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

The nature of two-dimensional incommensurate superlattices Ll(2)(MM) obtain ed in the precious-metals alloys Au3Cu and Cu3Pd is investigated on the bas is of first-principles calculations of the electronic structure. It is show n that their stability can be explained by the opening of energy gaps on co inciding sections of the Fermi surface in two mutually perpendicular direct ions. It is important that this explanation holds only if the superlattice is treated as a superstructure with respect to ordinary superstructures (Ll (2)): 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 quasicrystalline substances the Ll(2)(MM) phases fall between incommensurate systems and quasicrystals are presented. (C) 19 99 American Institute of Physics. [S0021-3640(99)00508-3].