Debye model

About: Debye model is a research topic. Over the lifetime, 7462 publications have been published within this topic receiving 133987 citations.

Velocity of sound in solid hexagonal close-packed H 2 and D 2

Abstract: Sound velocity measurements are reported on samples of hexagonal close-packed H2 and D2, believed to be single crystals. In the first part of the experiments, both the longitudinal and transverse velocities (v 1 and v t ) of crystals grown at a given melting pressureP M were measured at 4.2 K. For each mode, the velocities plotted vs.P M were found to lie between approximately parallel lines that represented the maximum and minimum observable velocities under the given experimental conditions set by the acoustic cell dimensions. From these extreme velocities v 1max, v 1min, v tmax, and v tmin an estimation of the elastic constants was made. Knowledge of these constants in turn permitted the calculation of the velocity surface, the bulk modulus, and the Debye temperature. In spite of the uncertainties in the analysis of the present data, a meaningful comparison could be made with results from other experiments. For both and D 2 , the elastic constants are on the average ∼20% below those derived from neutron scattering data. The transverse velocities, both for H 2 and D 2 , are consistent with those of Bezuglyi and Minyafaev for polycrystalline samples, but the longitudinal velocities are about 10% smaller than those of these authors. The bulk modulus and the Debye temperature from our experiments are compared with those from equation-of-state and calorimetric experiments. In the second part of this research, we have investigated the temperature dependence of the sound velocities at constant volume for both H 2 and D 2 with low concentrationsX of molecules with rotational angular momentumJ=1. From the measurements in H 2 , we are able to calculate the temperature change in the bulk modulus, which is then compared with that calculated from calorimetric data assuming the validity of the Gruneisen equation of state. Good agreement is obtained. In solid D 2 , were were able to deduce the temperature dependence of the adiabatic and isothermal modulusc 33 and make a rough estimation for that ofc 13 . In the third part we present measurements of v 1 and v t at 42 K and at constant volume as a function ofX in solid H 2 . It is found that as the orthopara conversion proceeds,v 1 increases andv t decreases. From these measurements the bulk modulus change withX is calculated. Comparison with the bulk modulus change calculated from static pressure measurements, assuming electric quadrupole-quadrupole interaction between the (J=1) molecules, shows very good agreement. The calculated dependence of the Debye temperature onX, as obtained from a combination of sound velocity and static measurements, is smaller than that reported from recent neutron scattering results. A short section is then devoted to absorption measurements in solid H 2 , which gave only qualitative results. Finally, in Section 4, we present measurements of the sound velocity in liquid D 2 at saturated vapor pressure as a function of temperature and for both liquid H 2 and D 2 along the melting curve.

Low‐temperature specific heat, ac susceptibility, and electrical resistivity of amorphous Fe90Zr10, Co90Zr10, and Co86Zr14 alloys

Abstract: The low‐temperature specific heat (CP) and magnetic susceptibility (χ) for the amorphous alloys Fe90Zr10, Co90Zr10, and Co86Zr14 are presented. A very large linear contribution to CP combined with a sharp decrease in χ below about 60 K show Fe90Zr10 to have spin‐glass or spin‐cluster glass behavior at low temperatures. The Co‐based alloys show no deviations from true ferromagnetic behavior at low temperatures. Values of the Debye temperature for all three alloys and the electronic density of states for the Co‐based alloys are obtained.

Quadrupolar Nuclear Relaxation in the III-V Compounds

Abstract: The results of nuclear quadrupolar spin-lattice relaxation time ${T}_{1}$ measurements in most of the III-V compounds and germanium are presented and discussed. It is shown that the ${T}_{1}'\mathrm{s}$ may be correlated with the quadrupole interaction for a free atom and appear to be relatively insensitive to different properties of the materials except for the Debye temperature. A theoretical derivation of the transition probabilities for a point charge zincblende lattice is given. This derivation follows Van Kranendonk's treatment for the NaCl lattice. An attempt is made to relate the point-charge model to the III-V compounds with the aid of experimental multiplication factors. A theoretical derivation, which is based on the spin-temperature concept, and an experimental verification of the dependence of the quadrupolar relaxation time on the nuclear spin are given. The spin dependence, $\frac{1}{{T}_{1}}\ensuremath{\propto}f(I)=\frac{(2I+3)}{{I}^{2}(2I\ensuremath{-}1)}$, is important in the interpretation of other experimental data. A theoretical derivation is given of a relaxation time that is isotropic as the orientation of the static field is varied with respect to the crystalline axes. This apparently accounts for the absence of an experimental observation of any systematic variations of the relaxation time with crystal orientation in this and other investigations. An experimental investigation of the temperature dependence of quadrupolar relaxation is reported. The observed temperature dependence varifies Van Kranendonk's predictions for a Raman "two-phonon" process. Debye temperatures of several III-V compounds are obtained from the temperature dependence of the relaxation times.

Novel silicon allotropes: Stability, mechanical, and electronic properties

Abstract: One quasi-direct gap phase (Amm2) and three indirect gap phases (C2/m-16, C2/m-20, and I-4) of silicon allotropes are proposed. The detailed theoretical study on the structure, density of states, elastic properties, sound velocities, and Debye temperature of these four phases is carried out by using first principles calculations. The elastic constants of these four phases are calculated by strain-stress method. The elastic constants and the phonon calculations manifest all novel silicon allotropes in this paper are mechanically and dynamically stable at ambient condition. The B/G values indicate that these four phases of silicon are brittle materials at ambient pressure. The anisotropy properties show that C2/m-20 phase exhibits a larger anisotropy in its elastic modulus, shear elastic anisotropic factors, and several anisotropic indices than others. We have found that the Debye temperature of the four novel silicon allotropes gradually reduces in the order of C2/m-20 > Amm2 > C2/m-16 > I-4 at ambient pressure.