Phase stability, ordering tendencies, and magnetism in single-phase fcc Au-Fe nanoalloys

Bulk Au-Fe alloys separate into Au-based fcc and Fe-based bcc phases, but L1$_0$ and L1$_2$ orderings were reported in single-phase Au-Fe nanoparticles. Motivated by these observations, we study the structural and ordering energetics in this alloy by combining density functional theory (DFT) calculations with effective Hamiltonian techniques: a cluster expansion with structural filters, and the configuration-dependent lattice deformation model. The phase separation tendency in Au-Fe persists even if the fcc-bcc decomposition is suppressed. The relative stability of disordered bcc and fcc phases observed in nanoparticles is reproduced, but the fully ordered L1$_0$ AuFe, L1$_2$ Au$_3$Fe, and L1$_2$ AuFe$_3$ structures are unstable in DFT. However, a tendency to form concentration waves at the corresponding [001] ordering vector is revealed in nearly-random alloys in a certain range of concentrations. This incipient ordering requires enrichment by Fe relative to the equiatomic composition, which may occur in the core of a nanoparticle due to the segregation of Au to the surface. Effects of magnetism on the chemical ordering are also discussed.