Model calculation based on parallel cylindrical fibrils with a distribution of radii are used to derive fibrillar radii obtained from the transverse intensity profile of the small-angle X-ray scattering (SAXS) peaks. The results are expressed in terms of moments of the distribution function of the radii. The traverse integral breadth of the peak leads to (/), the initial slope gives (/)^1/2, the asymptotic slope in the transverse wings yields or (/)^1/2 and the analysis of the characteristic function gives (/). The first two methods are applied to the SAXS patterns of well oriented samples of nylon 6, for which it is found that a positively skewed distribution of fibrillar radii. The relation between these analyses of uniaxially oriented systems and other SAXS and wide-angle diffraction methods is considered.

Procedures for correcting experimental diffraction intensities in the small-angle region for the determination of one-dimensional structures are presented. The diffraction patterns in question consist of meridional streaks which are transversely broadened due to: (1) finite fibril radius, (2) imperfect fibrillar orientation, (3) lamellar curvature or (4) instrumental broadening. Three methods are developed and compared for obtaining corrected intensities in the presence of these effects. One method uses direct integration over all reciprocal space. Two complementary techniques involve correction of integrated layer line or meridional peak intensities; the correction factors are shown to be the transverse integral widths of the layer lines, suitably modified for instrumental broadening.

Mixtures of model crystallizable copolymers, hydrogenated polybutadiene (HPB) and deuterated polybutadiene (DPB), were investigated by SANS in the intermediate q range (0.02 ≤ q ≤ 0.18 Å⁻¹). Linear and three-arm-star polymers were crystallized by quenching and slow cooling at rates differing by 3000-fold. Care was taken in subtracting the incoherent background scattering. The coherent cross section shows a q⁻² dependence which results in a constant Kratky plateau. Absolute SANS intensity is slightly greater than predicted for amorphous chains and is very insensitive to crystallization conditions in these polymers, changing by less than 10%. These observations are interpreted in terms of the gambler's-ruin model for chain configurations in semicrystalline polymers.

Several procedures for Fourier analysis of single diffraction peaks for microstrains and mosaic sizes are compared. A simple new method works well, especially when the size distribution is broad, and/or when the strains vary in an unusual manner.