Unit cells, dimensions

In optimisation on crystal properties, the first observables used were the unit cell dimensions, one to six data, which for technical reasons are concatenated to the conformational observables. Next, lattice energies were introduced, so far in a limited number. The use of other properties is being considered. 

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One of the things that can be done with a knowledge of the unit cell dimensions is to calculate the crystal density. This is examined in the following example. 

Use the unit cell dimensions cited above to determine the crystal density of polyethylene. Examine Fig. 4.10 to decide the number of repeat units per unit cell. 

Unit cell dimensions (A) Number of repeat units per cell Density (g cm 3)... 

For nosetip materials 3-directional-reinforced (3D) carbon preforms are formed using small cell sizes for uniform ablation and small pore size. Figure 5 shows typical unit cell dimensions for two of the most common 3D nosetip materials. Carbon-carbon woven preforms have been made with a variety of cell dimensions for different appHcations (27—33). Fibers common to these composites include rayon, polyacrylonitrile, and pitch precursor carbon fibers. Strength of these fibers ranges from 1 to 5 GPa (145,000—725,000 psi) and modulus ranges from 300 to 800 GPa. 

Fig. 5. Unit cell dimensions for carbon-carbon nosetip materials, parameters are...

The exchange energy coefficient M characterizes the energy associated with the (anti)paraHel coupling of the ionic moments. It is direcdy proportional to the Curie temperature T (70). Experimental values have been derived from domain-width observations (69). Also the temperature dependence has been determined. It appears thatM is rather stable up to about 300°C. Because the Curie temperatures and the unit cell dimensions are rather similar, about the same values forM may be expected for BaM and SrM. 

Sohd hydrogen usually exists in the hexagonal close-packed form. The unit cell dimensions are = 378 pm and Cg = 616 pm. SoHd deuterium also exists in the hexagonal close-packed configuration, and = 354 pm, Cg = 591 pm (57—59). 

Density. Although the polymer unit cell dimensions imply a calculated density of 1.33 g/cm at 20°C, and extrapolation of melt density data indicates a density of 1.13 g/cm at 20°C for the amorphous phase, the density actually measured is 1.15—1.26 g/cm, which indicates the presence of numerous voids in the stmcture. 

USY Zeolite ( 7 Al Atoms/u.c.) unit Cell Dimension =24.25 A (Si02/Ai203=54)... 

Relate unit cell dimensions to atomic or ionic radii (Examples 9.8,9.9 Problems 49-58) 51,53,56,76... 

Because of anomalous scattering by H the results for the as-precipitated Ni(OH)2 could not be refined. Nevertheless, cell constants and the O-H bond distance could be determined. The results showed that the as-precipitated material was different from the well-crystallized material. The unit cell dimensions were aQ =3.119 and c0 =4.686 A. Also the... 

An analogous case, of identical chain conformations as well as of similar unit cell dimensions, have been described for the two crystalline forms of poly-p-phenylene terephtalamide [33-36] (better known with the trade name of Kevlar). The projections along the c axis of the packing of the chains proposed for the two forms [36] has been sketched in Fig. 8, corresponding to the localization of the chain axes in (0,0, z) and (1/2,1/2, z) for the more common polymorph, in (0, 0, z) and (1/2,0, z) for the other polymorph. 

The distance of each reflection from the center of the pattern is a function of the fiber-to-film distance, as well as the unit-cell dimensions. Therefore, by measuring the positions of the reflections, it is possible to determine the unit-cell dimensions and, subsequently, index (or assign Miller indices to) all the reflections. Their intensities are measured with a microdensitometer or digitized with a scanner and then processed.8-10 After applying appropriate geometrical corrections for Lorentz and polarization effects, the observed structure amplitudes are computed. This experimental X-ray data set is crucial for the determination and refinement of molecular and packing models, and also for the adjudication of alternatives. 

The materials for solid solutions of transition elements in j3-rh boron are prepared by arc melting the component elements or by solid-state diffusion of the metal into /3-rhombohedral (/3-rh) boron. Compositions as determined by erystal structure and electron microprobe analyses together with the unit cell dimensions are given in Table 1. The volume of the unit cell (V ) increases when the solid solution is formed. As illustrated in Fig. 1, V increases nearly linearly with metal content for the solid solution of Cu in /3-rh boron. In addition to the elements listed in Table 1, the expansion of the unit cell exceeds 7.0 X 10 pm for saturated solid solutions " of Ti, V, (2o, Ni, As, Se and Hf in /3-rh boron, whereas the increase is smaller for the remaining elements. The solubility of these elements does not exceed a few tenths at %. The microhardness of the solid solution increases with V . Boron is a brittle material, indicating the accommodation of transition-element atoms in the -rh boron structure is associated with an increase in the cohesion energy of the solid. 

Fig. 7. A typical X-ray diffraction pattern of the Fepr protein fromZJ. vulgaris (Hil-denborough). The pattern was recorded on station 9.6 at the Synchrotron Radiation Source at the CCLRC Daresbury Laboratory using a wavelength 0.87 A and a MAR-Research image-plate detector system with a crystal-to-detector distance of 220 nun. X-ray data clearly extend to a resolution of 1.5 A, or even higher. The crystal system is orthorhombic, spacegroup P2i2i2i with unit cell dimensions, a = 63.87, b = 65.01, c = 153.49 A. The unit cell contains four molecules of 60 kDa moleculEu- weight with a corresponding solvent content of approximately 48%.

This is shown in the following diagram. Note that a simple shift in unit cell dimension is all that is required for the crystal structure change to take place. 

Table 1. Unit Cell Dimensions and Zn/Cu Ratios in Aurichalcite...

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