Phonon assisted energy transfer

Single-Step Resonant Energy Transfer.. Phonon-Assisted Energy Transfer. ... 

Keywords Oxalate networks [Cr(ox)3]3- [Cr(bpy)3]3+ 2E state Resonant energy transfer Phonon-assisted energy transfer Forster transfer Exchange interaction... 

Energy transfer between two inorganic ions can occur either by multipolar interaction or an exchange mechanism in dilute systems (Reisfeld and Jorgensen, 1977 Reisfeld, 1973, 1975, 1976a), or by multi-step migration in concentrated systems (Powell and Blasse, 1980). In addition to resonant transfer, phonon-assisted transfer is a quite common phenomenon (Reisfeld, 1976a, 1986). 

F ure 5.19 The energy-level schemes of donor D and acceptor A centers for (a) resonant energy transfer and (b) phonon-assisted energy transfer. 

The processes involved are stepwise energy transfer, cooperative sensitization of luminescence and cooperative luminescence. As an example of stepwise energy transfer a system containing Er and Yb may be considered. The latter ion absorbs at 970 nm (10,300 cm ) and in phonon assisted an Er ion... 

Van Uitert and Iida (55) suggested the applicability of the phonon-assisted-transfer mechanism to rare earth-rare earth energy exchange. They were able to correlate the emission intensity of the 5D0 level of trivalent europium or the5 D4 level of trivalent terbium with the closest, but definitely lower-lying, level observed for a second rare-earth ion. 

The first term is due to spontaneous radiative relaxation and nonradiative phonon relaxation as described in eq. (13), where / , is the probability of ion i in the excited state. The second term is due to energy transfer induced by ion-ion interaction, where W es and W A are rates of resonant and phonon-assistant energy transfer, which depend on distance between donor and acceptor RtJ. For resonant energy transfer... 

Energy transfer, particularly, phonon-assisted energy transfer processes must be considered in evaluating lanthanide luminescence decays, because they contribute in many cases to a major part of the observed lifetime. Based on the theoretical models described in section 3, we have conducted Monte Carlo simulations of energy transfer and its effect on luminescence decay for lanthanide ions in nanociystals and compared the calculated results with experi-... 

Direct pumping of poison centers as well as energy transfer from co-activators, and energy transfer from activators all represent an energy loss in the system. In addition, activators and co-activators also have non-radiative decay routes. Because non-radiative decay is usually phonon-assisted, non-radiative decay is exacerbated by increasing temperature and manifests itself by a characteristic temperature at which luminescence is quenched. The crystallographic relations that provide optimum sensitizer -activator energy transfer are outlined by Blasse (9)... 

As to the relaxation of the excitons in surfaces II and III by the bulk effect, a consistent discussion is as follows The bulk relaxation probability at the energy level s, PV(ES2), has been evaluated, at low temperatures, as few reciprocal centimeters and attributed to acoustical phonons (cf. Section II). With JSK 2cm"1, the direct probability (3.29) is evaluated as 0.2 cm"1, compatible with the observed value,141 while the phonon-assisted process (3.30) is drastically depressed and becomes comparable to direct transfer. 

The matrix element for one-phonon assisted energy transfer is then... 

Fig. 2. Phonon-assisted energy transfer for ions with a transition energy mismatch of AE,...

In certain cases involving very small energy mismatches two-phonon assisted transfer processes may be more important than the one-phonon processes. Numerous different types of two-phonon processes have been developed and found to predict a variety of different temperature dependences i2), The opposite limit of very large energy mismatch can be treated in a similar way to multiphonon relaxation processes 12,13). fhe matrix element in Eq. (2) is carried out to the Nth power where N is the number of phonons involved in the transfer process. The temperature dependence of the transfer rate for phonon emission processes then becomes... 

From the preceding section it is clear that certain important questions must be answered in characterizing host sensitized energy transfer in a specific material. The first question is whether the transfer is a single-step or multistep process. If it is a single-step process, the type of interaction mechanism must be identified and the strength of the interaction determined. The latter is usually characterized by the critical interaction distance Rq. Finally, it is important to determine whether the energy transfer is a resonant or phonon-assisted process. If the transfer is a multistep process, two distinct sets of parameters must be determined ... 

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