X-ray reflectivity from curved surfaces as illustrated by a graphene layer on molten copper

Konovalov, O.V.; Belova, V.; La Porta, F.; Saedi, M.; Groot, I.M.N.; Renaud, G.; Snigireva, I.; Snigirev, A.; Voevodina, M.; Shen, C.; Sartori, A.; Murphy, B.M.; Jankowski, M.

doi:10.1107/S1600577522002053

Figure 4
(a) Example of a fan of the reflected beam from the curved surface of the molten copper (Sample 3, ID10/ESRF data). Three white rectangles of equal area indicate the areas for calculation of the background (B_L, B_R) and the scattered signal (S) for each horizontal cut through the image. A halo below the white rectangles is the parasitic scattering of the primary beam. (b) Simulated angular spread value of the beam on a curved surface with a curvature radius of 200 mm and a vertical beam size of 50 µm. Inserts demonstrate the angular spread at effective grazing angles of 0.1 and 5° (from left to right) for the beam represented with nine rays and seen on a detector plane located at 1 m (scale of the vertical grid is 1 mm). In the case of 0.1°, only five rays reflect, and the four others go above the sample, while, in the case of 5°, all nine rays reflect from the sample surface. (c) 2D map of simulated X-ray reflectivity on the curved surface for a set of effective grazing angles. The ordinate of the map is the effective grazing angle α_i, while the abscissa is pixels of the effective 1D detector. The horizontal line at each α_i represents the reflected beam intensity distribution along the 1D profile in the XOZ plane. Each pixel on the map corresponds to a local grazing angle α_i,h. Parameters of the calculation: radius of the curved surface of liquid copper at T = 1400 K is 200 mm; incident beam size (2W_V) is 50 µm; detector pixel size is 55 µm, and sample-to-detector distance is 1.0 m. The vertical line at pixel 728 is a guide to the eye of the effective 1D detector center where α_i,h = α_i. The beam's intensity reaching the detector without reflection is not added to the graph. The color bar corresponds to the logarithm of intensity. (d) 2D map of the incident beam contribution fraction to the scattering in a pixel. These values are used for pixel-by-pixel normalization of intensity in Fig. 4

(c).

JOURNAL OF
SYNCHROTRON
RADIATION

ISSN: 1600-5775

Volume 29| Part 3| May 2022| Pages 711-720

https://doi.org/10.1107/S1600577522002053

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