Layer stacking sequences

Figure 5. Structure of LiC6. (a) Left schematic drawing showing the AA layer stacking sequence and the aa interlayer ordering of the intercalated lithium. Right Simplified representation [21. (b) In-plane distribution of Li in LiC6. (c) In-plane distribution of Li in LiC,.

Finally, as another simple example of description (and symbolic representation) of structures in terms of layer stacking sequence, we now examine structures which can be considered as generated by layer networks containing squares. A typical case will be that of structures containing 44 nets of atoms (Square net S net). The description of the structures will be made in terms of the separation of the different nets, along the direction perpendicular to their plane, and of the origin and orientation of the unit cell. 

The sphalerite- and wurtzite-type structures belong to a homeotect structure type set. The layer stacking sequence symbols (triangular nets) of the two structures are ... 

The structure can be described by the following layer stacking sequence triangular and kagome (T,K) nets ... 

The layer stacking sequence symbol of this structure may be compared with those of the hP2-WC and hP3-AlB2 types ... 

Ex-situ experiments by Fogg and co-workers suggested that the rhombo-hedral liAl- Cl LDH did not form staging intermediates when reacted with dicarboxylate salts [40]. In-situ measurements have confirmed that these reactions are indeed direct one-step processes. Similarly, staging is not seen for the intercalation of phosfonate salts (Fig. 13a). The alteration of the layer stacking sequence therefore has a profoimd effect on the reaction pathway [41 ]. 

Figure 26. Displacement of the layer stacking sequence (see text) on intercalation of lithium in graphite.11 Reprinted from J. Maier, Physical Chemistry of Ionic Materials. Ions and Electrons in Solids. Copyright 2004 with permission from John Wiley Sons, Ltd.

In addition, structural similarities can often be determined from careful interpretation of XRD powder patterns. The powder patterns of offretite and erionite look quite different, but are easily understood in terms of the crystallographic consequences of a change in the ordered layer stacking sequence (11), cf. Figure 4. In offretite, the layers are stacked in an AAB sequence, while in erionite, they are ordered in an AABAAC arrangement that doubles one of the crystallographic unit cell parameters. The doubled c-parameter is readily deduced from an analysis of the XRD powder pattern of erionite. Another framework structure effect, isomorphous substitution, can result in changing unit cell sizes, observed as shifts in XRD line positions for such systems as X and... 

TI2O is a variant of the anti-Cdl2 structure, which is the HCP counterpart to the anti-CdCl2 structure discussed in connection with CS2O (Section 3.2.2). For the thallium compound, there is a 12 layer stacking sequence in which the lone pair plays an important role. 

This raises the question of the carbon-layer stacking sequence. If the sequences were ordered, i.e., if we had ABAB. .. or AbCABC. .., the consequences of that ordering would be evident in the diffraction data. There is no evidence for such ordering. The ABAB sequence should produce easily detectable (10/) reflections based on a cell Oq - Hg(graphite) and c = 2/,. No sharp reflection occurs but the required d spacing of (103) is close to that of line C. The ordered ABCABC sequence would explain the absence of (100), but neither of the sequences can account for line B nor the general absence of (10/) reflections. 

The FCC structure is an equally close-packed arrangement. Its relation to the HCP structure is not immediately obvious, but Fig. 2-16 shows that the atoms on the (111) planes of the FCC structure are arranged in a hexagonal pattern just like the atoms on the (0002) planes of the HCP structure. The only difference between the two structures is the way in which these hexagonal sheets of atoms are arranged above one another. In an HCP metal, the atoms in the second layer are above the hollows in the first layer and the atoms in the third layer are above the atoms in the first layer, so that the layer stacking sequence can be summarized as A B A B A B. The first two atom layers of an FCC metal are put down in the same way, but the atoms of the third layer are so placed in the hollows of the second... 

Takeda H (1967) Determination of the layer stacking sequence of a new complex mica polytype A 4-layer Lithiirm Fluorophlogophite. Acta Crystallogr 22 845-853 Takeda H (1969) Existence of complex mica polytype series based on 2A7i sequence. Jpn Crystallogr Assoc Auturrm Meeting, Iwate, 2-3 (in Japanese)... 

If the framework structure proposed for ZSM-3 is a nine-layer stacking sequence of truncated octahedra, there are 256 possible structures. Many of these are identical, and in some cases limitations are imposed by space group symmetry but the number of possible framework structures is still large. 

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