Crystallization references

The term molecular crystal refers to crystals consisting of neutral atomic particles. Thus they include the rare gases He, Ne, Ar, Kr, Xe, and Rn. However, most of them consist of molecules with up to about 100 atoms bound internally by covalent bonds. The dipole interactions that bond them is discussed briefly in Chapter 3, and at length in books such as Parsegian (2006). This book also discusses the Lifshitz-Casimir effect which causes macroscopic solids to attract one another weakly as a result of fluctuating atomic dipoles. Since dipole-dipole forces are almost always positive (unlike monopole forces) they add up to create measurable attractions between macroscopic bodies. However, they decrease rapidly as any two molecules are separated. A detailed history of intermolecular forces is given by Rowlinson (2002). 

The much slower linear increase in density with the log of time after the primary crystallization, referred to as secondary crystallization. 

Millions of years ago, the Great Plains of the United States were ocean. As sea levels fell and at the same time the North American continent rose, many isolated pockets of seawater, called saline lakes, formed. Over time, these lakes evaporated, leaving behind the solids that had been dissolved in the seawater. Most abundant was sodium chloride, which collected in cubic crystals referred to by mineralogists as the mineral halite. When conditions were right, halite crystals like the ones in this chapter s opening photograph would grow to be several centimeters across. 

Formation of a crystalline material requires placement of molecules in a relationship described by the space group symmetry of the crystal lattice. In the following discussion, the sharing of symmetry elements between molecules in a crystal refers to only sharing... 

Index No. Cluster0 Color w J c 0 Other available spectral data0 Crystal Refer-structure ences ... 

RTase is a dimer composed of two polypeptide chains of 66 and 51 kilodaltons (kDa). The smaller subunit is identical to the larger, 66 kDa, subunit at the amino terminus, but lacks the 15 kDa segment at the carboxyl terminus of the larger subunit. This 15 kDa segment corresponds to the RNase H activity. Early attempts at the determination of the RTase structure were made difficult by the inability to obtain acceptable protein crystals (Wlodawer, 1992). Crystals capable of producing diffraction data could be obtained only by co-crystallization of RTase with either DNA and an anti-RTase antibody fragment (Arnold et al, 1992), or with a non-nucleoside inhibitor. Nevirapine (Kohlstaedt et al, 1992). These examples illustrate the vagaries involved in protein crystallization, referred to in an earlier section. 

Crystal polystyrene is produced by thermally initiated (Section 6.5.4) bulk polymerization of styrene at temperature of I20°C or more. (The term crystal refers to the optical clarity of products made from this polymer, which is not crystalline.) The rate of polymerization would decrease with increasing conversion and decreasing monomer concentration if the reaction were carried out at constant temperature. For this reason, the polymerization is performed at progressively increasing temperatures as the reaction mixture moves through a series of reactors. The exothermic heat of polymerization is useful here in raising the reaction temperature to about 250°C as the process nears completion. 

Quenching Excimers and Exciplexes.—By measurements of decay times and fluorescence anisotropy of pyrene and the excimer in cellulose acetate films it has been found that the medium consists of spaces where small pyrene molecules have considerable freedom, Dissado and Walmsley have developed a complete theory of excimer formation and exciton-induced lattice distortion in crystals. Reference is made to data on 9-cyanoanthracene. The spectroscopy of chemically linked dimers of l,3-(l,l -dinaphthyl)propane in a... 

Fig. 2 (a) A pure, equilibrium crystal (reference atom denoted by the arrow), (b) a reference atom (denoted by the arrow) in the alloy to be studied (atoms of other species denoted with other shading) and (c) the same reference atom in a monatomic crystal, with the identical structure of the alloy to be studied, but with all the atoms of the same atomic species as the reference atom, for the calculation of the strain energy term for the reference atom. The strain energy is the difference in energy of the reference atom between (c) and (a). 

For metals a reasonable approximation is obtained by assuming a uniform potential energy (- F) for the electrons within the crystal referred to a zero of energy for the free electron at rest outside the crystal. The separation of the allowed energy levels is very small if... 

Repeat the determinations of the preceding problem for the NaCl crystal, referring to Figure 21.16. 

Solidification and crystallization refer to the process in which a liquid changes to a solid. 

In different reference systems the strain and stress tensors have different components, the transformation being easily derived starting from the definitions. Let us consider, for example, the sample reference system (y ) and denote by Latin letters etm and stm the components of the strain and stress tensors in this system. If the transformation of the sample reference system (y,) into the crystal reference system (x ) is given by Equation (1) then the transformations of the strain tensors are the following ... 

Similar to the ODF for texture, SODF can be subjected to a Fourier analysis by using generalized spherical harmonics. However, there are three important differences. The first is that in place of one distribution (ODF), six SODFs are analyzed simultaneously. The components of the strain, or the stress tensor can be used for analysis in the sample or in the crystal reference system. The second difference concerns the invariance to the crystal and the sample symmetry operations. The ODF is invariant to both crystal and sample symmetry operations. By contrast, the six SODFs in the sample reference system are invariant to the crystal symmetry operations but they transform similarly to Equation (65) if the sample reference system is replaced by an equivalent one. Inversely, the SODFs in the crystal reference system transform like Equation (65) if an equivalent one replaces this system and remain invariant to any rotation of the sample reference system. Consequently, for the spherical harmonics coefficients of the SODF one expects selection rules different from those of the ODF. As the third difference, the average over the crystallites in reflection (83) is structurally different from Equations (5)+ (11). In Equation (83) the products of the SODFs with the ODF are integrated, which, in comparison with Equation (5), entails a supplementary difficulty. 

As noted in the introduction to the present chapter, the contemplation of thermal and elastic excitations necessitates that we go beyond the uninterrupted monotony of the perfect crystal. As a first concession in this direction, we now spell out the way in which the energy of a weakly excited solid can be thought of as resulting from excursions about the perfect crystal reference state. Once the total energy of such excursions is in hand, we will be in a position to write down equations of... 

The perfection of a crystal refers to the precision with which each and every unit cell associates. In a perfect crystal there are no dislocations in the laying down of one unit cell next to another as the crystal grows. In such a case the angular range over which a crystal is rocked, and that a given reflection occurs, is approximately given by the angle defined by... 

Fig. 9.15. Top Polar diagram of the puckering phase 0(°) vs. the puckering amplitude q(k) of 52 cyclopenten-2-one fragments with no cyclic substitution and cr(C-C)<0.01 A from the July 1987 release of the CSD. Since coordinates of chiral molecules from racemic crystals refer to an arbitrarily chosen enantiomer, all points were transferred into the range (p = 270 - 90° by adding 180° (corresponding to the enantiomeric structure) if necessary. Bottom Mean bond angles with standard deviations from the 26 fragments from the above structures with (t(C-C)< 0.005 A...

Studies on the mechanism of zeolite crystallization have received extensive attention from many investigators (4, 16, 22, 24, 29, 30, 33, 37, 39). However, the main questions of the mechanism of crystallization referring to kinetics, such as the autocatalysis of the crystallization process, alkalinity effect on the rate of crystallization, the nature of the induction period, and seeding effects, have been insufficiently studied. The question of the role of solid and liquid phases in the formation of zeolite crystals in the heterogenous aluminosilicate systems also is still being discussed (16,22,25, 30,31,37,39). 

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