A diffusion-transition model for the trapping and annihilation of positrons in grain boundaries having the form of a plane, cylinder or sphere was presented. This model provided closed-form expressions for the positron lifetime spectrum, the mean positron lifetime and the value of the S-parameter as evaluated from the annihilation line. This model was extended to the case where trapping centres for positrons were distributed within the grain. The validity of the model was confirmed for positron annihilation in a multi-layer system which was produced by the sequential magnetron direct-current sputtering of Cu and Sn layers.

Positron Annihilation Studies of the Multilayer Cu-Cu3Sn System. J.Dryzek, A.Czapla, E.Kusior: Journal of Physics - Condensed Matter, 1998, 10[48], 10827-38