Three-phonon decay

It is important to note at this point that the LA phonon lifetime against spontaneous decay varies as oT, i.e, high frequency LA phonons are predicted to decay much more rapidly than low frequency phonons. In simple systems near T 0, the spontaneous three-phonon decay of LA phonons, described above, should dominate the observed temporal evolution of nonequilibrium phonon distributions (Orbach and Vredevoe, 1964). 

At low ambient temperatures, such that tioiiy kgT, the spontaneous three-phonon decay of q=0, optical phonons into two acoustic phonons (plus the corresponding recombination process) should dominate all other phonon-phonon interactions (Orbach and Vredevoe 1964). 

The possible three-phonon decay channels are illustrated in the inset to figure 3. Channel (b) is not active since it would produce a phonon of higher energy than the LO phonon which is not... 

Equation (5), VER involves a higher-order anharmonic coupling matrix element, which gives rise to decay via simultaneous emission of several phonons nftjph (multiphonon emission). In the ACN case, three phonons must be emitted simultaneously via quartic anharmonic coupling (or four phonons via fifth-order coupling, etc.). 

In the gas phase, the asymmetric CO stretch lifetime is 1.28 0.1 ns. The solvent can provide an alternative relaxation pathway that requires single phonon excitation (or phonon annihilation) (102) at 150 cm-1. Some support for this picture is provided by the results shown in Fig. 8. When Ar is the solvent at 3 mol/L, a single exponential decay is observed with a lifetime that is the same as the zero density lifetime, within experimental error. While Ar is effective at relaxing the low-frequency modes of W(CO)6, as discussed in conjunction with Fig. 8, it has no affect on the asymmetric CO stretch lifetime. The DOS of Ar cuts off at "-60 cm-1 (108). If the role of the solvent is to open a relaxation pathway involving intermolecular interactions that require the deposition of 150 cm-1 into the solvent, then in Ar the process would require the excitation of three phonons. A three-phonon process would be much less probable than single phonon processes that may occur in the polyatomic solvents. In this picture, the differences in the actual lifetimes measured in ethane, fluoroform, and CO2 (see Fig. 3) are attributed to differences in the phonon DOS at 150 cm-1 or to the magnitude of the coupling matrix elements. 

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). 

In this section, per-deuterated n-octane (n-octane-dig) is used as the matrix material, and the emission properties of Pd(2-thpy)2 are compared with those obtained with a per-protonated n-octane matrix (n-octane-hig). This latter matrix was used for the investigations discussed in the preceding sections. Three different issues are addressed, namely the occurrence of different sites for Pd(2-thpy)2, changes of low-energy vibrational/phonon structures, and changes of the emission decay behavior. 

The situation at surfaces is more complicated, and richer in information. The altered chemical environment at the surface modifies the dynamics to give rise to new vibrational modes which have amplitudes that decay rapidly into the bulk and so are localized at the surface [33]. Hence, the displacements of the atoms at the surface are due both to surface phonons and to bulk phonons projected onto the surface. Since the crystalline symmetry at the surface is reduced from three dimensions to the two dimensions in the plane parallel to the surface, the wavevector characterizing the states becomes the two-dimensional vector Q = qy). (We follow the conventional notation using uppercase letters for surface projections of three-dimensional vectors and take the positive sense for the z-direction as outward normal to the surface.) Thus, for a given Q there is a whole band of bulk vibrational frequencies which appear at the surface, corresponding to all the bulk phonons with different values of (which effectively form a continuum) along with the isolated frequencies from the surface localized modes. 

Blasse et al. found in CaS04 Bi three stractureless excitation bands at 354,303 and 243 nm due to the transitions from Sq to Pi, P2, and Pi, respectively, and an intensive emission at 378 nm with a lifetime of 60 10 ns due to the transition of Pi So at room temperature [49]. This is the only report we have found so far on the absorption of So 2- The Stokes shift is 2000 cm, which is fairly low compared with the others (see Tables 14.1, 14.2 and 14.3). When the temperature was lowered to liquid heUum, the stractureless excitation and emission of CaS04 Bi " became structured. The emission red shifts from 378 to 400 nm, and the decay time becomes 330 20 ps. This is the typical forbidden transition of "Po So, which predominates over Pi Sq at liquid-helium temperature. The zero phonon... 

The N3 optical center is one of the best known in steady-state luminescence spectra diamond. It is connected with three substitutional nitrogen atoms botmded to a common carbon atom or a vacancy, the ground state being a level and the excited state where luminescence originates a state (C3V point group). The zero-phonon line occurs at 2.985 eV and absorption and emission spectra show very closely a mirror relationship (Bokii et al. 1986). The N3 prompt luminescence decay is exponential and equal to 40 ns. Time-resolved luminescence spectroscopy enables to detect that N3 center has some metastable levels between the emitting and ground state. One of the decay paths of these metastable levels is delayed N3 luminescence, which occurs... 

In general, the Hfting of the translational invariance of the bulk at a surface or interface must result in surface phonon modes that are localized at the surface and decay exponentially into the bulk. In contrast to bulk modes with their three-dimensional dispersion (u(q), that is, dependence of frequency (o or energy ha> as function of momentum q, surface modes do not possess a dependence on qx, that is, normal to the surface. 

Fig. 15. Energy level diagram fisr the three lowest excited states of [Ru(bpy-hg)j] in (Zn(bpy-hglgKClOJz.The spin-latice relaxations (sir) from state 111) to the states II) and 11) are very fast,but the relaxation from state II) to 11) is hindered at T = 1.2 K, due to a slow process of direct phonon emission. This leads to a decay time of 220 10 ns [165,166], while the emission from state 11) decays with the usual emission lifetime of t, = 230 ps. Since the states II) and 11) are deactivated differendy by Franck-Condon (FC) and Herzberg-Teller (HT) vibrations, respectively, the emission spectra change distincdy with time (see Fig. 16). Similar properties are also observed for partially and per-deuterated [Rulbpylg] chromophores...

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