Face-centred cubic close-packed structure

The sequence ABCABC... having a cubic symmetry is shown in Fig. 3.21. It is the cubic (face-centred cubic) close-packed structure, also described as cF4-Cu type structure. 

Figure 3.21. The face-centred cubic close-packed structure (Cu type). On the left a block of eight cells is shown (one cell darkened). On the right a section of the structure is presented it corresponds to a plane perpendicular to the cube diagonal. Notice that the plane is the same presented on the left in Fig. 3.19. The sequence of the layers in this structure is shown in Fig. 3.20 in comparison with other close-packed elemental structures.

Magnetite possesses an inverse spinel structure with oxygen ions forming a face-centred cubic closely packed structure. The formula for describing Fe occupancy is (Fe " ) [Fe ", Fe ]04 where the parentheses ( ) stand for cations at tetrahedral sites while brackets [ ] denote cations at octahedral lattice sites. Stoichiometric magnetite has all available substitutional sites occupied by Fe and Fe ions. Non-stoichiometric magnetites also exist, with various numbers of available sites being either vacant or occupied by impurity ions. 

Face-centred cubic close-packed structure... 

Their normal crystal structure, at ambient conditions, corresponds to the body-centred cubic cI2-W-type structure. At very low temperatures, the close-packed hexagonal hP2-Mg-type structure has been observed for Li and Na, while for Rb and Cs the face-centred cubic close-packed cF4-Cu-type structure is known at high pressure. No polymorphic transformation has been reported for potassium. 

The spinel structure is a common mixed oxide structure, typified by spinel itself MgAl204, in which the oxide ions are in a face-centred cubic close packed array (see Section 1.6.3 and Figure 1.43). For an array of TV oxide ions, there are TVoctahedral holes, and the trivalent ions (AP" ) occupy half of the octahedral sites (Figure 9.10). 

Metals atoms (cations) pack closely together in a regular structure to form crystals. Arrangements in which the gaps are kept to a minimum are known as close-packed structures. X-ray diffraction studies have revealed that there are three main types of metallic structure hexagonal close packed, face-centred cubic close packed and body-centred cubic. 

Figure 1.24(c) shows a unit cell of a face-centred cubic structure. If a single atom is placed at each lattice point then this becomes the unit cell of the ccp (cubic close-packed) structure. Find the 100, 110, and the 111 planes and calculate the density of atoms per unit area for each type of plane. (Hint Calculate the area of each plane assuming a cell length a. Decide the fractional contribution made by each atom to the plane.)... 

A section through the face centre of the cubic close-packed structure is shown in Figure 5.16. With randomly fluctuating electron density on all atoms it appears almost inevitable that some density should accumulate in... 

The cubic close packed structure may also be represented as a face centred cubic structure in which eight spheres are located at the centres of the faces (Figure 49). The relationship between this representation of the cubic close packed structure and that given in Figure 4Sby is that the plane III, which cuts the cube in Figure 4, represents a layer of spheres in Figure 48a,... 

Just as the edges of cation-centred polyhedra represent anion diffusion paths in a crystal, the edges of anion centred polyhedra represent cation diffusion paths. The polyhedra shown in Figures 7.18 reveal that cation diffusion in cubic close-packed structures will take place via alternative octahedral and tetrahedral sites. Direct pathways, across the faces of the polyhedron, are unlikely, as these mean that a cation would have to squeeze directly between two anions. There is no preferred direction of diffusion. For ions that avoid either octahedral or tetrahedral sites, for bonding or size reasons, diffusion will be slow compared to ions which are able to occupy either site. In solids in which only a fraction of the available metal atom sites are filled, such as the spinel structure, clear and obstructed diffusion pathways can easily be delineated. 

Pure silver has the cubic close-packed structure a (fig. 13.11). This phase is capable of accommodating up to 42 atomic per cent of cadmium in solid solution by the purely random replacement of silver atoms. The sites occupied are still those of the cubic face-centred structure, no change in which occurs except a progressive and approximately linear variation... 

There are four lattice points in the face-centred unit cell, and the motif is one atom at (0,0,0). The structure is typified by copper (Figure 5.17). The cubic close-packed structure is adopted by many metals (see Figure 6.1, page 152) and by the noble... 

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

Fig. 5.1. The close packing of hard-sphere atoms. The ABC slacking gives the face-centred cubic (f.c.c.) structure.

Crystalline copper and magnesium have face-centred-cubic and close-packed-hexagonal structures respectively. 

We begin by looking at the smallest scale of controllable structural feature - the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). 

Figure 29.1 Crystal structures of ZnS. (a) Zinc blende, consisting of two, interpenetrating, cep lattices of Zn and S atoms displaced with respect to each other so that the atoms of each achieve 4-coordination (Zn-S = 235 pm) by occupying tetrahedral sites of the other lattice. The face-centred cube, characteristic of the cep lattice, can be seen — in this case composed of S atoms, but an extended diagram would reveal the same arrangement of Zn atoms. Note that if all the atoms of this structure were C, the structure would be that of diamond (p. 275). (b) Wurtzite. As with zinc blende, tetrahedral coordination of both Zn and S is achieved (Zn-S = 236 pm) but this time the interpenetrating lattices are hexagonal, rather than cubic, close-packed.

The corresponding unit cells are shown in Figure 1.1 and an examination of simple ball-and-stick models (which the reader is strongly urged to carry out) shows that the face-centred cubic (fee) and hexagonal close-packed (hep) structures correspond to the only two possible ways of close-packing spheres, in which each sphere has twelve nearest neighbours. 

Figure 1.4 (a) Close packing of atoms in a cubic structure, showing six in-plane neighbours for each atom (b) An expanded diagram of the packing of atoms above and below the plane. A above and A below represents the location of atoms in the hexagonal structure, and A above with B below, the face-centred cubic structure... 

Although the face-centred cubic structure of metals is close packed, it is still possible for atoms which are much smaller than the host metal atoms to fit into interstitial sites inside the structure, while maintaining the essential properties of metals such as electrical conductivity and heat transport. These interstitial sites are of two kinds. The octahedral interstitial sites have six metal atoms at equal distances from the site, and therefore at the apices of a regular octahedron. The tetrahedral interstitial sites have four nearest neighbour metal atoms at the apices of a regular tetrahedron. A smaller atom can just fit into the octahedral site if the radius ratio is... 

The tI10-MoNi4 type is another superstructure based on face-centred cubic pseudo-cells. In the projection shown in Fig. 3.36, inside the true cell, the pseudo-cubic subcell (aps = 362 pm, cps = 356.4 pm) has been evidenced by dotted lines. Close-packed layers can be identified in this structure they are stacked in a 15 close-packed repeat sequence. 

This structure may be considered a superstructure based on a face-centred cubic pseudo-cell. The atoms form close-packed layers stacked in a 15 layer close packed repeat sequence. 

An alternative way of viewing this structure is to think of it as a cubic close-packed array of chloride Ions with sodium Ions filling all the octahedral holes. The conventional unit cell of a ccp array Is an F face-centred cube (hence the cubic in ccp) the close-packed layers lie at right angles to a cube diagonal (Figure 1.32). Filling all the... 

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