In ordered L$1_2$-type ${\mathit{A}}_3$B compounds, each A atom is coordinated by 8A+4B atoms, while each B atom is coordinated by 12A atoms. By symmetry, all A-A, A-B, and B-B bond lengths are equal. When this structure disorders to form the substitutionally random ${\mathit{A}}_{0.75}$${\mathit{B}}_{0.25}$ alloy, each atom acquires a distribution of different types of coordination shells. Concomitantly with this reduction in site symmetries, (i) topologically different A atoms (and separately, different B atoms) can have unequal charges, and (ii) the various bonds need not be of equal average lengths 〈R〉 (i.e., 〈${\mathit{R}}_{\mathit{A}\mathrm{-}\mathit{A}}$〉≠〈${\mathit{R}}_{\mathit{A}\mathrm{-}\mathit{B}}$〉≠ 〈${\mathit{R}}_{\mathit{B}\mathrm{-}\mathit{B}}$〉). Furthermore, (iii) there can be a distribution of bond-length values around 〈${\mathit{R}}_{\mathit{i}\mathit{j}}$〉 for each of the three chemical bond types. In this work we study the effects of such charge fluctuations (i) and relaxational fluctuations [(ii) and (iii)] on the electronic structure of ${\mathrm{Cu}}_3$Au and ${\mathrm{Cu}}_3$Pd. The random alloys are modeled by the special quasirandom structure (SQS), whereby the sites of a periodic supercell are occupied by A and B atoms so that the first few radial correlation functions closely reproduce the average correlation functions in an infinite substitutional random network. Instead of requiring that each atom ‘‘see’’ an identical, average medium, as is the case in the homogeneous site-coherent-potential approximation (SCPA), we thus create a distribution of distinct local environments whose average corresponds to the random alloy.

Application of a first-principles local-density method (linearized augmented-plane-wave method) to the SQS then provides the energy-minimizing equilibrium relaxations, charge density, density of states, and formation enthalpy. We find that charge and relaxational fluctuations neglected in the SCPA lead to a significant stabilization of the alloy (∼30% lowering in mixing enthalpy) and to substantial (∼1 eV) nonrigid shifts in the electronic energy levels.

• Received 2 January 1992

DOI:https://doi.org/10.1103/PhysRevB.45.10314