Small-angle scattering of x rays from groups of nonrandomly oriented ellipsoids of revolution of low concentration

Abstract

The small-angle scattering from low concentrations of ellipsoids of revolution is examined. For monodisperse ellipsoids having axes of 2a, 2a, and 2b and a fixed common orientation, it is shown that the scattering is equivalent to that of a ``Guinier sphere'' whose radius is H = (a2 sin2γ + b2 cos2γ)1/2, where γ is the angle between the axis of symmetry and the plane of observation. This affords a simple geometric interpretation of the ``average inertial distance'' of Guinier and also of the quantity analagous to the surface area in the Porod approximation. By analyzing the experimental data in the Guinier region for γ=0 and π/2, independent determinations of a and b are obtained. Comparisons of the data in the Porod region provide an independent determination of a/b. For ellipsoids having an orientation distribution described by a probability function, the scattering is equivalent to that of a group of Guinier spheres of radii in the range a to b. The general case of ellipsoids having both an orientation and size distribution is also treated. Methods of correction for beam height and the interpretation of experimental data are presented, along with an application to oriented inhomogeneities in pyrolytic graphite.