Using a density-functional-based tight-binding method we investigate the stability of various vacancy clusters up to a size of 17 vacancies. Additionally, we compute the positron lifetimes for the most stable structures to compare them to experimental data. A simple bond-counting model is extended to take into account the formation of new bonds. This yields a very good agreement with the explicitly calculated formation energies of the relaxed structures for V6 to V14. The structures, where the vacancies form closed rings, such as V6 and V10, are especially stable against dissociation. For these structures, the calculated dissociation energies are in agreement with experimentally determined annealing temperatures and the calculated positron lifetimes are consistent with measurements.
- Density-functional theory
- Positron annihilation