Faulting in finite face-centered-cubic crystallites

The effects that planar faults have on the powder diffraction peak profiles of a face-centered cubic (f.c.c.) material are studied considering the case of small crystallites. In doing so a new method to calculate the planar probability correlation function of a faulted crystallite is presented which considers the finite extent of the planar sequence. The resulting correlation function is demonstrated to be dependent on the position of a fault in a crystallite through its proximity to a crystallite boundary. The average correlation function found considering equal probability of a fault existing on each plane in a crystallite is compared with that found by solving a system of recursion relations. The broadened subcomponents of the f.c.c. powder profiles are shown to be related to the correlation function through a general Fourier series expression. This expression is then used to simulate peak profiles from the developed model, and then compare them with those predicted by the recursion relation treatment.