Paper:DNA-nanoparticle superlattices formed from anisotropic building blocks

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This is a summary/discussion of the results from:

This paper describes the formation of nanoparticle superlattices from anisotropic nano-objects. In the Supplementary Information information, the authors describe how to model x-ray scattering data from lattices of anisotropic nanoparticles.

Summary of Mathematics

Randomly oriented crystals give scattering intensity:

Where the structure factor is defined by an orientational average (randomly oriented crystal(s)):

and can be computed by:

Where c is a constant, and L is the peak shape; such as:

Note that the presented form of is closely-related to the lattice factor. The (isotropic) form factor intensity is an average over all possible particle orientations:

The form factor amplitude is computed via:

Form Factors

The SI also provides form factors for a variety of nano-object shapes: