Natural Quasicrystals

• Main Authors: Luca Bindi, Paul J. Steinhardt, Nan Yao, Peter J. Lu
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Koryak
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.672.9541; http://physics.princeton.edu/%7Esteinh/BindiSCIENCE.pdf

Quasicrystals are solids whose atomic arrangements have symmetries that are forbidden for periodic crystals, including configurations with fivefold symmetry. All examples identified to date have been synthesized in the laboratory under controlled conditions. Here we present evidence of a naturally occurring icosahedral quasicrystal that includes six distinct fivefold symmetry axes. The mineral, an alloy of aluminum, copper, and iron, occurs as micrometer-sized grains associated with crystalline khatyrkite and cupalite in samples reported to have come from the Koryak Mountains in Russia. The results suggest that quasicrystals can form and remain stable under geologic conditions, although there remain open questions as to how this mineral formed naturally. Solids, including naturally forming min-erals, are classified according to the orderand rotational symmetry of their atomic arrangements. Glasses and amorphous solids have disordered arrangements with no exact rota-tional symmetry. Crystals have atomic structures with long-range periodic order that can be de-scribed by a single atom or atomic cluster that repeats at regular intervals. According to the well-known theorems of crystallography derived nearly two centuries ago, the rotational symme-tries of crystals are highly restricted: Two-, three-, four-, and sixfold symmetry axes are allowed, but five-, seven-, and all higher-fold symmetry axes are forbidden. Quasicrystals (1, 2) (short for quasiperiodic crystals) have a more subtle kind of long-range order. In a quasiperiodic structure, the atomic positions along each symmetry axis are described by a sum of two or more periodic functions whose wavelengths have an irrational ratio (inexpressible as a ratio of integers). This difference exempts quasicrystals from the crys-tallographic restrictions: They can exhibit all the rotational symmetries forbidden to crystals, in-cluding fivefold symmetry. Just as square or hex-agonal tilings are commonly used as geometric analogs for periodic crystals, the Penrose tiling ...