1. Study of atomic hopping in quasicrystals
- Author
-
G. Coddens
- Subjects
Physics ,Nuclear and High Energy Physics ,Condensed matter physics ,Icosahedral symmetry ,Lattice (order) ,Quasiperiodic function ,Bravais lattice ,Rotational symmetry ,Quasicrystal ,Hexagonal lattice ,Crystal structure ,Atomic and Molecular Physics, and Optics - Abstract
It is a well-known fact that fivefold rotational symmetry is incompatible with crystalline lattice periodicity. Suppose that a Bravais lattice would contain a regular pentagon (Figure l), then it is possible to construct a smaller pentagon that also belongs to the lattice, as can be seen in Figure 1. This implies that a periodic lattice with fivefold symmetry can not satisfy the Delaunay condition. Thus, it came as a big surprise when Shechtman et al. (1) discovered quasicrystals (QC) (2) that exhibited diffraction patterns with five-fold (icosahedral) symmetry and sharp Bragg peaks characteristic of long-range order. Later, QC with eight-fold, tenfold and twelve-fold 2D symmetry were reported. The origin of this apparent paradox lies in a confusion between the concepts of long-range order and periodicity. Quasiperiodic lattices or tilings, such as illustrated in Figure 2 (for eightfold 2D symmetry), are not periodic but do give rise to diffraction patterns with sharp Bragg peaks due to their und...
- Published
- 1995