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

TL;DR

This paper presents a method to infer the orientation distribution of nano-layered crystallites in anisotropic powders from a single 2D WAXS image, applicable to different systems and requiring minimal data.

Contribution

A novel approach deriving orientation distributions from a single diffraction peak's azimuthal dependence, simplifying analysis of anisotropic powders.

Findings

Successfully applied to Na-fluorohectorite samples with different orientations.

Obtained Maier-Saupe functions describing the distributions.

Method only requires one scattering image, enabling efficient analysis.

Abstract

The wide-angle scattering of X-rays 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, we derive a relation providing f from the dependence of a given diffraction peak's amplitude on the azimuthal angle. The method is applied to two systems of Na-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 nanostacks 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 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. Besides, consistency can be checked by determining the orientation distribution from several diffraction peaks independently.