Interpretation of diffuse X-ray scattering via models of disorder

While Bragg diffraction data can only reveal average one-body information, such as atomic positions, thermal ellipsoids and site occupancies, diffuse scattering contains two-body information and is thus potentially a rich source of information on how atoms and molecules interact. The two major mathematical approaches that have been used to understand and analyse this diffuse part of the diffraction pattern are outlined and the difficulties and limitations which arise from the necessary complexity of these mathematical descriptions for any but the simplest of systems are discussed. Further, the progress that has been made in an alternative approach to understanding the local atomic and molecular arrangements in disordered materials, which overcomes some of these difficulties, is reviewed. The method consists of comparing diffraction patterns calculated from a computer model of the disordered structure with measured X-ray diffuse intensities. The advantage of the method is that it can be applied generally to all systems regardless of their complexity or size of the atomic displacements that might be present. Examples are taken from a variety of material systems and include oxygen-vacancy ordering and metal-atom displacements in yttria-stabilized cubic zirconia, disorder in the molecular crystal p-chloro-N-(p-methylbenzylidene)aniline, C₁₄H₁₂ClN (MeCl), and orientational disorder in crystals of 1,3-dibromo-2,5-diethyl-4,6-dimethylbenzene, C₁₂H₁₆Br₂ (BEMB2). The computer models are generated using both real-space Monte Carlo methods, which employ near-neighbour effective interactions, and a reciprocal-space synthesis approach. Diffraction patterns are computed in three dimensions using realistic atomic form factors so direct comparison can be made with mathematical descriptions of the diffuse scattering.