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Quasicrystals are solid materials that are ordered but not periodic. Unlike traditional crystals, which have atoms arranged in a repeating pattern, quasicrystals have atomic arrangements that lack translational symmetry. This means that while there is a definite pattern, it does not repeat itself exactly at regular intervals.

The discovery of quasicrystals in 1982 by Dan Shechtman revolutionized materials science. Prior to this, it was widely believed that crystalline solids could only possess rotational symmetries of 2-fold, 3-fold, 4-fold, or 6-fold. Shechtman's observation of 5-fold symmetry in an electron diffraction pattern of an aluminum-manganese alloy challenged this fundamental understanding.

The structure of quasicrystals can be described using aperiodic order. They often exhibit symmetries that are forbidden in periodic crystals, such as 5-fold, 8-fold, 10-fold, or 12-fold rotational symmetry. These structures can be generated by mathematical processes like cut-and-project methods or Penrose tiling.

Quasicrystals possess unique physical and chemical properties that differ significantly from their crystalline counterparts. These include low friction, high hardness, low adhesion, and resistance to corrosion. These properties make them attractive for various applications, such as protective coatings for tools, non-stick cookware, and electrical insulation. Research continues to explore the potential of quasicrystals in fields like catalysis and medicine.