Crystal lack

Unlike crystals that are packed with identical unit cells in 3D space, aperiodic crystals lack such units. So far, aperiodic crystals include not only quasiperiodic crystals, but also crystals in which incommensurable modulations or intergrowth structures (or composites) occur [14], That is to say, quasiperiodicity is only one of the aperiodicities. So what is quasiperiodicity Simply speaking, a structure is classified to be quasiperiodic if it is aperiodic and exhibits self-similarity upon inflation and deflation by tau (x = 1.618, the golden mean). By this, one recognizes the fact that objects with perfect fivefold symmetry can exist in the 3D space however, no 3D space groups are available to build or to interpret such structures. 

Crystals lack some of the dynamic complexity of solutions, but are still a challenging subject for theoretical modeling. Long-range order and forces in crystals cause their spectrum of vibrational frequencies to appear more like a continuum than a series of discrete modes. Reduced partition function ratios for a continuous vibrational spectrum can be calculated using an integral, rather than the hnite product used in Equation (3) (Kieffer 1982),... 

Cleavage The property of an individual crystal to fracture or break, producing planar surfaces along specific crystallographic directions dictated by the structure of the material. Some crystals lack cleavage others possess one or more crystallographi-cally distinct cleavage directions (see chapter 1). 

Triclinic sometimes called anorthic). Crystals lacking symmetry of any kind naturally have the most c general type of unit cell, the three axes of which are all inclined to each other at different angles and unequal in length. The addition of a centre of symmetry does not alter the situation, for this most general type of unit cell has a centre of symmetry and is appropriate for this class also. These two classes, 1 and 1, constitute the triclinic system (Fig. 32). 

Piezo-electricity is the property, possessed by some crystals, of developing electric charges when compressed or extended in particular directions. Conversely, when a potential difference is applied to suitable points on such a crystal, it expands or contracts. Piezo-electric properties can occur in all crystals lacking a centre of symmetry, except those belonging to the cubic class 432 (Wooster, 1938). A test for such properties, suitable for small crystals or even powders, is the following,... 

The Pockel s effect [3] refers to an electro-optical process wherein the application of large electric fields onto crystals lacking a center of symmetry can lead to nonlinear polarization effects and optical rotation. Pockel cells can be used in place of photoelastic modulators and can achieve very high modulation frequencies but often have the undesirable property of a nonzero birefringence in the absence of an applied field. 

The coupling between strain and electrical polarization that occurs in many crystals provides a means for generating acoustic waves electrically. When die structure of a crystal lacks a center of inversion symmetry , the application of strain changes the distribution of charge on the atoms and bonds comprising the crystal in such a manner that a net, macroscopic, electrical polarization of the crys-... 

For more than 50 years it has been known that the barely measurable differences between Fhki and F-n-k-t contained useful phase information. For macromolecular crystals lacking anomalous scattering atoms, this phase information was impossible to extract and use because it was below the measurement error of reflections. Anomalous dispersion was, however, sometimes useful in conjunction with isomorphous replacement where the heavy atom substitutent provided a significant anomalous signal. The difference between F ki and F-h-k-i was, for example, employed to resolve the phase ambiguity when only a single isomorphous derivative could be obtained (known as single isomorphous replacement, or SIR) or used to improve phases in MIR analyses. 

The name liquid crystal reflects the duality of such materials according to their properties they could be placed somewhere in between ordinary liquids and crystalline solids. Like liquids, liquid crystals lack long-range order in the positions of their molecules most liquid crystals are indeed fluid. At the same time, just like solid crystals, liquid crystals are anisotropic as their molecules are orientated in an anisotropic way. 

Parks, D. M. and Ahzi, S. (1990) Polycrystalline plastic deformation and texture evolution for crystals lacking five independent slip systems, J. Mech. Phys. Solids, 38, 701-724. 

Vice versa, mechanical stress changes the dimensions of the material. This does not usually result in an electrical polarization of the material because most materials have a so-called center of symmetry canceling opposite charge displacements. However, crystals lack such a center of symmetry, and they generate an internal polarization, P, when mechanically deformed. These materials are called piezoelectric, with a direct conversion from mechanical to electrical energy. 

It was reported recently, that polymeric can also form quasicrystals. Hayashida et al. [50] demonstrated that certain blends of polyisoprene, polystyrene, and poly(2-vinylpyridine) form starshaped copolymers that assemble into quaskrystals. By probing the samples with transmission electron microscopy and X-ray diffraction methods, they conclude that the films are composed of periodic patterns of triangles and squares that exhibit 12-fold symmetry. These are signs of quasicrystalline ordering. Such ordering differ from conventional crystals lack of periodic structures yet are well-ordered, as indicated by the sharp diffraction patterns they generate. Quasi-crystals also differ from ordinary crystals in another fundamental way. They exhibit rotational symmetries (often five or tenfold). There are still some basic questions about their stracture. 

We conclude that the best equipment is pulsed-neutron instrumentation and hl -resolution gamnm Spectrometers (lithium-drifted germahiuin crystals). Lacking ttiese, much can be done with less expensive instrumehts. 

One was steep, and close to the initial surface. It was attributed to self-diffusion in the titanite lattice. The other was a tail that stretched deeply into the sample. It was attributed to diffusion along so-called fast paths such as planar defects or pipes. Both mechanisms operated in crystals lacking euhedral morphology. In the case of dry experiments, the Arrhenius relationship was ... 

The application of an external electric field deforms the optical indicatrix (Fresnel ellipsoid) of crystals lacking a center of symmetry in such a way that its birefringence is changed. The dependence of the birefringence on the electric field E is linear, and can be analytically described by a change of the impermeability tensor a = (e ) by the electric field E [see Eq. (8.4a)] and the polarization P, respectively ... 

This effect is even less pronounced than the linear Pockels effect in crystals. In contrast to the linear electro-optic effect that is confined to crystals lacking a center... 

Lee B J, Ahzi S and Asaro R J (1995) On the plasticity of low symmetry crystals lacking five independent slip systems, Mech Mater, 20 1-8. 

The 50 50 blend (NIE50 50) (Fig. 11C) was composed of small spherulites measuring only 5-10 J,m in diameter. The interesterified sample (CIE50 50) contained fewer crystals. At the magnification used, these crystals lacked stmcture and measured only a few micrometers in size (Fig. lid). 

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