Four-phonon processes

We first consider the vibrational relaxation that can be induced by aijQqiqj (three-phonon processes) or Qq qi (four-phonon processes). In the three-phonon processes there are two accepting modes, while in the four-phonon processes there are three accepting modes. To calculate the rate of vibrational relaxation, we use... 

The s are then the generalized elastic constants. The third and fourth order s are directly proportional to the matrix elements for the three- and four-phonon processes respectively. 

All other terms that are not related to the above terms by permutation of the Indices are zero. As noted before, < gives the optical phonon frequency y gives the amplitudes for three-phonon processes and a and 3 give the amplitudes for the bare four-phonon processes. 

The similarity between the A C o spectra doped with different alkali metals again indicates that the observed modes are due only to the Cfio molecule, and that there are no observable A-Cfto modes above 100 cm The mode at 270 cm has a resolution-limited FWHM for CSftCfio, is broadened in nd is a doublet in K C q. The high-frequency mode of the doublet may result from a two-phonon process involving a low cnergy-A-Cfrequency modes (1383 cm and 1478 cm ). If this is the case, it is not clear that these modes should be broadened in the same way as the... 

Notice that it is not always easy to distinguish between these processes on an a priori basis. For example, three- or four-phonon asymmetric up-conversion rates vary approximately as the occupation number of some (low-frequency) phonon at low temperature and as T thereafter. The pure... 

This work contributed in two major ways. First, the calculation shows that it is now possible for the first time to calculate from first principles phonon-phonon interaction parameters that are inaccessible from experiment. Second, since all the effective four-phonon terms (direct plus mediated processes up to are attractive for the k = 0 optical phonons in diamond, the formation of the two-phonon bound state is unlikely in this system. 

This mechanism concerns the relaxation of vibrationally excited molecules near surfaces. It depends strongly on the ratio between the vibrational frequency of a molecule, coq, and the Debye frequency of the substrate, cup, which determines the upper limit of the phonon spectrum. If a>o < cod, relaxation through creation of a single phonon is possible. Usually the corresponding decay rates are of the order of lO -lO s . For (n — 1)cud < o o < ncup, the relaxation is accompanied by the generation of n phonons. The probability of an n-phonon process to occur rapidly decreases with order n. Typical values for the two-, three- and four-phonon decay rates are 10 -10 10 -10 and 10 -10 s, respectively (Zhdanov and Zamaraev 1982). 

From Table 5.1, it follows that there are four basic processes (i) absorption of a phonon with the creation of two other phonons, (ii) absorption of two phonons with the creation of another, (iii) simultaneous disappearance... 

A spin-dependent recombination rate is another consequence of the electron-hole correlation. The conservation of spin selection rule is preserved in amorphous materials. The final state of the recombination process has zero spin and both radiative and phonon-assisted non-radiative transitions occur without change in spin, so that recombination can only proceed from an initial state of zero spin. A weakly interacting electron-hole pair forms four possible spin states, one singlet and one triplet. Of the four states, only the singlet and one... 

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