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Debye model
About: Debye model is a research topic. Over the lifetime, 7462 publications have been published within this topic receiving 133987 citations.
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TL;DR: In this paper, the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Gruneisen parameters of B4C.
Abstract: Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic boron carbide (B4C) as functions of temperature in the range 160–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. B4C is an elastically stiff but extremely light ceramic: at 295 K, the longitudinal stiffness (C
L), shear stiffness (μ), adiabatic bulk modulus (B
S
), Young's modulus (E) and Poisson's ratio (σ) are 498 GPa, 193 GPa, 241 GPa, 457 GPa and 0.184, respectively. In general, the adiabatic bulk modulus B
S
agrees well with both experimental and theoretical values determined previously and is approximately constant over the measured temperature range. Both E and μ increase with decreasing temperature and do not show any unusual effects. The values determined at 295 K for the hydrostatic-pressure derivatives (∂ C
L/∂P)
P=O
, (∂μ/∂P)
P=O
and (∂B
S
/∂P)
P=O
are 5.7 ± 0.3, 0.78 ± 0.4 and 4.67 ± 0.3, respectively. The hydrostatic-pressure derivative (∂B
S
/∂P)
P=O
of the bulk modulus is found to be comparable with that estimated previously from dynamic yield strength measurements. The effects of hydrostatic pressure on the ultrasonic wave velocity have been used to determine the hydrostatic-pressure derivatives of elastic stiffnesses and the acoustic-mode Gru neisen parameters. The longitudinal (γL), shear (γS), and mean (γel) acoustic-mode Gruneisen parameters of B4C are positive: the zone-centre acoustic phonons stiffen under pressure in the usual way. Knowledge of the elastic and nonlinear acoustic properties sheds light on the thermal properties of ceramic B4C. Since the acoustic Debye temperature ΘD (=1480 K) is very high, the shear modes provide a substantial contribution to the acoustic phonon population at room temperature.
67 citations
TL;DR: In this article, a set of Mg2.08Si0.4−xSn0.6Sbx (0 ≤ x ≤ 0.072) compounds were investigated, and a peak ZT of 1.50 was obtained at 716 K in Mg 2.08 Si0.364sn0.036.
Abstract: Mg2(Si,Sn) compounds are promising candidate low-cost, lightweight, nontoxic thermoelectric materials made from abundant elements and are suited for power generation applications in the intermediate temperature range of 600 K to 800 K. Knowledge on the transport and mechanical properties of Mg2(Si,Sn) compounds is essential to the design of Mg2(Si,Sn)-based thermoelectric devices. In this work, such materials were synthesized using the molten-salt sealing method and were powder processed, followed by pulsed electric sintering densification. A set of Mg2.08Si0.4−xSn0.6Sbx (0 ≤ x ≤ 0.072) compounds were investigated, and a peak ZT of 1.50 was obtained at 716 K in Mg2.08Si0.364Sn0.6Sb0.036. The high ZT is attributed to a high electrical conductivity in these samples, possibly caused by a magnesium deficiency in the final product. The mechanical response of the material to stresses is a function of the elastic moduli. The temperature-dependent Young’s modulus, shear modulus, bulk modulus, Poisson’s ratio, acoustic wave speeds, and acoustic Debye temperature of the undoped Mg2(Si,Sn) compounds were measured using resonant ultrasound spectroscopy from 295 K to 603 K. In addition, the hardness and fracture toughness were measured at room temperature.
67 citations
TL;DR: In this article, the extended Dulong and Petit law in Neumann-Kopp rule is verified for zirconia and quaternary compounds using Debye theory.
67 citations
TL;DR: In this article, bound state wave functions were introduced related to the screening Coulomb potential (Debye model) using the Ritz variation method, and the bound energies were derived from an energy equation, which contains one unknown variational parameter.
Abstract: Plasma-screening effects are investigated on hydrogen atoms embedded in weakly coupled plasmas. In the present context, bound state wave functions are introduced related to the screening Coulomb potential (Debye model) using the Ritz variation method. The bound energies are derived from an energy equation, which contains one unknown variational parameter. To calculate the parameter numerically, fixed-point iteration scheme is used. The calculated energy eigenvalues for various Debye lengths agree well with the other available theoretical results. The radial wave functions and radial probability distribution functions are presented for different Debye lengths. The outcomes show that the plasma affects the embedded hydrogen atom.
67 citations
TL;DR: In this article, a Debye model is used to describe the phonon spectrum of the solid. But, it appears almost impossible to extract from a kinematical model reliable quantitative information about the average thermal displacements of the surface and bulk ion cores.
Abstract: The evaluation of the elastic scattering differential cross section of electron scattering from a planar surface of a vibrating lattice is reduced to the solution of a set of coupled algebraic equations for the associated scattering amplitude. This reduction is valid both for overlapping potentials (thus removing the restriction of previous analyses to muffin-tin potentials) and for the nonspherical potentials associated with ion cores at solid surfaces. The algebraic equations are solved using a double-diffraction analysis of the inelastic-collision model. Surface scatterers are taken to be geometrically equivalent but electronically and vibronically inequivalent to those in the bulk. A Debye model is used to describe the phonon spectrum of the solid. Numerical results are presented for a hypothetical fcc metal with the lattice parameters of aluminum. Thermal expansion alters the energies of peaks in the elastic intensity profiles ($I\ensuremath{-}V$ curves), whereas the thermal vibration of the ion cores alters the intensities of the peaks. The temperature dependence of the peak heights can be described by the kinematic model in which it is attributed to the Debye-Waller factor associated with an "effective" Debye temperature. However, the multiple scattering of the electron from the lattice causes these "effective" Debye temperatures to be related to the parameters of the model (e.g., bulk and surface electron---ion-core scattering phase shifts, the inelastic-collision mean free path, bulk- and surface-model Debye temperatures) in a complicated fashion. Although the trends evident in the dependence of the effective Debye temperature on the model parameters can be rendered plausible, it appears almost impossible to extract from a kinematical model reliable quantitative information about the average thermal displacements of the surface and bulk ion cores.
67 citations