Abstract
The sensational discovery ten years ago of quasicrystals with fivefold rotational symmetry and no periodic translation order made a strong impact on all solid state sciences based on crystals and crystallography, including metallurgy, materials science, chemistry, physics, mineralogy, etc. After a decennium of intensive study, many important aspects of this new class of materials and a new kind of ordered state with so-called ‘forbidden’ symmetry and quasiperiodicity have been made clear. The time is perhaps ripe to review the main advances in quasicrystal research made in the past ten years. The topics discussed in the present review are:(1) Quasicrystal or fivefold twins? (2) Why fivefold symmetry? (3) Why quasiperiodicity? (4) Stable quasicrystals; (5) Crystalline approximants.
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