Long-range order in a three-dimensional random-tiling quasicrystal

Abstract

Monte Carlo simulations are performed on the rhombohedral random-tiling model of icosahedral quasicrystals. Long-range order is observed in agreement with a squared-gradient form of the coarse-grained free energy, and the two independent phason elastic constants are determined. Schematic transmission electron micrographs, generated by two-dimensional projections of the tile vertices of a typical random configuration, display phason disorder only for sufficiently thin samples.