Polytypes unit cell

The different forms of carbynes were assumed to be polytypes with different numbers of carbon atoms in the chains lying parallel to the hexagonal axis and different packing arrangements of the chains within the crystallite. Heimaim et al [23] proposed that the sizes of the unit cells were determined by the spacing between kinks in extended carbon chains, Fig. 3A. They were able to correlate the Cg value for the different carbyne forms with assumed numbers of carbon atoms, n (in the range n = 6 to 12), in the linear parts of the chains. 

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). 

Table 2.2 The Major Serpentine Group Minerals Composition, Polytype, and Unit Cell Dimensions... 

Minerals Composition Polytype" Crystal System Unit Cell Dimension ... 

The unit cell for the different polytypes will naturally vary, as will the number of atoms per unit cell. This will affect the number of electronic bands and the phonon branches for a given polytype. 

In order to distinguish the polytypes a prefix is added to the formula. The integer corresponds to half the number of X layers within the unit cell, which is equal to the number of sandwiches, XMX. The letter of the prefix designates the symmetry of the unit cell, e. g. T trigonal, H hexagonal or R rhombohedral. 

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. 

Because of their structural relationship, wollastonite and pturawolla-stonite are better described as polytypes rather than as polymorphs. Other polytypes are possible (Deer, Howie, and Zussraan 1963). For example, a new polytype would be formed if regular stacking faults occurred in every third triclinic unit cell, producing the packing sequence... 

This family has many polytypes with a variety of ground state, some of which will be discussed in the following. The crystal structures of these are basically the same, i.e. composed of two-dimensional ET layers, but spatial arrangements of ET molecules in a unit cell are different, which result in drastically different ground states as described below. 

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