Two-phonon spectrum

The shape of the two-phonon spectrum is given by the convolution of the one-phonon spectrum with itself, g(a )ext g((i))ext- The shape of the three-phonon spectrum, n = 3, is obtained by convolving the one- and two-phonon spectra, and so on. The weight of each contribution is given by... 

In systems where inter-hydrogen forces are important, usually because of the close proximity of hydrogen neighbours, dispersion is clearly seen in the one quantum spectrum, as in Fig. 6.22. The higher order transitions from such systems would not then be expected to appear as sharp transitions, since the two phonon spectrum should resemble the self convolution of the one phonon spectrum ( 2.6.3). Occasionally, however, sharp transitions are observed, at E(2 o just below the energy of 2E(i o) If -d is the full width at half height of the (1<—0) transition. Then, provided that... 

After several reports between 1965 and 1980, no new information has been published on the spectroscopy of donors in GaP. Odd-parity transitions from the ground to excited states associated with the lowest X band for the Si, S and Te donors have been reported in the 55-100 meV ( 440-810cm-1) spectral domain [10,39,196,223]. The spectra are superimposed on the two-phonon spectrum of GaP and the FWHMs of the absorption lines at LHeT are - ()Ai meV. LHeT photoconductivity measurements in the photoionization region of shallow impurities in GaP revealed dips due to electronic transitions accompanied by the emission of LA(X) and LO (r) phonons with energies of 404 and 254 cm 1, respectively, and they have contributed to the understanding of the donor spectra [222]. LHeT transmission spectra of GaP Si samples at LHeT showing Si donor transitions are displayed in Fig. 6.45. 

Fig. 6.45. Transmission spectra of two epitaxied GaP samples in the spectral range 64.7-85.3 meV (the thickness is indicated) superimposed on the two-phonon spectrum. Apart from the weak line between lines 4/o and 3p i, due to the mylar beam splitter of the FTS, a weak local vibrational mode of 11BGa is also observed (after [39]). Reproduced with permission from the Institute of Physics...

The PL spectrum and onset of the absorption spectrum of poly(2,5-dioctyloxy-para-phenylene vinylene) (DOO-PPV) are shown in Figure 7-8b. The PL spectrum exhibits several phonon replica at 1.8, 1.98, and 2.15 eV. The PL spectrum is not corrected for the system spectral response or self-absorption. These corrections would affect the relative intensities of the peaks, but not their positions. The highest energy peak is taken as the zero-phonon (0-0) transition and the two lower peaks correspond to one- and two-phonon transitions (1-0 and 2-0, respectively). The 2-0 transition is significantly broader than the 0-0 transition. This could be explained by the existence of several unresolved phonon modes which couple to electronic transitions. In this section we concentrate on films and dilute solutions of DOO-PPV, though similar measurements have been carried out on MEH-PPV [23]. Fresh DOO-PPV thin films were cast from chloroform solutions of 5% molar concentration onto quartz substrates the films were kept under constant vacuum. 

Fig. 16 Raman spectrum of two-phonon processes in single crystalline a- 8g range 500-1000 cm , after [109]. The strong bands in the range 800-950 cm result from combinations of components of the stretching vibrations...

At higher temperatures, the two-phonon (Raman) processes may be predominant. In such a process, a phonon with energy hcOq is annihilated and a phonon with energy HcOr is created. The energy difference TicOq — ha>r is taken up in a transition of the electronic spin. In the Debye approximation for the phonon spectrum, this gives rise to a relaxation rate given by... 

The phonon spectrum of a crystal surface consists of two parts. The bulk... 

With further increase of the concentration (in p, phase range for H cLii cNb03) many new bands were observed. The fact that the low concentration boundary of the P phases is approximately x = 0.5 leads to the assumption for some kind of ordering of Li and as reported. On one hand, it can be assumed that the protons form a (nearly) ordered sub-lattice. Such a structure would have a phonon spectrum different from that of a pure LiNbOs, see . On the other hand, the PE probably leads to a reduction of the crystal symmetry, i.e. due to the incorporation of H, the two Li sites in the unit cell may become non-equivalent. In such case, the symmetry would be reduced from Csv to C3. As a result, the number of molecules per unit cell would remain the same, but new bands would appear in the vibration spectrum. 

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. 

The infra-red spectrum of Li-6 hydroxide was discussed by Decius and Lilley 69> who report that the major feature at 3681 400 cm"1 in the LiOH spectrum (which was previously assumed to involve a librational mode) is partly due to the absorption at 3681 290 cm 1 which involves a translator mode in which there is a significant amount of Li7-participation the rest may be a two-phonon process (see Oehler and Gunthard S6>). 

Puthoff et al. 77) found two polaritons associated with TO phonons of species Aj with tuning ranges from 630 to 500 cm 1 and 250 to nearly 0 cm-1. The Raman scattering at these extraordinary polaritons was used to study 36) the directional dispersion of the phonons in LiNb03. Recently Winter and Claus 78> also investigated the polaritons associated with the E phonons at 582 and 154 cm-1 by both photographic and photoelectric methods. These branches were important for the assignment of the phonon spectrum 39>. 

At low temperatures (/3ho)c>l) the contributions from one-phonon, two-phonon processes, etc., can be systematically extracted from the general expression for the rate constant, and the type of the dominant process is determined by the bath spectrum and temperature. The results of Leggett et al. [1987] show that quantum dynamics of a TLS crucially depends on the spectrum of the bath. For sufficiently strong coupling, the bath may dramatically slow the tunneling rate, even to the point of localizing the particle in one of the wells. This strong dependence on the bath spectrum is inherent to the quantum dynamics and does not show up in classical transitions. 

On the assumption that the electron correlations are relatively weak in the material, the model of Schulz [37], which takes into account the interaction between the conduction electrons and one acoustic phonon branch, has then been used to calculate the longitudinal phonon spectrum. In the model, two new optical modes are coming up at 2kF, corresponding to excitations in the phase and in the amplitude of the distortion. However, the agreement was still very poor in this case, the renormalization of the phase mode being considerably larger in the model than experimentally observed [34]. 

Figure 11.49. FT-IR spectrum of a diamond film in the C-H vibrational region. The band around 1700-2700 cm is the two-phonon band [352].

A spectrum of pristine Cfto sublimed in a tube and unexposed to air, O2, or alkali metal was taken (Fig. 2). We have previously shown (15) that exposure of vacuum-grown films to either air or oxygen alters the spectrum, especially in the frequency region of the symmetric mode at 1458 cm . In previous experiments (15) the Si substrate inhibited the identification of modes near 520 cm and 950 cm to 1000 cm . In the present experiments, the Si substrate has been eliminated and we can identify die mode at 522 em and the broad feature between 950 cm and 1000 cm as due to 60- The broad feature may result from a two phonon process involving the 490... 

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