Unit cell orientation

FIGURE 2.15. Some faces of sodium chloride crystals, labeled for a unit cell oriented as in Figure 2.5. Sodium cations are denoted Na, and chloride anions are denoted Cl. (a) When a crystal grows as a cube, its faces have equal numbers of sodium and chloride ions on their surfaces, (b) When the crystals grow as octahedra, the faces contain only one type of ion, either sodium or chloride. 

Figure 10. Relationships between unit cell orientations for lAlmcm, Pnma and Cmcm structures and the reference axes, X, Y, Z. Cell edges of the Pm3m unit cell are parallel to the reference axes. The P lmbm structure has the same unit cell as the IMmcm strac-ture, except that the c repeat of the former is half that of the latter (from Carpenter et al. 2000b).

The orientation of crystalline stems with respect to the interface of the microstructure in block copolymers depends on both morphology and the speed of chain diffusion, which is controlled by block copolymer molecular weight and the crystallization protocol (i.e. cooling rate). In contrast to homopolymers, where folding of chains occurs such that stems are always perpendicular to the lamellar interface, a parallel orientation was observed for block copolymers crystallized from a lamellar melt phase perpendicular folding was observed in a cylindrical microstructure. Both orientations are shown in Fig. 8. Chain orientation can be probed via combined SAXS and WAXS on specimens oriented by shear or compression. In PE, for example, the orientation of (110) and (200) WAXS reflections with respect to Bragg peaks from the microstructure in the SAXS pattern enables the unit cell orientation to be deduced. Since PE stems are known to be oriented along the c axis, the chain orientation with respect to the microstructure can be determined. 

Figure 7. Proposed nature of twin boundaries in Ba2YCu307. The unit cell orientation on either side of the twin boundary is labeled.

Lovinger AJ (1983) Microstmcture and unit-cell orientation in a-polypropylene. J Polym Sci Polym Phys Ed 21 97... 

Poly(ethylene oxide) has been investigated in both a single-crystal form and in normal or commercial, partially crystalline form. Single crystals have been examined by X-ray analysis and have been shown to be flat platelets with the c-axis of the unit cell oriented normal to the basal plane (34). Electron microscopy has shown bulk crystallized polymer to have a lamellar structure (35, 36), and single-crystal lamellae have been grown from dilute solution (37, 38). 

Finally, the crystal must be oriented in the laboratory axis system (X, Y, Z). The experiment is carried out with light polarized parallel to the long axis of the crystal (denoted X) in the lab frame = (1,0,0) and (perpendicular to the long axis of the crystal (denoted either the Y or Z) in the lab frame. = (0,1,0) or = (0,0,1). The intensity of polarized absorption for a given transition is proportional to the sum (over the four unit cell sites) of the squares of the site-projected and unit cell-oriented transition moments in the laboratory axis system (X, Y, Z). 

Second, only 20 reflection and its corresponding higher order reflections (see Figs. 9.3a, b) of Coir are visible in thin films, while several different hk reflections are observed for thick films (see Fig. 9.1). These results indicate a high preferential orientation of the rectangular unit cell in thin films so that (20) planes are parallel to the substrate surface. This unit cell orientation is consistent with a planar alignment... 

The presence of more than one molecule in the unit cell oriented in a different way leads to splitting of the IR band according the Bethe theory and the submaxima possess different polarization. In these cases the eUmination is obtained to an inflex point as shown in Figure 2.26, where the consequent elimination of the submaxima at 1738 cm- in 4 -cyanophenyl-4-n-heptylbenzoate is obtained. 

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