Invariant , crystal

Since crystallization invariably means more or less purification, even though by no more than the removal of the solvent, the ideas and processes of crystallization and purification are inextricably interwoven and it is impossible to consider crystallization... 

Finite chain extensibility is the major reason for strain hardening at high elongations (Fig. 7.8). Another source of hardening in some networks is stress-induced crystallization. For example, vulcanized natural rubber (cw-polyisoprene) does not crystallize in the unstretched state at room temperature, but crystallizes rapidly when stretched by a factor of 3 or more. The extent of crystallization increases as the network is stretched more. The amorphous state is fully recovered when the stress is removed. Since the crystals invariably have larger modulus than the surrounding... 

Crystal syntheses do not differ, in their essence, from classical chemical experiments in which molecules are modelled, synthetic routes devised, products characterized and their properties evaluated. However, this typical chemical approach needs, in a sense, to be repeated twice first, in order to prepare the building blocks (whether molecules or ions), and then to arrange the building blocks in a desired way via nucleation, precipitation and crystallization to attain and/or control crystal properties. Obviously, crystallization invariably implies the need to characterize the solid product, often in the form of a polycrystalline powder, for which routine analytical and spectroscopic laboratory tools are much less useful than in the case of solution chemistry. 

Application of group theory can also explain the important problem of degeneracy of excitonic states. This degeneracy can be conditioned by invariance of the crystal Hamiltonian upon elements of its space group (in this case it is sometimes called compulsory degeneracy, see (21), 40) or, as shown by Herring (23), it can result from the crystal invariance upon the time-reversal operation. 

Space group - A group of symmetry operations (reflections, rotations, etc.) that leave a crystal invariant. A total of 230 space groups have been identified. 

One issue might be the removal of the weakly bound water of crystallization invariably associated with the thicker films. For low temperature curing of apphed organics, for... 

Let us keep to the simple case of the smectic A phase. The discrete symmetries which leave smectic A liquid crystals invariant are clearly the same as those for nematic phases. Optical, magnetic, dielectric and other properties will simply... 

When synthesized with the aid of microorganisms, this polyester is expressed exclusively as the R enantiomer that crystallizes with left-handed helices in an orthohrom-bic unit cell. Lamellae of these crystals invariably have... 

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