# Paper:DNA-nanoparticle superlattices formed from anisotropic building blocks

This is a summary/discussion of the results from:

- Matthew R. Jones, Robert J. Macfarlane, Byeongdu Lee, Jian Zhang, Kaylie L. Young, Andrew J. Senesi, and Chad A. Mirkin DNA-nanoparticle superlattices formed from anisotropic building blocks
*Nature Materials***2010**,*9*, 913-917 doi: 10.1038/nmat2870

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:

- Pyramid
- Cube
- Cylinder
- Octahedron
- Rhombic dodecahedron (RD)
- Triangular prism