The Crystallographic Indexing

As mentioned in Section 5.1, adsorption of components of the electrolysed solution plays an essential role in electrode processes. Adsorption of reagents or products or of the intermediates of the electrode reaction or other components of the solution that do not participate directly in the electrode reaction can sometimes lead to acceleration of the electrode reaction or to a change in its mechanism. This phenomenon is termed electrocatalysis. It is typical of electrocatalytic electrode reactions that they depend strongly on the electrode material, on the composition of the electrode-solution interphase, and, in the case of single-crystal electrodes, on the crystallographic index of the face in contact with the solution. 

Recently, the In situ Raman scattering from Fe-TsPc adsorbed onto the low Index crystallographic faces of Ag was examined and the results obtained are shown In Fig. 5 (15). On the basis of the similarities of these spectra with those obtained for the macrocycle In solution phase, as well as the polarization behavior characteristics, It has been concluded that the most likely configuration Is that with the macrocycle edge-on with respect to the surface. This Is In agreement with conclusions reached from the UV-vlslble reflectance spectra. The preferred configuration, however, may depend on the particular macrocycle, as well as on the nature of the adsorption site. 

Figure 9.4. Characterization of mesoporous Si02 films with cylindrical mesopores (ca. 3nm in diameter) templated using Brij 58 surfactant TEM image a), 2D GISAXS pattern with crystallographic indexation b), and SRSAXS/XRR analysis c).The experimental data in c) thus correspond to a detailed scan along the sz axis in b), using a suitable diffractometer. The films were prepared according to Ref. 39 and analyzed by the methods described therein.

Different from the critical radius, Mori et al. [89] proposed a concept of effective crystallographic index to maximize the oxide ionic conductivity of doped ceria. The index, I, is defined as... 

Figure 3.13. Crystallographic index of a plane. The plane shown in (a) has the intercepts A - a,...

A certain anisotropy of the refractive index along specific crystallographic axes indicates that the microstructures in the porous network are not spherical but somewhat elongated along the PS growth direction [Mi4], This birefringence is below 1% for micro PS, while it may reach values in the order of 10% for meso PS films formed on (110) oriented silicon wafers [Ko22]. 

Single-crystal precession data indicate orthorhombic symmetry with the crystallographic space group Fddd. This system is not isostructural with any other known metal oxyfluoride or metal dioxide. The cell dimensions, determined from Guinier data, are a = 8.370 1 A. b = 10.182 1 A. and c = 7.030 1 A. The indexed powder data are given in reference 6. 

As mentioned earlier, the unit-cell space group can be determined from systematic absences in the the diffraction pattern. With the space group in hand, the crystallographer can determine the space group of the reciprocal lattice, and thus know which orientations of the crystal will give identical data. All reciprocal lattices possess a symmetry element called a center cf symmetry or point of inversion at the origin. That is, the intensity of each reflection hkl is identical to the intensity of reflection -h k -1. To see why, recall from our discussion of lattice indices (Section II.B) that the the index of the (230) planes can also be expressed as (-2 -3 0). In fact, the 230 and the —2 -3 0 reflections come from opposite sides of the same set of planes, and the reflection intensities are identical. (The equivalence of Ihkl and l h k l is called Friedel s law,but there are exceptions. See Chapter 6, Section IV.) This means that half of the reflections in the reciprocal lattice are redundant, and data collection that covers 180° about any reciprocal-lattice axis will capture all unique reflections. 

In producing an image of molecules from crystallographic data, the computer simulates the action of a lens, computing the electron density within the unit cell from the list of indexed intensities obtained by the methods described in Chapter 4. In this chapter, I will discuss the mathematical relationships between the crystallographic data and the electron density. 

In non-polar, isotropic crystals or in glasses, there is no crystallographic direction distinguished and the linear electro-optic effect is absent. Nevertheless a static field may change the index by displacing ions with respect to their valence electrons. In this case the lowest non-vanishing coefficients are of the quadratic form, i.e. the refractive index changes proportionally to the square of the applied field Kerr effect . 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

Such techniques were used by Benard and Oudar and co-workers (5) on polycrystalline Cu catalysts (9), on monocrystals of Ag (10), and on other metals (//). On the low-index Ag monocrystals, the bonding energy of chemisorbed sulfur follows the sequence (110) > (100) >(111), showing that the sulfur affinity changes with respect to the crystallographic orientation under consideration and therefore on the basis of the coordination number. 

These three numbers enclosed in parentheses and not separated with commas, that is, (M/), named the Miller indexes, denote the crystallographic plane. 

Henceforth, crystal structure analyses of carbohydrates (class 45), amino acids (class 48), purines and pyrimidines (class 44) and nucleosides and nucleotides (class 47) are referenced by means of their Cambridge Crystallographic Data Base REFCODES. All other crystal structure analyses are referenced in the General Index. 

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