Formation and binding energies of vacancies in the Al(111) surface: Density functional theory calculations confirm simple bond model

In terms of the density functional calculations on an Al(111) surface, we obtained reasonable results for the convergence of the formation energy of mono-vacancies with depth or supercell size and binding energy for di-vacancies in the first layer with supercell size. The formation energy of a mono-vacancy increases with the increase in the number of layers and the supercell size, and converges to the third layer and to a 4 × 4 supercell respectively. The binding energy of a di-vacancy on the surface will decrease with the supercell size. However, the lowest formation energy of a mono-vacancy and highest binding energy is in a 3 × 3 supercell because of the dimer formed by its two nearest neighbour Al atoms between two adjacent vacancies. The results are compatible with simple bond model theory, and the binding energy in a 2 × 2 supercell is in accord with experimental results.