Crystals and the cosmos might not seem like they have that much in common unless you're a new age amethyst junkie, but studying the mysteries of space is exactly how cosmologists discovered a new kind of crystal structure.
Latham Boyle, a cosmologist at the Perimeter Institute for for Theoretical Physics (PI) in Waterloo, Ontario, was trying to figure out how to design a network of four orbiting satellites. The goal: to use them as detectors to study gravitational waves—a notoriously elusive cosmological phenomenon. During his work, Boyle discovered a kind of symmetry based on repeated action called "choreographic symmetry." If you looked at a snapshot of the orbiting satellites, their arrangement would not look symmetrical but a "movie" view that followed them through time would reveal a highly precise and symmetric series of actions.
"If the satellites themselves—the building blocks of the orbit—are dynamical and [moving] in time, then the appropriate symmetry to go with that should be a sort of dynamical symmetry," Boyle said. "Very surprisingly, not only did this arrangement have the same amount of symmetry as a static tetrahedron, but it had even more symmetry."
Boyle had stumbled upon a new kind of mathematical object. With the help of his PI colleague Kendrick Smith, Boyle decided to tease out the implications of this discovery in the realm of crystallography. A paper describing their work is available on the ArXiv preprint server.
To be clear, Boyle and Smith are not saying that satellites flying around Earth are an actual crystal. The idea is that this particular way of arranging four artificial satellites in orbit is how this theoretical crystal would look at the atomic level. Its atoms actually move in time. Like the satellites, if you viewed them as a static image, they would look asymmetrical, but a "movie" view would reveal highly choreographed atomic movements. It's all theoretical at the moment, however.
Crystals are commonly understood as being composed of lattices made up of static atoms connected by electrical bonds. Ideal mathematical crystals have perfect atomic arrangements, making them great for futuristic endeavours like studying quantum communication. But another kind of crystal may exist—if not in nature, then as a mathematical concept—that doesn't rely on static arrangements of atoms or molecules. Instead, the kind of symmetry in these crystals would be dynamic much like Boyle's theoretical arrangement of satellites. These crystals—and the understanding of their dynamic structure—could open up new avenues of scientific inquiry.
For example, Pennsylvania State University researchers are currently using the theoretical concept of "anticrystals," crystals in a state of perfect disorder, to discover new, more efficient semiconductors. A new form of crystal cobalt salt developed by researchers at the University of Southern Denmark that can suck up oxygen and release it could allow us to breathe underwater for longer periods.
"We don't really know what the killer app for the idea is yet," said Boyle. "The suggestion that it could be the way atoms arrange themselves in actual, physical crystals is quite speculative—that's one guess as to how this formation could manifest. We don't really know if they exist in nature or not, but there is an experimental test you can do to find out if they're out there and how the atoms are doing their dance."
"I don't know whether it is difficult, or impossible, or easy to make such things in the lab"
Scientists in the past may have not known how to properly detect these new crystals, Boyle said, using methods like Bragg diffraction. In Bragg diffraction experiments, researchers shoot beams—X-rays or electrons, for example—at a crystal to project its structural pattern on a screen. The secret to detecting one of Boyle and Smith's choreographically symmetrical crystals could lie in measuring the frequency of the beam before and after it exits the crystal.
"When the particles are sitting still and you shoot a beam in at a certain frequency, it exits at the same frequency that you sent it in," Boyle explained. "Nothing interesting happens to the frequency, and so nobody measures it in a diffraction experiment. They just ignore it usually. We find instead that in these choreographic crystals that if you shine a beam in, the beam that comes out on the screen will have its frequency shifted up or down a little bit."
There is hope for Boyle, Smith, and other crystal-obsessed scientists—new crystal varieties have previously made the leap from speculation to reality.
In the 1970s, mathematician Roger Penrose invented a crystal structure now known as the "Penrose tiling"—a kind of tiling that can never form a repeating pattern. At the time, it was considered a mere mathematical curiosity. In the 1980s, however, materials scientist Dan Shechtman observed the pattern in what are known as quasicrystals in a lab environment using a diffraction experiment. He received the 2011 Nobel Prize in Chemistry for his work. In 2012, Princeton researchers discovered quasicrystal structures in a chunk of meteorite in Russia, confirming their existence in nature.
The ultimate significance of Boyle and Smith's discovery, and whether or not it will have wide-reaching implications for everything from data transfer to gravitational wave detection, will likely depend on whether their theoretical crystal structure is borne out in the lab or in nature.
"I don't know which way it will go—I don't know whether it is difficult, or impossible, or easy to make such things in the lab," said Boyle. "But I hope it is possible."