Cluster-based composition rule for stable ternary quasicrystals in Al-(Cu, Pd, Ni)-TM systems

Although hundreds of quasicrystals have been found, little is known about their quantitative composition rules that can help design new materials. In this paper we propose a cluster-based approach to decipher the composition rules. Our approach consists of the following steps: (1) selection of a known basic cluster in the constituent binary systems; (2) construction of a cluster line linking the binary cluster composition to a third element; and (3) the intersection of the two cluster lines points to a new quasicrystal composition if the e/a ratio falls in the appropriate range, typically from 1.8 to 2.0. The predicted compositions agree satisfactorily with experimental values.