Phonon spectrum, theory

Vibrational properties can also be computed using the total energy formalism. Here, the atomic mass is required as input and the crystal is distorted to mimic a frozen-in lattice vibration. The total energy and forces on the atoms can be computed for the distorted configuration, and, through a comparison between the distorted and undistorted crystal, the lattice vibrational (or phonon) spectrum can be computed. Again, the agreement between theory and experiment is excellent. [22]... 

The expression (9) for the non-adiabatic transition probability is correct, naturally, if the phonon spectrum is quasi-continuous one. Moreover, use of Fermi s gold rule or the first order of the perturbation theory on Fif is correct, if the following inequality is realized. 

The simple classical theory of a tetramerized chain with four different force constants was found to be unable to describe this phonon spectrum, however [36]. This is an indication that the conduction electrons could be involved in formation of the chain distortion. 

This review deals mainly with the electrical and thermal conductivities at temperatures T from 0 K to room temperature. It is the region where the lattice vibrations must be described by quantum mechanics, and the phonon spectrum determines much of the temperature dependence of the transport properties. The absolute magnitudes of the electrical and thermal conductivties depend crucially on a consideration of the quantum mechanical matrix elements for the scattering of electrons and phonons. They are difficult to calculate, not only for the refractory systems of interest here but for most solids. Theories of conduction properties therefore contain parameters, some of which are fairly well known while others are quite uncertain. 

Theoretically, the elasticity theory of continuous media may be used to study the long-wavelength modes. To determine the microscopic modes, numerical approaches are necessary. Most of them have used Born s model to estimate the inter-atomic forces. The semi-infinite crystals are modelled by thin films, whose thickness must be larger than the attenuation length of the surface modes. The complete MgO(OOl) phonon spectrum has been calculated, neglecting (Chen et al, 1977 Barnett and Bass, 1979) or taking into account (Lakshmi and de Wette, 1980) the surface relaxation. The same has been done for SrTiO3(001) (Prade et al, 1993). 

The theory of the effect of crystal structure on k is still in a very rudimentary state. It is generally observed that the larger the number of optical branches in the phonon spectrum, the lower the thermal conductivity. In garnets, there are 80 atoms in the primitive unit cells, and there are 97 optical modes at the zone center (Hurrell et al., 1%8). The combination of infrared and Raman studies has... 

The use of BCS theory to quantitatively compute for a given material requires detailed knowledge of both the electronic structure and the phonon spectrum. Information of this sort for complex materials (i.e., alloys and intermetallic compounds) is extremely difficult to obtain and one still relies on past experience and empiricism in the search for new materials. 

According to the quantum transition state theory [108], and ignoring damping, at a temperature T h(S) /Inks — a/ i )To/2n, the wall motion will typically be classically activated. This temperature lies within the plateau in thermal conductivity [19]. This estimate will be lowered if damping, which becomes considerable also at these temperatures, is included in the treatment. Indeed, as shown later in this section, interaction with phonons results in the usual phenomena of frequency shift and level broadening in an internal resonance. Also, activated motion necessarily implies that the system is multilevel. While a complete characterization of all the states does not seem realistic at present, we can extract at least the spectrum of their important subset, namely, those that correspond to the vibrational excitations of the mosaic, whose spectraFspatial density will turn out to be sufficiently high to account for the existence of the boson peak. 

Figure 19. The predicted low T heat conductivity. The no coupling case neglects phonon coupling effects on the ripplon spectrum. The (scaled) experimental data are taken from Smith [112] for a-Si02 (AsTj/ScOd 4.4) and from Freeman and Anderson [19] for polybutadiene (ksTg/Hcao — 2.5). The empirical universal lower T ratio l /l 150 [19], used explicitly here to superimpose our results on the experiment, was predicted by the present theory earlier within a factor of order unity, as explained in Section lllB. The effects of nonuniversaUty due to the phonon coupling are explained in Section IVF.

We used short broadband pump pulses (spectral width 200 cm 1, pulse duration 130 fs FWHM) to excite impulsively the section of the NH absorption spectrum which includes the ffec-exciton peak and the first three satellite peaks [4], The transient absorbance change signal shows pronounced oscillations that persist up to about 15ps and contain two distinct frequency components whose temperature dependence and frequencies match perfectly with two phonon bands in the non-resonant electronic Raman spectrum of ACN [3] (Fig. 2a, b). Therefore the oscillations are assigned to the excitation of phonon wavepackets in the ground state. The corresponding excitation process is only possible if the phonon modes are coupled to the NH mode. Self trapping theory says that these are the phonon modes, which induce the self localization. 

This subsection is devoted to the description of the upper excited states appearing in the excitation spectrum of the surface emission. The way this excitation is performed will be examined in Section III.B.3 below, in connection with the theory of Section III.B.l.b. The upper states examined are associated with the first singlet transition, b- and a-polarized, and are of two types purely electronic and vibronic states in an extended sense, as resulting from the coupling of electronic excitations to vibrations or to lattice phonons. 

The PPV spectra of Fig. 16 show all the signatures of exciton absorption and emission, such as in typical molecular crystals. The existence of well-defined structure in the absorption spectrum is not so easily accounted for in a band-to-band absorption model. In semiconductor theory, the main source of structure is in the joint density of states, and none is predicted in one-dimensional band structure calculations (see below). However, CPs have high-energy phonons (molecular vibrations) which are known (see, e.g., RRS spectra) to be coupled to the electron states. The influence of these vibrations has not been included in previous theories of band-to-band transition spectra in the case of such wide bands [176,183]. For excitons, the vibronic structure is washed out in the case of very intense transitions, corresponding to very wide exciton bands, the strong-coupling case [168,170]. Does a similar effect occur for one-electron bands Further theoretical work would be useful. 

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