On the powder diffraction pattern of crystals with stacking faults

Abstract

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.

Acknowledgements

One of the authors (E.E.R.) acknowledges support from the Humboldt Foundation through an Alexander von Humboldt fellowship. Part of this project was carried out under TWAS research grant 99-082 REG/PHYS/LA and under an Alma Mater grant from the University of Havana.

Notes

† The function P_t (m) can be seen as a generalization of the adopted by Warren (1990).

† It is worth noting that, for {111} faulting in a fcc lattice, is equal to L ₀=h+k+l as defined by Warren (1990). In our case the sign in the shift is implicit in whereas a sign function was introduced by Warren.