Crystals crystallographic systems

Figure 6-3. Top Structure of the T6 single crystal unit cell. The a, b, and c crystallographic axes are indicated. Molecule 1 is arbitrarily chosen, whilst the numbering of the other molecules follows the application of the factor group symmetry operations as discussed in the text. Bottom direction cosines between the molecular axes L, M, N and the orthogonal crystal coordinate system a, b, c. The a axis is orthogonal to the b monoclinic axis.

Nevertheless, fluoride does lead to a reduction in the solubility of hydroxyapatite in aqueous solution, even in the absence of trace levels of fluoride in solution, and hence can be seen to have an effect in the solid state as well [57], Apatites are complex and diverse materials which have the general formula Caio(P04)eX2 (X = F, Cl, OH) and they represent a crystallographic system, in which there can be considerable replacement of species. Thus, with little or no change in the dimensions of the crystal lattice, there can be exchanges of OH for F, Ca + for Sr +, and PO4 for CO and all of these are known to occur in biological systems. Natural hydroxyapatite, for example, is often partially carbonate substituted [58]. 

There are five main types of crystals, and these types have been arranged into seven crystallographic systems based on the crystal interfacial angles and the relative length of its axes. The treatment of the description and arrangement of the atomic structure of crystals is the science of crystallography. The material in this discussion will be limited to a treatment of the growth and production of crystals as a unit operation. 

Despite the fact that the triclinic system is the only crystallographic system that unequivocally allows singlecrystal orientations to provide both enhanced in-plane and out-of-plane NRVS spectra, many other crystalline heme derivatives fortunately have all porphyrin planes close to being parallel to a common crystallographic plane. For example, [Fe(TPP)(l-MeIm)(NO)] has four independent porphyrin plane orientations, but all planes are within 13.8° of a common plane in the crystal. Data were collected using this common plane as the crystal-orienting plane to obtain an in-plane and an out-of-plane spectrum. As shown in Figure 10, a comparison of the in-plane , out-of-plane , and powder spectra show that useful intensity enhancements are still evident. Moreover, and fortunately, this situation of nearly coincident planes appears to be moderately frequently observed. 

As regards to crystal shape and more information on crystallographic systems - see 5]. 

The crystals of silver iodide (Agl) resemUe ice crystals quite closely, both belonging to the hexagonal crystallographic system. As such, they can form the nuclei for the condensation and crystallization of water in a super-cooled and hence super-saturated moisture-laden atmosphere.Lead iodide (Pbl g) behaves similarly and the organic compounds metaldehyde and phloroglucinol have in the laboratory proved their activity. In fact, metaldehyde forms ice crystals from water vapor up to 31°F while silver iodide does this, according to the article, only up to 25 F. 

The elastic properties of an ideally elastic crystal may be characterized corrrpletely by the nrrmerical valrres of either the elastic stiffnesses c,yw or cxfi or else of its compliartces syu or These nrrmerical values, however, are referred to a specific coordirrate system arrd are, therefore, dependent on its choice. Usually they are reproduced in tables as referred to a Cartesian coordinate system with axes parallel to irrrportartt crystallographic directiorrs. It is chosen in a way that makes the representation of crystal properties as sirrtple as possible, as was shown already in Chap. 2, and is called the crystal coordinate system. 

Often, describing the crystal structure is easier if we rely on non-primitive elementary cell. To such a cell belong more particles whose position in the polyhedron is conditioned by the elements. For this reason, the non-primitive cells are not compatible with any crystallographic system (Goodhew, 2003). 

However, since this surface of refraction indices applies to a crystalline system, it will be subjected to the same limitations of symmetry to which the crystallographic system belongs. If the orientation of the direction of propagation of the incident radiation (represented by the optical axis, O.A.) coincides with the main symmetry axis of the crystal, the birefringence effect is therefore canceled. 

In conclusion, for the birefringence phenomena, its absence in any orientation or in one or two orientations of the O.A. can indicate the appurtenance of the crystal under concern to one of the set of the crystallographic systems that allow such a behavior it is thus more an indicator of the... 

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