A Cluster–Resonance Criterion for Al‐TM Quasicrystal Compositions

Abstract

Compositions of binary Al-TM (TM = Cr to Ni) quasicrystals are interpreted with a unified cluster formula [icosahedron](glue) 1 using the newly developed cluster-resonance model and the e/a formalism. The icosahedra are chosen from the corresponding approximants by considering large radial atomic density, high degree of isolation, and narrow distribution of the shell atoms. Icosahedral quasicrystals are expressed by an icosahedron plus one averaged icosahedron atom as the glue atom [icosahedron](icosahedron/13) 1 , characterized by e/a~1.83-1.85, while decagonal quasicrystals are expressed by an icosahedron plus one TM atom, with e/a~1.71-1.78. The total electrons accommodated in unit cluster formulas of different Al-TM quasicrystals have the same value approaching 24, which implies that the cluster formulas are both chemical and electronic structural units.

Compositions of Al-Based Quasicrystals Interpreted by Cluster Formulae

“…For QCs, the principal clusters are icosahedra adopted from crystalline approximants [6]. Take the Al 5 Co 2 phase for example, which is an approximant of decagonal quasicrystals [7].…”

“…By using the principal icosahedral clusters identied from corresponding approximants using the close atomic packing and isolation criteria [3], compositions of binary AlTM (transition metal) QCs were deciphered via the 24-electron cluster formulae [6]. The number of valence electrons per unit cluster formula e/u could be determined by e/u = (e/a)Z, with e/a = C i (e/a) i , C i and (e/a) i being the atomic fraction and the electron concentration of the i-th element.…”

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

“…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 key point is determination of the principal cluster entering into the cluster formula: [cluster](glue atoms) x . To resolve this problem, an effective method of central force field model 29 60 has been developed by combining interatomic force constants ( IFCs ) 61 62 and atomic close packing principle 14 22 , while its general utility has been validated by different CMAs in numerous alloy systems 27 28 29 . For a given alloy phase, the central force field model shows that those atoms with the largest IFCs act as the central atom of the cluster, those atoms with the smallest IFCs act as the glue atoms of the model, while those atoms with the IFCs locating between the max.…”

“…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.…”