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.

Expressions for the dimer and trimer formation of aliovalent cation—lattice-defect pairs in crystalline compensated lattices have been derived from the minimization of free energy expressions which are given in terms of canonical partition functions. Numerical calculations have been made for the KCl:Sr2+ system by assuming the principle of linear superposition. It is shown that while extensive dimer formation occurs through wide ranges of temperatures and concentrations, trimer and higher cluster formations are of significance only at relatively high concentrations. Although the uncertainties of the interaction energies in many cases may weaken some quantitative aspects of the theoretical calculations, the general procedure given in the paper can be readily applied to other compensated lattices such as alkaline-earth halides containing trivalent cations. The over-all qualitative features of the theory serve to elucidate some of the more puzzling experimental observations reported recently in the literature.

Hitherto undetermined symmetry origins of fluorescence lines occurring in the KCl:Sm2+5D0→7F5 transition region are examined in terms of lifetime measurements. From relative intensity measurements of all the dominant lines observed in the entire D0→75FJ(0≤ J ≤ 6) fluorescence spectrum and experimentally determined effective equilibrium distribution temperature of 219°K, the binding energies of the nearest-neighbor [C2ν(1,1,0)] and next-nearest-neighbor [C4ν(2,0,0)] Sm2+−K+ vacancy pairs are found to be −0.45 and −0.39 eV, respectively. At ordinary temperatures, the dominant sites, in the order of relative importance, are the C2ν(1,1,0), Cs(2,1,1), and C4ν(2,0,0) pairs. This observation is interesting in view of the predominance of the C4ν(2,0,0) site in the KCl:Sr2+ and KCl:Mn2+ systems.