Isotropic crystal structure

Whereas in many metals with relatively simple and isotropic crystal structures the parameter / has values between 0.5 and 1, it can have much more extreme values in materials in which the mobile species move through much less isotropic structures with 1-D or two-dimensional (2-D) channels, as is often the case with insertion reaction electrode materials. As a result, radiotracer experiments can provide misleading information about self-diffusion kinetics in such cases. 

When the two vectors are parallel, the crystal planes perpendicular to the line form a helix, and the dislocation is said to be of the screw type. In a nearly isotropic crystal structure, the dislocation is no longer associated with a distinct glide plane. It has nearly cylindrical symmetry, so in the case of the figure it can move either vertically or horizontally with equal ease. 

Kashiwagi et al.10) determined the second moment anisotropy for the one-way drawn polyethylene terephthalate sheets discussed above. The three lattice sums S00, S2q and S4o were calculated from the crystal structure determination of Daubeny et al., the proton positions being calculated on the basis of known bond angles and lengths. The isotropic lattice sum S00 was adjusted to a value consistent with the measured isotropic second moment of 10.3G2. The values for P200, P220 etc. were then used to predict the optical anisotropy. The predicted refractive indices for the sheets of draw ratio 2 1 and 2.5 1 are shown in Fig. 10, together with the experimental... 

Unlike low molar mass liquid crystals, these materials do not undergo a nematic-isotropic transition. Instead, they adopt liquid crystal behaviour throughout the region of the phase diagram for which they are in the melt. Above a particular temperature, rather than adopting an isotropic liquid structure, they decompose. 

In this section, we will describe the crystal structures of the mesogenic A -n-alkoxy-4-cyano-biphenyls (Fig. 1) [53-57]. The compounds have the phase sequences crystal-nematic-isotropic for CB05—CB07 and monotropic nematic for CB01-CB04 crystal-smectic A-nematic-isotropic for CB08. The crystal and molecular data of the investigated compounds CBOn are summarised in Table 2. 

Kurogoshi and Hori [ 104] determined the crystal structures of the mesogenic ethyl and butyl 4-[4-(4-n-octyloxybenzoyloxy)benzylidene]aminobenzoates. The compounds have different phase sequences crystal-smectic A-nematic-isotropic and crystal-smectic C-smectic A-nematic-isotropic for the ethyl and butyl compounds, respectively. Both compounds have layer structures in the solid phase. The butyl compound contains two crystallographically independent molecules. Within the layers, adjacent molecules are arranged alternately so as to cancel their longitudinal dipole moments with each other. In the ethyl compound the core moieties are almost perpendicular to the layer plane, while in the butyl compound these moieties are tilted in the layer. 

Small molecule crystallographers are familiar with these concepts, since it is routine to measure data at low temperature to improve precision by reduction of thermal motion, and structures are often done at multiple temperatures to assess the origins of disorder in atomic positions. Albertsson et al. (1979) have reported the analysis of the crystal structure of Z)(-l-)-tartaric acid at 295, 160, 105, and 35 K. Figure 22 shows the individual isotropic. S-factors for the atoms in the structure at each of these temperatures the smooth variation of B with T is apparent. Below 105 K, B is essentially identical for all atoms and is also temperature independent the value of B = 0.7 agrees well with the expected zero-point vibradonal value. However, even for this simple structure, not all of the atoms show B vs T behavior at high temperature which extrapolates to 0 A at 0 K. 

In particular, poly(amidoamine) dendrimers were peripherally modified with diimide moieties (see the structure shown in Scheme 1.43). After rednction with dithionite, this dendrimer was cast into a film, the electronic properties of which were isotropic. (This means that on the molecular and macroscopic levels, there is a three-dimensional (3-D) electron delocalization.) The conductivity was humidity dependent. Water molecules integrate into the material s crystal structure and take part in long-distance electron transfer. Such an effect of water was also observed to enhance electric... 

Chemical reactions in the sohd state have intrinsic features different from those for reactions performed in solution or in the gaseous state. For example, sohd-state organic reactions often provide a high regio- or stereoselectivity because the reactions and the structiue of a product are determined by the crystal structure of the reactant, i.e., the reaction proceeds under crystaUine lattice control [1-8]. When the reactant molecules are themselves crystalhne (molecular crystals) or are included in host crystals (inclusion compounds), the rate and selectivity of the reaction are different from those obtained in an isotropic reaction medium. 

Tables 1 through 7 giving positional and isotropic thermal parameters for most of the compounds discussed in this chapter. These data are taken, for the most part, from the literature, but, for a few materials that have not been structurally characterized, calculated positions are given. The tables also include lattice constants, space groups, and compositional data. Table 8 gives calculated x-ray powder diffraction information (26 (Cu), d-spacing, hkl, and intensity) for the same oxide compounds. In regard to the diffraction patterns, it should be remembered that preferred orientation and absorption effects, and cation substitutions will make the experimentally observed intensities differ from the calculated ones. Additional information on the crystal structures of high-Tc oxides can be found in a recent review (48).

The work of Cox, Cruickshank, and Smith (1958) on the crystal structure of benzene at — 3° C (a little below the melting-point) illustrates well this sort of application of the error synthesis. Fig. 215 shows the error synthesis (or difference synthesis) map in the plane of the benzene ring after a series of refinements in which only carbon atoms were included in the structure amplitude calculations, and thermal vibrations were assumed to be isotropic with a temperature factor B = 6-0 A2. 

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