Corrections for surface X-ray diffraction measurements using the Z-axis geometry: finite size effects in direct and reciprocal space

X-ray diffraction data have to be corrected by geometrical correction factors prior to any quantitative analysis. Here the case of grazing incidence X-ray diffraction measurements is considered, including the case of high exit angles. First, an approach taking into account the evolution of the diffracting area during an ω scan is presented. From the calculation of the effective part of the sample surface that participates in the diffraction phenomena at each step of the scan, a more accurate correction factor than those commonly used is derived and the evolution of the line shape along a zero-width rod is explained. Secondly, the case of finite-width rods, under the point-like sample approximation, is considered: the influence of the partial integration, as a result of the detector in-plane acceptance, of a rod with an anisotropic in-plane shape, is studied and leads to an analytical expression for the corresponding correction factor. Finally, a full numerical simulation is presented, which provides an alternative method for correcting the experimental intensities and shows in which conditions the previous formulae are no longer valid.