Investigation of the Hume–Rothery stabilization mechanism from ab initio band calculations for different electron compounds: Cu 5Zn 8 and Al–Mg–Zn, Al–Cu–Ru–Si approximants

Abstract

The origin of the pseudogap formed across the Fermi level has been studied in relation to the Fermi surface–Brillouin zone interaction and the sp–d hybridization effect by performing the LMTO–ASA (Linear Muffin–Tin Orbital–Atomic Sphere Approximation) band calculations for the three electron compounds: the γ-phase Cu 5Zn 8 alloy, the free-electron-like Al 30Mg 40Zn 30 Frank–Kasper-type 1/1-1/1-1/1 approximant and the Al 68Cu 7Ru 17Si 8 Mackay–Icosahedral-type 1/1-1/1-1/1 approximant. We revealed that, in the free-electron-like Al–Mg–Zn approximant, the Fermi surface–Brillouin zone interaction is solely responsible for the formation of the pseudogap at the Fermi level. In the case of the γ-phase and the Al–Cu–Ru–Si approximant, where d-states are involved across the Fermi level, we have demonstrated that the Fermi surface–Brillouin zone interaction is still strong enough to produce the pseudogap near the Fermi level but that its depth and width are substantially enhanced by the sp–d hybridization effect which splits the d-states into the bonding and antibonding states across the Fermi level.