Inferring orientation distributions in anisotropic powders of nano-layered crystallites from a single two-dimensional WAXS image

The wide-angle scattering of X-rays (WAXS) by anisotropic powders of nano-layered crystallites (nano-stacks) is addressed. Assuming that the orientation distribution probability function f of the nano-stacks only depends on the deviation of the crystallites' orientation from a fixed reference direction, a relation providing f from the dependence of a given diffraction peak's amplitude on the azimuthal angle is derived. The method is applied to two systems of sodium fluorohectorite (NaFH) clay particles, using synchrotron radiation and a WAXS setup with a two-dimensional detector. In the first system, which consists of dry-pressed NaFH samples, the orientation distribution probability function corresponds to a classical uniaxial nematic order. The second system is observed in bundles of polarized NaFH particles in silicon oil; in this case, the nano-stacks have their directors, on average, in a plane normal to the reference direction, and f is a function of the angle between a nano-stack's director and that of the plane. In both cases, a suitable Maier-Saupe function is obtained for the distributions, and the reference direction is determined with respect to the laboratory frame. The method only requires one scattering image. Consistency can be checked by determining the orientation distribution from several diffraction peaks independently.