Two-dimensional incommensurate superlattices in precious-metals alloys: Nature of formation

The nature of two-dimensional incommensurate superlattices Ll₂ (MM) obtained in the precious-metals alloys Au₃ Cu and Cu₃ Pd is investigated on the basis of first-principles calculations of the electronic structure. It is shown that their stability can be explained by the opening of energy gaps on coinciding sections of the Fermi surface in two mutually perpendicular directions. It is important that this explanation holds only if the superlattice is treated as a superstructure with respect to ordinary superstructures (Ll₂): the electronic spectrum of the superstructure and not the disordered alloy (as in the existing electronic theory of one-dimensional long-period structures) should serve as the starting spectrum. Arguments supporting the fact that in a number of quasicrystal-line substances the Ll₂ (MM) phases fall between incommensurate systems and quasicrystals are presented. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 548–554 (25 April 1999)