Screened Coulomb interactions in metallic alloys. I. Universal screening in the atomic-sphere approximation

We have used the locally self-consistent Green's-function (LSGF) method in supercell calculations to establish the distribution of the net charges assigned to the atomic spheres of the alloy components in metallic alloys with different compositions and degrees of order. This allows us to determine the Madelung potential energy of a random alloy in the single-site, mean-field approximation. The Madelung potential makes density-functional calculations by the conventional single-site, coherent potential approximation practically identical to the more rigorous LSGF supercell results obtained with a single-site local interaction zone. We demonstrate that the basic mechanism that governs the charge distribution is the screening of the net charges of the alloy components that makes the direct Coulomb interactions short ranged. In the atomic-sphere approximation, this screening appears to be almost independent of the alloy composition, lattice spacing, and crystal structure. A formalism which allows a consistent treatment of the screened Coulomb interactions within the single-site mean-field approximation is outlined. We also derive the contribution of the screened Coulomb interactions to the S-(2) formalism and the generalized perturbation method.