Hexagonal cells

The honeycomb roof is made from a hexagonal cell pattern similar to a beehive in appearance. The honeycomb is glued to a top and bottom aluminum skin that seals it. This roof rests directly on the Hquid. 

Different indices are used in hexagonal cells (we build a c.p.h. crystal up by adding bricks in four directions, not three as in cubic). We do not need them here - the crystallography books listed under Further Reading at the end of this chapter do them more than justice. 

Figure 6 The lateral cell dimensions of the hexagonal cell at 500 MPa. (a) Referred to the hexagonal axes and (b) referred to orthohexagonal axes. (From Ref. 57.) (c) Structural model of the intramolecular defect in the hexagonal crystal. (From Ref. 60.)...

Figure 10. Projection of of the crystal of lithiophorite, (Li,Al)Mn02(0H)2. along the LUO] direction of the hexagonal cell [58], The connections within the Mn06 and (Li,Al)(OH)6 octahedra layers are emphasized. For a better understanding the O - H bridging bounds between the two layer types are not shown.

The outermost layer of the skin appearing in the exploded epidermal sketch of Fig. 1(b) represents the stratum corneum (the horny layer). The principal barrier element of the skin, it is an essentially meta-bolically inactive tissue comprised of acutely flattened, stacked, hexagonal cell building blocks formed from once-living cells. These cellular building blocks are... 

Boron nitride may be obtained in three primary crystalline modifications (2) a, j3, and y. The most commonly encountered a form has a graphitic structure (hexagonal cell, a = 2.504 A, c = 6.661 A). For many years, this modification has been prepared from combinations of cheap boron and nitrogen containing reagents, e.g. B(0H)3 and (NH2)C0, B(0H)3, C and N2 or KBH4 and NH4C1 (3-5). More... 

As a first approximation, let us consider the X atoms as rigid spheres arranged in an ideal hexagonal close-packed (hep) sublattice. On transforming the usual hexagonal unit cell (a, 6, c ) to an ortho-hexagonal cell, defined by a0 = c, bo = b —a, and Co = + b, and introducing... 

Cl 6c +(u,u,u +m, + m, + m + w, + w, +m) w= This structure has a rhombohedral symmetry but is usually described in terms of a triple-volume hexagonal cell, which makes comparison with the idealized Cdl2 structure simpler. The idealized unit cell is adequate for the purposes of this book. In this representation the anion layers are in cubic closest packing. .. ABC ABC ABC... The metal and nonmetal stacking sequence is... 

Description of a rhombohedral unit cell in terms of the equivalent, triple-primitive, hexagonal cell (see Fig. 3.9). 

Figure 3.9. The relation between a primitive rhombohedral cell and an equivalent tripleprimitive hexagonal cell is shown. The cell orientations have been selected according to the criteria adopted by the International Tables (Hahn 2002).

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. 

Description of a hexagonal unit cell (ah, ch cell edges) in terms of an ortho-hexagonal cell (equivalent orthorhombic cell a0, b0, c0) (see Fig. 3.10). 

Figure 3.10. The relation between a hexagonal cell and an equivalent orthorhombic cell is shown by means of their projections on the a, b plane.

Description of a cubic (primitive, body centred or face centred) unit cell (ac) in terms of the equivalent, primitive rhombohedral, (a,-, a) and triple-primitive hexagonal, cells (ah, ch). See Fig. 3.11. 

In this book, the Pearson symbol will be used throughout and the convention has been adopted indicating in every case the number (ideal or effective) of atoms contained in the chosen unit cell. In the case, therefore, of rhombohedral substances for which the data of the (triple primitive) hexagonal cell are generally reported, the number of atoms is given which is in the hexagonal cell and not the number of atoms in the equivalent rhombohedral cell (Ferro and Girgis 1990). So, for instance,... 

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.

The Laves phases form a homeotect structure type set (a family of polytypic structures). In all of them, described in terms of a hexagonal cell, three closely spaced 36 nets of atoms are followed (in the z direction of the same cell) by a 3636 net. The 36 nets are stacked on the same site as the kagome 3636 nets which they surround. For instance (3-BAC- -CAB in the two slabs MgZn2-type (h) structure, (3-BAC- -CBA-a-ACB in the three slabs MgCu2-type (c) structure,... 

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 space group is R3, N. 148 with 42 atoms in the (triple primitive) hexagonal cell (14 atoms in the equivalent, primitive, rhombohedral cell). 

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

The hP3-A B2 type is presented as another example of the use of characteristic projections. A perspective view of the unit cell and the section sequence along the c axis of the cell are depicted in Fig. 7.5. Convenient representative projections in this case may be those on two perpendicular planes, that is on plane (001) and (110). The projection on the plane (001) of a portion (nine cells) of the structure is shown with the trace of the conventional hexagonal cells and the rectangular trace of the equivalent ortho-hexagonal cell (see the 3.6.1.3). The projection on a diagonal vertical plane (110), is also shown. 

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

Figure 7.17. The As-hR6 structure (a) a puckered layer of As atoms is viewed along the c axis of the hexagonal cell and (b) lateral view of two superimposed layers. Notice the coordination 3 of the atoms, characteristic for the element of the 15th group (five valence electrons).

Features of the hP2-WC type structure (characterized by an array of trigonal prisms alternatively centred by C atoms) are therefore present in the aforementioned structures. In the hP2-WC structure, of course, the prism axes are lying in the c direction of the hexagonal cell. 

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