Quantitative analysis of diffraction by liquids using a pink-spectrum X-ray source

A new approach for performing quantitative structure-factor analysis and density measurements of liquids using X-ray diffraction with a pink-spectrum X-ray source is described. The methodology corrects for the pink beam effect by performing a Taylor series expansion of the diffraction signal. The mean density, background scale factor, peak X-ray energy about which the expansion is performed, and the cutoff radius for density measurement are estimated using the derivative-free optimization scheme. The formalism is demonstrated for a simulated radial distribution function for tin. Finally, the proposed methodology is applied to experimental data on shock compressed tin recorded at the Dynamic Compression Sector at the Advanced Photon Source, with derived densities comparing favorably with other experimental results and the equations of state of tin.