Oblique unit cell

Cu(111) to a lesser extent than on the other two low-index planes. This adsorption results in formation of an ordered structure above 103 L at room temperature, which is displayed as an oblique unit cell [ ]. This pattern has been previously reported (16). It is interesting that it has not been observed by other workers, possibly because of the extreme O2 exposures required and the faintness of the pattern. 

The unit cells for the two-dimensional lattices are parallelograms with their corners at equivalent positions in the array (i.e., the corners of a unit cell are lattice points). In Figure 1.17, we show a square array with several different unit cells depicted. All of these, if repeated, would reproduce the array it is conventional to choose the smallest cell that fully represents the symmetry of the structure. Both unit cells (la) and (lb) are the same size but clearly (la) shows that it is a square array, and this would be the conventional choice. Figure 1.18 demonstrates the same principles but for a centred rectangular array, where (a) would be the conventional choice because it includes information on the centring the smaller unit cell (b) loses this information. It is always possible to define a non-centred oblique unit cell, but doing so may lose information about the symmetry of the lattice. 

Fig. 6 In the case of the oblique unit cell the intensity of the (—11) signal in the XRD pattern is usually higher than the intensity of the (11) signal (left). This indicates that the layer fragments in the crystallographic unit cell are inclined toward the shorter diagonal [the crystallographic plane (—11)] of the primitive unit cell (right). The electron density map was reconstructed from the X-ray data (see Sect. 3) bright regions are filled by the aromatic parts of molecules while the dark regions are filled by the alkyl chains. Dotted lines show midplanes of the blocks...

The closest analogues of thiols, alkaneselenols R—SeH, were found to form well-packed monolayers on the Au(lll) surface. The structure of these layers was studied by X-ray diffraction. An oblique unit cell was revealed, indicating a distorted hexagonal close-packed lattice of selenol molecules . Benzeneselenol and diphenyl diselenide form identical monolayers on gold, as shown with STM microscopy. Monolayers of benzeneselenol do not have vacancy pits typical for thiolate monolayers, but show the presence of small islands of gold (20-200 A) which were absent before deposition . 

Another unique characteristic of the rigid-rod fibers is that they are single-phase paracrystalline fibers, which is significantly different from many polymer fibers with a two-phase semicrystalline structure. Table 5 lists refined PBZT, PBZO, and PIPD crystal parameters. All of them have monoclinic crystal unit cells. For PBZT, two molecular chains pass through an oblique unit cell. Figure 15 shows the crystal structural models of PBZT suggested by Takahashi (218) and Fratini (217). In the Takahashi crystal model of PBZT, there is disorder... 

The Z)-enantiomer of N-docosyl-leucine 2D-crystallises in an oblique unit cell, as expected. However, GIXD revealed a different oblique unit cell for the racemic mixture suggesting miscibility of the two enantiomers [152]. For myristoyl alanine monolayers, GIXD data indicated that a racemic mixture separated into 2D-crystalline islands of opposite chirality [153]. 

Figure 16-16. Molecular packing of Oocl-OPV5 in the crystal lattice. Lett oblique view of (he unit cell of Oocl-OPV5 right projection of the unit cell on a plane perpendicular to the ci-axis.

The dimer chains of Ca -ATPase can also be observed by freeze-fracture electron microscopy [119,165,166,172-174], forming regular arrays of oblique parallel ridges on the concave P fracture faces of the membrane, with complementary grooves or furrows on the convex E fracture faces. Resolution of the surface projections of individual Ca -ATPase molecules within the crystalline arrays has also been achieved on freeze-dried rotary shadowed preparations of vanadate treated rabbit sarcoplasmic reticulum [163,166,173,175]. The unit cell dimensions derived from these preparations are a = 6.5 nm b = 10.7 nm and 7 = 85.5° [175], in reasonable agreement with earlier estimates on negatively stained preparations [88]. 

Analysis of the lanthanide-induced crystalline arrays by negative staining (Fig. 5) or freeze-fracture electron microscopy reveals obliquely oriented rows of particles, corresponding to individual Ca -ATPase molecules [119]. The unit cell dimensions for the gadolinium-induced Ca -ATPase crystals are a = 6. l A, b = 54.4 A and y = 111°. Similar cell constants were obtained for the crystals induced by lanthanum, praseodymium and calcium. The unit cell dimensions of the Ei crystals are consistent with a single Ca -ATPase monomer per unit cell. The space group of the Eptype crystals is PI [119], while that of the E2 crystals is P2 [88,90]. 

If unit cell is orthogonal there are layers lines on oblique texture electron diffraction pattern. These lines occur when certain reciprocal lattice planes lie perpendicular to the texture axis. In this case period c may be more accurately determined by measuring the minor semi-axis R of any ellipse (in the presence of layer lines it is measured directly, since there is a zero line with /=0) and H of any reflection on that ellipse (preferably with a large l) ... 

TABLE 9.5 Relationship Between the Spacing dhk and the Side Lengths 5 and 5 in the Two-Dimensional Unit Cells of Square, Rectangular, and Oblique Parallelogram Nets... 

Figure 11.3. The five distinct plane (2D) lattices (a) oblique, (b) primitive rectangular, (c) square, (d) and (e) are both centered rectangular but show alternative choices of unit cell, (/) hexagonal.

Suppose we were to center the oblique lattice of Figure 11.3a. This does not in any way improve its symmetry. All we have is another, denser oblique lattice, which would be properly defined as having a smaller set of defining translation vectors and a unit cell with half the area, as shown in Figure 11.6a. 

Fig. 11 XRD pattern of modulated SmCG general tilt structure with the synclinic tilt of molecules in the neighboring layers. The pattern corresponds to a structure with the body center oblique crystallographic unit cell note that for this phase the tilt of the unit cell is correlated to the tilt of the molecules...

A repeat of Fig. 2.4.) The primitive direct-lattice unit cell in a triclinic (lowest-symmetry) crystal is an oblique parallelopiped with sidesa, b, c, interfacial angles ot, ft, and y and unit vectors ea, eb, and ec. 

The actual infinite lattices are obtained by parallel translations of the Bravais lattices as unit cells. Some Bravais cells are also primitive cells, others are not. For example, the body-centered cube is a unit cell but not a primitive cell. The primitive cell in this case is an oblique parallelepiped constructed by using as edges the three directed... 

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