Soccer balls have it; so do virus capsids. It is a property known as icosahedral symmetry – a special type of rotational symmetry held by an icosahedron, the most complicated of the platonic solids. While at small scales, nature loves icosahedral symmetry – small clusters of particles prefer to pack densely with icosahedral symmetry, at large scales, nature abandons icosahedral symmetry. Like trying to tile a bathroom floor with pentagons, icosahedra do not nicely fill space. One way nature has sidestepped this problem is by forming icosahedral quasicrystals. First discovered by Daniel Schechtman in 1984, icosahedral quasicrystals (IQCs) have icosahedral symmetry at all scales by not being periodic in any direction. In other words, a shifted copy will never exactly match the original. IQCs challenged the assumption of generations of scientists as to what it means for atomic matter to be ordered. For this discovery, Dr. Schechtman was awarded the Nobel Prize in 2011.
Why do scientists care about IQCs? The answer lies in the fact that IQCs have almost orientationally uniform properties, thus making them candidates as specialized alloys. While other types of quasicrystals, however, have been discovered to form by many materials across many scales of matter, the IQC has proved elusive, discovered only in intermetallic compounds. Could long-range, complicated atomic interactions be necessary to stabilize this highly symmetric aperiodic form of matter?
Recently a team of researchers from the University of Michigan and Argonne National Laboratory showed this is not the case. Using molecular dynamics simulations, they showed that an IQC can be assembled from a one-component system of particles interacting via a relatively short-ranged isotropic pair potential. These results suggest that local geometric frustration alone is sufficient to stabilize very complex states of matter.
Intriguingly, the discovery of the self-assembled IQC in simulation was one of those serendipitous moments of science. “We were looking for complex structures,” said Carolyn Phillips, recipient of the Aneesur Rahman Postdoctoral Fellowship at Argonne National Laboratory, “but that particular pair potential was an anomaly. We weren’t supposed to be studying it. But, accidentally, we did, and there it was.”
Similar to Dr. Schechtman in 1984, one of the challenges facing the team was to show that what they had found was indeed an IQC and not an imposter. Compared with intermetallic compounds that form IQCs, the material assembled in simulation would be a barely-observable microscopic grain. The researchers began growing as large a sample as their computational resources would let them – 100,000 particles – and showed no degradation of the symmetry. Then, they used information about the sample that was readily available to them but nearly inaccessible to an experiment, the exact physical position of every particle. They used this data to measure properties of the sample and compare them to theoretically predicted properties of an IQC.
First, they showed the presence of phason flips, a rearrangement of the local atomic configuration unique to quasicrystals that leaves the free energy of the system unchanged. Then, using higher-dimensional crystallography, the researchers projected particle positions onto a six-dimensional hypercube lattice. The results showed that the samples had well-formed occupation domains with dodecahedral symmetry at two points in the hyperlattice unit cell. Again, these results were consistent with a high-quality IQC. These results also enabled the team to identify the quasicrystal as being body-centered in six dimensions.
“This was a surprising finding,” said Phillips. “All IQCs reported to date had been either primitive-icosahedral or face-centered icosahedral, never body-centered icosahedral.”
The research has left several questions open for future investigation. Are one-component quasicrystals of types other than body-centered IQCs possible? How are atoms able to arrange themselves rapidly into a long-range ordered configuration without the guidance of a unit cell? Are the IQCs thermodynamically stable?
“The ability to quickly assemble IQCs using a high-performance computer paves the way to begin answering these questions,” said Phillips. “Even further, by using molecular dynamic simulations, we have demonstrated that an IQC can be assembled with a relatively simple isotropic pair potential. We believe that nanoscale experiments can be designed to search for and find these IQCs.”
The paper discussing this research is available on the web:
http://www.nature.com/nmat/journal/v14/n1/full/nmat4152.html
“Computational self-assembly of a one-component icosahedral quasicrystal,” M. Engel, P. F. Damasceno, C. L. Phillips, and S. C. Glotzer, Nature Materials, advance online publication Dec. 8, 2014