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

Abstract

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.

Keywords:

• RT-type 1/1-1/1-1/1 approximants
• pseudogap
• FLAPW band calculations

Acknowledgements

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. He also wishes to thank Prof. P. Blaha, Technical University of Vienna, Austria, for providing information about “case.outputl” file generated from WIEN2k.

Notes

Notes

1. Note that Mizutani et al. 12 reported the Hume–Rothery plot data for the Al–Cu–TM–Si (TM = Fe and Ru) 1/1-1/1-1/1 approximants containing 144 atoms in a simple cubic lattice obtained by using a SUPERCOMPUTER at Department of Physics, Northwestern University. However, no FLAPW-Fourier analysis was made to extract the FsBz interactions.

2. For the sake of simplicity, at particular symmetry points is simply expressed as .