Quasi-crystal
A quasi-crystal is a solid with aperiodic structure, having a primarily discrete spectrum of diffraction. By this property it is attached to the crystals, although it differs from them by its structure. Since 1992 the International union of Crystallography modified the definition of its main object, the crystal, by retaining the single criterion of diffraction. Since one admits that the crystals are of two types: crystals periodic, well-known, and the aperiodic crystals which one calls quasicristaux. If the crystals are current (metals and mineral alloys, , ceramic, ice, salts…), it is not the same quasi-crystals. Their discovery. True a scientific Révolution followed this publication, although the news did not astonish of anything the mathematicians who knew already the not-periodicals objects. Indeed the mathematical framework in which was going to fit this discovery, was not new. It is based in particular on work of H. Bohr and A. Besicovic on the " functions presque-périodiques" and dating from the Years 1930, without forgetting the more recent work of Roger Penrose on the pavings not-periodicals (1974) which will remain the prototypes of the quasi-crystals. These pavings although not periodicals, are built starting from 2 tiles according to strict rules of joining which returns them perfectly ordered and have a symmetry of order 5 (at least from a local point of view).
The year even of discovered (1984), P. Steinhardt and D. Levine give the first geometrical interpretation and found the term of " quasi-cristal". The year 1985 will be marked by the fundamental work of A. Katz and Mr. Duneau of the polytechnic school on the description of the quasi-crystals in term of crystallography in a space with several dimensions. These structures result then from the " cut irrationnelle" of this periodic space. To illustrate the concept, let us take the simple example of a " quasi-cristal" with 1D. For that of a square network with two dimensions in which one placed small segments on the nodes (and whose size is astutely selected). Now one cuts this network with a line whose slope is irrational. When this slope is equal to the Golden section, one obtains a series of short and long segments which follow the nonperiodic sequence of Fibonnacci. In the same way a paving of Penrose can be built by the irrational cut of a space with 4 dimensions. The quasi-crystals of Dany Schechtman require a description in a periodic space with 6 dimensions.
The following year, this description is definitively adopted after concomitant work of Russian Kitaev, Levitov and Kalugin and of American Elser. From there, one manages to reconstitute the famous diagrams of diffraction of D. Shechtman.
It was thought whereas the only problem lay in the quasi-crystal growth of good size and good quality. At this point in time L. Bendersky discovered stable phases of symmetry décagonale. These phases have a structure quasi-periodical with two dimensions, the third dimension being periodic. Followed until today the discovery of a hundred phases of which the most studied: the ternary alloys aluminum, palladium, manganese (Al-Pd-mn) and aluminum copper iron (Al-Cu-Fe). When one cools a mixture in fusion of aluminum, palladium and manganese in precise quantity (70% Al, 20% Pd, 10% mn), it is possible to obtain beautiful quasi-crystals of macroscopic size showing of the pentagonal facets.
In the Years 1990, one bored the secrecy of the real structures in term of atomic positions whose frightening complexity leaves many open-ended questions. To illustrate this, let us take again the example of the cut with 2 dimensions. The small segments attached to the nodes of the network are called atomic surfaces. At first approximation, one can regard them as spheres whose concentric layers correspond has different chemical elements. The figure below represent a cross-section with 2D hyper-cubic network 6D centered faces of Al-Pd-mn quasi-crystalline lens. One finds the segments attached to the nodes (here N, and bc) of the network. Their intersection with space " réel" corresponds to the position and the nature of the atoms. The size and the form of atomic surfaces are adjusted in order to avoid too small atomic distances, a density and a composition in agreement with the experimental data. In space " réel" , one realized that 90% of the atoms were incorporated to form " amas" who interpenetrating to form the symmetry of the Icosahedral .
The principal interrogations remain related to the origin of the stability of these structures and their mode of growth. Think for example that to assemble a paving of Penrose by adding tile to tile, it is necessary to know the configuration of the whole of paving not to plant… which demon " shechtmannien" y-a it behind? Let us note to finish that the study of the quasi-crystals extends on all the fields from physics so much the atypical character from these structures affects broad its various physical properties. One can quote in particular his qualities of heat insulator and electric although they are metal alloys. From the point of view of its mechanical properties, they are extremely fragile and hard. This confers excellent tribological qualities to them, i.e. of wear to frictions. Thus one can imagine them returning in the composition of certain coatings (what was carried out in the case of an anti-adhesive frying pan) or as an heat insulator.