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Positron trapping and annihilation at interfaces between matrix and cylindrical or spherical precipitates modeled by diffusion-reaction theory

The exact solution of a diffusion$-$reaction model for the trapping and annihilation of positrons at interfaces of precipitate$-$matrix composites is presented considering both cylindrical or spherical precipitates. Diffusion-limitation is taken into account for interfacial trapping from the surrounding matrix as well as from the interior of the precipitate. Closed-form expressions are obtained for the mean positron lifetime and for the intensity of the positron lifetime component associated with the interface-trapped state. The model contains as special case also positron trapping at extended open-volume defects like spherical voids or hollow cylinders. This makes the model applicable to all types of cylindrical- and spherical-shaped extended defects irrespective of their size and their number density.