Approximants — the Key to the Structure of Quasicrystals

Abstract

AbstractThe relationship between approximant structures and quasicrystals is discussed on the example of quantitatively known decagonal quasicrystal and approximant structures in the thoroughly studied system Al-Co-Ni. The binary Al-Co as well as the ternary Al-Co-Ni approximants consist of the same basic pentagonal bipyramidal structure elements as the decagonal phase. The binary Al-Ni approximants, on the other hand, are vacancy ordered superstructures of the AlNi §-phase, which itself is related to the periodic average structure of decagonal Al-Co-Ni. Thus, the decagonal phase may be considered as a compromise between the competing driving forces to form pentagonal structural units on the one side and vacancy ordered superstructures of the AlNi §-phase on the other side. The broad stability range of decagonal Al-Co-Ni can be interpreted in terms of entropy gain by Co/Ni substitutional disorder and phasonic disorder of a part of the Al atoms.