Low density approximation for diffusion annealing

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Abstract
The problem of annealing of Frenkel-pairs in electron irradiated fee metals due to diffusion of interstitials is treated starting from exact equations for single particle densities, pair densities, etc. The mobile interstitials are considered to interact with vacancies (leading to recombination), impurity atoms (leading to interstitial-impurity complexes) and with each other (leading to interstitial clusters). By using the superposition approximation, i.e. replacing three-particle probabilities by products of two-particle probabilities we obtain generalized Waite equations. For low defect densities the annealing is at different times governed by different processes. For short times the important process is the recombination of an interstitial with the near-by correlated vacancy generated by the same electron impact event, the so-called correlated recovery. For long times the remaining interstitials undergo long range migration and interact with uncorrelated sinks. During this process interstitial impurity complexes and interstitial clusters are formed. The time dependence of the defect densities, the remaining fraction of defects after completion of diffusion annealing and the size distribution of interstitial clusters are calculated. Detailed comparison with experiments in Cu and Pt will be made.