Diffusion-reaction model of positron annihilation for complex defect pattern

The increasing structural complexity in modern material science is often associated with grain sizes in the µm- and the sub-µm-regime. Therefore, when positron annihilation is applied for studying free-volume type defects in such materials, positron trapping at grain boundaries (GBs) cannot be neglected, even when other defect types are in the primary focus. For this purpose, the available diffusion-reaction model for positron trapping and annihilation at GBs is extended to competitive trapping at two different types of intragranular defects. Closed-form expressions for the mean positron lifetime and the relative intensities of the defect-specific positron lifetime components are given. The model is presented for cylindrical-shaped crystallites, but is valid in the general sense for spherical symmetry as well with appropriate replacements. The model yields the basis for properly determining defect concentrations, even for the inconvenient but common case that one intragranular defect type exhibits a lifetime component similar to that in GBs. It turns out, that positron trapping at GBs matters even for µm-sized crystallites and should not be neglected for precise studies of intragranular defects.