用掠入射X射线衍射模式提取液体和汽液界面的对分布函数
Extracting the Pair Distribution Function of Liquids and Liquid-Vapor Surfaces by Grazing Incidence X-ray Diffraction Mode
摘要：
我们表明，水的结构因子$S(q)$可以得到从X射线同步辐射实验在掠入射角（反射模式），通过使用液体表面衍射仪。描述了用于获得自洽$S(q)$的校正。将这些校正应用于不同入射光束角度（临界角以上）的扫描，将测量的强度折叠成单个主曲线，而不需要拟合参数，其在比例因子内产生$S(q)$。在总反射率的临界角以下进行测量，得到水/蒸汽界面最顶层的结构因子。我们的研究结果表明，在蒸汽/水界面的水重组。我们还介绍了一种新的方法来提取$g(r)$，对分布函数（PDF），通过将PDF表示为误差函数的线性和，其参数通过应用非线性最小二乘拟合方法进行细化。这种方法可以直接确定PDF中的固有不确定性。我们的研究结果以前测量和理论预测的PDF的影响进行了讨论。
英文摘要：
We show that the structure factor $S(q)$ of water can be obtained from X-ray synchrotron experiments at grazing angle of incidence (in reflection mode) by using a liquid surface diffractometer. The corrections used to obtain $S(q)$ self-consistently are described. Applying these corrections to scans at different incident beam angles (above the critical angle) collapses the measured intensities into a single master curve, without fitting parameters, which within a scale factor yields $S(q)$. Performing the measurements below the critical angle for total reflectivity yields the structure factor of the top most layers of the water/vapor interface. Our results indicate water restructuring at the vapor/water interface. We also introduce a new approach to extract $g(r)$, the pair distribution function (PDF), by expressing the PDF as a linear sum of Error functions whose parameters are refined by applying a non-linear least square fit method. This approach enables a straightforward determination of the inherent uncertainties in the PDF. Implications of our results to previously measured and theoretical predictions of the PDF are also discussed.
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