Electronic structure of quasicrystalline Al-Zn-Mg alloys and related crystalline, amorphous, and liquid phases

We have studied the electronic structure of higher-order rational approximants to the icosahedral Al-Zn-Mg quasicrystal and of related crystalline, liquid, and amorphous phases. For the crystalline phases, self-consistent calculations using the linear muffin-tin orbital (LMTO) method have been performed, and the electronic structure of the higher-order approximants (with up to 12 380 atoms in the periodically repeated cell) and of the amorphous and liquid alloys has been calculated using the recursion method and a tight-binding LMTO method. Structure-induced pseudogaps at the Fermi level are predicted for the stable Frank-Kasper phase and for the higher-order approximants to the quasicrystal, but also for the amorphous alloy and some crystalline compounds. Hence, we conclude that although the pseudogap is a generic property of the quasicrystal, it is not a specific property distinguishing the quasiperiodic from the periodic or aperiodic phases. Crystalline, quasicrystalline, and amorphous alloys have to be considered as Hume-Rothery phases with a varying degree of band-gap stabilization.