N. Jedrecy, Coupling between spatial and angular variables in surface X-ray diffraction: effects on the line shapes and integrated intensities, J APPL CRYS, 33, 2000, pp. 1365-1375
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 samp
le, 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 illuminat
ed by the incident beam and viewed by the detector. Indeed, one must take a
ccount of the changes in the scattering direction that occur during the the
ta scan, and define at every theta the surface fraction A(theta) that scatt
ers into the detector. In a third step, a rod with finite width is consider
ed, and the spilling and travelling of the diffracted spot, arising from th
e centre of the sample, over the detector window is described. The spots em
erging from any other sample position are then considered. By coupling spat
ial and angular variables, the scan line shape can be simulated quantitativ
ely, by means of the inplane intensity distribution of the rod. The resulti
ng integrated intensity provides the correction factor to be applied to the
raw data for the derivation of the structure-factor amplitude. This correc
tion factor is compared to the usual correction (AL Deltal), where A is ass
umed to be constant, L is the Lorentz factor and Deltal is the l range as i
ntegrated during the scan (in the context of the Dirac-like rod). Significa
nt differences occur at large l values when using grazing-incidence conditi
ons.