Non-local first-principles calculations in Cu-Au, Ag-Au and Cu-Ag

Cu-Au is the prototypical alloy system used to exemplify ordering and compound formation, and serves as a testbed for all new alloy theory methods. Yet, despite the importance of this system, conventional density functional theory (DFT) calculations with semi-local approximations (GGA) have two dramatic failures in describing the energies of this system: 1) DFT predicts incorrect ordered ground states for Au-rich compositions, and 2) DFT formation energies of the observed Cu$_3$Au and CuAu compounds are nearly a factor of two smaller in magnitude than experimental values. Here, we show how modern extensions of DFT based on non-local interactions can rectify both of these failures. Using the self-consistent non-local HSE06 functional, the formation energies of Cu$_3$Au and CuAu are -71 and -91 meV/atom, respectively, which are in excellent agreement with the experimental measurements. The semi-local GGA predicted CuAu$_2$ is not a stable phase in the HSE06 calculations, and CuAu$_3$ with the L1$_2$ structure is theoretically predicted as a stable phase. For Ag-Au, both semi-local GGA and non-local HSE06 functionals give similar formation energies. The electronic structures are used to explain these different phenomena in Cu-Au and Ag-Au.