Showing papers on "Debye model published in 1968"
TL;DR: In this article, pressure and temperature dependence of isotropic elastic moduli of polycrystalline alumina, noting Gruneisen parameter, equation of state and Debye temperature.
Abstract: Pressure and temperature dependence of isotropic elastic moduli of polycrystalline alumina, noting Gruneisen parameter, equation of state and Debye temperature
129 citations
TL;DR: In this article, measurements of the elastic constants and thermal expansion of PbTe have been made from 4.2° to 303.2 degrees K. The linear coefficient of thermal expansion was found to be 20.4±0.6/°C at room temperature, and the 0°K Debye temperature was calculated to be 176.7°± 0.5°K.
Abstract: Measurements of the elastic constants and thermal expansion of PbTe have been made from 4.2° to 303.2°K. The extrapolated 0°K values for C44, (C11−C12)/2, and (C11+2C12)/3, respectively, are 1.514±0.009, 6.184±0.066, and 4.560±0.042×1011 dyn/cm2. At 303.2°K these values are 1.344±0.008, 5.016±0.057, and 4.107±0.037×1011 dyn/cm2. Intermediate values are presented graphically, as are the thermal‐expansion data. The linear coefficient of thermal expansion is found to be 20.4±0.4×10−6/°C at room temperature. The 0°K Debye temperature is calculated to be 176.7°±0.5°K.
127 citations
TL;DR: In this article, the elastic constants of GaP have been determined by the ultrasonic phase-comparison method and the compressibility, Debye temperature, and average longitudinal sound velocity in GaP are calculated.
Abstract: The elastic constants of GaP have been determined by the ultrasonic phase‐comparison method. The frequency range and temperature for the measurements were 8–20 MHz and 300°K, respectively. The compressibility, Debye temperature, and average longitudinal sound velocity in GaP are calculated. The elastic constants of GaP are found to agree with the regularities established from the measurement of these constants in other III–V compounds.
115 citations
TL;DR: In this paper, the adiabatic elastic constants of molybdenum and rhenium alloyed in solid solution with 7.0, 16.6, and 26.9 at.
Abstract: The adiabatic elastic constants of molybdenum and molybdenum alloyed in solid solution with 7.0, 16.6, and 26.9 at.% rhenium were measured in the temperature range −190°C to +100°C. Rhenium additions decrease (c11−c12)/2 and the twinning shear (c11−c12+c44)/3, and increase the bulk modulus and c44. The 26.9 at.% alloy is elastically isotropic. Alloy additions strengthen nearest‐neighbor interactions and weaken second‐nearest‐neighbor interactions. Debye temperatures calculated from the measured elastic constants agree well with those determined by calorimetry. Thermal expansion of the alloys was found to be essentially the same as for molybdenum in this temperature range.
59 citations
TL;DR: In this article, single crystals of cesium have been grown by a modified Bridgman technique and the adiabatic elastic constants were measured at 4.2° and 78°K by an ultrasonic pulse echo technique.
51 citations
TL;DR: In this article, the authors measured spin-lattice relaxation times for isolated (IrCl6)2-complexes in (NH4)2PtCl6 and (K 2PtCL6)Cl6 at frequencies from 95 to 24 GHz.
Abstract: Spin-lattice relaxation times have been measured at frequencies from 95 to 24 GHz for isolated (IrCl6)2- complexes in (NH4)2PtCl6 and K2PtCl6. The relaxation rate for the ammonium salt can be expressed as a sum of terms corresponding to a direct process, a Raman process and a concentration-dependent process as follows: for the ratio Ir:Pt = c less than about three per cent (f in Hz, T in °K). The value of Δ(similar 65 °K) agrees with the previously measured exchange interaction between nearest-neighbour (IrCl6)2- complexes. At higher values of c, a faster variation than c2 is found. Data for the potassium salt are similar except for the strongly enhanced Raman process, 1/T1 = 35 × 10-2T9. Theoretical estimates for the direct and Raman states indicate that a simple Debye model is not sufficient to explain all experimental data. All data regarding the concentration-dependent process agree with a mechanism in which single complexes cross relax to exchange-coupled clusters of three or more complexes, and relaxation of such clusters is discussed briefly. In particular, exchange-coupled pairs relax much too slowly to affect relaxation of single complexes (see also II).
51 citations
TL;DR: In this paper, the specific heat of high purity aluminum has been measured from 330 to 890°K with an estimated accuracy of ± 0.7 per cent, using dynamic adiabatic calorimetry.
44 citations
TL;DR: In this article, the complex dielectric behavior of ice doped with HCl has been measured in the concentration range 2'×'10−6' to 2 '×' 10−4' and the dissociation of HCl in ice was calculated as a function of temperature.
Abstract: The complex dielectric behavior of ice doped with HCl has been measured in the concentration range 2 × 10−6 to 2 × 10−4M The dissociation of HCl in ice was calculated as a function of temperature for ice doped at 2 × 10−6M The results at 1 × 10−5M and below conform to the Debye model with a single relaxation time The data suggest that, in a limited concentration range, HCl is substitutionally incorporated into the ice lattice
39 citations
TL;DR: In this article, the position of the P-atom in the ordered structure of chalcopyrite type ZnSnP2 was determined: X = 0.239 and the dependence of the degree of ordering on the cooling rate was established.
Abstract: The position of the P-atom in the ordered structure of chalcopyrite type ZnSnP2 is determined: X = 0.239. Crystals with various degrees of ordering are obtained by varying the cooling rate of the melt during growth. The partly ordered crystals show a mosaic structure and consist of blocks having chalcopyrite or sphalerite structure. The dependence of the degree of ordering on the cooling rate is established. From measurements at room and liquid nitrogen temperature the Debye temperature is found to be the same for crystals with different degree of ordering. The mean-square displacements of atoms as well as the microhardness increase with disordering, and may be related to defect formation. A decrease in the Hall mobility of holes is directly connected with the degree of disordering.
35 citations
TL;DR: In this article, the authors analyzed the ultrasonic velocity data for sodium measured under hydrostatic pressure by Martinson and applied the self-consistent Cook's method to calculate the adiabatic and isothermal elastic constants directly as a function of pressure and temperature.
TL;DR: Mean square atomic displacements variation with temperature in Zn, evaluating Debye temperature as mentioned in this paper, and evaluating the debye temperature of Zn in terms of mean square atomic displacement variation.
Abstract: Mean square atomic displacements variation with temperature in Zn, evaluating Debye temperature
TL;DR: In this article, the frequency distributions and dispersion curves of three cesium chloride-structure alkali halides (CCL, bromide, and iodide) were compared with three distinct models: the rigid ion model, the polarization dipole model, and two variations of the deformation dipoles model.
Abstract: Detailed calculations are presented for the frequency distributions and dispersion curves of the three cesium chloride‐structure alkali halides: cesium chloride, bromide, and iodide. Three distinct models have been used: the rigid ion model, the polarization dipole model, and two variations of the deformation dipole model. In each case combined frequency spectra and dispersion curves are presented and detailed critical‐point assignments made. Plots of the effective Debye temperature θD as a function of temperature are shown and compared with experiment. In addition, the moment functions of the frequency distributions ωD(n) = [13 (n + 3) μn] / n, where μn is the nth moment of a given distribution, have been computed, and plots of these results show that they provide a better means of discriminating between the various models than the θD curves, but unfortunately, no experimental data exist.
TL;DR: In this article, the specific heat of high purity platinum has been measured from 1.4 to 100°K and no anomalous temperature dependence of the lattice heat capacity is observed.
TL;DR: In this paper, the temperature dependence of the recoilless fraction in SnTe has been measured in 119Sn and 125Te nuclei in the range 85° < T < 250° K.
TL;DR: In this article, the specific heat of copper from 300 to 1200°K has been analyzed in order to estimate contributions from the formation of equilibrium lattice defects and anharmonic effects.
TL;DR: In this paper, the thermal conductivity of amorphous semiconducting system Se-Ge in the temperature range of 100 to 300°K was measured and the Debye model was used for the analysis of the experimental values and the calculated mean free path of phonons was related to the size of the basic structure units of the selenium glass.
Abstract: The thermal conductivity of the amorphous semiconducting system Se-Ge in the temperature range of 100 to 300°K was measured. The Debye model was used for the analysis of the experimental values and the calculated mean free path of phonons was related to the size of the basic structure units of the selenium glass. The shift of the thermal conductivity of amorphous selenium doped with germanium was explained by means of the increase of the velocity of sound observed together with the occurrence of the covalent bond Se-Ge between the basic structure units of the studied amorphous system.
TL;DR: In this article, the specific heat coefficient of hexagonal Zr-Ti, Zr Hf, and Zr Sc alloys was measured at 1.1 to 4.2 K. Maxima in both the electronic specific-heat coefficient and the superconducting transition temperature were observed at 60 at.
Abstract: The specific heats of hexagonal Zr-Ti, Zr-Hf, and Zr-Sc alloys were measured at 1.1 to 4.2\ifmmode^\circ\else\textdegree\fi{}K. Maxima in both the electronic specific-heat coefficient $\ensuremath{\gamma}$ and the superconducting transition temperature ${T}_{c}$ were observed at 60 at.% Ti in the Zr-Ti system. No superconductivity was found in the Zr-Sc system, although $\ensuremath{\gamma}$ rose to high values for pure scandium, and a minimum in $\ensuremath{\gamma}$ occurred near 10 at.% Sc. In the Zr-Hf system $\ensuremath{\gamma}$ was nearly linear between pure element values. The Debye temperatures ${\ensuremath{\Theta}}_{D}$, after correction for atomic mass and volume, deviate negatively near 60 at.% Ti in Ti-Zr, positively near hafnium in Zr-Hf, and in an S-type manner in Zr-Sc. The effects of scandium in depressing $\ensuremath{\gamma}$ in the zirconium-rich region are in qualitative agreement with dependence on electron/atom ratio indicated by earlier $B$-subgroup solute effects in zirconium-rich alloys. The $\ensuremath{\gamma}$ for Zr-Sc alloys, after a correction for phonon enhancement and with the assumption of a rigid band in the alloys, correlates fairly well with the electronic density of states for pure zirconium, calculated by Loucks. The rigid-band approximation, on the other hand, cannot explain the maxima in $\ensuremath{\gamma}$ and ${T}_{c}$ in Zr-Ti alloys, which involve no change of electron/atom ratio. Rather the maximum may arise from differences in the relative energies of the third and fourth bands in titanium and zirconium, with a crossing of these bands in the alloys. The $\ensuremath{\gamma}$ and ${T}_{c}$ are related to both the density of states and the electron-electron interactions, and although a clear separation of the two factors is not possible, a reasonable interpretation can be made, assuming that the electron-phonon interaction is nearly constant.
TL;DR: In this paper, it was shown that there appears to be a significant correlation between the Kapitza conductance of a solid and the reciprocal of its Debye temperature, with a linear dependence rather than the cubic dependence of Khalatnikov's theory.
TL;DR: The heat capacity of a single crystal of CaWO4 was determined by adiabatic calorimetry from 5° to 350°K and found to be without transitions or thermal anomalies as discussed by the authors.
Abstract: The heat capacity of a single crystal of CaWO4 was determined by adiabatic calorimetry from 5° to 350°K and found to be without transitions or thermal anomalies. Deviation of the curve from normal sigmate shape is shown to be due to internal vibrations of the WO4= ions. Apparent Debye θ's for the lattice‐only heat capacity and for that of the acoustical spectrum show “normal” deviation from simple Debye theory. Values of the heat capacity (Cp), entropy (S°), enthalpy function [(H°–H0°) / T], and Gibbs function [(G° / H0°) / T] at 298.15°K are 27.28, 30.21, 16.02, and −14.19, in calories per gram formula mass·degree Kelvin.
TL;DR: In this article, the superconducting electronic specific heat data are in accord with the BCS theory and fit the equation C es λT c = 10·71 exp ( -1·59T c T ).
TL;DR: In this paper, the allowed frequency modes for simple cubic microcrystallites with free boundaries, taking the nearest-neighbor interaction, have been calculated, and two different sets of force constants have been used.
Abstract: We have calculated the allowed frequency modes for simple cubic microcrystallites with free boundaries, taking the nearest-neighbor interaction. The mean-square displacement (m.s.d.) and the mean-square velocities (m.s.v.) in different directions, for atoms in different positions on the lattice, have been evaluated. Two different sets of force constants have been used. We find that for surface atoms, m.s.d. for motion along the surface is nearly the same as for motion perpendicular to the surface. m.s.d. is maximum for corner atoms and minimum for atoms in bulk. On the other hand, m.s.v. is maximum for atoms in bulk and minimum for corner atoms. At any fixed site, we find that both m.s.d. and m.s.v. increase with increasing crystal size, and tend to an asymptotic value. For one set of force constants we have also calculated the specific heat of microcrystallites at various temperatures, as a function of crystallite size. The effective Debye temperature is estimated, and its variation, both with crystallite size and sample temperature, is discussed.
TL;DR: In this paper, the Mossbauer effect was used to investigate ICN crystals at 100°K and it was concluded that the iodine promotes 0.27 p electrons (there is no sp hybridization) to the cyanide group.
Abstract: The Mossbauer effect in 129I (Er = 27.8 keV) has been used to investigate some properties of ICN crystals at 100°K. From the quadrupole split spectrum the value of e2qQ(127I) was found to be −2640 ± 20 Mc/sec and the isomer shift +0.119 ± 0.002 cm/sec with respect to a ZnTe source. The η parameter was found to be zero. From these values, it was concluded that the iodine promotes 0.27 p electrons (there is no sp hybridization) to the cyanide group. From considerations based on NQR data in BrCN and ICN and from the fact that no anisotropy was detected in the recoilless fraction, it was concluded that intermolecular (covalent) bonding to form a chain structure is negligible. The absolute recoilless fraction at 100°K was found to be 0.012 ± 002 corresponding to a Debye temperature of 61 ± 5°K.
TL;DR: In this article, the Debye temperature of the 27.7 −keV 129I transition in GeI4 and SiI4 was derived from the temperature dependence of the recoilless fraction.
Abstract: The Mossbauer effect of the 27.7‐keV 129I transition has been studied in GeI4 and SiI4 crystals. From the temperature dependence of the recoilless fraction, the characteristic Mossbauer temperatures have been derived. Using these temperatures and a simple model for the Mossbauer factor in a molecular crystal, the Debye temperatures of the crystals have been calculated. From the intensities of the peaks in the spectra, the absolute recoilless fractions have been calculated. The intensities of various transitions in the spectra show the existence of the Goldanski effect. From the quadrupole coupling and isomer shift measurements, the character of the Ge–I and Si–I bond is derived.
TL;DR: In this paper, three Born-von Karman lattice dynamical models obtained from neutron measurements and elastic constant measurements on Ni have been considered to calculate the Debye-Waller factor Debye temperature, θ M (T ).
TL;DR: In this article, the dependence of the Debye-Waller factor on the size of cubes and plates is calculated by assuming the debye theory, but using the frequency distribution which incorporates a term that is proportional to the surface area.
Abstract: The dependence of the Debye–Waller factor on the size of cubes and plates is calculated by assuming the Debye theory, but using the frequency distribution which incorporates a term that is proportional to the surface area. The ratio of B for small particles to B for large particles is less than 0.01 for cubes with 109 atoms or more and for plates which are more than 330 atoms thick. The inclusion or exclusion of the zero point energy terms has a large influence on the size correction which has to be applied to small particles and thin films.
TL;DR: In this article, the mean square displacement of polycrystalline I2, IBr, ICl, and I2Cl6 molecular crystals was obtained by means of the Mossbauer effect in the 27.8-keV line of 129I.
Abstract: Lattice‐dynamics information on polycrystalline I2, IBr, ICl, and I2Cl6 molecular crystals was obtained by means of the Mossbauer effect in the 27.8‐keV line of 129I. In the case of I2 and IBr, which are isomorphous, evidence was found that the mean‐square displacement is larger in the direction of the molecular axis, and from considerations regarding the molecular arrangements, it is concluded that the larger 〈x2〉 is in the ac plane. Similar evidence was found also for ICl. No anisotropy in 〈x2〉 was detected in the case of I2Cl6. From the temperature dependence of the recoilless fraction and from its absolute value, the Debye temperature was calculated and found to be 58° ± 2°K for both I2 and IBr, suggesting a similar density of phonon states, in accordance with far‐infrared results obtained with the halogens at 77°K. The 〈x2〉 found for I2Cl6 is compared with that calculated from Raman data for ICl4−, and it is concluded that the I‐Cl intramolecular vibrations are not excited by the recoilless mechanism...
TL;DR: The Debye temperatures of tellurium and cadmium have been determined by measurement of the x-ray integrated intensity of Bragg reflections from powder specimens in the temperature range 77 to 293°K as mentioned in this paper.
TL;DR: In this paper, the x-ray fine structure of niobium and copper was investigated at 300, 77, and 4.2 degrees K to determine the fundamental dependence of fine-structure variations on the Debye temperature and the location of scattering potentials.
Abstract: The x-ray $K$-absorption fine structure of niobium and copper has been investigated at 300, 77, and 4.2\ifmmode^\circ\else\textdegree\fi{}K to determine the fundamental dependence of fine-structure variations on the Debye temperature and the location of scattering potentials. The increase in the amplitude of the fine-structure fluctuations with a lowering of absorber temperature and the dependence of fine-structure temperature variations on the Debye temperature were found to agree with recent theory. No significant change was found in the energy positions of the fine structure as the temperature of the two absorbers was lowered.