A New Approach for Extracting the Pair Distribution Function of Liquds from X-Ray Scattering Experiments

A new approach for determining the pair distribution function (PDF, g(r)) from X-ray liquid structure factor in a reflection mode is described and applied to those of pure water and dilute water-salt solutions. The approach involves the construction of a model PDF function using parameterized generating functions that is refined by least square fitting procedure to the measured liquid S(Q). First, a histogram of the PDF is constructed using step-like functions that are convolved with width-varying gaussians for each interfacial step of the PDF to produce a smooth g(r). The structure factor S(Q) is then calculated from g(r) which is given by a linear combination of Error Functions. The fitted parameters are the positions and widths of the peaks of the g (r). The advantages of this procedure is that no absolute scaling of the intensity is necessary and it provides the uncertainties in calculated g(r). Measuring the S(Q) in reflection mode at grazing-angles of incidence (in particular below the critical angle for total reflectivity - GIXD mode) enables to obtain the liquid-gas interfacial S(Q) for which the new approach can be readily extended.