The most complicated crystal structure ever produced in a computer simulation has been achieved by researchers at the University of Michigan. They say the findings help demonstrate how complexity can emerge from simple rules.
The “icosahedral quasicrystal” they simulated looks ordered to the eye, but has no repeating pattern. At the same time, it’s symmetric when rotated, like a soccer ball with five-fold and six-fold patches. This property, called icosahedral symmetry, is frequently found on small scales around a single point. It’s in virus shells or buckyballs – molecules of 60 carbon atoms. But it is forbidden in a conventional crystal. Like trying to tile a bathroom floor with pentagons, icosahedra do not nicely fill space, said Michael Engel, a research investigator in the Department of Chemical Engineering and first author of a paper on the findings published in Nature Materials.
“An icosahedral quasicrystal is Nature’s way of achieving icosahedral symmetry in the bulk. This is only possible by giving up periodicity, which means order by repetition. The result is a highly complicated structure,” Engel said. Engel created an interactive visualization where visitors can explore the crystal.
Icosahedral quasicrystals are commonly found in metal alloys. The strange solids earned the chemist who discovered them more than 30 years ago a Nobel Prize. But engineers are still searching for efficient ways to make them with other materials. Due to their high symmetry under rotation, they can have a property called a “photonic band gap.” A photonic bandgap occurs when the spacing between the particles is similar to that of light. When particles are arranged in this way, as they are in this quasicrystal, they could trap and route light coming from all directions.
“If icosahedral quasicrystals could be made from nano- and micro-meter sized particles, they could be useful in a variety of applications including communication and display technologies, and even camouflage,” said Sharon Glotzer, the Stuart W Churchill Collegiate Professor of Chemical Engineering. Glotzer is also a professor of Materials Science and Engineering, Macromolecular Science & Engineering, and Physics in the College of Literature, Science and the Arts.
While these applications are tantalizing, they’re very much speculation. The researchers say the most exciting aspect of the findings is the insight they provide into how icosahedral quasicrystals form.
“When researchers study quasicrystals in the lab, they typically lack direct information about where the atoms are. They look at how the materials scatter light to figure that out. No one has ever gotten one with icosahedral symmetry to self-assemble thermodynamically in a computer model that’s not built by hand, and researchers have been trying for decades,” Glotzer said.
A conventional crystal forms one atom at a time, then column-by-column, and finally layer-by-layer, Engel said. This process is not possible in more exotic solids.
“There has recently been a swirl of activity in the field of crystallography with the goal to understand what is order, where are the limits, and how can we control it,” Engel said. “The simulation will allow researchers for the first time to observe how icosahedral symmetry develops.”
The team discovered the quasicrystal by accident. “Although we are always on the lookout for icosahedral quasicrystals in our work, without success, in this case we were trying to engineer particle interactions for a different sort of structure. When the quasicrystal appeared in the simulations, we were stunned,” said Pablo Damasceno, a graduate student in chemical engineering.
The U-M simulation was done using only one type of particle, which is unique. Typically, two or even three atomic elements are required to achieve a quasicrystal structure.
Even though the end product showed long-range order, the particles only interacted with those up to three particle-distances away. When the researchers looked closer, they found that the Golden Ratio governed those interactions. The Golden Ratio, which is about 1.61, is a mathematically and artistically important number that was first studied by the ancient Greeks. It’s related to the Fibonacci Sequence – the simple progression of numbers beginning with 0 and 1 in which the next number is the sum of the previous two – so 0, 1, 1, 2, 3, 5, 8, 13, etc. It’s visible in the arrangement of petals in flowers, seeds in a pinecone, branches in trees and spirals of nautilus shells, for example.
“These findings help answer fundamental questions that are important in all of nature: How do you get really complex arrangements of atoms and molecules from essentially local information? This is a beautiful example of something incredibly rich in structure emerging from very simple rules,” Glotzer said.
A paper on the findings titled “Computational self-assembly of a one-component icosahedral quasicrystal” is published online in Nature Materials. The research was funded by the U.S. Army Research Office, the Department of Defense, and the National Science Foundation.