Analysis of neutron double-crystal diffractometer scattering curves including multiple scattering

Double-crystal diffractometers (DCD) of the Bonse-Hart type are used for small-angle neutron scattering (SANS) experiments with very high resolution. Scattering from inhomogeneities in the size range of typically 100 nm to 10 µm can be detected with a DCD. The evaluation of DCD scattering curves is more complicated than for conventional SANS instruments with point collimation for two reasons: first, a DCD operates with a long-slit geometry, and second, owing to the high scattering power of large inhomogeneities, multiple small-angle scattering is likely to play a significant role in many DCD experiments. A numerical procedure is proposed for the determination of particle size distributions from DCD scattering curves influenced by multiple scattering. This procedure is based on an n-fold convolution of single-scattering cross sections, where n depends on the degree of multiple scattering. It makes use of the indirect Fourier transformation method and thus, firstly, size distributions of arbitrary shape can be determined, and secondly, the calculation is fast, allowing an interactive analysis. The procedure is demonstrated with scattering from latex particles with different degrees of multiple scattering. The results show that the size and volume fraction of the latex spheres can be determined with a reasonable error even from scattering curves that are strongly influenced by multiple small-angle scattering.