The 2011 Nobel Prize for Chemistry has been awarded to Dan Shechtman of Technion – Israel Institute of Technology, in Haifa for work that has a lot to do with math as well as chemistry.

The Nobel committee honored Shechtman for discovering natural ‘quasicrystals’ (‘almost-crystals’).

True crystals are materials built up in a repeating pattern. As every chemist learns, a true crystal can only have certain kinds of symmetry — two-, three-, four-  or six-fold. In other words, you can build a cubic crystal out of a lot of small cubes, or a lot of hexagons. But you can’t build a real crystal out of a symmetric shape with five, seven or eight sides.

At left: A quasicrystal with five-fold symmetry (Wikimedia Commons)

Quasicrystals were first discovered as mathematical objects by physicist Roger Penrose in the 1970s. They were regarded as pure, almost ‘recreational’ math, said Greg Kuperberg, a professor of mathematics at UC Davis.

“They were studied as pure math or just for fun,” Kuperberg said. Indeed, Kuperberg likes quasicrystals so much he put them on his bathroom floor — this picture shows a pattern with eight-fold symmetry.

In 1982, Shechtman discovered what appeared to be a crystal of a real compound, an alloy of aluminum and manganese, with five-fold symmetry. The atoms in the material were arranged in such a way that they could almost, but not quite, form a repeating pattern.

“The chemists had not known that these ‘almost crystals’ could exist, but Penrose and others had shown that they exist in pure mathematics,” Kuperberg said.

Since then, other quasicrystals have been discovered, both in the lab and in nature, with different levels of symmetry. Researchers are experimenting with these materials to see if they can bring new, useful properties to materials.

In another twist, it turns out that Penrose was anticipated several hundred years earlier by Islamic master masons. For example, the spectacular tiling of the Darb-i Imam shrine in Iran, built in 1453, turns out to be based on a quasiperiodic pattern that is symmetrical but never repeats. Researchers have discovered plans dating back as far as the 13th century setting out how to make the patterns.

“These would have been created by artists who were very good mathematicians,” Kuperberg said. But at some point, the knowledge behind these patterns was lost until being rediscovered in the 20th century.

(Picture credit: K. Dudley and M. Elliff)