Phonon energy spectrum

Fig. 13. Phonon energy spectrum with soft mode (Kohn anomaly) at q — Inlia ikp n/ia).

A phonon density of states can be obtained from the measured phonon energy spectrum for compounds, the partial phonon density of states for the specific element can be obtained. It should be noted that since the direction of the conversion electron and the direction of the... 

The phonon-energy spectrum from the heat capacity (heat capacity Cy versus temperature T) of sohds. 

In this section we continue to explore the consequences of the existence of the low temperature excitations in amorphous substances, which, as argued in Section III, are really resonances that arise from residual molecular motions otherwise representative of the molecular rearrangements in the material at the temperature of vitrification. We were able to see why these degrees of freedom should exist in glasses and explain their number density and the nearly flat energy spectrum, as well as the universal nature of phonon scattering off these excitations at low T < 1 K). 

Several types of spin-lattice relaxation processes have been described in the literature [31]. Here a brief overview of some of the most important ones is given. The simplest spin-lattice process is the direct process in which a spin transition is accompanied by the creation or annihilation of a single phonon such that the electronic spin transition energy, A, is exchanged by the phonon energy, hcoq. Using the Debye model for the phonon spectrum, one finds for k T A that... 

Nuclear absorption of incident X-rays (from the synchrotron beam) occurs elastically, provided their energy, y, coincides precisely with the energy of the nuclear transition, Eq, of the Mossbauer isotope (elastic or zero-phonon peak at = E m Fig. 9.34). Nuclear absorption may also proceed inelasticaUy, by creation or annihilation of a phonon. This process causes inelastic sidebands in the energy spectrum around the central elastic peak (Fig. 9.34) and is termed nuclear inelastic scattering (NIS). 

To understand the underlying rectifying mechanism, let s start from the energy spectrum of the interface particles. Fig. 8 shows the phonon spectra of the left and right interface particles at different temperature when the two lattices are decoupled kmt = 0). 

Phonon vibration spectrum was determined from force constant k which was determined from dependence of the calculated molecule average energy on volume ( a3), i.e. from compressibility k d2Etot(a,T)lda2. The pressure in the system was determined conventionally as P(a,T) = -dF(a,T) / 8V One can determine the lattice constant a(T) for every value of (P,T) by numerical inversion of the dependence P a,T) => a(P,T) ... 

Two of the more direct techniques used in the study of lattice dynamics of crystals have been the scattering of neutrons and of x-rays from crystals. In addition, the phonon vibrational spectrum can be inferred from careful analysis of measurements of specific heat and elastic constants. In studies of Bragg reflection of x-rays (which involves no loss of energy to the lattice), it was found that temperature has a strong influence on the intensity of the reflected lines. The intensity of the scattered x-rays as a function of temperature can be expressed by I (T) = IQ e"2Tr(r) where 2W(T) is called the Debye-Waller factor. Similarly in the Mossbauer effect, gamma rays are emitted or absorbed without loss of energy and without change in the quantum state of the lattice by... 

Light scattering is a useful tool for investigating a superconducting gap in the electronic energy spectrum because it is based on electron-phonon interaction and therefore is able to sensitively probe both phonon and electronic states. This idea and experimental studies have recently been developed for (BEDT-TTF)2I3 family superconductors [85,86]. The van-... 

The half width of the luminescence line by the phonon interaction mechanism, from Eq. (8.11), is 2[(2 In 2) ji This is 0.25 eV for the maximum phonon energy of 0.05 eV from the silicon network vibrations, which is a little less than the observed line width. Thus the phonon model indicates that the luminescence spectrum is dominated by the phonon interaction and that the disorder broadening contributes less. 

The NDR can be explained by the field effect, which splits the resonance scattering lines because of the frequency shifts at the turning points, and therefore the electron flow only partly contributes to the current. In accordance with the Pauli principle, the Fermi energy spectrum window given by the difference of Fermi functions results in a step-like increase of the current, when being overlapped with the transparency resonance at the bias voltage equals a multiple of the phonon quantum nil, as shown in Fig. 1. Since the transparency doublets are split faster than the Fermi windows are broadened out, after a... 

Fig. 7.17. Comparison between the Au and Pt p3/2 spectra in silicon obtained from photothermal ionization measurements at LHeT. To facilitate the assignment of the Pt phonon replicas, markers indicating 0, 1, and 2 phonon energies (hu> = 57 cm-1 or 7.1 meV) are included. The Au spectrum extends from about 600 to 650 meV and the Pt one from 910 to 960 meV [100]. Copyright 1988 by the American Physical Society...

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