Reconstructing the reflectivity of liquid surfaces from grazing incidence X-ray off-specular scattering data

Shen, C.; Zhang, H.; Ocko, B.M.

doi:10.1107/S1600576724002887

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Figure 2
Theoretical courses of the grazing incidence diffuse scattering R^* and of the specular reflectivity R from the water surface at 73 mN m⁻¹ at 293 K (a), and their ratio r = R^*/R (b). The calculation assumes an incident energy of 15 keV, a vertical angular resolution Δβ = 0.08° and two different horizontal angular resolutions Δ2θ: 0.004° (solid lines) and 0.08° (dashed lines). The incident angle for R^* is set to 0.07°. R^* and r corresponding to different off-specular positions Q_xy|_β=0 are color coded [ $[Q_{xy} |_{\beta = 0} = ({2\pi } / \lambda )\sqrt {(\sin 2\theta )^2 + (\cos 2\theta - \cos \alpha )^2} ]$ stands for Q_xy at β = 0]. Note that the blue lines are R^* and r in the plane of incidence (Q_xy|_β=0 = 0 Å⁻¹, i.e. 2θ = 0°). The legends provide the values of Δ2θ used (in parentheses), and the Q_xy|_β=0 value for R^*. In (a) the Fresnel reflectivity R_F (zero roughness, dash–dotted line) is shown as a reference. We use Q_xy|_β=0 rather than Q_x|_β=0 to define the off-specular position since at β= 0, Q_xy ≠ Q_x. At this position, Q_xy is not parallel to Q_x. A small Q_y component still persists [see the expression of Q_x and Q_y below equation (2)

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 57| Part 3| June 2024| Pages 714-727

https://doi.org/10.1107/S1600576724002887

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