Interpretation of diffuse scattering using superspace crystallography

Single crystal diffuse scattering is generally interpreted using correlation parameters that describe probabilities for certain configurations on a local scale. In this paper we present a novel interpretation of diffuse maxima using a disordered superspace approach. In (D+d)-dimensional superspace two modulation functions are disordered along the superspace axis $\vec{a}_{s,i}$ for i = 1,..,D, while the periodicity along the internal dimensions is maintained. This simple approach allows the generation of diffuse maxima of any width at any position in reciprocal space. The extinction rules that are introduced by superspace symmetry are also fulfilled by the diffuse maxima from structures generated using the disordered superspace approach. In this manuscript we demonstrate the disordered superspace approach using a simple a simple two-dimensional binary disordered system. The extension of the approach to (3+D)-dimensional superspace is trivial. The treatment of displacement and magnetic disorder in a similar approach is straight forward