Quasicrystal

In quasicrystals, the atoms or molecules in an ordered but aperiodic structure are arranged. Experimentally, they were discovered in 1982 by Daniel Shechtman, for the 2011 Nobel Prize in Chemistry was awarded. On its discovery, the name goes back Shechtmanit. Mathematically these structures were first described by Peter Kramer and Roberto Neri in 1984. Essential for their structure elucidation also wore Paul Steinhardt and Dov Levine 1984.

History

1984 Dan Shechtman discovered in the crystal structure of a rapidly cooled aluminum -manganese alloy (14% manganese) an unusual structure. This had the point group symmetry and hence the symmetry of an icosahedron. This is very unusual for crystalline substances, since this symmetry no lattice displacements are possible and thus no periodic structure, as necessary for the definition of a crystal, is available. Mathematically icosahedral quasicrystals were first designed by Peter Kramer and Roberto Neri in 1984. Later Dov Levine and Paul Joseph Steinhardt coined for this new phase type the term " quasicrystal " and compared the data found in the structure analysis of mathematical models.

An early pioneer of quasicrystals was Alan Mackay in the UK, who published a work on icosahedral sphere packings in 1962 ( a pack of five-fold symmetry ) and Penrose tilings in crystallography anwandte early 1980s. For this he received the 2010 Oliver E. Buckley Condensed Matter Prize with Levine and Steinhardt.

Patterns in quasicrystals

In a normal crystal, the atoms or molecules in a periodic structure are arranged. This structure is repeated in each of the three spatial directions, similar to honeycomb be repeated in two spatial directions. Each cell is surrounded by cells that form an identical pattern. In a quasi- crystal, the atoms or molecules, however, are only arranged " quasi-periodic ". Bar within the atoms in a regular structure, on a global scale, however, the structure aperiodic, each cell is surrounded by a different pattern.

Particularly noteworthy is the quasicrystals, that they have a five-, eight -, ten - or zwölfzählige symmetry. In a normal crystal, only one-, two -, three -, four -, and six-fold symmetry are also possible. This follows from the fact that the space can be filled only in this way with congruent parts. Before the discovery of quasicrystals, it was assumed that a five-fold symmetry has therefore could never occur because it is not possible to fill the space according periodically.

The discovery of quasicrystals helped to redefine what constitutes the essence of a crystal. Quasicrystals have no periodic structures, but they have sharp diffraction spots. There is an important relationship between quasicrystals and Penrose tiling, which Roger Penrose had already found before the discovery of quasicrystals: If you cut a suitable quasicrystal, the cut surface shows exactly the pattern of the Penrose tiling.

Geometric interpretation

A periodic pattern can be completely move a certain distance so that each displaced atom occupies the exact location of a corresponding atom in the original pattern. In a quasi-periodic pattern, such a complete parallel shift of the pattern is not possible, no matter what distance you choose. However, one can any cut, no matter what size he has to move so that he ( possibly after a rotation) is congruent with a corresponding cut.

There is a relation between periodic and non-periodic patterns. Each quasi-periodic pattern of dots may be formed from a periodic pattern of a higher dimension: In order to produce a three-dimensional quasicrystal, for example, one can start with a periodic arrangement of points in a six-dimensional space. The three-dimensional space is a linear subspace that penetrates the six-dimensional space at a certain angle. When projected every point of the six-dimensional space, which is located within a certain distance from the three-dimensional subspace of the subspace, and the angle is an irrational number, such as the Golden Section, the result is a quasi-periodic pattern.

Each quasi-periodic pattern can be generated in this way. Each pattern are obtained in this manner is either periodically or quasi- periodically. This geometric approach is useful to analyze physical quasicrystals. In a crystal lattice defects are positions where the periodic pattern is disturbed. In a quasi- crystal are the points where the three-dimensional sub-space is bent, folded or broken, when it passes through the higher-dimensional space.

Occurrence

Quasicrystals occur in many three-dimensional alloy systems. Most alloys containing quasicrystals are thermodynamically unstable, so they can only be formed by rapid cooling and transform themselves upon reheating into more stable crystals. However, there also exist a number of thermodynamically stable alloys which are quasi crystalline structured. These are usually ternary alloys, ie, those with three alloying elements and the elements of aluminum, zinc, cadmium or titanium as the main component. These alloys - and those with " neighboring" levels - often amorphous (or initially amorphous prior to the actual crystallization). Amorphous systems are therefore often competitors to the quasicrystals ( competition from so-called α -phase and the so-called i -phase ).

Among the rare two-element systems with quasicrystalline structure include CD5, 7YB, CD5, 7Ca in icosahedral structure and Ta1, 6th in a dodecahedral structure. Since the quasi-crystalline structure is generally stable only in a very narrow range of mixtures of the elements that quasicrystals can be also among the intermetallic compounds.

It has only been a naturally occurring quasi- crystalline mineral, the Icosahedrit known. It is an aluminum - copper -iron alloy with the composition Al63Cu24Fe13 that was found on the Chukchi Peninsula in Russia.

Use

There are various applications of quasicrystalline compounds studied. This applies to both composite materials in which alloys to improve certain properties of quasi-crystalline compounds are mixed, as well as quasi-crystalline coatings. As aggregate to allow steel quasicrystals a very solid, ductile, corrosion and aging -resistant steel. It is particularly interesting for medical devices, such as in surgery or acupuncture. Also aluminum alloys can be improved by the supplement of quasicrystals in their properties, such as the high temperature strength or ductility.

Quasicrystalline coatings allow by their hardness and oxidation stability a particularly low wear and low adhesion. This is for frying pans of interest, therefore quasicrystal coatings are investigated as an alternative to stainless steel pans and polytetrafluoroethylene coatings.

In Catalysis Quasicrystalline compounds investigated as possible catalysts, a quasicrystalline aluminum-copper -iron alloy for the steam reforming of methanol.