First-principles statistical mechanics of structural stability of intermetallic compounds

While as elemental solids, Al, Ni, Cu, Rh, Pd, Pt, and Au crystallize in the face-centered-cubic (fcc) structure, at low temperatures, their 50%-50% compounds exhibit a range of structural symmetries: CuAu has the fcc-based L${1}_{0}$ structure, CuPt has the rhombohedral L${1}_{1}$ structure, and CuPd and AlNi have the body-centered-cubic B2 structure, while CuRh does not exist (it phase separates into Cu and Rh). Phenomenological approaches attempt to rationalize this type of structural selectivity in terms of classical constructs such as atomic sizes, electronegativities, and electron/atom ratios. More recently, attempts have been made at explaining this type of selectivity in terms of the (quantum-mechanical) electronic structure, e.g., by contrasting the self-consistently calculated total electron+ion energy of various ordered structures. Such calculations, however, normally select but a small, O(10) subset of ``intuitive structures'' out of the ${2}^{\mathit{N}}$ possible configurations of two types of atoms on a fixed lattice with N sites, searching for the lowest energy. We use instead first-principles calculations of the total energies of O(10) structures to define a multispin Ising Hamiltonian, whose ground-state structures can be systematically searched by using methods of lattice theories. Extending our previous work on semiconductor alloys [S.-H. Wei, L. G. Ferreira, and A. Zunger, Phys. Rev. B 41, 8240 (1990)], this is illustrated here for the intermetallic compounds AlNi, CuRh, CuPd, CuPt, and CuAu, for which the correct ground states are identified out of \ensuremath{\sim}65 000 configurations, through the combined use of the density-functional formalism (to extract Ising-type interaction energies) with a simple configurational-search strategy (to find ground states). This establishes a direct and systematic link between the electronic structure and phase stability.