Face-centred cubic close-packed

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.

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). 

When the radius ratio is less than 0.59 the alloy is normal and the mclal—interstitial atom arrangement is face-centred cubic, close-packed hexagonal or body-centred cubic. The complex interstitial alloys have a radius ratio greater than 0.59 and are less stable. Carbon and nitrogen always occupy octahedral holes in interstitial alloys hydrogen always occupies the smaller tetrahedral interstices. In face-centred cubic and close-packed hexagonal lattices there are as many octahedral holes as metal atoms and twice as many tetrahedral holes. 

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... 

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 3.40 The face-centred cubic close packing of polystyrene spheres used as templates. Reprinted from Kuo and Lu, 2008 reference with permission from lOP Publishing Ltd...

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. 3.8 Some basic Bravais lattices (a) simple cubic, (b) body-centred cubic, (c) face-centred cubic and (d) simple hexagonal close-packed. (Figure adapted in part from Ashcroft N V and Mermin N D 1976. Solid State Physics.

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 3.16. WiditinnstiiUcn precipitation of a hexagonal close-packed phase from a face-centred cubic phase in i Cu Si alloy. Precipitation occurs on [ I I Ij planes of the matrix, and a simple epitaxial erystallographie correspondence is maintained. (0 0 0 Di, , (I I (after Barrett...

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... 

Table 2.2 CALPHAD-type representation of the thermodynamic properties of face-centred cubic (FCC), liquid and hexagonal close-packed (HCP) aluminium of the form (after Dinsdale [18]) ...

Figure 2.12 6/ -G, (A1 FCC) of hexagonal closed-packed (HCP) aluminium and aluminium melt relative to that of face-centred cubic aluminium [18].

Figure 2.30. Typical one-component systems (a) Room temperature, room pressure region of the well-known PIT phase diagram of water (notice the logarithmic scale of pressure), (b) P-T phase diagram of elemental Fe. The fields of existence of the different forms of Fe are shown a (body-centred cubic Fe), (face-centred cubic), 6 (body-centred cubic, high-temperature form isostructural with a), e (hexagonal close packed), L (liquid Fe). The gas phase field, owing to the pressure scale and the not very high temperatures considered, should be represented by a very narrow region close to the T axis.

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