Compositional short-range ordering in metallic alloys: Band-filling, charge-transfer, and size effects from a first-principles all-electron Landau-type theory

Abstract

Using a mean-field statistical description, we derive a general formalism to investigate atomic short-range order in alloys based on a density-functional description of the finite-temperature, grand potential of the random alloy. This ‘‘first-principles,’’ Landau-type approach attempts to treat several contributions (electronic structure, Fermi surface, electrostatics, magnetism, etc.) to the electronic energy on an equal footing. An important ingredient for the statistical averaging is the replacement of the molecular mean fields (Weiss fields) with Onsager cavity fields, which forces the diagonal part of the fluctuation-dissipation theorem to be obeyed. To show its general applicability and usefulness, we apply the theory to three fcc alloy systems. In ${\mathrm{Cu}}_{0.75}$ ${\mathrm{Pd}}_{0.25}$, the incommensurate atomic short-range order is driven by a Fermi-surface effect, in agreement with earlier work. In contrast, ${\mathrm{Pd}}_{0.5}$ ${\mathrm{Rh}}_{0.5}$ exhibits clustering tendencies, with both band-filling and charge-rearrangement effects being important in setting the spinodal temperature at 1150 K, in good agreement with experiment. In the final examples of three nickel-rich NiCr alloys, previously ignored electrostatic effects are found to play a significant role in determining the atomic short-range order.