Debye model

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

Re-Appearance of Cooperativity in Ultra-Small Spin-Crossover [Fe(pz){Ni(CN)4}] Nanoparticles†

Abstract: A reverse nanoemulsion technique was used for the elaboration of [Fe(pz){Ni(CN)4}] nanoparticles. Low-temperature micellar exchange made it possible to elaborate ultra-small nanoparticles with sizes down to 2 nm. When decreasing the size of the particles from 110 to 12 nm the spin transition shifts to lower temperatures, becomes gradual, and the hysteresis shrinks. On the other hand, a re-opening of the hysteresis was observed for smaller (2 nm) particles. A detailed 57Fe Mossbauer spectroscopy analysis was used to correlate this unusual phenomenon to the modification of the stiffness of the nanoparticles thanks to the determination of their Debye temperature.

Thermal resistance due to isotopes at high temperatures

Abstract: In pure dielectric crystals, the isotopic variations of atomic mass contribute a temperature-independent thermal resistance at high temperatures. This resistance has been calculated using a Debye model of the vibrational spectrum. Umklapp processes are treated as the dominant scattering mechanism. The distribution of the heat current over the vibrational modes is known for low frequencies. This distribution is considered to apply over the whole frequency spectrura. The calculated result is compared with the experiments of Geballe and Hull on isotopically pure germanium. A satisfactory agreement with experiment is obtained. (auth)

Phonon spectrum, thermodynamic properties, and pressure-temperature phase diagram of uranium dioxide

Abstract: We present a study of the structural phase transition and the mechanical and thermodynamic properties of UO${}_{2}$ by means of the local density approximation (LDA)+$U$ approach. A phase transition pressure of 40 GPa is obtained from theory at 0 K, and agrees well with the experimental value of 42 GPa. The pressure-induced enhancements of elastic constants, elastic moduli, elastic wave velocities, and Debye temperature of the ground-state fluorite phase are predicted. The phonon spectra of both the ground state fluorite structure and high-pressure cotunnite structure calculated by the supercell approach show that the cotunnite structure is dynamically unstable under ambient pressure. Based on the imaginary mode along the $\ensuremath{\Gamma}$$\ensuremath{-}$$X$ direction and soft phonon mode along the $\ensuremath{\Gamma}$$\ensuremath{-}$$Z$ direction, a transition path from cotunnite to fluorite has been identified. We calculate the lattice vibrational energy in the quasiharmonic approximation using both first-principles phonon density of state and the Debye model. The calculated temperature dependence of lattice parameter, entropy, and specific heat agrees well with experimental observations in the low temperature domain. The difference of the Gibbs free energy between the two phases of UO${}_{2}$ has predicted a boundary in the pressure-temperature phase diagram. The solid-liquid boundary is approximated by an empirical equation using our calculated elastic constants.

Interpretation of mechanical properties and structure of TeO2-Li2O-B2O3 glasses

Abstract: Lithium borate glasses containing TeO2 as Li0.6 TexB1.4� 2xO2.4� x have been prepared by the conventional rapid quenching method over a wide range of composition (x ¼ 0, 0.1, 0.2, 0.3, and 0.35). Ultrasonic velocities (longitudinal and shear) were measured in these glasses at room temperature. The elastic moduli, and the Debye temperature, were calculated and discussed quantitatively in terms of the glass transition temperature, the cross-link density, and the packing density. The monotonic decrease in the velocities, the glass transition temperature, and the elastic moduli as a function of TeO2 modifier content reveals the loose packing structure, which is attributed to the increase in the molar volume and the reduction in the vibrations of the borate lattice. The compositional dependence of these parameters suggested that TeO2 changes the rigid character of Li0.6B1.4O2.4 to a matrix of ionic behavior bonds by breaking down the lithium borate structure. This was attributed to the creation of more and more discontinuities and defects in the glasses. r 2007 Elsevier B.V. All rights reserved.

Thermal expansion and atomic displacement parameters of cubic KMgF3 perovskite determined by high-resolution neutron powder diffraction

Abstract: The structure of KMgF3 has been determined by high-resolution neutron powder diffraction at 4.2 K, room temperature and at 10 K intervals from 373 K to 1223 K. The material remains cubic at all temperatures. The average volumetric coefficient of thermal expansion in the range 373–1223 K was found to be 7.11 (3) × 10−5 K−1. For temperatures between 4.2 and 1223 K, a second-order Gruneisen approximation to the zero-pressure equation of state, with the internal energy calculated via a Debye model, was found to fit well, with the following parameters: θD = 536 (9) K, Vo = 62.876 (6) A3, K_{o}^{\,\prime} = 6.5 (1) and (VoKo/γ′) = 3.40 (2) × 10−18 J, where θD is the Debye temperature, Vo is the volume at T = 0, K_{o}^{\,\prime} is the first derivative with respect to pressure of the incompressibility (Ko) and γ′ is a Gruneisen parameter. The atomic displacement parameters were found to increase smoothly with T and could be fitted using Debye models with θD in the range 305–581 K. At 1223 K, the displacement of the F ions was found to be much less anisotropic than that in NaMgF3 at this temperature.