# Quasicrystalline order in self-assembled binary nanoparticle superlattices

Original entry: Sujit S. Datta, APPHY 225, Fall 2009.

## Reference

D. V. Talapin, E. V. Schevchenko, M. I. Bodnarchuk, X. Ye, J. Chen, and C. B. Murray, *Nature* **461,** 964 (2009).

## Keywords

quasicrystal, self-assembly, packing

## Key Points

Equilibrium phase transformations are ubiquitous in nature. Because of their complexity, it is often useful to focus on the 'simple' case of hard spheres, whose equilibrium phase diagram is dictated purely on entropic grounds. For monodisperse Brownian spheres with purely hard-sphere interactions, volume fraction is the only control parameter: for small volume fractions, the system is fluid-like; for intermediate volume fractions (between ~49% and 55%), a fluid and crystal phase coexist; for volume fractions larger than ~55%, up to the maximum FCC packing fraction of ~74%, the system is crystalline.