An exact diffusion-reaction model solution was presented for the trapping and annihilation of positrons in the grain boundaries of polycrystalline materials. The model went beyond the description of boundaries as ideal sinks, and allowed for positron de-trapping from the boundaries. The diffusion limitation gave rise to an infinite sequence of decay rates. However, only a few of them had to be taken into account in practical applications. The other components had either low intensities or parallel decay rates. Closed-form expressions were provided for the mean positron lifetime, for the intensity of the decay time that was associated with positron annihilation in the grain boundaries (in the case of negligible de-trapping), and for the 2-component positron lifetime spectrum which occurred in the case of small grain sizes and/or high positron diffusivity. The variation of the positron annihilation characteristics as a function of grain size was analyzed, as well as the possibility of making reliable determinations of positron diffusivities from positron lifetime measurements of fine-grained polycrystalline materials.

R.Würschum, A.Seeger: Philosophical Magazine A, 1996, 73[5], 1489-501