Monte Carlo study of the quasicrystal-to-crystal transformation using an approach based on the Gummelt covering

A tiling representation and associated possible tiling flips are developed for the “unit-cluster” description of decagonal quasicrystals with reference to the example of decagonal Al₇₀Co₁₅Ni₁₅. A perfect P1 tiling is a suitable model of the ideal quasiperiodic structure and a 180° flip of a pentagon tile can be used as an analogue of the hexagon flips in Penrose rhomb tilings. Monte Carlo simulations and calculated diffraction patterns are used to study the effect of those tiling flips on the cluster scale for some example cases. Some of these have a special importance for the quasicrystal-to-crystal transformation. Starting with the perfect P1 tiling the system is allowed to evolve using phason fluctuations whose probabilities depend on the resulting local tile configurations. The degree of order/disorder introduced and its effects on the diffraction pattern are investigated.