The Pattern of Crystallization

Nevertheless, it has subsequently been suggested that, for polyethylene, there could be a phase inversion at small lamellar thickness which could make the hexagonal the precursor of orthorhombic crystallization from the melt even at atmospheric pressure [4]. The basis of this proposal will now be outlined and the conclusion reached that it is inapplicable, in part because the effective fold surface energy during growth of hexagonal lamellae is not sufficiently low. 

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For powder photographs, the use of the charts described on p. 143 and in Appendix 3 will show whether the substance is cubic, tetragonal, or hexagonal if it is not, the numerical methods of indexing the patterns of crystals of low symmetry may be tried or, if it is. possible to pick out single crystals, or if the specimen can be recrystallized to give suitable crystals, the unit cell dimensions may be determined by the methods described earlier. A search may then be made in the tables of Donnay and Nowacki (1954), in which, for each crystal system, the species are arranged in order of the axial ratios. 

Although the structure of the surface that produces the diffraction pattern must be periodic in two dimensions, it need not be the same substance as the bulk material. Thus LEED is a particularly sensitive tool for studying the structures and properties of thin layers adsorbed epitaxially on the surfaces of crystals. 

A larger number of smaller spherulites are produced at larger undercoolings, a situation suggesting nucleation control. Various details of the Maltese cross pattern, such as the presence or absence of banding, may also depend on the temperature of crystallization. 

The pattern of hydrogen bonding between a pair of acylurea derivatives revealed by X-ray analysis was consistent with that predicted by spectroscopic studies. Typical examples are illustrated in Figs. 11 and 12 35-37) two NH — O intermolecular hydrogen bonds connect the two molecules. This holds true for the other acylurea derivative 20 (R8 = CH2Ph)38) and 1 1 complexes whose crystal structures were so far determined. 

The pattern of variation of the multiplets differ among the samples. The relative intensities are not constant and they are not in the ratios of small numbers as would be expected if they arose from different points within a single unit cell. The spectral intensities are also not consistent within a single unit cell. The spectral intensities are also not consistent with the possibility of three independent crystal forms. According to Atalla therefore a model based on two independent crystalline forms seems most possible. In Fig. 5, the spectrum of pure cellulose II is given. 

If we prescribe rules for one type of cell in Figure 5.6, where the, a, faces form strong bonds with each other, while the, bb, and, ab, junctures are not strong, we anticipate a particular pattern of crystal structure to form. 

The next most importtmt parameters in Czochralski growth of crystals are the heat flow and heat losses in the system. Actually, aU of the parameters (with the possible exception of 2 and 9) are strongly ciffected by the heat flow within the crystal-pulling system. A tj pical heat-flow pattern in a Czochralski sjretem involves both the crucible and the melt. The pattern of heat-flow is important but we will not expemd upon this topic here. Let it suffice to point out that heat-flow is set up in the melt by the direction of rotation of the cr5rstal being pulled. It is also ctffected by the upper surface of the melt and how well it is thermally insulated from its surroundings. The circular heat flow pattern causes the surface to radiate heat. The crystal also absorbs heat and re-radiates it... 

In many foods, it is essential to control either sugar or ice crystal patterns and in others there is a problem of controlling both. In Table I are listed the foods in which we encounter crystalline structure problems and the type of crystals with which we are concerned. 

It is important to note that this second choice is possible because expression (25) includes the smooth background belonging to the crystalline phases, so it can be separated from the background due to the amorphous phase. A typical example, where the amorphous phase is not available, is the study of crystallization process. In this case, the composition and the diffraction pattern of the amorphous phase can change a lot. 

II, and III), two were monohydrates (termed a-monohydrate and /3-monohydrate) and one was a ferf-butylamine disolvate. The differences in the powder patterns of the phases were readily evident (Table 1). This study demonstrates the unique ability of x-ray diffractometry for the identification of (1) anhydrous compound existing in both crystalline and amorphous states, (2) different polymorphic forms of the anhydrate, (3) the existence of solvates where the solvent of crystallization is water (hydrate) or an organic solvent (in this case, /m-butylamine), and (4) polymorphism in the hydrate. 

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