Multi-phonon processes

G. Herzberg, Molecular Spectra and Molecular Structure, Vol. II - Infrared and Raman Spectra of Polyatomic Molecules, Van Nostrand Reinhold, New York, 1945 In the crystalline state, it is more convenient to speak about multi-phonon processes since the modes from the whole dispersion range of the first Brillouin zone are allowed to contribute according to the conservation of energy and momentum of the phonons involved in the process... 

Estimation of Low-Energy Excitation Modes. An absorption line profile of each dye molecule at low temperature consists of two components a sharp zero-phonon line and a broad phonon side band. Tbe energy difference between the zero-phonon line and the phonon side band coincides with the low-energy excitation mode or phonon frequency of the matrix when multi-phonon processes can be ignored. 

Fig. 3. Schematic representation of emission probability and absorption cross section for nuclei bound in a solid after Visscher (1960). The sharp line arises from zero-phonon processes, the broad distribution from one- and multi-phonon processes. The / factor equals the ratio of the area under the sharp line to the total area. Height and width of the zero-phonon line are not to scale. The energy scale corresponds to the case of Np. [Taken from Dunlap and Kalvius (1985).]...

In general, for a multi-phonon process p = Ajlj, the total transition probability is given as... 

Accordingly, if multi-phonon processes were not involved, the phonon density corresponds to the amplitude-weighted frequency distribution as multiplied with the Debye-Waller factor. Actually, however, multiphonon scattering is not negligible and peaks due to multi-phonon processes appear in the phonon density curves. 

The region between 860 and 2400 cm is believed to be caused by multi-phonon processes in which one photon generates two or more phonons. The a values for the two-phonon processes are about 10 times as large as the one-phonon processes, and the three-phonon processes give a values about 10 times as large. 

Fig. 3.7. Polarized micro-Raman spectra of a (0001) ZnO bulk sample (a) and a (0001) ZnO thin film (d 1,970 nm) on (0001) sapphire (b). The vertical dotted and dashed lines mark ZnO and sapphire (S) phonon modes, respectively. MP denotes modes due to multi-phonon scattering processes in ZnO. Excitation with Ar+-laser line A = 514.5 nm and laser power P < 40 mW. Reprinted with permission from [38]...

Figure 13.35 Schematic energy level diagrams showing typical UC processes for Er, Tm, and Ho +. The dashed-dotted, dotted, and full arrows represent excitation, multi-phonon relaxation, and emission processes, respectively. The notations used to label the f levels refer to spin (5), orbital (L),...

The absorption coefficient for a multi-phonon combination can be expressed as the product of three terms. The first one is the matrix element of the coupling term between the phonons involved in the process. It is non-zero only for specific phonon combinations determined by selection rules derived from symmetry considerations. The second one describes the temperature... 

We have mentioned the existence of CPs in the one-phonon density of states, but this can be measured only for compound crystals. The situation is different in multi-phonon absorption because the high-frequency phonons of the BZ boundary are mostly involved (note that in three-phonon processes, the q = 0 zone-centre phonons can also be involved without problem for momentum conservation). For the two-phonon absorption, the density of states is proportional to an integral similar to the one in expression 3.20, with wt replaced by the sum of the two pulsations and of the phonons of the combination. Besides the trivial case where = u> = 0, the condition Vq (wt (q) + wt (q)) = 0 is fulfilled when Vq (wt) = Vq(uv) = 0 or when Vq (wt) = — Vq (wt ). The observed two-phonon absorption is the sum of the contributions of the possible two-phonon processes. Figure 3.2 shows the RT absorption of silicon in the two- and three-phonon absorption region. In the two-phonon region, it is fitted with the two-phonon dispersion curves... 

R is the effective radius of the dislocation core, p is the density of the crystal. G is the shear modulus, v is the Poisson ratio. The second term in Equation (6) applies to very rapid deformation processes due to strong shock loading and is dominated by the resonant condition Ei - E. i T(T,U)vo /d that occurs as T(i,U) 1. This term leads to resonant multi-phonon molecular excitation and dissociation associated with detonation and is discussed elsewhere [18]. 

Some authors approach the study of impact and shock sensitivities as if it were a single type of initiation. However, from the standpoint of the way the impulse energy is transferred to the reaction centre of the molecule there are two different initiation processes (Sect. 4). On the basis of his multi-phonon up-pumping model of initiation of EMs, Dlott considers the impact initiation to be a kind of low velocity initiation (LVI) [1,74]. 

In this section we review the important theoretical developments relevant to host-sensitized energy transfer. The basic interaction between two isolated ions or molecules is discussed first, then the effects of having an ensemble of sensitizer and activator ions is presented. The mathematical description of energy transfer by multi-step migration among sensitizer ions is developed and the effects of trapping at activator sites is discussed. The importance of phonons in both single-step and multi-step transfer processes is also described. 

Fig. 2 a Energy migration, that is multi-step energy transfer between chemically identical chromophores. b Within the inhomogeneous distribution it can proceed via an resonant process (straight arrow) or via a phonon-assisted process whereby the energy mismatch between the donor and the acceptor is made up by lattice phonons (curly arrows)... 

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