Diffuse X-ray scattering and strain effects in disordered crystals

It is shown in this paper that a feature that has been observed in the diffuse scattering patterns of a wide variety of different materials - a diffuse `ring' or `doughnut'-shaped region of scattering - can be understood in terms of a simple model that has been borrowed from the field of sol-gel science. In this, it is supposed that there is a balance between the local attractive forces that are trying to make a particular structure and a rather longer range repulsive force. In the present context, it is believed that this latter force has its origin in the strain that builds as the preferred local structure tries to fit into the average crystal lattice. Simple Monte Carlo (MC) computer simulations are described that demonstrate this principle for three example materials: cubic stabilized zirconia, the p-didecylbenzene/urea inclusion compound and the pure molecular compound 1,3-dibromo-2,5-diethyl-4,6-dimethylbenzene, C₁₂H₁₆Br₂ (BEMB2).