Improvement of data treatment in small-angle neutron scattering

Small-angle neutron scattering has been successfully used since the 1970s. As a general rule, methods to extract the useful signal from that received by the detector are well known and give good results. At the Laboratoire Leon Brillouin, for example, these methods have been employed for a long time. However, the data reduction software has been changed for the following reasons. Problems are encountered if the container of the sample gives a spurious signal or if the scattering angle is so large that its cosine cannot be approximated by 1. In the present paper, generalizations of formulas are made in order to account for these difficulties. The decrease of scattered intensity delivered by an incoherent sample that is often observed at large angles is shown to be only due to a geometrical effect. The consequent modifications of the relations used for the normalization of cells of position-sensitive detectors and for the absolute calibration are given. As for the inherent background of the sample, the contribution of density fluctuations is usually neglected. This contribution is formally given as a function of the contrast lengths and of the isothermal compressibility of the sample. This new result allows numerical evaluations of the different terms of the inherent sample background. Practical examples are given. Finally, several methods, developed at the Laboratoire Leon Brillouin, are given to determine the background properly. They are based on systematic measurements of transmissions and background levels of suitably prepared blank samples.