Structural orientation functions for anisotropic small-angle scattering

Porod's invariant analysis of small angle X-ray scattering is re-examined for an oriented system of anisotropic scattering elements. Starting with the Patterson function, a one-dimensional pseudo-invariant is defined. By comparing pseudo-invariants taken at various azimuthal angles, the extent of orientation in the specimen can be explored. This is done for four different carbon fibre specimens by comparing the ratio of the pseudo-invariant taken along the fibre radius to that taken along the fibre axis as well as for the averaged preferred angle of orientation (sin 2 phi ). For these fibres, it was found that the modulus and the break strength of the fibres increased as the orientation of the scattering particles increased.