Showing papers on "Debye model published in 1980"

Equation of state and melting properties of He 4 from measurements to 20 kbar

Abstract: We measured simultaneously the pressure, volume, temperature, and ultrasonic longitudinal velocity in fluid $^{4}\mathrm{He}$ from 75 to 300 K and 2 to 20 kbar. The data were fitted to a Benedict-type equation of state from which various thermodynamic quantities were calculated. From 75 to 97 K the measurements extended into the solid region, yielding values of the melting properties and new constants for the Simon melting equation. We used the Lindemann relation to determine a Debye temperature from which the ultrasonic transverse velocity of solid. $^{4}\mathrm{He}$ was estimated. The melting entropy was analyzed to determine the contribution due to disordering of the atoms.

Magnetic susceptibility, specific heat, and the spin-glass transition in Hg 1 − x Mn x Te

Abstract: A systematic study of the low-dc-field magnetic susceptibility and the specific heat has been carried out on mixed ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ crystals, in the composition range $0l~xl~0.35$. The alloy with $x=0.35$ showed spin-glass behavior below $T=10.9$ K. At this Mn concentration the sample is a very poor conductor at low temperatures, so that the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism cannot be responsible for the spin-glass transition. Also, since the Mn ions interact only antiferromagnetically, the observed spin-glass phase does not result from competition between ferro- and antiferromagnetic interaction. It must therefore be ascribed to the frustration of the antiferromagnetic interactions inherent in an fcc sublattice over which the Mn ions are distributed. For $xl~0.25$, the ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$ samples remain paramagnetic down to 1 K. Experimental results for the specific heat and the susceptibility for $xl0.1$ are discussed in terms of a cluster model which leads to an estimated value of the antiferromagnetic exchange constant $\frac{J}{k}\ensuremath{\approx}\ensuremath{-}0.7\ifmmode\pm\else\textpm\fi{}0.3$ K. When a random distribution of Mn ions over the fcc sublattice is assumed, calculated values for the specific heat and the susceptibility differ substantially from the experimental results for the low Mn concentration. This therefore indicates that in real crystals the distribution of Mn ions is very different from random. To obtain agreement between calculated and experimental results, the number of single ions has to be reduced to less than 30% of the number corresponding to a purely random distribution, leading to the conclusion that the magnetic ions prefer to cluster rather than to remain isolated in ${\mathrm{Hg}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{Te}$. For HgTe, the Debye temperature ${\ensuremath{\Theta}}_{D}$ is 141 K at $T=0$ K, and goes through an anomalously low minimum value of ${\ensuremath{\Theta}}_{D}=77$ K at 7 K. A very small linear term in the low-temperature specific heat of HgTe gives an estimate of the electric charge carrier density in the ${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ range.

Asymmetric effects in the extended X-ray absorption fine structure analysis of solid and liquid zinc

Abstract: Extended X-ray absorption fine structure (EXAFS) results are presented for solid and liquid Zn for the temperature range 273 to 782 K. At the higher temperatures the distribution of nearest neighbour atoms is asymmetric. Neglect of the asymmetry and use of EXAFS analysis methods developed for symmetric distribution functions gives an underestimate of the nearest neighbour distance R1 and the disorder parameter σ12. It is shown that a transform analysis can be useful in detecting asymmetric effects, and methods of analyzing the EXAFS of asymmetric distributions are presented. An anharmonic oscillator model is applied to the EXAFS data of polycrystalline Zn to correct the values of R1 and σ12. The corrected values of σ12 are found to be~20% higher than those predicted by a Debye model. An empirical, analytically simple asymmetric distribution function is fitted to the liquid data to obtain promising agreement with the nearest neighbour structure as deduced from X-ray diffraction studies. Finally it is shown...

THERMAL EXPANSION OF MODIFIED SPINEL, β-Mg2SiO4

Abstract: Thermal expansion of β-Mg2SiO4 (modified spinel; orthorhombic symmetry) was measured by the X-ray powder diffraction method in the temperature range between 20°C and 800°C. Gruneisen's theory of thermal expansion was applied to the linear and volume expansion data, and thermal expansion coefficients were obtained to be αa=9.14, αb=5.46, αc=5.92, and αv=20.6 in unit of 10-6/K, at 293K. Gruneisen's parameter γG=1.26 was obtained by assuming the Debye temperature to be 952K. The magnitude of volume expansion coefficient of β-Mg2SiO4 is located between those of γ- and α-phases. β-Mg2SiO4 is found to be a significantly anisotropic material both in thermal expansion and elasticity.

Temperature and pressure dependence of intrinsic anharmonic and quantum corrections to the equation of state

Abstract: Results of detailed calculations of the anharmonic and the quantum corrections to the equation of state and to Gruneisen's parameter γ are given for pressures P from zero to 2B0 (where B0 is the bulk modulus at P = 0 and T = 0) and for temperatures T from zero to (0.6) Te (where Te = ∈/k,∈ is the depth of the potential well and k is Boltzmann's constant). Interionic potentials of the form A/r+ϕR with ϕR proportional to r−12, r−8, and e−αr were used. It was found, for example, that at T = (0.2) T∈ the anharmonic corrections to P for the potentials in the order just given were approximately 7, 6, and 4% at P = (0.1)B0, while they were approximately 1, 1, and ½% at P = (0.5)B0. Quantum corrections to P were found to depend very weakly on P and to be about 1% or less for (0.2)B0 < P < 2B0 for temperatures above the zero-pressure Debye temperature. Anharmonic corrections decreased the values of γ and of P, while quantum corrections decreased the value of γ but increased the value of P.

Thermal expansion in insulating materials

Abstract: A model of thermal expansion in terms of the Morse potential which was developed earlier for low temperatures is extended to high temperatures and applied to a semiempirical calculation of thermal expansion in insulating materials. In this model, the localized quantum mechanical solutions of the Morse potential are combined with the Debye model to give a localized-continuum description of thermal expansion. A set of empirical rules is developed for characterizing the interatomic potential in terms of the Morse potential. These are then applied to the quantitative calculation of thermal expansion in the alkali halide crystals and a group of binary high temperature materials with the aid of the known crystal structures, compressibilities, and Debye temperatures of these materials. Good agreement between calculated and experimental values is obtained for temperatures ranging between 0 K to values near the melting points. A discussion of the underlying basis of the empirical rules is given as well as their likely applicability to a wide range of insulating materials.

Thermal expansion of ZnTe and HgTe and heat capacity of HgTe at low temperatures

Abstract: The linear coefficient of thermal expansion of ZnTe and HgTe is measured between 1.5 and 30K by means of a three-terminal capacitance dilatometer; the heat capacity of HgTe is measured in this temperature range. Values gamma 0th=0.07+or-0.07 (ZnTe) and -1.2+or-0.2 (HgTe) are obtained for the zero-temperature limit of the Gruneisen parameter. The former value is in good agreement with gamma 0el=0.05 calculated from the pressure derivatives of the elastic moduli. The low-temperature limiting value of the Debye temperature theta 0th=147.5+or-2K for HgTe. The variation of gamma (T) and theta D(T) as functions of reduced temperature, T/ theta D, fit the patterns established previously for other II-VI compounds of zincblende structure.

A New Low Temperature Phase (fct) of Fe–Pd Invar

Abstract: A new fct phase of disordered Fe–Pd Invar alloys was found at low temperatures. The low temperature phase diagram was obtained from X-ray diffraction experiments (4.2 K to 300 K). The fct phase ranges from 28% to 33.5% Pd at 0 K and the temperature dependence of lattice constants was determined. A decrease of the X-ray Debye temperature associated with a lattice softening was observed for 34% Pd in the low temperature region.

Low-temperature specific heat of the graphite intercalation compounds K C 8 , Cs C 8 , Rb C 8 , and their parent highly oriented pyrolytic graphite

Abstract: The specific heat of the graphite intercalation compounds KC/sub 8/, CsC/sub 8/, and RbC/sub 8/ and their parent material, highly oriented pyrolytic graphite (HOPG), has been determined between 0.48 and 90 K. The results are analyzed in terms of electronic and lattice contributions. The electronic contribution to the specific heat of these compounds is enhanced by at least 29 times above that for HOPG. Comparisons are made to theoretical band-structure calculations. The lattice contribution shows deviations from a Debye model for T>5 K, which can be mathematically fitted by an Einstein specific-heat function. While our results for RbC/sub 8/ are unique, comparison with previous results for powder-based KC/sub 8/ and CsC/sub 8/ samples over a limited temperature range suggest that the type of parent graphite and/or details of preparation technique may influence the physical properties of these compounds.

The Fokker-Planck-Langevin model for rotational Brownian motion. II. Comparison with the extended rotational diffusion model and with observed infrared and Raman band shapes of linear and spherical molecules in fluids

Abstract: A detailed comparison of two extensions of the Debye model for molecular reorientation in liquids, Gordon’s extended J‐diffusion model and the rotational Fokker–Planck–Langevin model, is presented It is shown that the two models, although they represent very different physical pictures of rotational dynamics in fluids, lead to remarkably similar reorientational correlation functions, memory functions, correlation times and spectral densities Only for values of the angular momentum correlation time appropriate to low density fluids do the two models give significantly different results, but the validity of the FPL model is questionable in this region The results of an infrared study of the ν3 band of N2O in N2O/O2 along the coexistence curve from 105–153 K, and in N2O/N2 along the 80 bar isobaric line from 100–300 K are presented The reorientational correlation functions from these measurements, and from earlier infrared studies of CO/N2 and Raman studies of CF4 and N2O liquids are compared with correl

Effect of high-magnetic fields on the electronic specific heat in the strongly Pauli-paramagnetic compound LuCo/sub 2/

Abstract: The low-temperature (1.3 to 20.0 K) heat capacity of the strongly Pauli-paramagnetic Lu${\mathrm{Co}}_{2}$ compound was measured in magnetic fields up to \ensuremath{\sim}10 T. The measured results show that the electronic-specific-heat constant decreases with increasing magnetic field (11% at 10 T), while the Debye temperature does not change. This is probably due to the depression of spin fluctuation enhancement of the heat capacity by moments induced on the cobalt atoms by the high magnetic fields. These results appear to be in accord with recent theoretical predictions.

Influence of the lattice and electronic factors on the hydrogenation properties of the RNi5-base (R is a rare earth) haucke compounds: Results of low temperature heat capacity measurements

Abstract: The low temperature heat capacities (1 – 20 K) and the hydrogen absorption properties of some ternary Haucke compounds — LaNi5−xAlx (0 ⩽ x ⩽ 1.5), LaNi5−xPtx (0 ⩽ x ⩽ 5) and La1−xThxNi5 (0 ⩽ x ⩽ 1)—were investigated to examine any correlation between the ability of these compounds to absorb hydrogen and their physical properties, e.g. their electronic structure and elastic properties. The density of states at the Fermi level has a minimum near x = 1 in LaNi5−xAlx. The electronic specific heat constants of LaNi5−xPtx decrease in a smooth fashion as the concentration of nickel decreases. La1−xThxNi5 alloys, however, only exhibit a slight change in their electronic specific heat constants. The low temperature heat capacities were also measured for the hydrides of these compounds. The electronic specific heat constant γ and the Debye temperature θD of the LaNi5−xAlxHy phase do not change as drastically, relative to the corresponding LaNi5−xAlx phase, as those for the RH2 compounds change relative to the corresponding pure metal R. This is probably caused by filling of the new bonding states formed in these compound hydrides with the added electrons of hydrogen.

Plasma shifts of hydrogenic-ion lines

Abstract: Systematic red shifts for the Paschen ..cap alpha.., ..beta.., and ..gamma.. lines (n=4,5,6..-->..n=3) of He II are observed over an electron density range of (1--8) x 10/sup 22/ m/sup -3/. The measurements are compared with combined estimates for plasma polarization and ion quadrupole effects. It is demonstrated that previous theoretical estimates have left out an important contribution to the polarization shift, which we estimate using the Debye model.

Optical and thermal properties of BeO thin films prepared by reactive ionized‐cluster beam technique

Abstract: Preparation of BeO thin films is successfully achieved by the reactive ionized‐cluster beam technique developed by the authors. Transparent BeO films with the c‐axis preferential orientation which is peculiar to a hexagonal structure are obtained on glass substrates, and single‐crystal epitaxial films are formed on sapphire substrates at low substrate temperatures up to 400 °C. Optical and thermal transport properties of films are investigated in detail. A strong reststrahlen reflection peak is observed in the vicinity of wavelength 13.5 μm, from which the frequencies of the transverse and longitudinal vibration modes are determined. Anisotropic lattice thermal conductivities parallel and perpendicular to the c axis of the films are measured, and the values of κ∥ph ?2.6 W/cm deg and κ⊥ph ?0.6 W/cm deg at 300 K are obtained. It is also shown that the thermal conductivities of BeO films are proportional to T−2 below Debye temperature ϑD?1053 K of this material.

Lattice dynamics of Na2S

Abstract: Inelastic neutron scattering has been used to measure the phonon dispersion relation along (001), (110) and (111) directions of a single crystal of Na2S at 50K. A simple shell model has been successfully fitted to the data. Dynamic quantities such as density of states, Debye temperature, displacement-displacement correlation functions and mean square ionic displacement are computed from the model and compared with CaF2. Finally some remarks on the ionic conductivity of antifluorites are given.

Enhancement of Superconductivity through Lattice Softening.

Abstract: The superconducting transition temperature of an iridium-yttrium eutectic is enhanced extraordinarily through lattice softening. This is shown by a drastically reduced Debye temperature.

Mossbauer effect study of lattice vibration of small iron particles

Abstract: The recoilless fraction fa has been determined as a function of temperature for small iron particles (average diameter 100 to 150 AA). The effect of the motion of the particle as a whole on the observed fa is averted by embedding the particles in matrices. The particles have an oxide surface layer 1-2 layers thick. It is concluded, from the comparison of the temperature dependences of fa for the particles and a bulk specimen, that the lattice vibration of the metallic core of the particles is not softened as compared with the bulk, while the lattice vibration of the oxide surface layer is very soft. The Debye temperature of the metallic core is found to be 470+or-30K.

X-Ray Diffraction Study of Fine Gold Particles Prepared by Gas Evaporation Technique. : II. Characteristic Temperature

Abstract: From an analysis of the X-ray Debye-Scherrer lines from fine gold particles with the mean size of 100 A, the mean square atomic displacement, , was determined at several temperatures in a range from 112 to 298 K. The temperature dependence of was analysed on the basis of the Einstein approximation for the thermal vibrations of atoms and a characteristic temperature θ M =143±3 K was obtained. This is 15% less than the Debye temperature θ M =168 K for the bulk crystal. It was found that the observed includes the temperature independent component, impling the existence of some kind of static lattice distortions. The contribution from such lattice distortions depends on the preparation condition of fine gold particles.

Hot electrons in metals at low temperatures

Abstract: Hot electrons in metals at helium temperatures under steady conditions can be produced by passing an electric current of moderate density (≲ 106 A/cm2) through thin, narrow (~1 Μm wide) metallic films in good thermal contact with bulk single-crystal dielectric substrates. This paper is concerned with the theory of hot electrons in normal metals at low temperatures (when θ ≪ θD, where θ is the average electron energy and θ D is the Debye temperature). The theory is formulated in terms of realistic electron and phonon dispersion laws, taking into account the experimental possibility of heat removal from the sample. In the case in which the temperature approximation of Kagnov, Lifshitz, and Tanatarov is not satisfied when elastic scattering of electrons is dominant in a steady state electric field, the kinetic equation is derived for the energy-dependent, hot electron distribution function, which determines the associated nonlinear responses. The solution of this equation is discussed for a simple model. It is shown that the experimental information on the electron-phonon interaction in a metal can be obtained in terms of the well-known spectral functions S(Ω) ≡ α2 F(Ω) and g(Ω) ≡ αtr 2 F(Ω). This is illustrated by experiments determining the nonlinear field dependence of the resistance, by tunnel experiments, and by critical current hysteresis measurements (for superconducting metals). Theoretical estimates which support the observability of the effects under discussion are presented.

Diffractive scattering of H atoms from the (001) surface of LiF at 78 K

Abstract: We have built an apparatus for the measurement of high resolution diffractive scattering of hydrogen atoms from crystal surfaces. The apparatus comprises a hydrogen atom beam source, a hexapolar magnetic field velocity selector, a variable temperature UHV crystal manipulator, and a rotatable bolometer detector. The diffraction pattern of a beam of hydrogen atoms scattered by a (001) LiF surface at 78 K has been obtained for different angles of incidence and different orientations of the crystal. The Debye–Waller factor has been measured leading to a surface Debye temperature ϑS=550±38 K. The corrugated‐hard‐wall‐with‐a‐well model of Garibaldi et al. [Surf. Sci. 48, 649 (1975)] has been used for the interpretation of the intensities of the diffracted peaks. By means of a best fit procedure we obtain a main ’’corrugation’’ parameter ξ0=0.095 A. By comparison of the data with the theory of Cabrera et al. [Surf. Sci. 19, 70 (1967] at the first order, the strength parameters of a periodic Morse potential have ...

Low-temperature lattice specific heats of an amorphous Pd-Si alloy subjected to various heat treatments

Abstract: The low-temperature specific heats of an initially amorphous Pd-Si alloy subjected to various heat treatments are measured in the temperature range 1.5-4.2K. All the results fit well to the usual equation C= gamma T+ alpha T3+ delta T5. As recovery, or crystallisation, proceeds with heat treatment, the Debye temperature theta D is found to increase, while the delta coefficient decreases. It is found that the lattice specific heat behaviour can be interpreted on the basis of a comparison to the observed relationship between theta D and delta in a number of crystalline metals and alloys. This comparison suggests that the lattice vibrational modes of an amorphous and of a crystalline Pd-Si alloy at low temperatures are rather similar to those of many crystalline metals and alloys, and that the observed change in the theta D and delta coefficients due to the heat treatment merely results from an increase in the packing fraction of the constituent atoms.

Vibrational states in a model amorphous Cu57Zr43

Abstract: The vibrational density of states of a model amorphous Cu57Zr43 alloy was calculated by the recursion method. A general agreement was obtained between the calculated result and the experimental one reported for amorphous Cu44Zr56 alloy. The wavenumber-dependent spectra for both longitudinal and transverse excitations were also calculated. The elastic constants estimated from the sound velocity (Young's modulus E=0.80 Mbar, shear modulus G=0.30 Mbar) agreed fairly well with the experimental results (E=0.745 Mbar, G=0.244 Mbar). The Debye temperature was estimated to be 327K, which is 30K higher than that determined from experimental DOS spectra.

Thermal Conductivity, Thermal Diffusivity and Specific Heat of Lithium Fluoride Crystals Containing Dislocations

Abstract: The thermal conductivity and thermal diffusivity of lithium fluoride single crystals have been measured simultaneously by the temperature wave method at 1.5–20 K. The specimens were successively deformed by compression and dislocations with densities of 10 6 –10 8 cm -2 were introduced. The diffusivity data were used to analyze the scattering of phonons by dislocations. The analysis was made with the Callaway's method, and the empirical representation of the relaxation rate for the dislocation scattering was found to be a sum of two rates with different dependences on phonon frequency: τ F -1 ∝ω -1 and τ A -1 ∝ω 2 . The former corresponds to the phonon scattering by the fluttering of dislocations, while the latter represents other unknown scattering mechanism effective at high temperatures. Specific heat of the crystals was also determined from the conductivity and diffusivity data. The Debye temperature was found to decrease or the specific heat to increase by fairly large amount when dislocations were i...