Crystals can be impossible

Quasicrystals show sharp diffraction and a symmetry — including five-fold — that classical crystallography had proved a repeating lattice cannot have.

A classical crystal repeats a unit cell by translation. That constraint forbids icosahedral and five-fold axes. Shechtman’s aluminium–manganese alloy, rapidly cooled, diffracted like a crystal and showed ten-fold patterns. He was asked to leave his group. In 2011 he received the Nobel Prize.

The order is quasiperiodic: it never quite repeats, and it never quite loses its rules, the way a Penrose tiling covers a plane with two tiles and no translational repeat. Atoms can do that. ‘Crystal’ had to grow a new definition. Nature had already published one in a metal.