# 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. For binary systems consisting of particles of two different sizes, the equilibrium phase diagram is much richer (e.g. see "Entropy-driven formation of a superlattice in a hard-sphere binary mixture" by Daan Frenkel's group in 2003), with three control parameters now - the volume fraction of each size particle, and the relative size difference between them. Further complexity develops in the equilibrium phase diagram with deviations from hard sphere behavior, such as the incorporation of van der Waals, Coulombic, and dipolar interactions. Different crystalline phases of nanoparticle systems have been experimentally observed (and theoretically predicted) as a result. This work is the first to demonstrate an equilibrium quasicrystalline phase, with clues suggesting that the phase is solely a general result of entropy, *not* the interparticle interactions.

The nanoparticles used in this study are made of two different materials, and have two different sizes, respectively (with size ratio ~2.7:1). Because of their surface chemistry, they do not aggregate due to van der Waals interactions, but have additional short range steric repulsions. Thus, the key control parameter in this system is the relative composition of the different nanoparticle components. Consistent with previous work, Talapin et al. found that "normal" crystalline superlattices of different structures form when one component dominates the composition of the system. These themselves have intriguing structures, resembling regular 2D Archimedean tilings of squares and triangles. More surprisingly, Talapin et al. found that for intermediate composition ranges, superlattices with *quasicrystalline* order formed -- specifically, the superlattices consisting of square and triangle packing motifs organized into a dodecagonal quasicrystal (possessing 12-fold rotational symmetry, and no translational symmetry).

superlattices crystals, etc. by relative composition slow evaporation saw dodecagonal quasicrystal! interface, wetting layer

- IN PROGRESS*