Partial multiplicity factors for texture correction of cubic structures in the disc-shaped crystallite model

The correction of integrated intensities for preferred orientation in the disc-shaped crystallite model is analyzed. The partial multiplicity factors have been derived to describe the relationships between the prominent – preferentially oriented – HKL pole density P_H(α) and the total pole density P^T_h(α = 0) for any set of symmetry-equivalent planes {hkl}. (The angle α is referred to the sample-surface normal.) The analysis of partial multiplicity factors revealed, in all crystal systems, the preferentially oriented planes {HKL} for which the general and partial multiplicity factors are equal for all (hkl) and showed the {HKL} planes that require the introduction of partial multiplicity into the intensity formula. Present results enable the application of the disc-shaped crystallite model with a simple texture correction for all kinds of preferentially oriented planes {HKL} in all crystal systems, which is especially useful for cubic structures, where the special multiplicity factors have to be used for every {HKL}.