Many-body tetrahedral-cluster model for binary and ternary alloys

An exact solution of a four-site tetrahedral crystal model with periodic boundary conditions, the smallest face-centered-cubic crystal, is presented in the case of binary and ternary alloy systems. The model consists of (a) a single s orbital per site with nearest-neighbor-only hopping, (b) a Coulomb repulsion between electrons on the same site, and (c) a single electron per atom. The model, which represents Cu, Ag, Au, and their alloys, shows all the segregational, solutional, and compound-forming tendencies of the real systems. Such characteristics are absent in noninteracting independent-electron approaches. Calculations demonstrate extreme sensitivity to the input one-electron parameters, with minor differences resulting in widely different alloying properties.