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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.
Acknowledgements
We wish to thank Prof. P. Blaha, Technical University of Vienna, Austria, for providing us valuable information needed to perform the WIEN2k-FLAPW-Fourier analysis and the Hume-Rothery plot for the present MI-type approximants. One of the authors (UM) is grateful for the financial support of the Grant-in-Aid for Scientific Research (Contract No.23560793) from the Japan Society for the Promotion of Science.