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

Abstract

The equations taking into account refraction at the sample surface in grazing-incidence small-angle X-ray scattering (GISAXS) when the angle between the incoming beam and the sample surface is slightly larger than the critical angle are derived and discussed. It is demonstrated that the refraction of both the incoming and the scattered beam at the sample surface affects the GISAXS pattern and that, when a planar bidimensional detector perpendicular to the incoming beam is used, the effect depends on the azimuthal detector angle. The smearing of the pattern depending on the size of the illuminated sample area in grazing incidence is estimated by simulations with Cauchy functions of different widths. The possibility of integrating the recorded intensities over a suitable azimuthal angular range and then of making the correction for refraction is also analysed, employing simulations involving the intensity function of monodisperse interacting hard spheres. As a case study, the refraction correction is applied to the investigation of a Cu-Ni implant on silica glass

Small-angle scattering in materials science - a short review of applications in alloys, ceramics and composite materials

“…Generally speaking, one has to deal not only with the incoming, but also with the reflected X-ray beam (Martorana et al, 2001). This means that the Born approximation is generally not valid in this case.…”

Nucleation of atomic-layer-deposited HfO2 films, and evolution of their microstructure, studied by grazing incidence small angle x-ray scattering using synchrotron radiation

“…In principle, these data must be corrected for refraction and reflection effects related to the experimental geometry. [10][11][12] However, for the present case, corrections for refraction and incident beam normalization vary negligibly across the q range of interest. Also, with an incidence angle of 0.35°, the entire ALD film thickness is sampled, and the correction for the sampling volume is calculated to vary by less than 6%.…”

“…Complete experimental details of GISAXS studies may be found elsewhere. [10][11][12] Specular reflected intensity was measured with the incident beam collimation and linear detector slits set to equal angles of grazing incidence and specular reflection. The intensity was measured as a function of angle over the range from 0°to 6°, corresponding to q values perpendicular to the substrate of 0 -10 nm −1 .…”

Analysis of 2D GISAXS patterns obtained on semiconductor nanocrystals

“…2b). The 2y 0 angle is determined from the scattering geometry and refraction indexes (n i ) for a given material [11]. The second effect, which also arises due to different refraction indexes, is the transmission coefficient for exiting beam, which varies depending on the incidence angle.…”