Ion-Lattice Coupling

To take the above-mentioned ion-lattice coupling into account, the full ion-plus-lattice system must be considered, so that the static Hamiltonian given by Equation (5.2) must be replaced by... 

The 3d orbitals in TM ions have a relatively large radius and are unshielded by outer shells, so that strong ion-lattice coupling tend to occur in TM ions. As a result, the spectra of TM ions present both broad (S > 0) and sharp (S 0) bands, opposite to the spectra of (RE) + ions, discussed in section 6.2.1, which only showed sharp bands (S 0). 

The situation for actinide ions is ambiguous due to a lack of experimental data. Because of the larger crystal-field parameters of the actinides, one would anticipate that the ion-lattice coupling is stronger. This assumption was not obviously shown to be true in the recent line width measurements of neptunium (47). Experimental measurements of the temperature dependence of the fluorescence lifetimes and quantum efficiencies will provide a direct test for the multiphonon coupling and the universality of the energy gap dependence of the multiphonon spontaneous transition rate. 

Electric-dipole oscillator strength Ion-lattice coupling... 

The constants W (0) and a are dependent on the host and strength of the ion-lattice coupling but not on the specific rare earth ion or electronic state. Data for multiphonon relaxation in several different crystals and in a glass are summarized in fig. 35.7. Experimental points correspond to different electronic states and ions. The numbers in parentheses are the phonon energies which, based upon the temperature dependence of multiphonon rates and vibronic spectra, appear to be most important for relaxation. In general, the major contribution to multiphonon processes involves the highest energy vibrations... 

A number of cases have been reported in the literature where the exchange between pairs of ions in a lattice is piedominant, i.e., ions aie exchange coupled in pairs because of their proximity. An example of this is copper acetate 168), where the copper ions occur in pairs which are relatively close, so that the spins of pairs of copper ions are coupled together to form a singlet state (paired spins) and a triplet state (unpaired spins). Resonance measurements 158) permit determination of the magnitude and sign of J. 

Equation 13 can be solved numerically for Tc as a function of the proton-lattice coupling. The parameters are chosen so as to fit the experimental value of Tc for KDP. For C = 21 732 K/A and g2ygAyf close to those used for perovskite oxides, Tc Ikdp = 115 K. In Fig. 3 Tc is shown as a function of C with all other parameters fixed. Including the deuteration effects (Table 2), Ter = C Idkdp/C Ikdp 1 2. With this estimate TcIdkdp = 168 K. C itself depends only weakly on /, g2y g4 but a strong dependence on/ is observed, which is the coupling between the PO4 shells and the K" " ions. This, on the other hand, should not be dependent on deuteration. 

Fillpescu et al. [556], and Schmitschek and Schwarz [657] in 1962 were the first to point out the possibility of using the rare earth complexes as laser materials due to the low pump power necessary to excite these complexes via the IMET process and the relatively high quantum yield. The diminished lattice coupling of the rare earth ions in complexes may be very important in the liquid laser where quenching is quite serious. 

Nanophenomena due to size confinement in lanthanide nanoparticles may indeed occur because of ion-phonon coupling that directly affect excited state lifetime and energy transfer. Namely, the size confinement is not on electronic states, but lattice vibra-... 

Here g is the electron-lattice coupling constant, suffixes S and A are sensitizer and activator ions respectively, n is the number of phonons excited at the temperature of the system, hco is the phonon energy which contributes dominantly to these multiphonon processes and N is the number of phonons emitted in the processes, namely,... 

Fig. 3.26. Schematic representation of the transition from the free-ion state (apex) to the condensed-matter state (base). See also text. Ei, indicates the electron-lattice coupling, J the otbital overlap. Along the right-hand leg localisation increases, along the left-hand leg delocalisation. The examples concern the Bi ion. In CsrNaBiCIf, the spectra can be described by a small Huang-Rhys coupling parameter (S), in Bi4Ge30i2 the value of S is very large, whereas Cs3Bl2Br9 is a semiconductor...

The existence of vibronic transitions in rare earth crystals shows that the rare earth ions are coupled to the vibronic modes of the lattice we shall also show that such coupling plays a dominant role in the energy transfer process between rare earth ions in glasses. We believe that this treatment of phonon-assisted energy transfer can be extended to biologically active organic molecules such as DNA, ATP, DTP and similar molecules. 

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