Diffraction patterns of stacked layer crystals

The relation between diffraction and planar faulting is studied. The layer displacement probability correlation function is shown to be related to the Fourier coefficients of the decomposed diffraction pattern. Peak displacement can be considered as a consequence of the departure of the faulted structure from the original periodicity, while peak broadening is associated with the loss of correlation. Several definitions of distance are introduced to compare stacking sequence and measure their degree of randomness. A run-length encoding procedure is considered, well suited for the identification of mixed polytypes and as a measure of disorder. The problem of identification of faulting complexes is discussed in terms of the pair correlation function of the binary sequence representing the layer stacks.