Coupling between spatial and angular variables in surface X-ray diffraction: effects on the line shapes and integrated intensities

Abstract

The intensity line shape, as provided by a rocking scan, and the derivation of the structure factor from the integrated intensity are reviewed in the context of surface X‐ray diffraction, focusing on the z‐axis geometry. In a first step, under the assumption of a Dirac‐like rod and a point‐like sample, the effects of the detector slit settings on the scan width and on the integrated rod height are described. In a second step, it is shown that it is incorrect to treat the integrated intensity as being proportional to the active area A of the surface, defined as the sample area that is illuminated by the incident beam and viewed by the detector. Indeed, one must take account of the changes in the scattering direction that occur during the θ scan, and define at every θ the surface fraction A(θ) that scatters into the detector. In a third step, a rod with finite width is considered, and the spilling and travelling of the diffracted spot, arising from the centre of the sample, over the detector window is described. The spots emerging from any other sample position are then considered. By coupling spatial and angular variables, the scan line shape can be simulated quantitatively, by means of the in‐plane intensity distribution of the rod. The resulting integrated intensity provides the correction factor to be applied to the raw data for the derivation of the structure‐factor amplitude. This correction factor is compared to the usual correction (ALΔl), where A is assumed to be constant, L is the Lorentz factor and Δl is the l range as integrated during the scan (in the context of the Dirac‐like rod). Significant differences occur at large l values when using grazing‐incidence conditions.

Scherrer grain-size analysis adapted to grazing-incidence scattering with area detectors

“…Although the limits between GIWAXS and GID are somewhat fluid, in the following it will be understood that GIWAXS measurements are primarily concerned with collecting diffuse scattering with an area detector, while in GID typically higher-resolution scans using point or line detectors are performed, in conjunction with collimating slits or Soller collimators (see, for instance, Smilgies et al, 2005). The use of collimation significantly changes the resolution function and has been discussed by Robach et al (2000) and Jedrecy (2000). In the following, we will be concerned with the GIWAXS case, which follows the same considerations as apply for GISAXS.…”

Layer relaxation and intermixing inFe∕Cu(001)studied by surface x-ray diffraction

“…Symbols represent the structure factor amplitudes ͉͑F obs ͉͒ obtained from the integrated intensities after correcting for apparative factors. 47,48 Standard deviations ͑͒ of the ͉F͉ values are derived from the counting statistics and the reproducibility of symmetry-equivalent reflections. 49,50 In general, error bars are about the size of the symbols in Fig.…”

Flat-top silver nanocrystals on the two polar faces of ZnO: An all angle x-ray scattering investigation

“…The same geometry is used for GIXD except that the scattering centers are the atoms and that the two outgoing angles ␣ f , ␦ f may vary between 0°and 90°. 22 The experiments were performed at the European Synchrotron Radiation Facility ͑ESRF͒ using the UHV surface diffraction setup of the CRG BM32 beamline. 23 A doubly focused x-ray beam of 18 keV was used, with a typical 0.4 ϫ 0.3 mm 2 horizontal times vertical size.…”