A two-dimensional model of crystal-growth disorder

A simple two-dimensional (2D) model of crystal-growth disorder is described. The model assumes growth probability parameters which involve the interaction of a crystallizing molecule with neighbours in two crystal directions. The disorder that results from this process is described mathematically and with the use of an optical simulation technique. It is found that the correlations between neighbours that result in the completed crystal are not simply related to the initial probabilities, but when a special linearity restriction is made the correlations can be used to retrieve these probabilities. The direction in which the crystal is grown is inherently different from other directions and this is evident in the diffuse diffraction patterns that are obtained from the model.