3 K for the Sn-and Pb-ternaries, respectively. The ratio of the electronic heat capacity to susceptibility indicates a lower limit for λ, the electron-phonon mass enhancement, of unity for both materials. The effective Debye temperature of each material varies with temperature much more strongly than that for a simple metal, and suggests, as does the crystal structure, that the molybdenum-sulfur units can, to at least a low-order approximation, be regarded as molecular units, which are weakly bound to each other and to the Sn or Pb. Average internal-and external-mode frequencies are obtained using a simple harmonic model phonon spectrum to fit the heat-capacity data.