view article
Figure 3
(a) Position along the vertical direction detector (qz) for various experimental features, as a function of grazing-incidence angle ([\theta _{\rm i}]), for 13.5 keV X-rays. The horizon (H, dashed gray line) is the plane of the sample itself; sub-horizon scattering must transit through the substrate (and suffer from absorption) while scattering above the horizon exits the film and travels through a vacuum. The specular reflected beam (R, red) appears at [2\theta _{\rm i}]. When the exit angle matches the critical angle ([\theta _{\rm c}]) of the film or substrate, one observes enhanced intensity on the detector. This Yoneda (Y, yellow) scattering is offset from the horizon by [\theta _{\rm c}]. The circles are experimental data, where the position of maximum low-q scattering was identified as the Yoneda, for a block-copolymer thin film on a Ge-coated silicon substrate. The solid yellow line is the theoretical expectation for the critical angle for this substrate. When the incident angle is below the critical angle for the polymer film, the Yoneda shifts to this lower critical angle instead. The transmitted beam (T, blue) is shifted from the direct-beam position (qz = 0) because of beam refraction (the dashed line denotes the position of the transmitted beam within the polymer layer). (b) The refraction distortion ([\Delta q_{z}]) as a function of position along the detector is strongly nonlinear, and depends on both qz and the incident angle ([\theta _{\rm i}]). The positions of the various features are denoted by vertical lines: transmitted beam (blue), horizon (dashed gray), substrate Yoneda (yellow), and specular reflection (red). There is a gap in the data between the horizon and the film critical angle. Data close to this gap are generally unusable for reconstruction owing to the large and strongly non-linear distortion. The gray shaded region denotes the area unusable for reconstruction because of the finite range of qz sampling (refer to Results and discussion[link]); the horizontal arrow denotes the span of qz used for reconstruction.

IUCrJ
Volume 5| Part 6| November 2018| Pages 737-752
ISSN: 2052-2525
https://doi.org/10.1107/S2052252518012058