Modeling decagonal quasicrystals : random assembly of interpenetrating decagonal clusters

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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

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