Crystal interaction

Crystallization is one of the oldest unit operations in the portfoho of industrial and/or laboratory separations. Almost all separation techniques involve formation of a second phase from a feed, and processing conditions must be selected that allow relatively easy segregation of the two or more resulting phases. This is a requirement for crystallization also, and there are a variety of other properties of the sohd product that must be considered in the design and operation of a crystallizer. Interactions among process, function, product, and phenomena important in crystallization ate iRustrated in Figure 1. 

Politzer 1992b). This is consistent with fluorine in organic crystals interacting only with electrophiles and in an intermediate-type orientation. 

The second step in Ten Cate s two-step approach was to focus on crystal-crystal interaction by means of an explicit two-phase DNS of the turbulent suspension that completely resolves the translational and rotational motions and collisions of the spherical particles plus the turbulence of the liquid between the particles. The particle motions are driven by the turbulent flow and the particles affect the turbulent flow of the liquid in between. When particles approach one another down to a distance smaller than the grid spacing, lubrication theory is exploited to bridge the gap between them. 

Crystal interactions may lead to a number of readily observable consequences. The molecular geometries may be different in different polymorphic forms of a given compound or, as in the case above, in symmetry-independent sites in a given crystal a change of molecular substituents remote from the torsionally flexible bonds may change the molecular conformation, as a result of modification... 

In crystallography, the difiiraction of the individual atoms within the crystal interacts with the diffracted waves from the crystal, or reciprocal lattice. This lattice represents all the points in the crystal (x,y,z) as points in the reciprocal lattice (h,k,l). The result is that a crystal gives a diffraction pattern only at the lattice points of the crystal (actually the reciprocal lattice points) (O Figure 22-2). The positions of the spots or reflections on the image are determined hy the dimensions of the crystal lattice. The intensity of each spot is determined hy the nature and arrangement of the atoms with the smallest unit, the unit cell. Every diffracted beam that results in a reflection is made up of beams diffracted from all the atoms within the unit cell, and the intensity of each spot can be calculated from the sum of all the waves diffracted from all the atoms. Therefore, the intensity of each reflection contains information about the entire atomic structure within the unit cell. 

The two previously described interactions are sufficient to provide a two-dimensional or sheeted chromatin structure. The intermolecular interaction that provides the third dimensional packing of chromatin sheets is most likely the metalion interaction described previously. While it is tempting to describe this feature as a general chromatin interaction, it is absent in the histone octamer crystal interaction (PDB access number 1HQ3). Instead the contact residues (the side chains of Gin 76 and Asp 77 of 2H3 and the main chain carbonyl of Leu 22 of 2H4... 

Silinsh EA, Capek V (1994) Organic molecular crystals. Interaction, localization and transport properties. American Institute of Physics, New York... 

E. A. Silinsh, V. Capek, Organic molecular crystals Interaction, localization, and transport phenomena, AIP Press, New York, 1994. 

Crystals interact with molecules of the environment via the surfaces that delineate them. Consequently, several of their properties, such as their morphology, structure and symmetry of solid-solutions and their etch-pit patterns formed upon partial dissolution, depend on an interplay between the surface structures of the crystal faces and the composition of the solution. For example, crystallization of a racemate undergoing spontaneous resolution in the... 

M. Pope and C.E. Swenberg, Electronic Processes in Organic Crystals (Clarendon, Oxford, 1982) E.A. Silinsh and V. Capek, Organic Molecular Crystals Interaction, Localization and Transport Phenomena (Am. Inst. Phys., New York, 1994). 

Silinsh, E. A., and Capek, V., in Organic Molecular Crystals Interaction,... 

Silinsh, E. A., in Organic Molecular Crystals, Springer-Verlag, Berlin, 1980. Silinsh, E. A., and Capek, V., in Organic Molecular Crystals Interaction,... 

For the particular case of longitudinal optical modes, we found in Eq. (9-27) the electrostatic electron-phonon interaction, which turns out to be the dominant interaction with these modes in polar crystals. Interaction with transverse optical modes is much weaker. There is also an electrostatic interaction with acoustic modes -both longitudinal and transverse which may be calculated in terms of the polarization generated through the piezoelectric effect. (The piezoelectric electron phonon interaction was first treated by Meijer and Polder, 1953, and subsequently, it was treated more completely by Harrison, 1956). Clearly this interaction potential is proportional to the strain that is due to the vibration, and it also contains a factor of l/k obtained by using the Poisson equation to go from polarizations to potentials. The piezoelectric contribution to the coupling tends to be dominated by other contributions to the electron -phonon interaction in semiconductors at ordinary temperatures but, as we shall see, these other contribu-... 

As shown within, accounting for crystal interactions can lead to improved results in most cases [C(N3H)], however, not for C(N1). Thus, the newly proposed mechanism should not be discarded based solely on these arguments... 

When a diffraction grating, such as a crystal, interacts with X rays, the electron density that causes this diffraction can be described by a Fourier series, as discussed in Chapter 6. The diffraction experiment effects a Fourier analysis, breaking down the Fourier series (of the electron density) into its components, that is, the diffracted beams with amplitudes, F[hkl). The relative phases a(hkl) are, however, lost in the process in all usual diffraction experiments. This loss of the phase information needed for the computation of an electron-density map is referred to as the phase problem. The aim of X-ray diffraction studies is to reverse this process, that is, to find the true relative phase and hence the true three-dimensional electron density. This is done by a Fourier synthesis of the components, but it is now necessary to know both the actual amplitude F[hkl) and the relative phase, a[hkl), in order to calculate a correct electron-density map (see Figure 8.1). We must be able to reconstruct the electron-density distribution in a systematic way by approximating, as far as possible, a correct [but so far unknown) set of phases In this way the crystallographer, aided by a computer, acts as a lens for X rays. 

Shear-induced crystallization had a much greater effect in bulk systems than emulsified systems (Fig. 6) and resulted in an accelerated rate of crystallization. Prior to, and during, the initial stages of crystallization, intradroplet fat is protected from interdroplet crystallization by the spherical shape and pressure of the droplet and is not directly available to the shear field, i.e., no protruding crystals. This observation is consistent with microstructure work where limited destabilization was observed in droplets with no visible crystals. Initially, droplet interfaces in the PSCO system showed that the crystallized fat was not available at the surface, limiting the occurrence of crystal-induced flocculation and coalescence. Droplets remained stable until their interfaces were disturbed by the shear fleld or crystal interaction. 

Tricyanomethanide ion. The very small deviations from planarity of this ion observed in certain salts have been attributed to crystal interactions. This ion can form interesting polymeric structures with metal ions. In the argentous compound the group acts as a 3-connected unit in layers based on the simplest 3-connected plane net, and these layers occur as interwoven pairs as described on p. 90. 

The 320 nm electronic spectrum of naphthalene was the first for which the theory was developed in detail [67]. In the vapour spectrum there are two interpenetrating band systems. One system with oscillator strength f=0.0002 is very weakly electronically allowed and long-axis polarized. The other stronger (f=0.002) system is short axis polarized, and is induced by vibrational perturbation. In the crystal the effect of the crystal field on these systems is different. We had shown experimentally [66] that the origin transition on the one hand and the vibrationally induced transition on the other, were differently affected by crystal interactions. The origin band is split by 151 cmJl and the vibrational by less than 1 cm-1. 

The value of the exponent b is usually between 1 and 2.5, considerably lower than any predictions based on primary nucleation. The value of the exponent k is usually between 2 and 4. The value of j is generally close to 1, implying that collisions with the impeller(s) and other parts of the crystallizer are more important than crystal-crystal interactions. 

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