J. Phys. I France 2 (1992) 695-706
Modeling decagonal quasicrystals : random assembly of interpenetrating decagonal clustersS. E. Burkov
Cornell University, Laboratory of Atomic and Solid State Physics, Ithaca, NY 14853-2501, U.S.A.
(Received 11 February 1991, revised 26 November 1991, accepted 22 January 1992)
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.
© Les Editions de Physique 1992