Modeling decagonal quasicrystals : random assembly of interpenetrating decagonal clusters

(Received 11 February 1991, revised 26 November 1991, accepted 22 January 1992)

Abstract
Conventional tiling models of quasicrystals imply the existence of two or more elementary cells (tiles). A new approach is proposed that allows a quasicrystal to be thought of as a random assembly of identical interpenetrating atomic clusters. This model is shown to be equivalent to a decagonal binary tiling. On applying a random tiling hypothesis, originally postulated by Elser, to the present cluster model it is found that the free energy as a function of the alloy composition has a cusp at a point exactly corresponding to the decagonal quasicrystal. This fact helps to explain an old mystery, namely why a system is phase locked in a quasicrystalline state even thought it is incommensurate.