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

## TL;DR

This paper presents an exact diffusion-reaction model for positron trapping and annihilation at interfaces of spherical or cylindrical precipitates, accounting for diffusion limitations and providing closed-form solutions for positron lifetime and intensity.

## Contribution

It introduces a comprehensive analytical model for positron trapping at various extended defects, including precipitate interfaces and voids, applicable across different shapes and sizes.

## Key findings

- Closed-form expressions for positron lifetime and intensity.
- Model encompasses trapping at precipitate interfaces and voids.
- Applicable to all cylindrical and spherical extended defects.

## Abstract

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.