We present a diffusion-transition model of the trapping and annihilation of positrons in the grain boundaries in the form of a plane, cylinder and sphere. This model provides the closed-form expressions for the positron lifetime spectrum, the mean positron lifetime and the value of the S-parameter evaluated from the annihilation line. The comparison of this model with the standard trapping model has been performed. In our theoretical consideration we have extended this model for the case when trapping centres for positrons are distributed inside the grain. The validity of the model has been tested with positive results for study of the positron annihilation in the multilayer system which was produced by a sequential magnetron dc sputtering of copper and tin layers.
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