Electronic Theory of Disordered Ternary Alloys: Coherent-Potential Approximation and Its Diagrammatic Equivalent

The one-particle electronic theory of a disordered-ternary-alloy model is studied in the single-site approximation in terms of the averaged-Green's-function formalism recently developed for the substitutionally disordered binary-alloy case. The model is formed by randomly distributing fractional concentrations $C_A$, $C_B$, and $C_C$ of atoms $A$, $B$, and $C$, respectively, on the sites of a regular lattice. The corresponding Hamiltonian is separated into a perfect-crystal part with diagonal energy of the $A$ atom and compositionally independent off-diagonal nearest-neighbor hoppings, while perturbations are contributed by $B$ and $C$ atoms replacing $A$ atoms. The self-consistent diagrammatic-resummation technique of Leath, and the coherent-potential theory of Soven and others provide equivalent means for establishing a pair of simultaneous equations for the determination of the self-energy of the electron and the averaged one-electron Green's function. Numerical results based on Hubbard's simple model density of states for the reference crystal are displayed for the self-energy, the total density of states, and the component densities of states over a wide range of concentrations and scattering-potential strengths.