Numerically efficient real space theory of scattering from colloidal crystals

Abstract

The production of high-quality colloidal crystals demands precise quantitative characterization of their nanostructures. While small-angle radiation scattering is the technique of choice, a procedure for a comprehensive quantitative modeling of the data is still pending. A novel theory based on the pertinent radial pair distribution which takes into account orientational, positional, stacking disorder and grain effects is developed here. We also show how the scattering length density of the particles can be estimated from the positions of minima in the form factor. The obtained results can be cast as sums of analytical functions over the distribution function and, as such, are suitable for easy (automatic) parallelization. On the experimental side, we report on a strong extinction effect coming from grazing incidence specular reflection that we have been able to model analytically. © 2011 American Chemical Society.