Long-Period Structures in Noble-Metal Alloys: New Aspects

Proceeding from precise calculation of the electronic structure and the generalized electronic susceptibility, a systematic study of the relationship between the nesting properties of the Fermi surface (FS) and the character of long-period ordered superstructures (LPSs) in noble-metal alloys, Cu–Au, Cu–Pd, and Ag–Mg, is performed. An answer is provided as to why in Cu–Au, Cu–Pd, and Cu–Pt alloys so-called incommensurate LPSs, characterized by an irrational period and smeared antiphase boundaries, are formed. The reasons for occurrence of such LPSs within a short temperature range only are clarified. The dependence of the long period M on the long-range order parameter in Cu–Au alloys is accounted for. The causes for formation of two-dimensional LPSs in Au₃Cu and Cu₃Pd alloys are found. It is shown that their stability may be explained for by energy gaps opening on coinciding patches of FS in two mutually perpendicular directions. Arguments are drawn in favor of the fact that among quasicrystalline substances, phases with incommensurate LPSs occupy an intermediate position between incommensurate systems and quasicrystals. An attempt is made to identify the reasons for qualitatively different behavior of LPSs with large and small superperiods. It is shown that the dependence of LPS's behavior on the value of 2M is controlled by the quality of nesting on FS and the nesting vector sensitivity (2k _F) to variations in the long-range order parameter .