quasikrystals

Quasikrystals are crystalline materials that possess atomic arrangements lacking translational periodicity but exhibiting long-range orientational order. Unlike conventional crystals, which have repeating patterns in a specific direction, quasikrystals do not repeat in a simple, linear fashion. However, they do display symmetries that are forbidden in classical crystallography, such as five-fold or ten-fold rotational symmetry. This unique structure was first discovered by Dan Shechtman in 1982, a finding that challenged existing paradigms and earned him the Nobel Prize in Chemistry in 2011.

The atomic structure of quasikrystals can be understood as being composed of interpenetrating lattices that are incommensurate with each other. This means their repeating units do not align perfectly. Common examples include alloys of aluminum with transition metals like manganese, iron, or cobalt. Their discovery has opened up new avenues in materials science, leading to the development of materials with unusual properties. For instance, some quasikrystals exhibit exceptional hardness, low friction, and high resistance to heat and oxidation, making them potentially useful in coatings, cutting tools, and even specialized cookware. The mathematical description of quasikrystals often involves concepts from higher-dimensional crystallography and aperiodic tilings, such as the Penrose tiling, which demonstrates a similar lack of periodicity with ordered structure.