Face-Centred Cubic structure,

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. 

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... 

The atomic structure of the nuclei of metal deposits, which have the simplest form since they involve only one atomic species, appear to be quite different from those of the bulk metals. The structures of metals fall mainly into three classes. In the face-centred cubic and the hexagonal structures each atom has 12 co-ordination with six neighbours in the plane. The repeat patterns obtained by laying one plane over another in the closest fit have two alternative arrangements. In the hexagonal structure the repeat pattern is A-B-A-B etc., whereas in the face-centred cubic structure the repeat pattern is A-B-C-A-B-C. In the body-centred cubic structure in which each atom is eight co-ordinated, the repeat pattern is A-B-A-B. (See Figure 1.4.)... 

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... 

Most of the metals which form polynuclear carbonyls adopt the 12 co-ordinate face-centred cubic structure ( = 12) in the solid state so that the relation between Aland T can be revised to... 

Nevertheless it may be observed that, in some specific cases, reference to a pseudo-face-centred tetragonal cell may be useful, for instance to compare the structure under examination with a face-centred cubic structure. 

A) Face-centred cubic structure of NaCI (B) Body-centred cubic structure... 

AFMs have also been used to eshmate the cohesive energy of ionic materials with face-centred-cubic structure (Fraxedas et al., 2002a). In these experiments an ultrasharp AFM hp (hp radius / < 10 nm) indents a hat surface of a single crystal and the dynamical mechanical response of the surface during indentahon is transformed into a force plot (applied force vs. penetrahon). It turns out that the... 

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.)... 

Photonic crystals have only been studied in the laboratory for two decades, but naturally occurring examples exist, with the best known being the gemstone opal. Opals consist of tiny spheres of silica arranged in a face centred cubic structure. These are thought to have formed from colloidal silica solutions, and the colour depends on the size of the spheres. 

Scandium complexes with chloride ion in aqueous solution, and there is ion-exchange evidence for anionic species, presumably ScClJ aq, in concentrated hydrochloric acid,119 while values of K = 90 and K2 - 37 for the first two association constants have been reported.1211 Solid salts of the anions ScClt-, St Cll- and ScCl2- have been isolated with alkali metal cations.121,122 It seems likely that both the first two species are octahedral and bridged-octahedral respectively, in line with Cs2NaScCl6 which has an X-ray powder pattern in accord with a face-centred cubic structure.123... 

Berret et al. (1996) have investigated the effect of steady shear, applied using a Couette cell, on the orientation of a face-centred cubic structure in PE0i27PP04aPE0127 (Pluronic F108) using SAXS, and transitions between shear-... 

Although the Prussian blue phases exhibit remarkable magnetic properties, their face-centred cubic structures mean that no magnetic anisotropy can be expected. 

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,... 

The four reactions above in isolation each contribute 3.7, 5.5, 3.0 and 3.5% to the hydrogen mass percentage, which for the combined reaction system is about 5.6%. Figures 2.59a-c show the molecular structure of the sodium alanates. In particular, NajAlH has two forms of which the simple face centred cubic structure (Fig. 2.59c) only dominates at temperatures above 252°C (Arroyo and Ceder, 2004). 

Solid ammonia has an approximately face-centred cubic structure, the lone pair of electrons being involved in hydrogen bonding to three other molecules. There is thus no free inversion of the molecule in the solid, a conclusion supported by infrared spectroscopic evidence. 

A likely explanation for these facts lies in the disordered stacking of the molecules in planes pormal to the c axis. It is well known that the positions taken by spheres in the third layer of stacking determines which of the close-packed structures occurs, the stacking arrangement in a face-centred cubic structure being ABCABC... whereas that in a hexagonal close-... 

Closest distance of approach of atoms in body-centred cubic structures Closest distance of approach of atoms in face-centred cubic structures... 

Up to and including x = 3 the intercalates maintain the face-centred cubic structure and fill the octahedral and tetrahedral sites accordingly. However, the materials A C q (where A = K, Rb, Cs) transform and form a new structure, consisting of a body-centred cubic array of molecules with a cluster of metal atoms at the centre. 

This composition has produced the class of superconductors which has the highest of any non-cuprate based system. The phases KjC q, Rb3CgQ and CsRb2CgQ (maximum = 33 K) have the intercalated face-centred cubic structure at all temperatures, with both octahedral and tetrahedral holes filled. 

A study of europium niobates showed that the crystallization processes and kinetics of growth were similar to those reported for the yttrium niobates. The emission spectra of Cs2NaEuCl and Cs2Na(EUjcYi, )Cl6 confirmed that the europium atom in each compound was situated at a site of perfect octahedral symmetry and was surrounded by six chloride ions in a face-centred cubic structure. ... 

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