Extended Lattice Gas Interactions of Cu on Cu(111) and Cu(001): Ab-Initio Evaluation and Implications

We present ab-initio calculations of a variety of different lattice-gas interaction energies between Cu adatoms on Cu(001) and Cu(111). We find the next-nearest-neighbor (NNN) interactions to be negligible on Cu(111), explaining the success of the nearest-neighbor (NN) Ising model when describing the Cu(111) step stiffness. On Cu(001), however, we find that NNN interactions are roughly (1/7) the attractive NN interaction strength. On both surfaces, we find longer-range pair interactions to be small, although there are relatively large trio interactions. On Cu(111) these include two orientation dependent trios composed of adatoms forming a NN-triangle. We calculate the interaction energies of these trios and show that they can account for the difference in formation energies between Aand B-steps. On Cu(001), we find the trio interaction composed of adatoms forming a NN-isosceles right triangle to be quite large and repulsive. This contradicts our theoretical expectations, which suggest the interaction should be attractive to account for the Cu(001) step stiffness. Finally, by calculating the bulk energy per atom in multiple ways, we show our calculations are self-consistent.