Debye model

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

Thermodynamics and lattice vibrations of minerals: 1. Mineral heat capacities and their relationships to simple lattice vibrational models

Abstract: This is the first of a series of five papers in which the thermodynamic properties of minerals are interpreted in terms of lattice vibrational spectra. In this paper, measured heat capacities for minerals are examined in terms of the Debye theory of lattice vibrations, and it is demonstrated that heat capacities of silicates show large deviations from the behavior expected from Debye theory. The underlying assumptions of Debye theory are critically reviewed, and it is shown that the observed thermodynamic deviations in minerals probably arise from four effects not included in the Debye model: anisotropy of elastic parameters, dispersion of acoustic waves toward Brillouin zone boundaries, optic vibrations in excess of the Debye spectrum at low frequencies, and optic vibrations at frequencies much greater than the Debye cutoff frequency predicted by acoustic measurements. Each of the four effects influences the heat capacity in a particular temperature range: anisotropy, dispersion and low-frequency optic vibrations are important at low temperatures (0°K to ∼100°K); high-frequency vibrations are important at higher temperatures. It is necessary to include all four effects in a generalized lattice vibrational model for minerals; such a model is developed in papers 2-5 of this series. The minerals included in this study are halite, periclase, brucite, corundum, spinel, quartz, cristobalite, silica glass, coesite, stishovite, rutile, albite, microcline, jadeite, diopside, enstatite, tremolite, talc, muscovite, forsterite, zircon, kyanite, andalusite, sillimanite, pyrope, grossular, andradite, spessartine, almandine and calcite.

Lattice dynamics of hexagonal Mo S 2 studied by neutron scattering

Abstract: Phonon-dispersion curves for the hexagonal-layered compound Mo${\mathrm{S}}_{2}$ have been measured at room temperature by inelastic-neutron-scattering techniques for the [100] and [001] directions. The results have been analyzed on the basis of a model which includes valence forces between atoms in a layer and axially symmetric forces between atoms in neighboring layers. While the model reproduces the essential over-all features of the data, the present analysis indicates the need for a more sophisticated treatment of valence forces and/or for the inclusion of the atomic polarizabilities. The temperature dependence of the specific heat and the Debye temperature have been calculated from the model.

Resonant Ultrasound Spectroscopy

Abstract: When a new crystalline material is discovered, one of the first fundamental properties to be determined is the atomic structure, defined by the minimum in the free energy with respect to the positions of the atoms. Another fundamental characteristic of interest is the curvature of the free energy in the vicinity of the minimum, and this would be manifest in the elastic constants for the material. As derivatives of the free energy, elastic constants are closely connected to thermodynamic properties of the material. They can be related to the specific heat, the Debye temperature and the Gruneisen parameter (which relates the thermal expansion coefficient to the specific heat at constant volume), and they can be used to check theoretical models. Extensive quantitative connections among thermodynamic properties can be made if the elastic constants are known as functions of temperature and pressure. The damping of elastic waves provides information on anharmonicity and on coupling with electrons and other rela...

Experimental and theoretical studies of phonons in hexagonal InN

Abstract: The first- and second-order Raman scattering and IR reflection have been studied for hexagonal InN layers grown on (0001) and (1102) sapphire substrates. All six Raman-active optical phonons were observed and assigned: E2(low) at 87 cm−1, E2(high) at 488 cm−1, A1(TO) at 447 cm−1, E1(TO) at 476 cm−1, A1(LO) at 586 cm−1, and E1(LO) at 593 cm−1. The ratio between the InN static dielectric constants for the ordinary and extraordinary directions was found to be e⊥0/e∥0=0.91. The phonon dispersion curves, phonon density-of-state function, and lattice specific heat were calculated. The Debye temperature at 0 K for hexagonal InN was estimated to be 370 K.

Electronic and elastic properties of the light actinide tellurides

Abstract: The elastic constants c11, c12 and c44 of U, Np, Pu, and Am telluride single crystals have been obtained by Brillouin scattering from the measured sound velocities in prominent crystallographic directions. In case of the U chalcogenides also by ultrasound techniques. The Cauchy pressure, the Poisson ratio, the anisotropy ratio, the bulk modulus and the Debye temperature have been derived from these data. U and Pu telluride have a negative c12, implying intermediate valence. AmTe has a very low bulk modulus, but a positive c12. It is extremely soft, with a very low sound velocity. For AmTe also the LO and TO phonon frequencies could be determined. The elastic data point to a divalent Am state. The optical reflectivity of the light actinide tellurides (and sometimes of all chalcogenides) has been measured between UV and infrared wavelengths, in the case of AmTe down to the far infrared. The plasma edge of the free carriers has been determined, which yields the ratio of n/m*. Together with the γ value of the specific heat and magnetic data a consistent proposal for the electronic structure of the light actinide chalcogenides can be given. Thus, the Pu chalcogenides are intermediate valent and represent the high-pressure phase of the corresponding Sm chalcogenides. AmTe, as judged by the electronic, optic and magnetic properties seems to be in the 5f7 configuration, i.e. divalent Am, but with a narrow, half-filled (24 meV) wide 5f band, about 0.1 eV below the bottom of the 6d conduction band. We thus propose a new kind of unhybridized heavy fermion. Also AmTe seems to represent a high-pressure phase of EuTe.