Abstract
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.