Direct and quantitative comparison of pixelated density profiles with high-resolution X-ray reflectivity data

A method for comparing pixelated density profiles (e.g. obtained from molecular dynamics or other computational techniques) with experimental X-ray reflectivity data both directly and quantitatively is described. The conditions under which such a comparison can be made quantitatively (e.g. with errors <1%) are determined theoretically by comparing calculated structure factors for an intrinsic continuous density profile with those obtained from density profiles that have been binned into regular spatial increments. The accuracy of the X-ray reflectivity calculations for binned density profiles is defined in terms of the inter-relationships between resolution of the X-ray reflectivity data (i.e. its range in momentum transfer), the chosen bin size and the width of the intrinsic density profile. These factors play a similar role in the application of any structure-factor calculations that involve the use of pixelated density profiles, such as those obtained from iterative phasing algorithms for inverting structures from X-ray reflectivity and coherent diffraction imaging data. Finally, it is shown how simulations of a quartz-water interface can be embedded into an exact description of the bulk phases (including the substrate crystal and the fluid water, below and above the actual interface) to quantitatively reproduce the experimental reflectivity data of a solid-liquid interface.