Local cluster networks and the number of valence states in aluminium–transition metal face-centred icosahedral quasicrystals

Abstract

Abstract Coordination environments of a special class of clusters which are related to the valence states in aluminium–transition metal face-centred icosahedral quasicrystals were analysed on the basis of the six-dimensional model of Katz and Gratias for the atomic sites and that of Yamamoto for the centres of the clusters. The number of the clusters per atom in the model (≈0.263) is comparable with that of Al–Cu–Ir cubic approximant crystal (≈0.258), and it indicates that the model reasonably represents the distribution of the clusters. We identified all the possible local cluster networks of short distances, which are related to the inter-cluster bonds, and evaluated the number of the valence states by assuming two possible configurations of inter-cluster bonds. The number of the valence states per atom was derived as a function of the fraction of transition-metal atoms, and the value is in good agreement with that expected from the compositions of real quasicrystals. Notably, the number of the part of the valence states which do not depend on the fraction of transition-metal atoms is numerically similar to the electron to atom ratio known as e/a, which is phenomenologically related to the stability of quasicrystals.