On the powder diffraction pattern of crystals with stackings faults

The so-called direct solution of the powder diffraction pattern for a faulted layered crystal is discussed. It is shown how, in the general case, peak profiles can be split into a symmetric and an antisymmetric component. The relationships between peak profile parameters and the underlying faulting structure, as given by the probability correlation function, are evidenced. The formalism reduces to known equations when applied to particular faulting models. Warren's equations for peak profile of fcc materials with {111} planar faulting are derived within the framework of a general theory. Possible strategies for incorporating the proposed formalism into a general powder pattern refinement procedure are also discussed.