Theory of Concentration Quenching in Inorganic Phosphors

A theory is presented for concentration quenching in solid systems, based on the migration of excitation energy from one activator center to another and eventually to an imperfection which may act as an energy sink. Calculations are made on the dependence of the fluorescence yield on concentration, and to indicate typical activator concentrations at which appreciable quenching may be expected to occur. If the transition in the activator is of the electric dipole or electric quadrupole type, appreciable quenching may arise when the activator concentration is 10-3 to 10-2; if it is a magnetic dipole transition, transfer will occur by exchange, rather than by overlapping of magnetic dipole fields, and the critical concentration will be of the order of a few percent. The implications of transfer phenomena upon the observed absence of luminescence in most ``pure'' inorganic crystals are discussed, and it is concluded that transfer rates are so high in strongly absorbing crystals that the energy can easily migrate to a very few sinks dispersed throughout the lattice.