Ground states of a ternary fcc lattice model with nearest- and next-nearest-neighbor interactions

The possible ground states of a ternary fcc lattice model with nearest- and next-nearest-neighbor pair interactions are investigated by constructing an eight-dimensional configuration polytope and enumerating its vertices. Although a structure could not be constructed for most of the vertices, 31 ternary ground states are found, some of which correspond to structures that have been observed experimentally.