A general recursion method for calculating diffracted intensities from crystals containing planar faults

The method exploits the self-similar stacking sequences that occur when layers stack non-deterministically. Recursion gives a set of simple relations between average interference terms from a statistical crystal, which can be solved as a set of simultaneous equations. The diffracted intensity for a polycrystalline sample is given by the incoherent sum of scattered intensities over an ensemble of crystallites. The relations between this and previous approaches are discussed. Calculations for diamond-lonsdaleite and for several synthetic zeolite systems that contain high densities of stacking faults are presented as examples. -from Authors