Computer simulations of two-dimensional quasiperiodic crystal and random tiling models

The recent discovery23,24 of quasicrystalline materials exhibiting resolution-limited diffraction peaks focusses attention on those quasicrystalline models which predict long-range translational order. Two such models have been suggested: the quasiperiodic crystal model (for which the Penrose tiling is the prototype) and the random tiling model (analogous to allowing arbitrary spacefilling arrangements of the Penrose rhombuses). Physically, the two models are distinguished by primary dependence on energy and entropy, respectively, in stabilizing the quasicrystal phase. Here we describe computer simulation results for simple two-dimensional realizations of each models. (author). 24 refs, 13 figs