Stability and mobility of vacancy nanoclusters on Cu(111) surface: An {\it ab initio} study*

We used {\it ab initio} calculations to study stability and mobility of vacancy nanoclusters on Cu(111) surface. We found that the formation energies for single vacancies in the vicinity of surface are $\approx$0.3\,eV lower than that in bulk. Interestingly, calculations yield strongly bonded 1$^{st}$NN divacancy on the surface than in bulk. In addition a trivacancy binds very strong on the surface, indicating that formation of loop-like vacancy nanoclusters are most energetically favored on the surface. These findings imply the ease of nucleation of vacancy nanoclusters on the surface. We also examined migration of mono-, di- and trivacancy on the surface. A zigzag motion for divacancy diffusion on the surface is predicted with the migration barrier higher on the surface than in the bulk due to larger binding energy and elastic contribution.