An analytical expression was developed for the scattering intensity from single crystals of close-packed polytypes (hexagonal close-packed, face-centered cubic and more complex ones) having arbitrary concentrations of random shearing stacking faults; provided that the stacking-fault planes were parallel to each other. In order to obtain simulated powder-diffraction patterns in the case of a finite crystallite size, the single-crystal intensity was substituted into an integral formula. The same approach permitted an analytical description of the scattering intensity from a face-centered cubic crystal having differently-oriented random shearing stacking faults, under the assumption that the atomic displacements which were associated with each stacking-fault orientation were independent. The latter approximation was valid for moderate stacking-fault concentrations.

Calculation of Diffraction Patterns of Close-Packed Polytypes with Random Shearing Stacking Faults. E.V.Shelekhov, T.A.Sviridova: Materials Science Forum, 2000, 321-324, 97-102