Quasicrystal structure modelling

We have developed a package of computer codes for the diffraction refinement of the tiling-decoration models of decagonal quasicrystals. Since up to now all such refinements have been carried out within hyperspace approach, we discuss the relationships of the two approaches, emphasizing the fact that the model of quasicrystal is not completely specified by assigning chemical identities to a nonperiodically arranged set of points: in addition, the integral part of the model is the hypothesis about the physically relevant degrees of freedom, assigned to each of these points. The machinery of the tiling-decoration refinement is illustrated on the case of the decagonal AlPdMn quasicrystal, for which we present the results obtained by fit to the single-crystal diffraction data [1].