Treatment of grazing-incidence small-angle X-ray scattering data taken above the critical angle

The equations taking into account refraction at the sample surface in grazi ng-incidence small-angle X-ray scattering (GISAXS) when the angle between t he incoming beam and the sample surface is slightly larger than the critica l angle are derived and discussed. It is demonstrated that the refraction o f both the incoming and the scattered beam at the sample surface affects th e GISAXS pattern and that, when a planar bidimensional detector perpendicul ar to the incoming beam is used, the effect depends on the azimuthal detect or angle. The smearing of the pattern depending on the size of the illumina ted sample area in grazing incidence is estimated by simulations with Cauch y functions of different widths. The possibility of integrating the recorde d intensities over a suitable azimuthal angular range and then of making th e correction for refraction is also analysed, employing simulations involvi ng the intensity function of monodisperse interacting hard spheres. As a ca se study, the refraction correction is applied to the investigation of a Cu -Ni implant on silica glass.