Quasicrystals: A New Class of Ordered Structures

1984/12/24 by Dov Levine, Paul J. Steinhardt · 2,098 citations
Chemistry · Materials Science · Mathematics · #Chemistry #Computer science #Condensed matter physics #Crystal (programming language) #Crystallography #Diffraction #Geometry #Homogeneous space #Icosahedral symmetry #Ideal (ethics) #Law #Materials science #Mathematics #Physics #Quantum mechanics #Quasicrystal #Quasicrystal Structures and Properties #Quasiperiodic function #Rotation (mathematics) #Symmetry (geometry) #Theoretical physics #Translational symmetry #X-ray Diffraction in Crystallography

paper · pdf · doi:10.1103/physrevlett.53.2477

published in Physical Review Letters 53(26), 2477-2480 (American Physical Society)

openalex publication_date 1984/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A quasicrystal is the natural extension of the notion of a crystal to structures with quasiperiodic, rather than periodic, translational order. We classify two- and three-dimensional quasicrystals by their symmetry under rotation and show that many disallowed crystal symmetries are allowed quasicrystal symmetries. We analytically compute the diffraction pattern of an ideal quasicrystal and show that the recently observed electron-diffraction pattern of an Al-Mn alloy is closely related to that of an icosahedral quasicrystal.

Citations

• Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
• Complex alloy structures regarded as sphere packings. I. Definitions and basic principles
• Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures
• Mathematical Games

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• Quasicrystal [wikipedia]