Origin of the DOS pseudogap and Hume–Rothery stabilization mechanism in RT-type Al₄₈Mg₆₄Zn₄₈ and Al₈₄Li₅₂Cu₂₄ 1/1-1/1-1/1 approximants

Full-potential linearized plane wave (FLAPW) band calculations with subsequent FLAPW-Fourier analyses have been performed for two RT-type Al48Mg64Zn48 and Al84Li52Cu24 1/1-1/1-1/1 approximants containing 160 atoms per unit cell. The FLAPW-Fourier analysis revealed that the Fermi surface–Brillouin zone (FsBz) interactions involving more than two sets of lattice planes are responsible for the formation of a pseudogap across the Fermi level in both compounds. The most critical sets of lattice planes interfering with electrons at the Fermi level are deduced to be {543} + {710} + {550} with = 50 in the former and {631} with = 46 in the latter. The square of the Fermi diameter is determined to be 49.9 ± 0.1 and 47.1 ± 0.4 in units of , respectively, where a is the lattice constant. Hence, the matching condition holds well in both compounds. It is also shown that, while a shallow pseudogap in the Al48Mg64Zn48 approximant can be ascribed solely to the FsBz interactions, a much deeper one in the Al84Li52Cu24 approximant is explained as a superposition of the FsBz interactions and the formation of strongly directional bonding states between Cu-4p and Al-3p orbitals.