Hexagonal cell positions

A detailed example of the alternative descriptions of a given compound, both in terms of its hexagonal unit cell and of the corresponding rhombohedral primitive cell is presented in Chapter 4 the rhombohedral compound Mo6PbSx (the prototype of the family of the so-called Chevrel phases) is described and unit cell constants and atomic positions are listed for its conventional hexagonal cell and for the rhombohedral primitive cell. 

Figure 3.20. A lateral view of different stacking sequences of triangular nets. They correspond to some typical close-packed structures. The first layer sequence shown corresponds to a superimposition according to the scheme ABABAB... (equivalent to BCBCBC... or CACACA... descriptions) characteristic of the hexagonal close-packed, Mg-type, structure. With reference to the usual description of its unit cell, the full stacking symbol indicating the element, the relative position of the superimposed layers and their distance is Mg Mg. The other sequences correspond to the schemes ABC.ABC. (Cu, cubic), ABAC.ABAC. (La, hexagonal), ACACBCBAB. (Sm, hexagonal). For Cu the constant ch of the (equivalent, non-conventional) hexagonal cell is shown which may be obtained by a convenient re-description of the standard cubic cell (see 3.6.1.3). ch = cV 3, body diagonal of the cubic cell.

Figure 3.23. Hexagonal, 63, net of points, a, b and c are the codes corresponding to the different positions relative to the cell origin. Notice that the unit cell contains two points (every point in a comer is in common with four adjacent hexagonal cells). The coordinate doublets of the points are reported.

Figure 3.24. The kagome , 3636, net of points. The codes a, (3,corresponding to the different positions of the net (relative to the hexagonal cell origin) are shown. Notice that the unit cell contains three points of the net (every point in an edge belongs to two adjacent cells). For the different positions the coordinate doublets of the three points are reported.

Mo bSg. It is rhombohedral (hR45), space group R3, N.148, with the following atomic positions (45 atoms in the triple primitive hexagonal cell) ... 

The atomic positions, in the hexagonal cell of the prototype Mo3Se4, are ... 

Atomic positions (in the triple primitive hexagonal cell) ... 

The only measurements of the isotope effect for a long bond are those of Meg aw [5] who compared the axial parameters of light and heavy ice. The expansion of the edge a of the unit hexagonal cell at 0°C is 0 003 0-001 A. Since the hydrogen bond occurs twice per unit cell in its direction in the 0001 plane, its expansion will be 0 0015 i 0 0005 A. In ice the oxygens occupy lattice positions and so the calculation does not involve any assumptions. 

In discotic phases the orientation of the molecules is perpendicular to the molecular plane. Here, the columns can be arranged in a nematic or columnar manner. In the nematic phase the molecules possess a centre of gravity randomly ordered, but with the short molecular axis of each molecule more or less parallel. In the columnar phase, beside the preferable orientation of the short molecular axes, the disc-like molecules are ordered forming columns. Depending on the correlation strength between he columns these phases can be subdivided into ordered or disordered. A third possibility is to have a thermodynamically preferable position of the columns in the mesophase, like in a hexagonal cell. Additionally, a tilt of the columns is also possible. 

The structure of BaNiCh is closely related to perovskite (CaTiC>3, 3 2Pi/4 3/4O1/4), but the packing sequence is hep rather than ccp as for perovskite. The hexagonal cell contains two molecules, CB , C63me, a0 = 5.580 and c0 = 4.832 A. As shown in Figure 5.40, each Ni atom is at the center of an octahedron formed by six O atoms. With P layers at B and C positions all Ni atoms in O layers are at A positions, sharing three O atoms with another Ni atom. The Ba atom is at the center of a trigonal prism formed by six Ni atoms. The packing sequence of this structure is shown below ... 

The structure of s-TaN is fairly simple as seen in Figure 8.20. The hexagonal cell contains three molecules, D, P6/m mm, a0 = 5.191, and c0 = 2.908 A. There are two different environments for Ta. In the first layer (the base of the cell at 0) there are four Tai atoms at the comers, one N at the center and four N in the edges, all at A positions, giving The next layer contains two Tan atoms at 50, a half-... 

Figure 12.2. A projection along c showing the A, B, and C positions for a hexagonal cell.

Figure 12.4. The projection along c of a hexagonal cell with A, B, and C positions shown, (a) The large dark balls represent a one-quarter filled layer and large light balls represent a three-quarter filled layer. (b) The large light balls represent a one-third filled layer and the large dark balls represent a two-third filled layer.

The patterns for positions in a hexagonal cell can vary, depending on the occupancies of layers. Four patterns are shown in Figures 12.2, 12.3, and 12.4a and b. Usually comer positions are labeled A. These positions were labeled C in Figure 12.3 to agree with Figure 6.8, where comers are not occupied. 

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