Controlled Self-Assembly of Gold Nanotetrahedra into Quasicrystals and Complex Periodic Supracrystals

The self-assembly of shape-anisotropic nanocrystals intolarge-scalestructures is a versatile and scalable approach to creating multifunctionalmaterials. The tetrahedral geometry is ubiquitous in natural and manmadematerials, yet regular tetrahedra present a formidable challenge inunderstanding their self-assembly behavior as they do not tile space.Here, we report diverse supracrystals from gold nanotetrahedra includingthe quasicrystal (QC) and the dimer packing predicted more than adecade ago and hitherto unknown phases. We solve the complex three-dimensional(3D) structure of the QC by a combination of electron microscopy,tomography, and synchrotron X-ray scattering. Nanotetrahedron vertexsharpness, surface ligands, and assembly conditions work in concertto regulate supracrystal structure. We also discover that the surfacecurvature of supracrystals can induce structural changes of the QCtiling and eventually, for small supracrystals with high curvature,stabilize a hexagonal approximant. Our findings bridge the gap betweencomputational design and experimental realization of soft matter assembliesand demonstrate the importance of accurate control over nanocrystalattributes and the assembly conditions to realize increasingly complexnanopolyhedron supracrystals.