Quasi-crystals

Crystals are sohds. Sohds, on the other hand can be crystalhne, quasi-crystal-hne, or amorphous. Sohds differ from liquids by a shear modulus different from zero so that solids can support shearing forces. Microscopically this means that there exists some long-range orientational order in the sohd. The orientation between a pair of atoms at some point in the solid and a second (arbitrary) pair of atoms at a distant point must on average remain fixed if a shear modulus should exist. Crystals have this orientational order and in addition a translational order their atoms are arranged in regular lattices. 

A pecuhar sohd phase, which has been discovered not too long ago [172], is the quasi-crystalline phase. Quasi-crystals are characterized by a fivefold or icosahedral symmetry which is not of crystallographic type and therefore was assumed to be forbidden. In addition to dislocations which also exist in normal crystals, quasi-crystals show new types of defects called phasons. Computer simulations of the growth of quasicrystals [173] are still somewhat scarce, but an increasing number of quasi-crystalline details are studied by simulations, including dislocations and phasons, anomalous self-diffusion, and crack propagation [174,175]. 

The extraordinary bonding properties in 16 can also be seen in a diagram of 16 (Fig. 34). In 16, an almost perfect five-numbered axis is attained, distorted only by the central Ga2 unit. This is the first time that a symmetry close to the five-numbered symmetry is observed for molecular metalloid clusters. A few solid-state modifications with five-numbered symmetry have, however, been found for compounds involving Group 13 elements. Because there is no crystallographic space group with a five-numbered axis, these compounds are summarized under the collective name quasi-crystals .83 For a better understanding of quasi-crystals,... 

A special case of coagulation is the "quasi crystal" formation by unit layers of mont-morillonite bearing exchangeable Ca2+ cations (cf. Fig. 3.10). As Sposito (1989) points out, "one can imagine that the competition between the repulsive electrostatic forces and the attractive van der Waals force will, along with random thermal motions, largely determine the behavior of two siloxane surfaces approaching each other to a distance of separation >10 nm. However, at a separation distance of... 

To date, little use has been found for quasi crystals in bulk, but they have proved very effective as coatings, notably in cookware. Recent cookware, with a different appearance and feel, has appeared in the marketplace. These pots, pans, and so on, have a hardness equal to that of hardened alloy steel and thus are practically immune to scratching. They also are thermally stable and corrosion and oxidation resistant. 

Abstract. A number of observations and critical remarks were made dealing with perspectives of the metallic materials (both classical alloys and quasi-crystals) and nano-sized carbon materials as reversible accumulators of hydrogen. 

Also, quasi-crystals of apparent macroscopic fivefold symmetry do exist, despite the toological restriction that an object with a fivefold axis cannot tile two-dimensional space these funny quasi-crystals do have voids in them, which "fill" the remainder of the space needed. 

III. Quasi-crystal. A quasi-crystal is made up of ions with a certain arrangement which does not repeat itself indefinitely. 

The strength of electron microscopy as a characterization technique lies not only in its ability to probe at near atomic resolution, the internal structure of minute amounts of material, but also in its capacity to reveal directly structural imperfections of the most subtle kind.(1-4) Other investigative methods such as x-ray or neutron diffraction as well as many spectroscopic techniques possess their own individual merits but they utilize procedures which provide only spatially averaged information. And this is often far less suitable for the characterization of defective, multi-phasic or heterogeneous crystalline (or quasi-crystal 1ine) materials. 

Figure 9-64 shows some beautiful representatives of quasicrystals and Figure 9-65 depicts another quasicrystal and a modern sculpture that could be taken as an artistic expression of a quasicrystal although the artist was not aware of the existence of such materials. The artistic appearance of quasi crystals, however, predates their scientific entry by centuries [150], The discovery of such cultural monuments has generated lively discussions even in the general press [151], Concluding, we quote again Mackay [155], who stated that... 

A. L. Mackay, Quasi-Crystals and Amorphous Materials. J. Non-Cryst. Solids 1987, 97 98, 55-62. 

L. Pauling, Unified structure theory of icosahedral quasi crystals Evidence from neutron diffraction patterns that AlCrFeMnSi, AlCuLiMg, and TiNiFeSi icosahedral quasicrystals are twins of cubic crystals containing about 820 or 1012 atoms in a primitive unit cube. Proc. Natl. Acad. Sci. (USA) 85. 8376-8380 (1988). 

An approach with consideration of the two states (i.e, free with concentration c, and bound with concentration a,) of the B and A counterions is consistent with the loose quasi-crystal molecular model [41] that states that mass transfer in the exchanger may not occur by transfer of the complete counterions mass, as suggested by the classical quasi-homogeneous exchanger model [1-5,7-12,16,17], but solely by the free counterions that are not bound to the fixed exchanger groups. 

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... 

M.V. Jaric, "Introduction to Quasi-Crystals". Academic Press, (1988 and 1989), New York Academic Press. 

Non-uniformity also brings the question of where within each span each new knot should be inserted. Forcing it always to be at the centre is a totally arbitrary choice. A second question is close behind, whether to insert in every span anyway. Quasi-crystal theory, which inserts knots only one at a time, but where they are most needed, does not lead to obvious efficiency, but could provide some theoretical insight. 

Maimed and Klein [6.20] found two-dimensional defects (probably cluster boundaries) in the quasi-crystal Al Mn. The sizes of clusters (quasi-crystallites) comprise 102u, and the boundary thickness equals approximately a. 

Other interesting directions are hardening with intermetallics, quasi-crystals, borides, silicides, discrete fibres, creation of natural composites. Conscious regulation of structure and properties of such materials requires studying phase equlibria in multi-component systems, in particular on the basis of light metals like aluminum, magnesium, titanium. The important direction is also a creation of specially organized porous structures. To some extent these directions are presented in a number of papers of the present book. 

Whenever an electric field, E, is applied across a thin film quasi-crystal system, such as found in these metallic oxides, a force is exerted on the charged particles in a quasi-crystal. If an ion or a defect has a charge, Qi, then the force, Fi, on this ion or defect film is given as (21) (28) ... 

The process of crystal nucleation and growth is equivalent to a phase transition. The initial phase might be a gas, liquid, solution or solid (e.g. glass or another crystal) and the final phase need not be a crystal as traditionally defined. It could be a liquid crystal, a quasi-crystal, a polytype or some other defect solid. The phase transition proceeds via a critical state, which is intermediate between the two phases of the transition and holds the key to the understanding of crystal growth. 

---