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Creating a self-assembling quasicrystal

Creating a self-assembling quasicrystal

A quasiperiodic crystal, also known as a quasicrystal, is an organized but nonperiodic structure. A quasicrystalline design may occupy all available space indefinitely, although it lacks translational symmetry. While crystals can only have two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals reveals distinct peaks with additional symmetry orders, such as five-fold.

Metal alloys, generally aluminum with one or more other metals, were the first quasicrystalline materials found. These materials have thus far been used as nonstick coatings for frying pans and anti-corrosive coatings for surgical equipment. However, there has been a lot of interest in developing new forms of quasicrystal materials, such as those produced from self-assembling nanoparticles.

Brown University researchers have described a quasicrystalline superlattice (QC-SL)  that self-assembles from a single type of nanoparticle building block, a truncated tetrahedral quantum dots (or TTQD) . According to the researchers, this is the first definitive observation of a quasicrystalline superlattice produced from a single component. The study sheds fresh light on how these unusual crystal-like formations form.

“Single-component quasicrystal lattices have been predicted mathematically and in computer simulations, but hadn’t been demonstrated before this,” said Ou Chen, an assistant professor of chemistry at Brown and the paper’s senior author. “It’s a fundamentally new type of quasicrystal, and we’ve been able to figure out the rules for making it, which will be useful in the continued study of quasicrystal structures.”

QC order generated through a flexible polygon tiling rule.

Much of Chen’s research has focused on connecting the nanoscale and macroscale worlds by constructing superstructures out of nanoparticle building pieces. He created a new form of nanoparticle building block, a tetrahedral (pyramid-shaped) quantum dot, around two years ago. Whereas most research on nanoparticle architectures has used spherical particles, Chen’s tetrahedra can pack more densely and potentially produce more complex and resilient structures.

Chen and his colleagues were curious about the shapes the particles would form when formed on top of a liquid surface, which offers the particles additional degrees of freedom while assembling themselves. The team was astounded to discover that the final structure was a quasicrystalline lattice.

The video shows the structure of a quasicrystalline superlattice made from single-component nanoparticle building blocks. The nanoparticles form decagons, which stitch together to form a lattice. In order to fill in space in the lattice, the decagons flex into polygons with five, six, seven eight or nine sides. In the video, the large red dots show the center of the polygons. The lines indicate the distance from one polygon center to the closest and next-closest polygon center. The smaller red dots denote the number of sides a polygon has. Credit: Chen Lab / Brown University

“When I realized the pattern I was seeing was a quasicrystal, I emailed Ou and said ‘I think I’ve found something super-great,'” said Yasutaka Nagaoka, a postdoctoral scholar in Chen’s lab and the lead author of the new paper. “It was really exciting.”

The particles were formed into discrete decagons (10-sided polygons), which stitched themselves together to form a quasicrystal lattice with 10-fold rotational symmetry, the researchers demonstrated using transmission electron microscopy. The 10-fold symmetry, which is prohibited in normal crystals, was a sign of a quasicrystalline structure.

 10-fold QC-SLs assembled from TTQDs.
Tomography reconstruction of the QC-SL with a double-decker stacking.
 Schematic representation of the TTQD assembly pathways.

The researchers were also able to deduce the “laws” that guided the formation of their structure. While decagons are the fundamental units of the structure, they are not – and cannot be – the sole units. Creating a quasicrystal is similar to tiling a floor. The tiles must fit together in such a way that they cover the whole floor without gaps. That cannot be done with simple decagons since there is no way to put them together without gaps. Other shapes are required to fill the gaps.

The same is true for this novel quasicrystal structure: secondary “tiles” that can cover the gaps between decagons are required. The researchers discovered that the flexible edges of the decagons are what allowed their structure to operate. One or more of their points might be smoothed off if required. They may then transform into polygons with nine, eight, seven, six, or five sides, depending on what was needed to fill the gap between decagons.

“These decagons are in this confined space that they have to share peacefully,” Chen said. “So they do it by making their edges flexible when they need to.”

The researchers were able to design a new method for creating quasicrystals based on this discovery, which they term the “flexible polygon tiling rule.” Chen believes that this rule will be beneficial in future research into the relatively new field of quasicrystals.

Single-component quasicrystalline nanocrystal superlattices through flexible polygon tiling rule, Yasutaka Nagaoka, Hua Zhu, Dennis Eggert, Ou Chen

Published: December 2018
DOI: 10.1126/science.aav0790

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