Abstract
Quasicrystals are materials whose structure cannot be understood within classical crystallography rules. Quasiperiodic lattices, with long-range order but without periodic translations in three dimensions, are shown to describe correctly these new structures. They are also derivable from structures that are periodic in a higher dimensional space. Neutron diffraction patterns, with contrast variation effects, have recently provided reasonable insight into the description of one icosahedral quasicrystal so that it is now possible to say where the atoms should be in a perfect quasicrystal.
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