Original version With this story appeared in Quanta Magazine.
Since their discovery in 1982, exotic materials called quasicrystals have plagued physicists and chemists. Their atoms arrange themselves in chains of pentagons, decagons and other shapes, creating patterns that are never repeated. These patterns seem to defy physical laws and intuition. How can atoms “know” how to form complicated, non-repeating arrangements without advanced understanding of mathematics?
“Quasicrystals are one of those things that as a materials scientist, when you first learn about them, you think, ‘This is crazy,’” he said Wenhao Sunmaterials scientist from the University of Michigan.
But recently, a series of results have revealed some of their secrets. IN one studySun and colleagues adapted a method of studying crystals to determine whether at least some quasicrystals are thermodynamically stable – their atoms will not arrange themselves in a lower-energy arrangement. This discovery helps explain how and why quasicrystals form. AND second examination enabled a modern way to construct quasicrystals and observe them as they form. A third research group has already done this logged in previously unknown properties of these unusual materials.
Historically, creating and characterizing quasicrystals has been challenging.
“There is no doubt that they have interesting properties,” he said Sharon Glotzera computational physicist who also works at the University of Michigan but was not involved in this work. “But being able to mass produce them and scale them up at an industrial level…[that] didn’t seem possible, but I think this will help us start to show how to do it in a repeatable way.”
“Forbidden” symmetries
Almost a decade before the Israeli physicist Dan Shechtman discovered the first examples of quasicrystals in the laboratory, British mathematical physicist Roger Penrose invented 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 without gaps or overlaps, creating patterns that do not and cannot be repeated. Unlike tessellations composed of triangles, rectangles and hexagons – shapes that are symmetrical on two, three, four or six axes and whose spacing is arranged in periodic patterns – Penrose tiles have a “forbidden” fivefold symmetry. The tiles form pentagonal arrangements, but the pentagons cannot fit tightly together to cover the plane. Thus, while the tiles are arranged along five axes and form an infinite mosaic, the different sections of the pattern only look similar; exact repetition is impossible. Penrose’s quasiperiodic stories made the cover Scientific American in 1977, five years before the transition from pure mathematics to the real world.