Single and multiple X-ray small-angle scattering of carbon fibres

The theory of single and multiple small-angle scattering of fibres with a two-phase system of densities is revised. Luzzati's fundamental treatment of multiple scattering has been applied to systems with cylindrical symmetry. It is shown that the results of measurements with an `infinite' slit parallel to the fibre axis cannot give the specific internal surface directly, but that this information can be obtained by a combination of `infinite' slit measurement and measurements with a pin-hole system in the case of needle-like pores with preferred orientation. The experimental results obtained indicate that the scattering at very small angles is a multiple scattering determined by the filament cross-section. It is shown that parameters related to the size and the shape of the filament cross-section as wall as the specific surface of the filaments can be computed from this scattering. The scattering at somewhat wider angles is essentially a single scattering and can contain two components. The predominant component is a scattering of needle-like pores with diameters in the 10-20 Å range and lengths of at least 200-300 Å. The porosity is around 30%. The needle axes show a preferred orientation parallel to the fibre axis. The angular distribution of the needle axes is very similar to that of the graphitic layers. A second component can be observed, which is produced by density fluctuations in the parallel stacking of graphitic layers. Studies on powdered fibres indicate changes in the microstructure due to the grinding.