Short-range order diffuse scattering in quasicrystals

A theory for the diffuse scattering intensity owing to short-range order (SRO) in quasicrystals is given. The diffuse scattering intensity can be calculated based on higher-dimensional cluster models of quasicrystals. It is determined by the overlapped area (or volume) of occupation domains separated from each other by distances up to the correlation length and the SRO correlation functions. It is applied to a random atom distribution in phason flip sites in the Penrose pattern. To confirm the validity of the derived formula, analytical and numerical results for this case have been compared. Both results give similar diffuse scattering intensity, suggesting the validity of the theory.