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

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 (2k(F))(2) is determined from the Hume-Rothery plot to be close to 50 without exception in units of (2 pi/a)(2), where a 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 vertical bar G vertical bar(2) = 50 wave, in which the Fourier coefficients are most evenly and densely distributed across EF, is selected as the critical one satisfying the matching condition (2k(F))(2) = vertical bar G vertical bar(2). 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 vertical bar G vertical bar(2) is found to hold well for structurally complex intermetallic compounds obeying the Hume-Rothery stabilization mechanism.