From Goldene to Noblene: exhaustive enumeration of the ordered Au-Ag-Cu monolayer alloys

Abstract

Two-dimensional metals became a laboratory reality with the isolation of Goldene, a gold sheet one atom thick released by chemical exfoliation, which raises the question of what alloying can achieve on the same close-packed lattice. Here we combine an exhaustive enumeration of derivative superstructures with density functional theory to map the ordered Au-Ag-Cu monolayer alloys, relaxing every symmetry-inequivalent arrangement up to four atoms per cell and extending the set with larger cells selected by a fitted model. We find that the arrangement of the atoms, and not their proportion, controls the mixing energy, since the spread among the orderings of a single composition is several times the step between neighboring compositions, one composition spans more than 50~meV/atom between two arrangements of the same three atoms, and at two compositions the arrangement decides the sign. The energetics is carried by a competition between Au-Cu contacts, which bind, and Ag-Cu contacts, which do not, and bulk enthalpies computed under the same protocol show that this chemistry is not uniformly rescaled in two dimensions, since Au-Cu orders more strongly in the monolayer than in the crystal while the other two weaken. A pair model completed by an elastic size-mismatch term reproduces the computed energies to a few meV/atom and returns a composition landscape whose convex hull no balanced ternary composition reaches. One equimolar ordering, which we name Noblene, is the only structure in which every atom is surrounded exclusively by unlike species, and it is dynamically stable and metallic, and carries a Poisson's ratio above one half, higher than that of any of the three pure monolayers. Since Noblene sits on the lattice that Goldene already realizes, the route that produced Goldene is a plausible starting point for its synthesis.