The original version of this story appeared in Quanta Magazine.

Since their discovery in 1982, exotic materials known as quasicrystals have bedeviled physicists and chemists. Their atoms arrange themselves into chains of pentagons, decagons, and other shapes to form patterns that never quite repeat. These patterns seem to defy physical laws and intuition. How can atoms possibly “know” how to form elaborate nonrepeating arrangements without an advanced understanding of mathematics?

“Quasicrystals are one of those things that as a materials scientist, when you first learn about them, you’re like, ‘That’s crazy,’” said Wenhao Sun, a materials scientist at the University of Michigan.

Recently, though, a spate of results has peeled back some of their secrets. In one study, Sun and collaborators adapted a method for studying crystals to determine that at least some quasicrystals are thermodynamically stable—their atoms won’t settle into a lower-energy arrangement. This finding helps explain how and why quasicrystals form. A second study has yielded a new way to engineer quasicrystals and observe them in the process of forming. And a third research group has logged previously unknown properties of these unusual materials.

Historically, quasicrystals have been challenging to create and characterize.

“There’s no doubt that they have interesting properties,” said Sharon Glotzer, a computational physicist who is also based at the University of Michigan but was not involved with this work. “But being able to make them in bulk, to scale them up, at an industrial level—[that] hasn’t felt possible, but I think that this will start to show us how to do it reproducibly.”

Vikram Gavini, Sambit Das, Woohyeon Baek, Wenhao Sun, and Shibo Tan hold examples of geometric shapes that appear in quasicrystals. The University of Michigan researchers have shown that at least some quasicrystals are thermodynamically stable.

Photograph: Marcin Szczepanski Michigan Engineering

‘Forbidden’ Symmetries

Nearly a decade before the Israeli physicist Dan Shechtman discovered the first examples of quasicrystals in the lab, the British mathematical physicist Roger Penrose thought up the “quasiperiodic”—almost but not quite repeating—patterns that would manifest in these materials.

Penrose developed sets of tiles that could cover an infinite plane with no gaps or overlaps, in patterns that do not, and cannot, repeat. Unlike tessellations made of triangles, rectangles, and hexagons—shapes that are symmetric across two, three, four or six axes, and which tile space in periodic patterns—Penrose tilings have “forbidden” fivefold symmetry. The tiles form pentagonal arrangements, yet pentagons can’t fit snugly side by side to tile the plane. So, whereas the tiles align along five axes and tessellate endlessly, different sections of the pattern only look similar; exact repetition is impossible. Penrose’s quasiperiodic tilings made the cover of Scientific American in 1977, five years before they made the jump from pure mathematics to the real world.