Physical Properties of the Crystal

Simple descriptors of crystal compactness include the crystal density, and the Kitaigorodski packing coefficient, Cr [5]  

A more sensitive index is the bulk modulus, which, at zero pressure and 60 7o of the melting temperature, can be estimated as [21]  

Kq is related to the overall hardness of the crystal the sublimation enthalpy A//s may be estimated from the calculated packing energy. 

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Given the information above, the question remains as to the nature of the monolayer states responsible for the stereo-differentiation of surface properties in racemic and enantiomeric films. Although associations in the crystalline phases are clearly differentiated by stereochemical packing, and therefore reflected in the thermodynamic and physical properties of the crystals, there is no indication that the same differentiations occur in a highly ordered, two-dimensional array of molecules on a water surface. However, it will be seen below (pp. 107-127) that conformational forces that are readily apparent in X-ray and molecular models for several diastereomeric surfactants provide a solid basis for interpreting their monolayer behavior. 

Most of the four above-mentioned properties for Raman spectra can be explained by using a simple classical model. When the crystal is subjected to the oscillating electric field = fioc " of the incident electromagnetic radiation, it becomes polarized. In the linear approximation, the induced electric polarization in any specific direction is given by Pj = XjkEk, where Xjk is the susceptibility tensor. As for other physical properties of the crystal, the susceptibility becomes altered because the atoms in the solid are vibrating periodically around equilibrium positions. Thus, for a particular... 

All these models for the calculation of the hardness need empirical parameters which cannot be explained by physical properties of the crystals. This problem is solved if the hardness of crystals is described as a volumetric cohensive energy as suggested by Plendl et. al.(20). Then the hardness can be written as the ratio of the cohensive energy U to the molecular volume V, as to be seen in Equation 5. 

Since Eqs. (B.7) and (B.8) are equal, this implies that a rotational symmetry element of direct space is also a rotational symmetry element of reciprocal space. This result must be correct since X-ray scattering is a physical property of the crystal, it must at least have the point-group symmetry of the crystal. 

In this section we have explained the relation between a bulk ambient phase and a bulk crystal (where the crystal is assumed to have an ideal, regular structure). Since the 1930s, theoretical and experimental investigations have indicated that a real crystal contains defects of lattice order, and that these defects have a significant effect on the physical properties of the crystal. This understanding has led to the present day semiconductor industry. 

This study showed that the overall crystallization processes for mor-denite, zeolite X, and zeolite A were similar. However, the physical properties of the crystallizing system determine the rate-limiting step for a particular zeolite synthesis. In the case of mordenite in which both the viscosity of the batch composition and the morphology of seed crystals were varied, it was observed that diffusion in the liquid phase was the ratedetermining step. For zeolite X the actual growth rate on the crystal-liquid interface was the rate-limiting factor as shown by identical conversion rates for the seeded and unseeded systems. For zeolite A in the system chosen, both processes influenced the conversion rate. 

A perfect crystal is one in which the crystal structure would be that of an ideal space lattice. No such crystals exist, all real crystals containing imperfections which have a strong influence on the physical properties of the crystal. 

Another useful physical property of the crystal is its density, which can be used to determine several useful microscopic properties, including the protein molecular weight, the proteinlwater ratio in the crystal, and the number of protein molecules in each asymmetric unit (defined later). Molecular weights from crystal density are more accurate than those from electrophoresis or most other methods (except mass spectrometry) and are not affected by dissociation or aggregation of protein molecules. The proteinlwater ratio is used to clarify electron-density maps prior to interpretation (Chapter 7). If the unit cell is symmetric (Chapter 4), it can be subdivided into two or more equivalent parts called asymmetric units (the simplest unit cell contains, or in fact is, one asymmetric unit). For interpreting electron-density maps, it is helpful to know the number of protein molecules per asymmetric unit. 

If the chemical contents of a polymorph are different than other forms, it is designated as a pseudopolymorph.Most often this occurs due to the presence of differing amounts of solvent, and may alter physical properties of the crystals such as melting points and solubilities. Polymorphism and pseudopolymorphism may be observed when different experimental conditions are used for synthesis. For example, if crystals are grown by sublimation, changing the temperature will often yield different crystal structures, possibly even metastable phases that are kinetically favored. 

When the absolute structure has been determined, the result must be correlated with some physical property of the crystal, otherwise the result has no use to the chemist. The obvious correlation is with the direction of rotation of the plane of plane-polarized light, that is, whether the compound or crystal is dextrorotatory or levorotatory. Another correlation can be made with crystal appearance this was shown for zinc blende with its matte and shiny faces, and for silica and sodium ammonium tartrate crystals for the disposition of their hemihedral faces. If such data are not available, it may be necessary to list physical properties of diastereomers made with chiral complexing agents. Then, whenever this same compound is encountered by a chemist, its absolute structure is well known. 

The physical properties of the crystallized APT can be influenced by crystallization conditions to some extent. They are of importance for the further processing to metal powder by hydrogen reduction. 

X traps are localised at a particular point in the lattice, without extending over larger distances in one or more dimensions. They thus belong to the class of point defects. Other point defects can be caused by missing molecules in the lattice, i.e. lattice vacancies or so-called Schottky defects, or by interstitial molecules, i.e. Frenkel defects, or finally by improperly oriented molecules on regular lattice sites. Point defects can usually be observed only indirectly, through the effects they have on other physical properties of the crystal. 

For the limiting case (Cd g) > we find that (VAg) — (CdAg). That is, the vacancy concentration is completely fixed by the addition of CdBr2. This is called the region of exclusively extrinsic disorder, as opposed to the region of intrinsic disorder. In the extrinsic region, those physical properties of the crystal which depend upon the point defect disorder are functions only of the concentration of dopant. However, in deriving eq. (4-26), it has been tacitly assumed that point defects do not form complexes. This assumption, as shown later, must eventually be modified. 

The analysis of the statistical or preferred orientation of the crystallites in solid polycrystaUine materials is commonly referred to as texture analysis. Again, the diffraction technique allows the definition of the relationship between a microscopic property, i.e. the orientation of the crystallites defined as coherent diffraction domains, and the macroscopic physical properties of the crystal aggregate. Texture studies are of course crucial in the characterization of oriented synthetic materials such as cold-rolled metals or oxide thin films, but they are also of great relevance in the study of the formation processes of mineral assemblages. As an example, the texture features of olivine or pyroxene minerals in meteoritic chondrules yield information on the early condensation sequence... 

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