Compositions of Al-Based Quasicrystals Interpreted by Cluster Formulae

Abstract

It is known previously that bulk metallic glass compositions satisfy cluster formulae [cluster](glue atom)1,3 of 24 valence electrons as deduced from our cluster-resonance model. In the present work, it is further shown that compositions of Al-based binary and ternary quasicrystals are also explained by 24-electron cluster formulae of the types [icosahedron](glue atom)0,1, where the icosahedral cluster is identied from a corresponding crystalline approximant according to dense atomic packing and cluster isolation criteria, and the glue atom site is either vacant for an icosahedral quasicrystal or equal to one for a decagonal quasicrystal. Ternary quasicrystals are formulated with the same formulae as their basic binary ones but the icosahedron shell sites are substituted by third elements. The 24-electron cluster formulae are then the chemical and electronic structural units of quasicrystals, mimicking the molecular formulae of chemical substances.

Hidden electronic rule in the “cluster-plus-glue-atom” model

“…Based on the cluster-resonance model 20 69 , it has been found that the valence electrons’ number per unit cluster formula ( N e/u ) for typical QCs and BMGs 24 26 , is also close to the specific constant of eight-multiples and twelve-multiples 24, as shown in Fig. 4 .…”

“…In this work, an electron counting rule hidden in the cluster formula for CMAs is revealed. Our analysis on the cluster structure and electron concentration for typical kinds of CMAs 20 22 24 26 54 (including intermetallic compounds, quasicrystals and metallic glasses), indicates that the valence electrons’ number per unit cluster formula for these CMAs are close to specific constants of eight-multiples and twelve-multiples. It is thus termed as CMAs’ specific electrons cluster formula.…”

“…While the Z value is acquired from the cluster formula of these QCs and BMGs, which has been successfully used to explain their experimental compositions (see Supplementary Table SVI and SVII ). Hence, the N e/u values for these Al-based QCs and BMGs 24 26 are obtained, and the results are presented in Fig. 4 and Supplementary Figure S6 .…”

“…Among these cluster-based models, Dong’s “cluster-plus-glue-atom” model 15 can be used to describe the atomic structure of nearly all materials. Denoted by a uniform cluster formula of [cluster](glue atoms) x 18 19 20 21 , this cluster-plus-glue-atom model regards the atomic structure of any materials, no matter whether crystalline or non-crystalline, to be composed of the clusters part and the glue atoms part 22 23 24 25 26 27 28 . Accordingly, all atoms in a given structure belong to three kinds of the central atoms, the shell atoms and the glue atoms 29 30 , as the red spheres, the blue spheres and the green spheres shown in Supplementary Figure S1 , respectively.…”

Electrochemical Potential Derived from Atomic Cluster Structures

“…Because the ECP is relevant to the electron density for the system of interest, and certain electronic rule associated with the electron density upon atomic cluster structures has been deduced from the “cluster-plus-glue-atom” model, − we speculate that the correlations between the ECP and atomic cluster structures can be established accordingly. In this Letter, a method for correlating the ECP with the atomic cluster structures is presented.…”