Crystallization general considerations

Emsley, J.W. Liquid crystals general considerations, vol. 4, Wiley, Chichester 1996. 

W.J. Emdey, Liquid Crystals general considerations. Encyclopedia of Nuclear Magnetic Resonance, in D.M. Grant, R.K. Harris (Eds.), vol. 4, John Whey Sons, Chichester, UK, 1996, p. 2788. 

Effect of Crystal Defects on Corrosion—General Considerations... 

It follows from general considerations that the role of the shape of the filler particles during net-formation must be very significant. Thus, it is well-known that the transition from spherical particles to rod-like ones in homogeneous systems results in such radical structural effect as the formation of liquid-crystal phase. Something like that must be observed in disperse systems. 

In general, Cv is obtained from Cp by taking the isobaric expansivity and isothermal compressibility of the crystal into consideration ... 

The same general considerations apply to nonazo pigments. Attempts have been made to theoretically interpret absorption spectra of polycylic compounds by quantum mechanics. These studies compared the absorption of systems such as indigo [1] with known spectra of polymethine dyes. However, the investigation of solid state spectra is aggravated by interactions within the crystal lattice and has rarely been studied. 

General Considerations.—Solid crystallisable substances are usually obtained at the end of a reaction in the form of a crude product which separates in more or less pure form from the solvent on cooling, either directly or after concentration. The rate at which organic substances crystallise varies within very wide limits, and their tendency to form supersaturated solutions is extraordinarily great. But even when supersaturation is counteracted by dropping a crystal into the solution—by seeding —the attainment of equilibrium in the cold saturated solution is often exceedingly slow. The cause is indeed the slow rate of crystallisation. Hence the full yield of crude product is often obtained only after the solution has been left for many hours. 

The above remarks refer only to the relative dimensions of crystals. A consideration of the indices of the principal bounding faces may lead to further conclusions, at any rate for molecular crystals. The bounding faces on crystals are apparently those planes having the greatest reticular density of atoms or molecules the indices of the bounding faces may therefore indicate the general arrangement of the molecules. For instance, when a crystal is found to be bounded entirely or mainly by faces of 110 type (110, Oil, 101, etc.) it is likely that there are molecules... 

Noncrystalline materials exist in many different forms. A huge variety of atomic and molecular structures, ranging from liquids to simple monatomic amorphous structures to network glasses to dense long-chain polymers, are often complex and difficult to describe. Diffusion in such materials occurs by a correspondingly wide variety of mechanisms, and is, in general, considerably more difficult to analyze quantitatively than is diffusion in crystals. 

In Eq. (10), E nt s(u) and Es(in) are the s=x,y,z components of the internal electric field and the field in the dielectric, respectively, and p u is the Boltzmann density matrix for the set of initial states m. The parameter tmn is a measure of the line-width. While small molecules, N<pure solid show well-defined lattice-vibrational spectra, arising from intermolecular vibrations in the crystal, overlap among the vastly larger number of normal modes for large, polymeric systems, produces broad bands, even in the crystalline state. When the polymeric molecule experiences the molecular interactions operative in aqueous solution, a second feature further broadens the vibrational bands, since the line-width parameters, xmn, Eq. (10), reflect the increased molecular collisional effects in solution, as compared to those in the solid. These general considerations are borne out by experiment. The low-frequency Raman spectrum of the amino acid cystine (94) shows a line at 8.7 cm- -, in the crystalline solid, with a half-width of several cm-- -. In contrast, a careful study of the low frequency Raman spectra of lysozyme (92) shows a broad band (half-width 10 cm- -) at 25 cm- -,... 

Several theories have been developed to explain how energy absorbed by one molecule is transferred to a second acceptor molecule of the same or a different species. At first sight exciton theory,20 66 which accounts for excitation transfer in molecular aggregates or crystals and the Davydov splitting effects connected with it, appears to bear little relationship to the treatment of long-range resonance transfer as developed, for example, by Forster.81-32 However, these theories can be shown to arise from the same general considerations treated at different well-defined mathematical limits.33-79... 

For the preparation of inorganic materials with well-defined morphologies, liquid phase syntheses are preferred. These synthetic reactions proceed at relatively lower temperatures and therefore require lower energies. The sol-gel (alkoxide) method is one of these methods - however, this method usually gives amorphous products, and calcination of the products is required to obtain crystallized products. In this chapter, solvothermal methods are dealt with, which are convenient for the synthesis of a variety of inorganic materials. General considerations for solvothermal reactions are discussed first and then the solvothermal synthesis of metal oxides is reviewed. 

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