Metallic Phase with Long-Range Orientational Order and No Translational Symmetry

Abstract

We have observed a metallic solid (Al -14-at. /o-Mn) with long-range orientationai order, but with icosahedral point group symmetry, which is inconsistent with lattice translations. Its diffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice.

Inhomogeneous chiral condensates

“…Therefore they cannot be ordinary crystals, and it was suggested in Ref. [123] that they might belong to the class of "quasi-crystals" [186,187] which, besides crystals and amorphous structures, is known from condensed matter physics as a third category of solids.…”

Aperiodic Spin State Ordering of Bistable Molecules and Its Photoinduced Erasing

“…On the one hand, macroscopic ordering is manifested by the appearance of regular patterns, which in some cases never repeat themselves periodically in 3D space but only in a higher dimension space: this so-called aperiodicity 5,6,7 plays a central role in the structure and physical properties of materials as diverse as quasicrystals 8 , charge-density 1 and spin-density waves 9,10 , or new superconductors 11 for instance. On the other hand, some materials exhibit more or less cooperative switching between bi-stable functional molecular states 12,13,14,15 , controllable with temperature, pressure, light… The relationship between molecular bistability in the solid state and aperiodicity has not been considered so far.…”

Structure determination of quasicrystals

“…Composite structures (intergrowth or inclusion compounds) correspond to the case where two icommensurate sublattices interact. Quasicrystals, discovered by Shechtman in 1982 [1], have a diffraction pattern whose symmetry is incompatible with lattice translation symmetry, for instance the icosahedral symmetry.…”