Instrumental effects on measurements of surface X-ray diffraction rods: resolution function and active sample area

This paper describes the effect of instrumental resolution on the line shapes and intensities of surface diffraction rods when the component of the scattering vector perpendicular to the surface (Q_z) is not small. Using a square-wave shape for the resolution function perpendicular to the scattering plane but an arbitrary in-plane shape, it is calculated how the resolution affects line shapes when the scattering vector is scanned parallel to the surface (Q_|| scans). The approach used is to measure the line shape in Q_|| scans at small Q_z and from this to determine how the Q_|| line shapes depend on Q_z. Line shapes calculated in this manner are compared with data from an Ag(111) surface with excellent agreement, confirming the treatment. A similar approach is used to calculate the resolution correction that is needed to convert the measured diffraction-rod intensities into structure factors. Measurements of both peak intensity and integrated intensities in rocking scans are treated and the results are compared with those of previous treatments. Finally, the active sample area for an incident beam that is spatially nonuniform is calculated, as appropriate for experiments using focusing optics and wide incident slits. This approach accounts for the active area more accurately than the usual calculation assuming a uniform rectangular beam. The results described in this paper permit a better understanding of the effects of instrumental resolution on the line shapes of surface diffraction rods, enable more accurate determination of structure factors along these rods and are valid for nearly all Q_z.