In this paper, we present a detailed study of the concentration and temperature dependences of the quantum efficiency of energy transfer between Ce3+ and Tb3+ in La1−x−yCexTbyPO4. The determination of the transfer quantum efficiency in terms of the donor luminescence lifetimes is critically compared with that in terms of the donor luminescence intensities. It is shown that for the latter determination it is important to take into account any overlap in the donor and acceptor absorption spectra in the excitation wavelength region. From the exponential behavior, the concentration, and thermal dependences of the donor luminescence decay, it is shown that the diffusion of donor excitation plays an important role in the energy transfer process.

In this paper, the adiabatic relaxation theory is applied to investigate the origin of rare-earth fluorescence quenching involving multiphonon transitions. The energy level schemes for BaCl,:Sm2+ and BaBr,:Sm H have been obtained from the observed fluorescence spectra. The phonon cutoff frequencies, 210 and 140 cm-1 for BaCl, and BaBr" respectively, have been determined from vibronic sidebands. From the observed temperature dependence of the fluorescence intensities and lifetimes, it is shown that the 5 D, and 5 Do levels are thermally quenched through radiationless excitation to the 4f 5 5 d band and that the population of the 5DO level from 5D, involves the 4f 5 5d band as an intermediary. This indirect f(--;d)--;f relaxation mechanism appears to have resulted from the proximity and relatively large displacement between the adiabatical surfaces of the low-lying 4f 5 5 d and the 5D, states of Sm2+ in BaCl, and BaBr,.

The rate of multiphonon relaxation of rare-earth ions in crystals has been calculated using the Kubo representation of the rate constant in terms of linear response time correlation functions. The nonadiabatic electron-phonon operator arising from the effect of the kinetic energy of the ions on the Born-Oppenheimer basis functions is employed in the first-order perturbation theory. The calculations yield the explicit dependence of the decay rate on the temperature, the transition energy gap, the phonon energy, and the displacements of the adiabatic potentials. Excellent agreement between theory and experiment has been obtained for the multiphonon relaxation phenomenon observed in LaF3:Er3+, LaCl3:Dy3+, LaCl3:Nd3+, and LaBr3:Dy3+. Although the comparison of theory and experiment is specialized to the nonradiative relaxation of rare earth ion excited states in crystals, the treatment given in the present paper is also generally valid for the relaxation of excited states by internal conversion in large molecules.

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It is shown that many-body interactions can play a dominant role in nonradiative energy transfer processes between ions in crystals. These interactions formally arise from the Coulomb and exchange interactions between the electrons of the donor ion and two or more acceptor ions. In particular, three-body transfer processes arising from the dipole-dipole perturbation Hamiltonian through virtual transitions are considered in some detail. Such processes are manifested by the quadratic concentration dependence of the per-ion nonradiative energy transfer rate observed in concentration quenching and sensitized luminescence experiments. Many-body interactions are important in rare-earth ions because of the narrow widths of the 4fn crystal states and because of the large moments of the virtual transitions involving the opposite parity 4fn−1 5d states.