Quasicrystals nature

Zeng X, Ungar G, Liu Y, Percec V, Dulcey AE, Hobbs JK (2004) Supramolecular dendritic liquid quasicrystals. Nature 428(6979) 157-160. doi 10.1038/nature02368... 

Another characteristic point is the special attention that in intermetallic science, as in several fields of chemistry, needs to be dedicated to the structural aspects and to the description of the phases. The structure of intermetallic alloys in their different states, liquid, amorphous (glassy), quasi-crystalline and fully, three-dimensionally (3D) periodic crystalline are closely related to the different properties shown by these substances. Two chapters are therefore dedicated to selected aspects of intermetallic structural chemistry. Particular attention is dedicated to the solid state, in which a very large variety of properties and structures can be found. Solid intermetallic phases, generally non-molecular by nature, are characterized by their 3D crystal (or quasicrystal) structure. A great many crystal structures (often complex or very complex) have been elucidated, and intermetallic crystallochemistry is a fundamental topic of reference. A great number of papers have been published containing results obtained by powder and single crystal X-ray diffractometry and by neutron and electron diffraction methods. A characteristic nomenclature and several symbols and representations have been developed for the description, classification and identification of these phases. 

The basic modem data describing the atomic stmcture of matter have been obtained by the using of diffraction methods - X-ray, neutron and electron diffraction. All three radiations are used not only for the stmcture analysis of various natural and synthetic crystals - inorganic, metallic, organic, biological crystals but also for the analysis of other condensed states of matter - quasicrystals, incommensurate phases, and partly disordered system, namely, for high-molecular polymers, liquid crystals, amorphous substances and liquids, and isolated molecules in vapours or gases. This tremendous... 

Let us return to quasicrystals and investigate the nature of their intrinsic ordering. It is possible to solve their structure by (almost) classical crystallographic techniques if one admits structural solutions in six-dimensions. Clearly however this is of little help when we try to grasp the real structure of the crystals. To arrive at the true three-dimensional structure... 

Quasicrystal structures have been known for a long time to occur in condensed matter and rejected as inexplicable curiosities. They may emerge naturally too in mathematical descriptions of surfaces. (The decagonal variant certainly arises, cf. [36]). It is not an entirely idle speculation to conjecture, e.g. that the principles exploited in construction of quasi-crystals may be precisely those used by nature to build protems that solve the problem... 

Dubost, B., Lang, J-M., Tanaka, M., Saintfort, P., and Audier, M. Large Al-CuLi single quasicrystals with triacontahedral solidification morphology. Nature (London) 324, 48-50 (1986). 

Since our surroundings are three-dimensional, we tend to assume that crystals are formed by periodic arrangements of atoms or molecules in three dimensions. However, many crystals are periodic only in two, or even in one dimension, and some do not have periodic structure at all, e.g. solids with incommensurately modulated structures, certain polymers, and quasicrystals. Materials may assume states that are intermediate between those of a crystalline solid and a liquid, and they are called liquid crystals. Hence, in real crystals, periodicity and/or order extends over a shorter or longer range, which is a function of the nature of the material and conditions under which it was crystallized. Structures of real crystals, e.g. imperfections, distortions, defects and impurities, are subjects of separate disciplines, and symmetry concepts considered below assume an ideal crystal with perfect periodicity. ... 

Molecular quantum potential and non-local interaction depend on molecular size and the nature of intramolecular cohesion. Macromolecular assemblies such as polymers, biopolymers, liquids, glasses, crystals and quasicrystals are different forms of condensed matter with characteristic quanmm potentials. The one property they have in common is non-local long-range interaction, albeit of different intensity. Without enquiring into the mechanism of their formation, various forms of condensed matter are considered to have well-defined electronic potential energies that depend on the nuclear framework. A regular array of nuclei in a structure such as diamond maximizes cohesive interaction between nuclei and electrons, precisely balanced by the quantum potential, almost as in an atom. 

First, in quantum physics, problems of an electron in complex potentials have been formulated to explain properties of the naturally existing crystals, disordered solids and quasicrystals. Similar structures in optics were mainly man-made for the purpose of optical engineering. 

The concept of quaternion groups i.s useful for the understanding of icosahedral quasicrystals and shows how the existence of icosahedral quasicrystals is a natural consequence of the use of quaternions to represent symmetry groups. In this connection a real quaternion is defined as an ordered quadruple of four real numbers w,x, y, z). subject to the following rules of addition and multiplication where q = (w, x, y, z) and q = (w, r. /, c ) ... 

Just as we think we know everything about how matter is constructed, nature always has a way of surprising us. Quasicrystals, crystals with fivefold S5nnmetry that were not supposed to exist, actually do. Their discovery has opened exciting new areas of research into their structure and properties, especially when it was found that, even though they are metaUic systems, in many respects they behave more like ceramics and semiconductors than metals. 

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