Two-phonon

For polyatomics, ordinarily only the last two tenns of equation (C3.5.6), the cubic and quartic anlrannonic tenns, need be considered [34]. In a cubic anlrannonic process, excited vibration D relaxes by interacting with two other states, say airother vibration cr aird one phonon (or alternatively two phonons). In the quartic process, D relaxes by interacting with tlrree other states, say two vibrations aird one phonon. The total rate constairt for energy loss from Q for cubic... 

The role of two-phonon processes in the relaxation of tunneling systems has been analyzed by Silbey and Trommsdorf [1990]. Unlike the model of TLS coupled linearly to a harmonic bath (2.39), bilinear coupling to phonons of the form Cijqiqja was considered. In the deformation potential approximation the coupling constant Cij is proportional to (y.cUj. There are two leading two-phonon processes with different dependence of the relaxation rate on temperature and energy gap, A = (A Two-phonon emission prevails at low temperatures, and it is... 

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. 

Figure 9-14. Absorption (top) and elecuuabsorplion of a mLPPP film at 21) K. Note the resolution of at least two phonon progressions (sec text).

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 Orbach process is a two-phonon process that takes place via population of an excited electronic state with energy Eq. The temperature dependence of the relaxation rate is given by... 

When Wqi / Wq2 the magnetization recovery may appear close to singleexponential, but the time constant thereby obtained is misleading [50]. The measurement of 7) of quadrupolar nuclei under MAS conditions presents additional complications that have been discussed by comparison to static results in GaN [50]. The quadrupolar (two phonon Raman) relaxation mechanism is strongly temperature dependent, varying as T1 well below and T2 well above the Debye temperature [ 119]. It is also effective even in cases where the static NQCC is zero, as in an ideal ZB lattice, since displacements from equilibrium positions produce finite EFGs. 

Fig. 6. Vibrational states corresponding to axial H-atom vibrations (y-coordinate) and perpendicular B-atom vibrations (atj, x2 — coordinates) in the absence and presence of anhar-monic coupling (see text). For state mn,n2>, the m is the H-vibrational quantum number, and the n s are the B-vibrational quantum numbers. The infrared absorption corresponding to the m = 0 to m = 1 transition is sensitive to the B-isotope, as seen in the figure (solid vertical lines). Also, the transition n = 0 to n = 2 is now weakly allowed due to the mixing with the H-mode these two-phonon transitions are indicated by dashed vertical lines. Less important vibrational states are not shown on the figure.

This two-phonon transition was subsequently observed as predicted in infrared-absorption (Stavola et al., 1989a). Furthermore, its polarization is the same as the fundamental one-phonon (111) transition from which it gains its oscillator strength, providing further support for the BC model. Finally, a considerably weaker two-phonon infrared absorption was observed for nB, also consistent with predictions based on this model. 

One-phonon interactions are described in general by formula (A2.14). An analogous expression for two-phonon interactions appears as ... 

To estimate the above expression, consider a particular case of the symmetric two-well potential in which the two-phonon interaction //- can approximately be derived from expansion (A2.32) ... 

Under even more intense photoexcitation ( 10mJ/cm2), the coherent A g and Eg phonons of Bi and Sb exhibit a collapse-revival in their amplitudes (Fig. 2.10) [42,43], This phenomenon has a clear threshold in the pump density, which is common for the two phonon modes but depends on temperature and the crystal (Bi or Sb). At first glance, the amplitude collapse-revival appears to be analogous to the fractional revival in nuclear wavepackets in molecules [44,45]. However, the pump power dependence may be an indication of a polarization, not quantum, beating between different spatial components of the coherent response within the laser spot [46],... 

Contents Lattice Dynamics. - Symmetry. - Inter-molecular Potentials. - Anharmonic Interactions. - Two-Phonon Spectra of Molecular Crystals. -Infrared and Raman Intensities in Molecular Crystals. 

Notice the second, weaker oscillator at 640 cm-1 from a quantum viewpoint, this oscillator is interpreted as the excitation of two phonons by a photon. In order for momentum to be conserved, two phonons with almost equal and opposite momenta must be created a photon has negligible momentum compared with phonon momenta. Such two-phonon transitions usually occur to a noticeable extent in ionic crystals, which necessitates a multiple-oscillator correction to the main one-oscillator Reststrahlen band. 

Inelastic scattering of radiation in solids is typified by the Raman effect, which involves the creation or annihilation of phonons or magnons. If a single phonon is involved, the scattering event is referred to as the first-order Raman effect in second-order Raman effect two phonons are involved. The polarizability associated with a phonon mode can be represented as a power series of the phonon amplitude, u, as follows ... 

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. 

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