Optical transforms of disordered systems containing symmetry-related scattering sites

A previously described method of synthesizing a real-space distribution of scattering points which will give rise to virtually any required diffraction pattern has been extended to include the possibility of multiple symmetry-related sites per unit cell. The distribution may be used in the form of an optical diffraction screen to give an immediate visual check on both the real-space and reciprocal-space distributions. The method has been applied successfully to two examples which exhibit strong diffuse X-ray scattering effects: a molecular crystal sample, 1,3-dibromo-2,5-diethyl-4,6-dimethylbenzene (BEMB2), in which disorder occurs because the molecule can take up two different orientations in any given molecular site, and a mineral mullite, Al₂(Al_{2 + 2x}Si_{2 − 2x})O_{10 − x}⊗_x, where disorder diffuse scattering occurs as a result of the oxygen vacancies ⊗ and the accompanying cation displacements.