Atomic ordering in Au-(42 to 50) at.%Pd: A diffuse scattering and first-principles investigation

Abstract

Atomic ordering in Au-Pd alloys was studied by diffuse x-ray scattering and first-principles methods. Diffuse scattering was done of a single crystal of Au-48 at.% Pd that was aged at 703 K for 24 days. The weakly modulated short-range-order scattering exhibits diffuse maxima with an incommensurate wave vector, which can be related to a Fermi-surface nesting mechanism. From effective pair interaction parameters determined by the inverse Monte Carlo method, a one-dimensional long-period superstructure of the CH structure, LPS1, was found for AuPd. Concurrent electronic-structure calculations of the effective cluster interaction (ECI) parameters indicated the presence of another closely related superstructure, LPS2, at 0 K. At the same time, direct first-principles calculations of the total energies of the CH structure and further one-dimensional long-period superstructures predicted the stabilization of LPS4. Although the energy differences between these structures are small and a complex behavior of the effective interactions is expected due to the Fermi-surface nesting, experimental data and theoretical results both support the stabilization of a long-period superstructure of the CH structure for AuPd at 0 K. The ECI parameters determined by the screened generalized perturbation method also predicted a ground-state structure different from Au${}_{7}$Pd${}_{5}$, previously obtained from cluster expansion calculations. Its energetic preference was confirmed by direct total-energy calculations.