Hexagonal-primitive packing

Hexagonal-primitive packing of Si-V one unit cell is outlined. Si-VI only atomic contacts within the layers parallel to the b-c plane have been drawn Numbers x coordinates... 

In the WC type the metal atoms do not have a closest-packing, but a hexagonal-primitive packing the metal atoms form trigonal prisms that are occupied by the C atoms. 

Fig. 6.8. Hexagonal dose-packed surface, (a) Real. space, (b) Reciprocal space. The length of the primitive reciprocal lattice vector is b = (4Tr/y 3 a).

Figure 1.32 Rod packings (a) hexagonal (honeycomb) packing (b) tetragonal packing (c) tetragonal layer packing and (d) primitive cubic rod packing. (After O Keeffe Andersson, 1977).

Figure 16.3. (a) Construction of the Wigner-Seitz cell in a 2-D hexagonal close-packed (hep) lattice, (b) Primitive unit cell of the hep lattice. 

The extended structure of a hexagonal close-packed metal is shown in A FIGURE 12.14(a). There are two atoms in the primitive hexagonal unit cell, one from each layer. Neither atom sits directly on the lattice points, which are located at the comers of the unit cell. The presence of two atoms in the unit cell is consistent with the two-layer ABAB. .. stacking sequence associated with hep packing. 

The scheme of the SCM model reaUzation, discussed in Sect. 10.1.3, requires in stage 1 the calculations of the perfect crystal. The perfect corundum crystal has a rhombohedral structure with the space group R3c D, see Chap. 2). The oxygen atoms form a hexagonal close-packed structure, the almnimun atoms occupy 2/3 of the octahedral vacancies so that aU A1 atoms have the same environment. Every O atom has two neighboring A1 atoms at a distance of ri = 1.86 A and two others at a distance of r2 = 1.97 A. The primitive rhombohedral unit cell consists of two AI2O3 formula imits with experimental lattice parameters a = 5.128 A and a = 55.333°. 

Figure 5 Most frequently observed macrolattices, (a) Lamellae (b) hexagonal packed cylinders (c) BCC (d) FCC (e) hexagonal close-packed spheres (f) primitive cubic (g) double gyroid (Ia3d) (h) double diamond (DD) (i) Pm3n and (j) Fddd.

For additional symbols of further packings cf. [38, 156], T (triangular) refers to hexagonal layers, Q to layers with a periodic pattern of squares. The packing Qs yields a primitive cubic lattice (Fig. 2.4), Qf a body-centered cubic lattice (cf. Fig. 14.3, p. 153). Sometimes the symbols are set as superscripts without the angular brackets, for example Ti[Ca03]c. 

Many metals have close-packed structures, with the atoms stacked in either a hexagonal or a cubic arrangement close-packed atoms have a coordination number of 12. Some metals have body-centered cubic structures, but primitive cubic structures are rare. 

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