Showing papers on "Debye model published in 1974"

Phonon-Assisted Jump Rate in Noncrystalline Solids

Abstract: An exact calculation of the acoustic-phonon-assisted jump rate has been carried out. It is found that while the Miller-Abrahams (single-phonon) approximation is adequate for the study of shallow-impurity conduction at helium temperatures, it is typically inappropriate for the study of hopping between deep states in noncrystalline solids. In particular, the multiphonon jump rate will display a nonactivated temperature dependence below the Debye temperature which is similar to the often-seen $\mathrm{exp}[\ensuremath{-}{(\frac{{T}_{0}}{T})}^{\frac{1}{4}}]$ behavior.

Correlation of Properties of Materials to Debye and Melting Temperatures

Abstract: Many solid state properties are correlated to simple parameters like the atomic mass, the interatomic distance and some measure of the strength of the interatomic interaction, e.g. the melting temperature Tm or some Debye temperature θD. Such empirical relations are investigated for elastic properties, melting temperature, thermal expansion, vacancy formation energy, grain boundary and surface energy, cohesive energy, heat of fusion, activation energies for bulk, grain boundary, surface and dislocation pipe diffusion, viscosity, activation energy for creep, recrystallization temperature and other properties. When experimental data are available, both elements and diatomic compounds (alkali halides, oxides, carbides, III-V semiconductors) are considered. The correlations to Tm, θD(T = 0) and a high temperature effective θD are compared. It is found that for all practical purposes Tm gives the best correlation. For diatomic compounds, the average mass is not uniquely defined and various averages are discussed. The purpose of the paper is not only to present empirical relations but also to give a short account of the possibilities to calculate the considered parameters using solid state theory in its most advanced present state.

Elastic constants of some MAl2 single crystals

Abstract: Elastic constants of single crystals of the cubic Laves phases CaAl2, YAl2, LaAl2, and GdAl2 have been measured over the temperature range 4.2–300 K. The ferromagnetic transition in GdAl2 near 170 K is evident by changes in slope in plots of the three independently measured elastic constants of GdAl2 as functions of temperature. Debye temperatures at 0 K were evaluated as 474 K for CaAl2, 484 K for YAl2, 374 K for LaAl2, 399 K for magnetically disordered GdAl2, and 406 K for magnetically ordered GdAl2. It was inferred from the data that the valence electron distributions in nonsuperconducting YAl2 and GdAl2 are much alike, but the valence electron distribution in superconducting LaAl2 is significantly different. Thus the results support a theoretical calculation indicating an admixture of 4f character into the valence bands of LaAl2.

Pulse-induced critical scattering (pics) from polymer solutions

Abstract: Pulse-induced critical scattering (PICS) is a new, fast technique for determining thermodynamic and kinetic parameters of polymer solutions. Relative intensities of scattered laser light are measured over periods of seconds after a fast temperature step into the region of Debye critical opalescence. In the mode of operation using thermal pulses to progressively lower temperatures, the intensity pulse shape gives sensitive information on the fluctuation equilibrium and on the kinetics of phase separation with formation of emulsions of sub-wavelength particles, Spinodal and critical loci for the system polystyrenecyclohexane (PS–CH) are measured about 10 times faster and more accurately than in recent work based respectively on conventional light scattering equipment and on turbidimetry. The classical Debye theory of scattering near a critical point, or Scholte's extension to spinodal points, gives excellent semi-empirical extrapolations to spinodal temperatures T s . Though there are signs that the classical theory needs amendment in the sense of the generalized nonlinear theory of Fisher, Chu, and co-workers, this would generally give results on T s in close agreement with the simpler classical theory in the experimental range accessible to PICS. The effects of heterodispersity on the phase diagram are studied, comparing data by Scholte and new data by PICS on PS–CH. The evidence suggests that spinodal loci are governed mostly by M w (as suggested by recent theories). Marked secondary effects seem, however, to arise, not (as recently suggested) from M n , but from M z . Results obtained by the technique of approaching phase equilibrium from the heterogeneous side, using an emulsion carefully ‘seeded’ by a thermal step, suggest that supercooling is more serious in cloud-point determinations of dilute polymer solutions than hitherto thought. The formation of sub-wavelength droplets follows kinetics bearing more than formal resemblance to that for the nucleation and growth of spherulitic crystals in bulk.

Some effects of phonon dynamics on electron lifetime, mass renormalization, and superconducting transition temperature

Abstract: Effects of the dynamical properties of phonons on the electronic properties of metals are treated through the use of the phonon spectral weight function. It is shown that the leading behavior of the electron quasiparticle lifetime is lowered to quadratic in the frequency or temperature from the cubic behavior which is well known to occur for infinitely sharp phonons. Explicit evaluations of $\frac{1}{\ensuremath{\tau}}$ are made using an extension of the Debye model which allows for a finite phonon lifetime. The mass-enhancement parameter $\ensuremath{\lambda}$ is discussed and is shown formally to be related to the static phonon propagator. Thus if there is a difference between the phonon relaxation at zero frequency and at the phonon frequency, it is possible for the phonon frequencies which determine $\ensuremath{\lambda}$ to differ significantly from the peak frequencies observed in inelastic neutron scattering. The implications of these results for superconducting transition temperatures are discussed with particular reference to recent neutron scattering experiments in ${\mathrm{Nb}}_{3}$Sn.

Thermal expansion, Debye temperature and Gruneisen constant of carbides and nitrides

Abstract: The experimental data on the thermal expansion of the carbides and nitrides of the early transition metals (with B 1 structure) have been collected and evaluated, and average curves of α against temperature and composition have been determined. Some of the difficulties encountered in making good thermal expansion measurements peculiar to this class of compounds are briefly discussed. The resultant values of α, together with the experimental specific heat and elastic constants, are used to determine the temperature dependence on the Debye temperature and the Gruneisen constant.

Thermal Conductivity of Borosilicate Glass

Abstract: The thermal conductivity of a borosilicate glass has been measured in the temperature range 0.05-50 K. The samples contained well-defined holes to provide a source of phonon scattering. The results are consistent with the predictions of the Debye model using experimentally measured sound velocities. The results also indicate that thermal transport at temperatures below \ensuremath{\approx} 30 K is provided by low-frequency phonons having a characteristic temperature \ensuremath{\lesssim} 3 K.

Electrical Properties of Ni1-xS

Abstract: Hexagonal nickel sulfide NiS shows a metal-nonmetal transition with the appearance of antiferromagnetism as temperature is lowered below 265 K ( T t ). Measurements of conductivity, Hall coefficient, thermoelectric power and magnetoresistance were made on polycrystalline samples of hexagonal Ni 1- x S (0.004≦ x ≦0.050). The low temperature phase is found to be a degenerate semiconductor with a high hole density from 3.13×10 20 cm -3 ( x =0.004) to 1.60 ×10 21 cm -3 ( x =0.020), which is essentially due to ionized nickel vacancies. Carriers are mainly scattered by ionized and neutral impurities associated with nickel vacancies. The effective mass is estimated from Seebeck coefficients to have a value between 1.50 m 0 and 2.90 m 0 . Above T t , the compound is a normal metal without a magnetic moment. The low temperature resistivity has revealed the Debye temperature to be 175 K for the metallic phase. There is no apparent evidence of a strong correlation effect although the electronic state densities are l...

A determination of the Debye–Waller temperature factor and the X‐ray Debye temperature for Ni, Cr, Fe, Mo and W

Abstract: The integrated intensities of high-order reflexions for Ni, Cr, Fe, Mo, and W powder samples were measured at 296 and 77°K with Mo Kα radiation. The values 397 ± 6, 510 ± 6, 435 ± 6, 407 ± 6, and 333 ± 6°K respectively were obtained for the Debye temperatures after correction for thermal diffuse scattering. These values are in good agreement with those calculated from force-constant models determined by inelastic neutron scattering.

The specific heat of high purity gadolinium between 1.5 and 14K

Abstract: The specific heat of high purity gadolinium, prepared by solid electrotransport processing, has been measured in the temperature range 1.5 to 14K, and the data analysed for electronic, Debye and magnetic contributions to the total specific heat. The electronic coefficient gamma was found to be 3.7+or-0.2 mJ mol-1 K-2 and the magnetic specific heat, assumed to be of the form CM=BTn, yielded B=1.94+or-0.04 mJ mol-1 K-(n+1) with n=1.75+or-0.05. The Debye temperature between 1.5 and 5K was calculated to be 187+or-3K, while for temperatures in excess of 5K it was found to decrease with temperature to a constant value of 160+or-3K above 12K.

Elastic constants of niobium‐rich zirconium alloys between 4.2 K and room temperature

Abstract: The adiabatic elastic constants were determined for niobium and for its alloys containing 1.4, 3.6, and 6.0 at.% zirconium. The c11, c12, and c44 constants as well as the shear constant C′ = (1/2)(c11 − c12) and the bulk modulus were tabulated between 4.2 and 290 K. The unusual temperature dependence of the shear constant c44 found in niobium was also observed in the alloys. The Debye temperatures were computed from the constants at 4.2 K.

Interference Effects in Neutron and X Ray Scattering

Abstract: The properties of interference between the one and multiphonon contributions to the dynamic and static scattering functions, S(Q, a) and S(Q), first considered by Ambegaokar er al., are discussed in detail for b.c.c 3He and 4He for comparison with recent neutron and proposed X ray scattering experiments. Calculations of interference for Na and of the Debye temperature appropriate to the Debye-Waller factor in b.c.c 3He are also presented. In all cases the on shell interference term which alters the one phonon scattering intensity is found to be more important than the off shell term which alters the one phonon line shape. This is characteristic of systems in which anharmonic effects produce a large phonon frequency shift but in which the phonon Iifetimes remain long. The difficulty in establishing the one phonon sum rules experimentally in the presence of interference is emphasized. As noted by Horner, existing unusual variations of scattering intensity observed in solid 4He can be satisfactorily explained by taking account of interference and this difficulty without introducing an anomolous Debye-Waller factor. Comparisons with liquid 4He suggest a similar difficulty in establishing the sum rules there.

Specific heat of 2H NbSe2

Abstract: The specific heats of four samples of 2H NbSe2 have been measured in the temperature range from 1 to 54 K. No anomalous behavior was found near 40 K where x‐ray, NMR, and Hall‐effect measurements have indicated the presence of a phase transition. An upper limit of 0.3 J/mole K has been placed on the magnitude of any anomaly in the heat capacity associated with this transition. Measurements of high‐purity stoichiometric 2H NbSe2 sample gave a superconducting transition temperature of 7.23 K, a specific heat jump (ΔC) in zero field of 240 mJ/mole K, and a Debye temperature of 204 K. A deviation from the usual T3 behavior for the lattice contribution to the heat capacity was observed and assumed to be due to the two‐dimensional layer structure of the compound. Our best estimate for the electronic coefficient of specific heat (γ) is about 10±5 mJ/mole K2. Based on the values for Tc and ΔC, the value for γ calculated from BCS theory is 23 mJ/mole K2 for 2H NbSe2 which is in disagreement with our estimated valu...

Mössbauer Spectroscopy of 125Te — Some New Results and Applications

Abstract: Narrow and reproducible linewidths for the 35.5-keV Mossbauer resonance in 125Te have been observed with a 2.7-year 125Sb source diffused in Cu. Measurements made on cubic ZnTe as a function of absorber thickness reveal that the linewidth of these sources is Γsource = 5.20 ± 0.08 mm/sec. This result is in good agreement with the minimum observable line-width 2Γnat as calculated from the measured half-life of the 3/2 level, t½ = 1.475 ± 0.010 nsec. From this Mossbauer measurement the Debye temperature of cubic ZnTe is found to be 175 ± 9 °K. The Mossbauer effect in 125Te provides a useful technique for characterizing amorphous chalcogenide semiconductors. Investigations on sputtered thin films of amorphous GexTe1-x were performed as a function of composition, temperature, and heat treatment. The variation of the quadrupole splitting as a function of composition exhibits discontinuities in slope at x = 0.33 and 0.50. These results are indicative of chemical ordering in the amorphous GexTe1-x system at these compositions. A structural model of amorphous GexTe1-x alloys based on two inequivalent Te sites is developed for the Te rich phase and is found to fit the data well. Annealing of the films is shown to lead to a greater degree of structural order on a microscopic scale. Crystallizing the films is shown to lead to phase separation of the system into crystalline GeTe and Te metal.

Specific heat of single crystal NiO from 3.2 to 18.75 K

Abstract: The specific heat of single crystal NiO has been measured from 3.2 to 18.75 K. The Debye temperature was found to be 595±20 K.

Electron distribution in BN

Abstract: The Compton profiles of cubic and hexagonal BN have been measured with AgKα X-rays on polycrystalline samples and reveal a somewhat broader distribution in electron momenta for the cubic form The structure factors for cubic BN were measured on a polycrystalline sample with monochromatic MoKα and CuKα The values of the 111 and 200 structure factors (the latter is absent in diamond) reveal a significant change in the valence electron distribution as compared to a superposition of free-atom charge densities Solid state theoretical structure factors are available for comparison in the following paper (Euwema, Surratt, Wilhite and Wepfer 1974) The Debye-Waller factor for cubic BN indicates an effective Debye temperature only about one half that of diamond (750°K compared to 1500°K) but this is consistent with specific heat measurements for diamond and cubic BN The magnitude of the (420) structure factor suggests that the thermal mean-square displacement of the boron atoms is larger than that of t