A novel real space scattering theory: efficient characterization of colloidal crystals

Recent advances in self-organized 3D ordered structures of submicron particles as colloidal crystals demand a precise quantitative characterization of the produced nano-structures. Small angle scattering is the technique of choice for such a task but a comprehensive quantitative modeling of the measurements is far from being straightforward. We have developed a theory based in the pair distances distribution which take into the account orientational, positional and staking disorder as well as finite size effects. We show also how the radial scattering length density of the constituent particles, essential for a comprehensive modeling of the experimental data, can be estimated from the position of the form factor local minima. The results reduce to sums of analytical functions over the distribution of pair distances and as such, are suitable for easy (automatic) parallelization.