Hume-Rothery stabilization mechanism and e/a determination for RT- and MI-type 1/1-1/1-1/1 approximants studied by FLAPW-Fourier analyses.

Full-potential linearized augmented plane wave (FLAPW) electronic band calculations were performed for two RT- (rhombic triacontahedron) and five MI- (Mackay icosahedron) type 1/1-1/1-1/1 approximants plus several complex metallic compounds in Al-TM (TM = transition metal element) binary alloy systems in order to elucidate the origin of a pseudogap from the viewpoint of Fermi surface-Brillouin zone (FsBz) interactions. The square of the Fermi diameter (2k(F))(2) and square of the critical reciprocal lattice vector |G|(2) or the critical set of lattice planes, with which electrons at the Fermi level E(F) are interfering, can be extracted from the FLAPW-Fourier method. We revealed that a pseudogap in both RT- and MI-type 1/1-1/1-1/1 approximants universally originates from interference phenomenon satisfying the matching condition (2k(F))(2) = |G|(2) equal to 50 in units of (2π/a)(2), where a is the lattice constant. The multi-zone effect involving not only |G|(2) = 50 but also its neighboring ones is also claimed to be responsible for constituting a pseudogap across E(F). The value of e/a for Mn, Fe, Re and Ru elements in the periodic table is deduced to be positive in the neighborhood of unity. All 1/1-1/1-1/1 approximants, regardless of RT- or MI-type atomic cluster involved, are stabilized at around e/a= 2.7, while their counterpart quasicrystals are at around e/a= 2.2. A new Hume-Rothery electron concentration rule linking the number of atoms per unit cell, e/uc, with a critical|G|(2) holds well for all complex intermetallic compounds characterized by a pseudogap at E(F).