materiały: Quasicrystal

Evidence: 100 • authority: 72

A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. The discovery changed our understanding of crystalline order, as it demonstrated that the presence of long-range order is not necessarily associated with periodicity. While crystals, according to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction pattern of quasicrystals shows sharp peaks with other symmetry orders—for instance, five-fold. Aperiodic tilings were discovered by mathematicians in the ear…

Evidence: 72 • authority: 72

The crystallographic restriction theorem characterizes the possible orders of rotational symmetry in a lattice. In 2 or 3 dimensions, the rotational symmetries are restricted to 2-fold, 3-fold, 4-fold, and 6-fold. The theorem's name comes from geological crystals, whose rotational symmetries are generally limited to these same values. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; these were not discovered until 1982 by Dan Shechtman. Crystals are modeled as discrete lattices, generated by a list of independent finite translations (Coxeter 1989). Because discreteness requires that the spacings between lattice points have a lower bound, the group…

Evidence: 38 • authority: 72

crystal classes by using the crystallographic restriction , consistent with Haüy's laws, that only 2, 3, 4 and 6- fold rotational axes are permitted. 1830 -

Evidence: 33 • authority: 80

Removal of Conflicting Molecular Symmetries Restores a Hexagonal Array of Six-Fold Phenyl Embraces in a bis(Trityl)-Containing Compound. I. Crystals of 1, 1, 1, 6, 6, 6-Hexaphenyl-2, 4-hexadiyne

Evidence: — • authority: 72

The law of symmetry is a law in the field of crystallography concerning crystal structure. The law states that all crystals of the same substance possess the same elements of symmetry. The law is also named the law of constancy of symmetry, Haüy's law or the third law of crystallography.

Evidence: — • authority: 72

A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals gives rise to X-ray diffraction and that the atomic lattices (crystal structure) of semiconductors affect their conductivity of electrons. Photonic crystals occur in nature in the form of structural coloration and animal reflectors, and, as artificially produced, promise to be useful in a range of applications. Photonic crystals can be fabricated for one, two, or three dimensions. One-dimensional photonic crystals can be made of thin film layers deposited on each other. Two-dimensional ones can be made…

Evidence: — • authority: 72

A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated them in the 1970s. There are several variants of Penrose tilings with different tile shapes. The original form of Penrose tiling used tiles of four different shapes, but this was later reduced to only two shapes: either two differ…

Evidence: — • authority: 80

A rigorous proof on the crystallographic restriction theorem

Evidence: — • authority: 80

Quasicrystalline overlayers with crystallographic orders of rotational symmetry

Evidence: — • authority: 88

Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry. Micelles are the simplest example of self-assembly found in nature. As many other colloids, they can self-assemble in aqueous solution to form ordered periodic structures. These structures so far all exhibited classical crystallographic symmetries. Here we report that micelles in solution can self-assemble into quasicrystalline phases. We observe phases with 12-fold and 18-fold diffraction symmetry. Colloidal water-based quasicrystals are physically and chemically very simple systems. Macroscopic monodomain samples of centimeter dimension can be easily prepared. Phase transitions between the fcc phase and the two quasicr…

Evidence: — • authority: 88

DYNAMIC CRACK PROPAGATION IN FIVE-FOLD SYMMETRY QUASICRYSTALS. Based on the elasto-/hydro-dynamic model the dynamic properties of the five-fold symmetry quasicrystals with point groups 5, [Formula: see text] are investigated, by using the finite difference method. The problems including dynamic initiation of crack growth and fast crack propagation of this material are studied. The results show that the phonon–phason coupling effect plays an important role to the dynamic properties of the quasicrystals.

Evidence: — • authority: 80

Five-fold symmetry: Millimetre-sized quasicrystals grown from aluminium alloy