Unit cell hexagonal close-packed lattice

The rhombohedral unit cells for rhodium and iridium trifluorides (44) contain two formula units. The structure can be related to the first structure type by considering anion positions, which here correspond to a hexagonal, close-packed array. There are no vacant anion sites and the cations occupy one-third of the octahedral holes. This leads to M—F—M angles of 132°, characteristic for filling adjacent, octahedral holes in a hexagonal close-packed lattice. Alternatively, the structure can be described as a linking of octahedra through all corners, but the octahedra are now tilted with respect to each other. 

Various schemes have been proposed for the classification of the different alumina structures (Lippens and Steggerda, 1970). One approach was to focus attention on the temperatures at which they are formed, but it is perhaps more logical to look for differences in the oxide lattice. On this basis, one can distinguish broadly between the a-series with hexagonal close-packed lattices (i.e. ABAB...) and the y-series with cubic close-packed lattices (i.e. ABCABC...). Furthermore, there is little doubt that both y- and j/-A1203 have a spinel (MgAl204) type of lattice. The unit cell of spinel is made up of 32 cubic close-packed O2" ions and therefore 21.33 Al3+ ions have to be distributed between a total of 24 possible cationic sites. Differences between the individual members of the y-series are likely to be due to disorder of the lattice and in the distribution of the cations between octahedral and tetrahedral interstices. 

Fig. 5.4 Unit cells of (a) a cubic close-packed (face-centred cubic) lattice and (b) a hexagonal close-packed lattice.

The closest analogues of thiols, alkaneselenols R—SeH, were found to form well-packed monolayers on the Au(lll) surface. The structure of these layers was studied by X-ray diffraction. An oblique unit cell was revealed, indicating a distorted hexagonal close-packed lattice of selenol molecules . Benzeneselenol and diphenyl diselenide form identical monolayers on gold, as shown with STM microscopy. Monolayers of benzeneselenol do not have vacancy pits typical for thiolate monolayers, but show the presence of small islands of gold (20-200 A) which were absent before deposition . 

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

Figure 5.1. Unit cells of the face-centered cubic (fee), body-centered cubic (bcc), and hexagonally closed packed (hep) lattices.

Figure 16.2. Unit cells of the three most important lattice types (a) face-centered cubic (b) hexagonal close-packed (c) body-centered cubic. (From Ref 1, with permission from Noyes.)...

The host crystal of chrysoberyl has a hexagonal-close-packed structure. The space group is orthorhombic Pnma with four molecules per unit cell. The AP ions are octahedrally coordinated by the oxygen ions and occur in two not equivalent crystal field sites in the lattice. The AP" sites lying in the mirror-... 

Adsorption in many different adsorption sites simultaneously is expected for overlayers with an incommensurate lattice (cf. Sect. III). This has been confirmed by LEED intensity analyses for the case of an incommensurate overlayer of Xe on Ag(l 11), where both the substrate and the overlayer consist of hexagonally close-packed layers (with unrelated unit cells) parallel to the surface. 

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. 

Crystalline solids consist of periodically repeating arrays of atoms, ions or molecules. Many catalytic metals adopt cubic close-packed (also called face-centred cubic) (Co, Ni, Cu, Pd, Ag, Pt) or hexagonal close-packed (Ti, Co, Zn) structures. Others (e.g. Fe, W) adopt the slightly less efficiently packed body-centred cubic structure. The different crystal faces which are possible are conveniently described in terms of their Miller indices. It is customary to describe the geometry of a crystal in terms of its unit cell. This is a parallelepiped of characteristic shape which generates the crystal lattice when many of them are packed together. 

The next degree of complexity is encountered when two or more atoms of the same kind are associated with each point of a Bravais lattice, as exemplified by the hexagonal close-packed (HCP) structure common to many metals. This structure is simple hexagonal and is illustrated in Fig. 2-15. There are two atoms per unit cell, as shown in (a), one at 0 0 0 and the other at f (or at i, which is an equivalent position). Figure 2-15(b) shows the same structure with the origin of the unit cell shifted so that the point 1 0 0 in the new cell is midway between... 

Most pure metals adopt one of three crystal structures, Al, copper structure, (cubic close-packed), A2, tungsten structure, (body-centred cubic) or A3, magnesium structure, (hexagonal close-packed), (Chapter 1). If it is assumed that the structures of metals are made up of touching spherical atoms, (the model described in the previous section), it is quite easy, knowing the structure type and the size of the unit cell, to work out their radii, which are called metallic radii. The relationships between the lattice parameters, a, for cubic crystals, a, c, for hexagonal crystals, and the radius of the component atoms, r, for the three common metallic structures, are given below. 

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