Cluster expansions of alloy energetics in ternary intermetallics

Ternary alloy energetics are examined for substitutional systems by a formal cluster expansion. In contrast to the binary-alloy problem, several distinct basis sets are possible for the ternary cluster expansion. Several of these sets of ternary basis functions are examined and compared, and relationships are derived between the expansion coefficients, or effective cluster interactions, expressed in various bases. The method of direct configurational averaging (DCA) (based on a tight-binding, linearized muffin-tin-orbital Hamiltonian) is extended to treat ternary alloy systems. Using the DCA, ternary, fcc-based effective pair and triplet interactions are computed for the Rh-V-Ti, Pd-Rh-V, and Ag-Pd-Rh systems, and convergence of the expansion is examined. By combining the cluster expansion with the results of the DCA computations, formation energies are obtained for the completely disordered state as a function of alloy composition. Both pair and triplet interactions are seen to be crucial towards obtaining quantitatively converged energetics.