Hume-Rothery stabilization mechanism and e/a determination in MI-type Al–Mn, Al–Re, Al–Re–Si, Al–Cu–Fe–Si and Al–Cu–Ru–Si 1/1-1/1-1/1 approximants – a proposal for a new Hume-Rothery electron concentration rule

Abstract

Full-potential linearized augmented plane wave (FLAPW) band calculations with subsequent FLAPW-Fourier analyses have been performed for five MI-type Al–TM (transition metal)-based 1/1-1/1-1/1 approximants in order to elucidate the origin of a pseudogap from the point of view of the Fermi surface–Brillouin zone (FsBz) interactions. The square of the Fermi diameter is determined from the Hume-Rothery plot to be close to 50 without exception in units of , where is the lattice constant. The FsBz interactions involving several reciprocal lattice vectors are claimed to be responsible for constituting the pseudogap structure across E F. This is referred to as the multi-zone effect. Among them, the wave, in which the Fourier coefficients are most evenly and densely distributed across E F, is selected as the critical one satisfying the matching condition . The d-states-mediated-splitting appears to be absent in spite of substantial occupations of TM-d states in the valence band. All MI-type approximants studied are found to obey the Hume-Rothery stabilization mechanism. A new Hume-Rothery electron concentration rule linking the number of atoms per unit cell, e/uc, with a critical reciprocal lattice vector is found to hold well for structurally complex intermetallic compounds obeying the Hume-Rothery stabilization mechanism.