Electronic structure of random ${\mathrm{Ag}}_{0.5}$${\mathrm{Pd}}_{0.5}$ and ${\mathrm{Ag}}_{0.5}$${\mathrm{Au}}_{0.5}$ alloys

The electronic density of states and mixing enthalpies of random substitutional ${\mathit{A}}_{1\mathrm{-}\mathit{x}}$ ${\mathit{B}}_{\mathit{x}}$ alloys have often been described within the single-site coherent-potential approximation (SCPA). There one assumes that each atom interacts with a fictitious, highly symmetric average medium and that at a given composition x, all A atoms (and separately, all B atoms) are equivalent (i.e., have the same charges and atomic sizes). In reality, however, a random alloy manifests a distribution of different (generally, low-symmetry) local environments, whereby an atom surrounded locally mostly by like atoms can have different charge-transfer or structural relaxations than an atom surrounded mostly by unlike atoms. Such ‘‘environmental effects’’ (averaged out in the SCPA) were previously studied in terms of simple model Hamiltonians. We offer here an efficient method capable of describing such effects within first-principles self-consistent electronic-structure theory. This is accomplished through the use of the ‘‘special-quasirandom-structures’’ (SQS) concept [Zunger et al., Phys. Rev. Lett. 65, 353 (1990)], whereby the lattice sites of a periodic ‘‘supercell’’ are occupied by A’s and B’s in such a way that the structural correlation functions closely mimic those of a perfectly random infinite alloy. The self-consistent charge density, total and local density of states, and mixing enthalpies are then obtained by applying band theory (here, the linearized augmented-plane-wave method) to the SQS. Application to ${\mathrm{Ag}}_{0.5}$ ${\mathrm{Pd}}_{0.5}$ and ${\mathrm{Ag}}_{0.5}$ ${\mathrm{Au}}_{0.5}$ alloys clearly reveals environmental effects; that is, the charge distribution and local density of states of a given atomic site depend sensitively not only on the composition and occupation of the site but also on the distribution of atoms around it. This SQS approach provides a rather general framework for studying the electronic density of states of alloys.