Effect of cell-size on the energetics of vacancies in aluminum studied via orbital-free density functional theory

We investigate the effect of cell-size on the energetics of vacancies in Aluminum using orbital-free density functional theory with non-local kinetic energy functionals. Extending the recently developed coarse-graining techniques based on quasi-continuum reduction to include non-local kinetic energy functionals, we consider cell-sizes up to a million atoms in this study. We find remarkable cell-size effects that are present in computational domains consisting up to 103 − 104 atoms, even in simple defects like vacancies. These results indicate the presence of important long-ranged interactions that have not been considered in prior electronic structure studies of defects conducted on a few hundred atoms. These cell-size effects are more striking in the computed di-vacancy binding energies, where vacancies are found to repel each other in small computational cells, but become attractive in larger computational cells representative of realistic vacancy concentrations. PACS numbers: 61.72.jd,31.15.es,02.70.-c,02.70.Dh