J. Phys. I France
Volume 2, Number 5, May 1992
Page(s) 695 - 706
DOI: 10.1051/jp1:1992160
J. Phys. I France 2 (1992) 695-706

Modeling decagonal quasicrystals : random assembly of interpenetrating decagonal clusters

S. 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.

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