Showing papers on "Debye model published in 1972"
TL;DR: In this paper, the thermal conductivities of over twenty single crystals of synthetic ZnO, ZnS and HgTe have been measured from temperatures of 3 to 300 K.
Abstract: The thermal conductivities $\ensuremath{\kappa}$ of over twenty different single crystals of synthetic ZnO, ZnS, ZnSe, ZnTe, CdTe, and of natural, cubic ZnS have been measured from temperatures of 3 to 300 K The results for the undoped crystals above 30 K can be scaled using the parameter $\overline{M}\ensuremath{\delta}{\ensuremath{\Theta}}^{3}$, where $\overline{M}$, $\ensuremath{\delta}$, and $\ensuremath{\Theta}$ are the average mass, interatomic spacing, and Debye temperature, respectively A comparison of these results with those in the literature for BeO, CdS, CdSe, HgSe, HgTe, Si, Ge, GaAs, and InSb show that the same scaling parameter applies for most of them The compounds HgSe and HgTe exhibit anomalously low $\ensuremath{\kappa}$ values Crystals doped with ${\mathrm{Fe}}^{2+}$ show a resonant-type one-phonon scattering from the five low-lying energy levels of this $3{d}^{6}$ ion Group theory shows that the strongest scattering occurs for phonons of energy $2\ensuremath{\Delta}$, where $\ensuremath{\Delta}$ is the interlevel spacing of the ${\mathrm{Fe}}^{2+}$ ion
155 citations
TL;DR: In this paper, the hydrodynamic velocity υϕ along the path of constant crystallographic structure was approximated by the formula ∂ ln υ ϕ/∂ lns ρ = − ½[1−(∂ln VM/∆ ln A)]−1, where ρ is the density and VM is the molar volume.
Abstract: Simple approximations for the lattice vibrational spectrum allow the regularities of velocity-density plots with structure and composition to be semiquantitatively explained from a simple and unified point of view. It is possible to explicitly separate paths of constant mean atomic weight A where velocities change because of compression or phase changes from paths of constant crystallographic structure where the mean atomic weight is changed. One can approximate the hydrodynamic velocity υϕ along the path of constant crystallographic structure by the formula ∂ ln υϕ/∂ ln ρ = − ½[1−(∂ ln VM/∂ ln A)]−1, where ρ is the density and VM is the molar volume.
122 citations
TL;DR: In this paper, the surface Debye temperature of a LiF crystal was derived from measurements of the specularly reflected intensity of a thermal beam of atomic hydrogen impinging on the surface of the crystal.
94 citations
TL;DR: In this article, it was shown that LaAl2 behaves as a B.C.S. superconductor and the electronic specific constant, γ, is anomalously high compared to YAl2 and LuAl2.
86 citations
TL;DR: In this article, the Debye characteristic temperature at 0 K was calculated from the elastic constants, which was shown to be at most 221.0$ K for all previously measured face-centered-cubic alkali halides.
Abstract: The adiabatic elastic constants have been measured in single crystals of rubidium fluoride over the temperature range of 300 to 4.2 K to investigate a discrepancy with neutron scattering data. The values of the elastic constants at 0 K, extrapolated from 4.2 K, are ${C}_{11}=6.527$, ${C}_{44}=0.952$, and ${C}_{12}=1.255$ in units of ${10}^{11}$ ${\mathrm{d}\mathrm{y}\mathrm{n}/\mathrm{c}\mathrm{m}}^{2}$. The Debye characteristic temperature at 0 K (${\ensuremath{\Theta}}_{D}$) as calculated from the elastic constants is ${\ensuremath{\Theta}}_{D}=221.0$ K. A summary of Debye temperature values calculated from elastic constant data at 0 K is presented for all previously measured face-centered-cubic alkali halides.
72 citations
TL;DR: In this paper, the adiabatic elastic constants for Niobium and niobium-molybdenum alloys of the following nominal compositions: 15, 25, 35, 50, 75, and 90 wt.% Mo.
Abstract: The adiabatic elastic constants were determined for niobium and niobium‐molybdenum alloys of the following nominal compositions: 15, 25, 35, 50, 75, and 90 wt.% Mo. The c11, c12, and c44 elastic constants of these bcc alloys were tabulated between −190 and +100°C. The effects of compositional changes on the elastic constants were far greater than those due to temperature. An anomalous temperature dependence for c44 was found for the niobium‐rich alloys. An analysis of the elastic constants in terms of central forces revealed that nearest‐and second‐nearest‐neighbor force constants rise with molybdenum additions, with the latter tending towards a maximum as the composition of pure molybdenum is approached. This is thought to be associated with the filling of a d subband. The Debye temperatures were computed and found to be generally in good agreement with the calorimetrically determined values reported in the literature.
69 citations
TL;DR: In this paper, a quantum-mechanical treatment of the one-phonon inelastic scattering of gas atoms in three dimensions by a solid surface is presented, where the gas-surface interaction is represented by a potential which consists of an infinite repulsive step with zero well-depth.
60 citations
TL;DR: In this paper, an analysis of the Mossbauer effect spectrum of a well-characterized sample of the marcasite-type compound FeSb 2 showed that the unusual temperature dependence of the quadrupole splitting is a result of the promotion of electrons across an energy gap.
46 citations
TL;DR: The static magnetic susceptibility from 1.6 to 300°K and the heat capacity in fields of 0 and 5 kG from 0.9 to 10.2°K have been measured on polycrystalline samples of the complex of 1,3-bisdiphenylene-2-phenylallyl with benzene, commonly abbreviated BDPA.
Abstract: The static magnetic susceptibility from 1.6 to 300°K and the heat capacity in fields of 0 and 5 kG from 0.9 to 10.2°K have been measured on polycrystalline samples of the complex of 1,3‐bisdiphenylene‐2‐phenylallyl with benzene, commonly abbreviated BDPA. The data are shown to correspond to antiferro‐magnetic Heisenberg linear chains characterized by a nearest‐neighbor exchange integral of −4.6°K. Weak interchain coupling results in a paramagnetic—antiferromagnetic phase transition at 1.695°K in zero field, as evidenced by the sharp heat capacity anomaly at that temperature. Resolution of the heat capacity into a lattice T3 contribution and a magnetic contribution yields a Debye temperature of 52.5°K and a magnetic entropy per mole of 101% of the expected Rln2.
41 citations
38 citations
TL;DR: In this article, the Debye-Waller theory is applied to atomic helium scattering from various solid surfaces and a gas-surface potential well depth of ∼500 cal/mol is calculated.
Abstract: The Debye‐Waller theory is applied to atomic helium scattering from various solid surfaces. The theory agrees well with all experimental data currently available with which comparisons may be made, namely, helium scattering from silver, platinum, tungsten, and tungsten carbide surfaces. Qualitative agreement is obtained between the surface Debye temperature of the materials cited above found from the helium scattering data and deduced from LEED measurements. Alternatively, if the surface Debye temperature obtained from LEED data is used in conjunction with the Debye‐Waller theory for atomic scattering, the interaction energy between helium and the solid surfaces may be calculated. Very reasonable values of this interaction energy are obtained in this way. The theory is also applied to the interaction of molecular hydrogen and a silver surface, and a gas‐surface potential well depth of ∼500 cal/mol is calculated.
TL;DR: In this article, the normal spinel Fe[Cr2]S4 has been studied using the Mossbauer effect over the temperature range 7-170 °K, and it has been shown that the magnetically split spectra can be fitted using a zero value of the asymmetry parameter over a temperature range of 2-500 °K.
Abstract: The normal spinel Fe[Cr2]S4 has been studied using the Mossbauer effect. Spectra have been collected over the temperature range 2–500 °K. Results are presented for the quantity , the hyperfine field, and the isomer shift. We find that the magnetically split spectra can be fitted using a zero value of the asymmetry parameter over the temperature range 7–170 °K. But for an asymmetry parameter is required to fit the spectrum. Experiments in applied fields at 7 and 81 °K show that the quadrupole interaction is not produced by a crystallographic distortion. Attention is drawn to features of the spectra which suggest the presence of relaxation effects in the compound. The isomer shift shows deviations from the Debye model behavior. A model, which allows explanations of the observations, is proposed.
TL;DR: In this article, the total cross-sections of gold, aluminium and copper were determined as a function of neutron energy in the range 10−7
Abstract: By transmission measurements at the time-of-flight spectrometer for ultracold neutrons at the FRM Munich, the total cross-sections of gold, aluminium and copper were determined as a function of neutron energy in the range 10−7
TL;DR: In this paper, the effects of temperature on the intensity-energy spectra of specular LEED beam from Cu(100) and (111) were investigated, and it was shown that all peaks in the spectra can be characterised by an effective Debye temperature, but that this temperature is sensitive to the diffraction conditions operating, varying in a somewhat random manner.
TL;DR: In this paper, the adiabatic elastic constants of terbium were determined in the temperature range 78-300 K, using high-purity single crystals, and the constants were obtained from the ultrasonic wave velocities (20 MHz) measured by the pulse-superposition method.
Abstract: The adiabatic elastic constants of terbium were determined in the temperature range 78–300 K, using high‐purity single crystals. The constants were obtained from the ultrasonic wave velocities (20 MHz) measured by the pulse‐superposition method. The values of the constants c33, c44, c11, c12, and c13 at room temperature in units of 1011 dyn/cm2 are 7.225, 2.140, 6.788, 2.432, and 2.299, respectively. Using these values, the Debye temperature was computed to be 176.6 K. The velocities tend to vary with temperature in an anomalous fashion near the magnetic phase transitions, i.e., the Neel and Curie temperatures, 229 and 221 K, respectively. The relative change of the longitudinal velocity in the [0001] direction, near the Neel temperature, TN, could be described by a logarithmic function of the reduced temperature (T‐TN)/TN. The rate of the relaxation process of this relationship was estimated to be 6×109 sec−1.
TL;DR: In this article, Longitudinal and shear velocities have been measured as a function of temperature in polycrystalline samples of ScH1.99, YH 1.93, and Er H1.81.
Abstract: Longitudinal and shear velocities have been measured as a function of temperature in polycrystalline samples of ScH1.99, YH1.93, and ErH1.81. From these measurements values of the limiting Debye temperature, θ0, the bulk modulus, Young's modulus, the shear modulus, and Poisson's ratio are calculated.
TL;DR: In this article, it is suggested that the low-temperature heat capacity difference between glasses and their crystal may be computed by considering the simple process, Cx(Vx) ⇒(a) Cx (Vg) ⇔(b) Cg(Vg), where Vg is the constant volume heat capacity of the crystal at its equilibrium volume at normal pressures, Vx is the substance of identical structure as the crystal but of a volume, Vg, equivalent to that of the glass.
Abstract: It is suggested that the low‐temperature heat‐capacity difference between glasses and their crystal may be computed by considering the simple process, Cx(Vx) ⇒(a) Cx(Vg) ⇒(b) Cg(Vg), where Cx(Vx) is the constant volume heat capacity of the crystal at its equilibrium volume at normal pressures, Vx, Cx(Vg) is the heat capacity of the substance of identical structure as the crystal but of a volume, Vg, equivalent to that of the glass, and Cg(Vg) is the constant volume heat capacity of the glass. Estimates are made of the change in heat capacity due to step (a) (the change in heat capacity at constant crystal structure due to a volume change) and to step (b) (the change in heat capacity due to disordering at constant volume) for a one‐dimensional model of a glass and crystal. These suggest that step (a) contributes more to the heat‐capacity difference than does step (b). Contributions to step (a) from a three‐dimensional Debye model show reasonable agreement with experiment.
TL;DR: In this article, the quantum theory of the one-phonon inelastic scattering of gas atoms in three dimensions by a solid surface, presented recently by F. O. Goodman [Surface Sci. 30, 1 (1972), is used to calculate energy accommodation coefficients for the system He•W. The approximations used are the same as those in the above paper, except that the gas surface interaction is represented by the exponential repulsive potential with zero well depth.
Abstract: The quantum‐mechanical theory of the one‐phonon inelastic scattering of gas atoms in three dimensions by a solid surface, presented recently by F. O. Goodman [Surface Sci. 30, 1 (1972)] is used to calculate energy accommodation coefficients for the system He‐W. The approximations used are the same as those in the above paper, except that the gas‐surface interaction is represented by the exponential repulsive potential with zero well‐depth. The theory is compared with experimental data on both equilibrium and nonequilibrium energy accommodation coefficients for He‐W. With a gas‐surface interaction potential inverse‐length parameter corresponding to a Morse parameter for He‐W in the range 1.3–1.6 A−1, and with a (bulk) Debye temperature for W in the range 320–380°K quantitative agreement is found between theory and experiment in regimes in which the theory may be expected to be applicable. These regimes are those in which effects of bound states of gas atoms at the surface, which are neglected in the theory, are relatively unimportant.
TL;DR: In this article, the phonon-dispersion curves along the [001, [110, and [111] directions in Pb at room temperature have been measured by neutron inelastic scattering.
Abstract: The phonon-dispersion curves along the [001], [110], and [111] directions in ${\mathrm{Mg}}_{2}$Pb at room temperature have been measured by neutron inelastic scattering. Although these curves are qualitatively similar to those for ${\mathrm{Mg}}_{2}$Sn, marked differences exist in some of the longitudinal branches which show large dips at small $q$ for ${\mathrm{Mg}}_{2}$Pb, suggesting large screening effects of free carriers. A reasonable fit to the measured dispersion curves has been obtained with a nine-parameter shell model. The model was used to calculate the phonon density of states and the temperature dependence of the Debye temperature. The calculated Debye temperature agreed well with the Debye temperature obtained from heat-capacity measurements.
TL;DR: In this article, the energy difference between the parallel and the antiparallel pairs of NH4 ions is estimated to be 1.46 kj mol−1 from the low-temperature tail of the heat capacity anomaly near Tλ.
Abstract: Heat capacity of NH4Cl was measured between 8 and 300 K with an adiabatic calorimeter. The low-temperature limit of the Debye temperature is 352 K and its high-temperature limit in the harmonic approximation is 285 K. The λ transition point Tλ is 242.502±0.004 K with the heat of transition 1168 J mol−1 and the entropy of transition 5.00 JK−1 mol−1. It is very close to the first-order transition. From the analysis of the heat capacity between 242 and 300 K, an extra contribution to the heat capacity that amounts to 11.5 JK−1 mol−1 at 300 K is extracted and explained by a simple model which assumes an additional type of order-disorder in the arrangment of NH4 ions above Tλ. The energy difference between the parallel and the antiparallel pairs of NH4 ions is estimated to be 1.46 kj mol−1 from the low-temperature tail of the heat capacity anomaly near Tλ.
TL;DR: In this article, a discussion of the effect of lattice vibrations on the effective electron-ion-core elastic scattering vertex is given using the model of Duke and Laramore.
Abstract: A discussion of the effect of lattice vibrations on the effective electron-ion-core elastic scattering vertex is given using the model of Duke and Laramore. The renormalization introduced by the lattice vibrations can substantially increase the number of partial waves necessary to describe this scattering. The vertex approximation using the $s$-wave part of the phonon renormalization factor and phase shifts from a realistic potential to describe the electron-rigid-ion scattering is compared with the vertex approximation using the full phonon renormalization factor and the constant phase shift $s$-wave model to describe the electron-rigid-ion scattering. Model calculations of low-energy-electron-diffraction (LEED) intensity profiles are presented for a system having the geometrical parameters of Al(100), and effective Debye temperatures are obtained for the Bragg peaks in the intensity profiles. The dependence of these effective Debye temperatures on the inelastic-collision mean free path and on the characteristic falloff of the vibrational amplitude of the ion cores with distance from the surface is investigated. Even for a constant mean free path the ${{\ensuremath{\Theta}}_{D}}^{\mathrm{eff}}$ exhibit a pronounced energy dependence. By comparing the calculated ${{\ensuremath{\Theta}}_{D}}^{\mathrm{eff}}$ with the experimental measurements of Quinto et al., a crude estimate of the inelastic-collision mean free path in the surface region of aluminum is obtained.
TL;DR: The temperature dependence of diffracted intensity from the clean (100) surface of aluminum has been measured in the range of 298 to 598°K effective Debye temperatures have been extracted from the data for five prominent intensity peaks of integral and nonintegral order.
TL;DR: In this paper, an absolute measurement of the atomic scattering factor of chromium by x-ray diffraction was made at room temperature, using an imperfect single crystal in transmission and applying a measured secondary-extinction correction to the integrated intensities obtained with monochromatic K-ensuremath{\alpha}$ radiation.
Abstract: Absolute measurements were made to determine the atomic scattering factor of chromium by x-ray diffraction. This study was made at room temperature, using an imperfect single crystal in transmission and applying a measured secondary-extinction correction to the integrated intensities obtained with monochromatic $\mathrm{Mo}K\ensuremath{\alpha}$ radiation. The measurements were placed on an absolute scale using a value of the Debye temperature of 525\ifmmode^\circ\else\textdegree\fi{}K and a measured mass-absorption coefficient of 30.15 ${\mathrm{cm}}^{2}$/g. As in previous measurements on nickel, the apparent scattering factors of the (110) and (200) reflections were found to depend linearly on the reciprocal of the reflection half-width, thus indicating the presence of primary extinction. The true atomic scattering factors for the (110) and (200) reflections, determined from an extrapolation to zero reciprocal half-width, were found to be considerably lower than the theoretical values obtained from free-atom Hartree-Fock calculations. From the paired reflections (330)-(411) and (600)-(442) the ${t}_{2g}$ population of $3d$ electrons was found to be about 72%, thus indicating a marked departure from spherical symmetry.
TL;DR: In this paper, an expression that approximates Debye-Waller B values by a sum of three terms is derived from the theory of lattice dynamics in the harmonic approximation.
Abstract: An expression that approximates Debye-Waller B values by a sum of three terms is derived from the theory of lattice dynamics in the harmonic approximation. For cubic crystals (M is the mass of the th atom in the unit cell): B = T + 22h2/3k TM + /M2T3, where T D/2 and and are constants, depending on interatomic forces only. It is shown that for temperatures above the Debye temperature D of the lattice, the second and third terms in the above expression can be neglected. From this, it follows that above the Debye temperature Debye-Waller B values become independent of the atomic masses. Consequently, the heavier atoms in a lattice do not necessarily have the smaller B values.
TL;DR: In this article, the electron-density distribution in solid aluminum has been determined and the Debye parameter is found to be 0.849 ± 0.005 A2 at 293°K, varying with temperature to 362 ± 9°K at 559°K.
Abstract: Accurate photographic X-ray intensities have been obtained for nearly all reflexions within the Mo Kα limiting sphere for two single crystals of aluminum. These intensities have been used to give the X-ray Debye temperature, Θd, in the first part of an experimental determination of the electron-density distribution in solid aluminum. The results of this work show that Θd = 393 ± 1°K at 293°K, varying with temperature to Θd = 362 ± 9°K at 559°K. The Debye parameter is found to be 0.849 ± 0.005 A2 at 293°K.
TL;DR: The amplitude of the de Haas-van Alphen oscillations in mercury has been studied at temperatures between 1 and 17 K and fields between 20 and 90 T as discussed by the authors, and no evidence of any appreciable temperature dependence of X has been found.
Abstract: The amplitude of the de Haas-van Alphen oscillations in mercury has been studied at temperatures between 1 and 17 K and fields between 20 and 90 T. Because of the low Debye temperature of mercury, the Dingle temperature X might be expected to increase appreciably with temperature because of increased scattering of electrons by phonons. Such a temperature dependent X would also cause the appropriate logarithmic plot of amplitude against temperature to depart appreciably from linearity. Measurements of X as a function of temperature and of the temperature dependence of amplitude at a number of fields have however provided no evidence of any appreciable temperature dependence of X. This apparently paradoxical result turns out to be explicable by a recent many-body theory due to Engelsberg & Simpson of the effects of electron-phonon scattering on the de Haas-van Alphen amplitude.
TL;DR: The adiabatic elastic stiffness constants of single crystal gallium antimonide were measured as a function of temperature from 4·2°K to 300°K by the ultrasonic pulse-echo technique as mentioned in this paper.
TL;DR: In this article, a simple model of a cubic lattice with piecewise linear nearest-neighbor interactions is presented for the motion of a straight screw dislocation at finite temperature T, under the action of a constant applied stress.
Abstract: In a simple model of a cubic lattice with piecewise linear nearest‐neighbor interactions, a solution is obtained for the motion of a straight screw dislocation at finite temperature T, under the action of a constant applied stress. This external stress is balanced by the frictional stress due to the scattering and emission of phonons by the core of the dislocation. The results are compared with those obtained by the authors and others for the case of zero temperature. It is found that the thermal agitation greatly affects the dislocation motion for T comparable to the Debye temperature. At low T, the shape of the stress‐velocity curve is the same as at T=0, except that an additional phonon‐scattering term, proportional to the number of phonons, is present.
TL;DR: In this paper, low-temperature specific heat measurements have been made on random poly(L-alanine) (Pilot), and the effective one-dimensional (intra-molecular polymeric) Debye temperature is 323°K, and the corresponding three-dimensional temperature is 54°K.
Abstract: Low-temperature specific heat measurements have been made on random poly(L-alanine) (Pilot). The effective one-dimensional (intra-molecular polymeric) Debye temperature is 323°K, and the corresponding three-dimensional temperature is 54°K. An anomaly, similar to that seen in polyethylene and other high polymers, is observed. The method will be a useful tool for the study of low-frequency vibrations in polypeptides.
TL;DR: In this paper, it was shown that the free energy terms arising from charge-charge interactions in the Debye theory and in modern statistical-mechanical treatments of electrolyte solutions can be brought into close agreement when it is borne in mind that the ''ionic diameter'' is an adjustable parameter of both theories.
Abstract: It is shown that the free energy terms arising from charge‐charge interactions in the Debye theory and in modern statistical‐mechanical treatments of electrolyte solutions can be brought into close agreement when it is borne in mind that the ``ionic diameter'' is an adjustable parameter of both theories. By considering the case of an ideal nonelectrolyte solution, it is shown that the imperfect gas (co‐volume) term in the modern theories is an artefact of the ``primitive model'' which cannot validly be included in comparisons with experimental data.