Diffusion-reaction model for the trapping of positrons in grain boundaries

The exact solution of a diffusion-reaction model for the trapping and annihilation of positrons in grain boundaries of polycrystalline materials is presented. The model goes beyond the description of boundaries as ideal sinks and allows for positron detrapping from the boundaries. The diffusion limitation gives rise to an infinite sequence of decay rates of which, however, only a few have to be taken into account in practical applications. The other components have either low intensities or coinciding decay rates. Closed-form expressions are given for the mean positron lifetime, for the intensity of the decay time associated with positron annihilation in the grain boundaries in the case of negligible detrapping, and for the two-component positron lifetime spectrum which occurs in the case of small grain sizes and/or high positron diffusivity. The variation of the positron annihilation characteristics with the grain size as well as the possibilities of a reliable determination of the positron diffusivities from positron lifetime measurements on fine-grained polycrystalline materials are discussed.