Modelling local disorder and diffuse scattering in quasicrystals

Higher-dimensional and three-dimensional techniques are complementary approaches for modelling disorder and diffuse scattering in quasicrystals. The concept of phasonic disorder allows a higher-dimensional description of disorder and calculation of diffuse intensities without knowing the atomic structure of the quasicrystal. In three-dimensional space, disorder can be analyzed by application of Patterson techniques. Local order may be modelled quantitatively without considering medium or long-range order properties of the quasicrystal. Furthermore, a priori knowledge about the structure of clusters present in the crystal can be easily utilized with Patterson methods. Potential and limitations of the techniques are discussed and demonstrated by means of experimental data.