The Lorentz-Polarization Factor and Preferred Orientation in Oriented Clay Aggregates

A closed-form equation was derived that describes the powder-ring distribution factor as a function of 2 θ , soller slit collimation, and σ *, which is defined as the standard deviation of an axially symmetrical Gaussian orientation function. Methods were developed for measuring σ * in the reflection mode by means of a θ /2 θ diffractometer. Six experimental arrangements for a sedimentary chlorite showed widely different intensity ratios of the 001/005 reflections and gave a standard deviation of ±5.8% when corrected by the theory. The absolute integrated intensities of the 003 reflection from eleven illite samples provided an eight-fold maximum range which, when corrected, yielded a standard deviation of ±7.7%. The intensity distributions within each of two X-ray powder diffraction patterns obtained from instruments with different soller-slit configurations could not be directly compared at low diffraction angles unless corrections, based on σ *, were introduced to allow for the differences in axial divergence.