X-ray diffraction analysis of stacking and twin faults in f.c.c. metals: a revision and allowance for texture and non-uniform fault probabilities

A revision is presented of the original description by Warren [X-ray Diffraction, (1969), pp. 275–298. Massachusetts: Addison-Wesley] of the intensity distribution of powder-pattern reflections from f.c.c. metal samples containing stacking and twin faults. The assumptions (in many cases unrealistic) that fault probabilities need to be very small and equal for all fault planes and that the crystallites in the sample have to be randomly oriented have been removed. To elucidate the theory, a number of examples are given, showing how stacking and twin faults change the shape and position of diffraction peaks. It is seen that significant errors may arise from Warren's assumptions, especially in the peak maximum shift. Furthermore, it is explained how to describe powder-pattern reflections from textured specimens and specimens with non-uniform fault probabilities. Finally, it is discussed how stacking- and twin-fault probabilities (and crystallite sizes) can be determined from diffraction line-profile measurements.