INDEX polytypes

The identity of the polytype present in a given LDH sample may, in principle at least, be determined from the powder XRD pattern, although as we shall see for many LDHs this is not possible, as the amoimt of useful information therein is limited. By convention, the indexing of powder patterns for rhombohedral polytypes is based on a triple hexagonal unit cell (see Fig. 3). 

Fig. 8 Examples of diffraction patterns of poorly crystalline LDHs that can best be indexed as one layer polytypes. Reprinted with permission from [118]. Copyright American Chemical Society...

Perhaps the more important questions raised by Rule 5, as Burdett and McLarnan (1984) point out, concern the extent to which it really is borne out by observation. For example, Baur et al. (1983) have developed a numerical index for the degree of parsimony in a crystal structure and have shown that, using this measure, many crystal structures are not parsimonious but lavish in their use of different local environments. Also, the dominance of short-range forces is by no means obvious when ordered structures with extremely large unit cells are observed (e.g., a c dimension of 1500 A in some SiC polytypes Shaffer, 1969). The explanation of such structures poses problems for electrostatic as well as covalent models. 

Table 5a. Conversion of characters appearing in the OD s nnbols of mica polytypes. The individual operations are characterized by their extended Hermann-Mauguin (H-M) symbols and by the corresponding operations indexed in orthogonal (ORT) C2 -setting axes. Cf. Table 1 and Backhaus and Durovic (1984).

Subfamily B polytypes show two reflections along D rows. However, polytypes of this subfamily either are orthogonal or belong to Class b, for which the non-right angle is a (before the axes interchange) and the /c index of the superlattice nodes does not depend on h. The reciprocal sublattice in this case matches for all polytypes, which is consistent with the fact that the primitive cell of the family structure is hexagonal. 

Syngony of the individual Lattice of the individual Twin lattice Kind of twinning Twin laws Twin index Rotation between pairs of individuals Polytypes... 

In micas, and more generally in layer compounds, plesiotwinning represents a generalization of the concept of twinning, at least from the lattice viewpoint. In twins the CSL produced in each plane (orthogonal polytypes) or in one plane out of three (non-orthogonal polytypes) has E factor 1, whereas in plesiotwins the CSL has E factor of n > 1 (n > 7 for the hp lattice). The twin/plesiotwin index is thus 1 (twinning by merohedry)... 

Figures 37-40 present the diffraction patterns from three SX planes. The shortest separation between successive reflections along c of X rows is c i/6 the apparent period is six layers and thus the / index of all the reflections are expressed as (mod 6). Figure 40 shows the diffraction pattern from an SD plane of the same sample which, with one reflection for c i repeat, has the typical appearance of a subfamily A polytype. The presence of twinning is not evident from this plane.

The cell of the allotwin lattice has a period of 6cq along c and contains six lattice planes of the IM polytype and three lattice planes of the 2M polytype. Of these, only the plane with z = 0(mod 6) has all the nodes from both polytypes overlapped by the allotwin operation, whereas in all the other lattice planes the nodes from the two polytypes are separated. Consequently, the allotwin index of IMis 6, and that of 2M is 3. 

This Datareview outlines the data on optical absorption and refractive index in the various polytypes of SiC. The optical transitions give rise to the characteristic colour of each polytype. Values for both the ordinary and extraordinary refractive indices versus wavelength are given. 

Optical absorption and refractive index of SiC TABLE 3 Refractive index of SiC polytypes. 

The interband transitions in SiC polytypes give rise to the characteristic colours of green (6H), yellow (15R) and green-yellow (4H). Cubic SiC exhibits a pale yellow colour when undoped and greenish yellow in the doped state. The variations of refractive index with wavelength for the 3C, 2H, 4H, 6H and p-SiC polytypes are listed. 

Thirdly, in eoexistenee with the polytype DyAls erystals, there are some isolated erystals with different struetures. Some of them are eomplex. Only one has been indexed as a primitive eubic (a = 7.20 A) or a bee one (a = 10.15 A). 

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