On a Problem in Random-Lattice Statics

Abstract

The quenching of fluorescense in pure solid phosphors due to the well-known mechanism involving the resonance transfer of the excitation energy from one luminescent centre to another and eventually to randomly distributed imperfections acting as sinks, or traps, is reformulated as a problem in random-lattice statics. Here the question of configurational averaging over the random sinks, involvied in the calculation of the fluorescence yield, or efficiency, has been treated in an approximation that goes beyond the virtual-crystal approximation (VCA), and presumably incorporates the quasicrystalline approximation (QCA). An expression has been derived for the efficiency of fluorescence (η) in terms of the trap concentration C t and the phenomenological rate constants 1/τ, Γ and χ characterizing, respectively, the de-excitation of the luminescent centre by re-radiation, resonance transfer to another luminescent centre, and through capture by a trap. This has been done for the case of an idealized phosphor consisting of a lattice of luminescent centres with randomly substituted traps, assuming nearest-neighbour transfers only. It is found that η falls off rapidly with increasing Γ in qualitative agreement with some recent experiments on the extinction of luminescence in certain weakly exchange-coupled paramagnetic phosphors.