Every crystal must have a periodically repeating atomic pattern.

A familiar crystal can be pictured as a three-dimensional wallpaper pattern: one small arrangement of atoms repeats again and again through the material. For a long time, that kind of periodic repetition was part of the definition of a crystal.

In 1982, Dan Shechtman examined an aluminium–manganese alloy using electron diffraction. Electrons scattered from the atoms produced a pattern that revealed how regularly those atoms were arranged. Shechtman saw sharp, orderly spots, so the material clearly had strong internal order. But the pattern had a symmetry that an ordinary repeating crystal could not produce.

The result was initially difficult to accept because it seemed to violate the rules of crystallography. Other experiments reproduced it, and researchers showed that atoms can form structures that are ordered across long distances without ever repeating the same pattern periodically.

These materials became known as quasicrystals. They are not disordered like glass; their atoms follow a precise arrangement. The discovery changed the definition of a crystal by showing that long-range order does not require periodic repetition.