Debye model

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

The lattice thermal conductivity of a semiconductor nanowire

Abstract: It has been found experimentally as well as theoretically that the lattice thermal conductivity can be largely reduced by the size confinement effect. The significant boundary scattering effect is one of the dominant factors. In most existing lattice thermal conductivity models, an empirical relation is used for this scattering rate. An unconfined or confined phonon distribution obtained based on the phonon Boltzmann equation and the relaxation time approximation is then employed to calculate the lattice thermal conductivity. In this work, we first attempt to derive an analytical form of the boundary scattering rate for phonon conduction in a semiconductor nanowire and then claim two reasonable ways to take it into account correctly. Consistent mathematical models in the sense that the effects of the size confinement on (i) the phonon dispersion relation, (ii) the phonon distribution, (iii) the phonon group and phase velocities, and (iv) the Debye temperature are finally proposed.

First-principles study of pressure-induced phase transition in silicon carbide

Abstract: The phase transition of SiC from the zinc blende (ZB) structure to the rocksalt (RS) structure under pressure is investigated by the first principles plane-wave pseudopotential density functional theory method. The results obtained are in good agreement with the experimentally measured data and other theoretically calculated results. It is found that the pressures of transition of SiC from the ZB structure to the RS structure are 74.6 GPa from total energy–volume data and 75.4 GPa from the enthalpy calculations. Moreover, through the quasi-harmonic Debye model, in which the phononic effects are considered, the dependences of relative volume V/V0 on pressure P at T=0, 1400 K are successfully obtained. The calculated volume reduction at the transition is 18%. In particular, from the high-pressure elastic constants obtained, the ZB structure SiC is found unstable when the applied pressure is larger than 126.6 GPa. This value is in excellent agreement with the experimental data and the molecular dynamics (MD) simulation results.

On the Electron-Phonon Interaction in Normal Metals. I

Abstract: By the use of Frohlich's Hamil!onian and the method of Green's functions, the electron­ phonon interaction in a normal metal under a steady magnetic field is studied. It is shown that the period of the de Haas-van Alphen effect is not modified by the interaction. The resonance frequency of the Azbel'-Kaner effect, on the other hand, is modified and the cyclotron mass of the electron takes essentially the same value as the thermal mass which is also modified by the interaction as shown previously. The conclusion is in accord with the recent experimental results obtained by Kip and Grimes on Na and K. The same conclusion, however, is obtained also by applying Landau's theory of Fermi liquids to the inter-electronic Coulomb correlation without introducing the electron-phonon interaction, though the mass shift caused by the former seems too small. § I. Introduction In a previous paper'> we examined how the electron-phonon interaction modifies the density of one-electron states (i.e. the thermal mass of the electron) and electric conductivity of a normal metal. As emphasized there, the physical point is the dynamical character of the interaction. This character is already evident in the lowest order process in the perturbation theory of the electron self-energy. Thus, between emission and reabsorption of a phonon by an elec-. tron, there exists retardation which makes the time dependence of the self­ energy essential. Indeed, as we have shown, this dynamical part of the self­ energy becomes singular when the velocity of sound v. is much less than the electron velocity Vp at the Fermi surface and appreciably modifies the thermal mass. It results also in some anomalous dispersion of the one~electron excita­ tion spectrum when excitation energies are comparable to the Debye temperature. On the other hand, in the case of electric conductivity, the renormalization of the wave function explicitly comes into play in addition to the mass renormali­ zation mentioned above. These two effects are cancelled by each other both in static and anomalous limits and there appears the bare (band theoretical) electron mass in the expression for conductivity. The aim of the present paper is to extend the theory so as to include a steady magnetic field. We thus deal with de Haas-van Alphen effect and Azbel'­ Kaner effect, taking into consideration the electron-phonon interaction. As for the de Haas-van Alphen effect, Luttinger 2> and Gor'kov and Bychkov3> have already

LV. A surface contribution to the Debye specific heat

Abstract: The vibrations of a bounded lattice are identified with those of an elastic medium (isotropic, arbitrary elastic constants) having stress free surfaces. The densities of the representative points in wave number space for the four possible types of vibration are estimated. These estimates are carried one step further than the usual (Debye) method by including terms proportional to the surface. Summing over the densities, the total number of excited modes and the intrinsic energy of the lattice vibrations are obtained in the usual manner. From these we calculate surface terms for the Debye temperature and specific heat and for the free energy of the lattice vibrations.

Two unique measurements related to flash experiments with yttria‐stabilized zirconia

Abstract: We report two measurements related to flash experiments. One is concerned with electroluminescence in yttria-stabilized zirconia; in this case we have measured the broadening of the (UV) absorption edge in single crystal cubic zirconia below the conduction band, suggesting the generation of energy levels that are consistent with the electroluminescent spectra. The second measurement relates to the universal nature of the power density at the early onset of the flash transition in Stage I, for several ceramics flashed under a wide range of electric fields and temperature, which may be related to nonlinear thermal vibrations, so that the Debye temperature would be a lower bound for the flash-onset.