Face centred cubic

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.

In Figure 8.19 is shown the X-ray photoelectron spectrum of Cu, Pd and a 60 per cent Cu and 40 per cent Pd alloy (having a face-centred cubic lattice). In the Cu spectrum one of the peaks due to the removal of a 2p core electron, the one resulting from the creation of a /2 core state, is shown (the one resulting from the 1/2 state is outside the range of the figure). 

Figure 8.19 X-ray photoelectron spectrum, showing core and valence electron ionization energies, of Cu, Pd, and a 60% Cu and 40% Pd alloy (face-centred cubic lattice). The binding energy is the ionization energy relative to the Fermi energy, isp, of Cu. (Reproduced, with permission, from Siegbahn, K., J. Electron Spectrosc., 5, 3, 1974)...

EXAFS spectra of platinum metal, having a face-centred cubic crystal stmcture, have been obtained at 300 K and 673 K. Explain what qualitative differences you might expect. How many nearest-neighbour atoms are there in this stmcture Illustrate your answer with a diagram. 

In the face-centred cubic structure tirere are four atoms per unit cell, 8x1/8 cube corners and 6x1/2 face centres. There are also four octahedral holes, one body centre and 12 x 1 /4 on each cube edge. When all of the holes are filled the overall composition is thus 1 1, metal to interstitial. In the same metal structure there are eight cube corners where tetrahedral sites occur at the 1/4, 1/4, 1/4 positions. When these are all filled there is a 1 2 metal to interstititial ratio. The transition metals can therefore form monocarbides, niU ides and oxides with the octahedrally coordinated interstitial atoms, and dihydrides with the tetrahedral coordination of the hydrogen atoms. 

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...

Except for Ceo, lack of sufficient quantities of pure material has prevented more detailed structural characterization of the fullerenes by X-ray diffraction analysis, and even for Ceo problems of orientational disorder of the quasi-spherical molecules in the lattice have exacerbated the situation. At room temperature Cgo crystallizes in a face-centred cubic lattice (Fm3) but below 249 K the molecules become orientationally ordered and a simple cubic lattice (Po3) results. A neutron diffraction analysis of the ordered phase at 5K led to the structure shown in Fig. 8.7a this reveals that the ordering results from the fact that... 

Crystal structure Martensite (body centred cubic) austenite (face centred cubic)... 

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