Quasiperiodic structures, or quasicrystals, because of their unique ordering of atoms and a lack of periodicity, possess remarkable crystallographic, physical and optical properties not present in regular crystals.
Figure Caption: Two-dimensional Penrose type quasicrystal made using only two tile shapes: a thick rhomb and a thin rhomb. The structure proposed by Roger Penrose lacks translational symmetry and exhibits five-fold rotational symmetry not allowed in regular crystals.
Periodic structures are known for their predictable symmetry, both rotational and translational, and they were believed to be the only kinds of repeating structures that could occur in nature. From basic solid state physics, these structures are only allowed to exhibit strict 2, 3, 4 or 6-fold rotational symmetry, i.e., upon rotation by a certain angle about a crystallographic axis, the shape would still look identical upon each rotation. It was not believed that there could be a structure that existed which violated these four symmetry rules. Random systems, the other big area of research, looks at amorphous or disordered media like gases.
The introduction of quasicrystals – an ordered structure that lacks periodicity, exhibits some properties similar to periodic structures (such as atomic ordering over large-length scales) while violates rotational symmetry rules associated with them (i.e., a quasicrystal can exhibit 5 or 8 fold rotational symmetry) – was an area initially met with resistance from the research community. Agrawal explores this transition from skepticism to the ultimate acceptance by a growing number of researchers exploring the potential of these unique structures.
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