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We show that the structure factor $S(q)$ of water can be obtained from X-raysynchrotron experiments at grazing angle of incidence (in reflection mode) byusing a liquid surface diffractometer. The corrections used to obtain $S(q)$self-consistently are described. Applying these corrections to scans atdifferent incident beam angles (above the critical angle) collapses themeasured intensities into a single master curve, without fitting parameters,which within a scale factor yields $S(q)$. Performing the measurements belowthe critical angle for total reflectivity yields the structure factor of thetop most layers of the water/vapor interface. Our results indicate waterrestructuring at the vapor/water interface. We also introduce a new approach toextract $g(r)$, the pair distribution function (PDF), by expressing the PDF asa linear sum of Error functions whose parameters are refined by applying anon-linear least square fit method. This approach enables a straightforwarddetermination of the inherent uncertainties in the PDF. Implications of ourresults to previously measured and theoretical predictions of the PDF are alsodiscussed.

Extracting the Pair Distribution Function of Liquids and Liquid-Vapor Surfaces by Grazing Incidence X-ray Diffraction Mode