Face-centered cubic structure octahedral

Only large clusters usually adopt the face-centered cubic structure of metallic platinum. A novel cuboctahedral cluster [Pt15Hx(CO)8(PBut3)6] has been reported by Spencer et al.512 and the first octahedral cluster [Pt6(CO)6(/i-dppm)3]2+ was only reported recently.573... 

Fluorite oxides are the most common and classical oxygen ionconducting materials. The crystal structure consists of a cubic oxygen lattice with alternate body centers occupied by 8-coordinated cations. The cations are arranged into a face-centered cubic structure with the anions occupying the tetrahedral sites. This leaves a rather open architecture, with large octahedral interstitial voids, as shown in Figure 1-6. 

FIGURE 4.23 Left the diamond type structure right tetrahedral T and octahedral Oj interstices highhghted in face-centered cubic structure after Heyes (1999). 

Writing the total number of aminoacids (20) as the exact available number of tetrahedral (T ) and octahedral (Oj ) interstices (excluding central octahedral interstice) in face-centered cubic structure this way providing the crystalline paradigm of the genetic code ... 

As previously described, FeO is an oxygen excessive (Fe defect) non-stoichiometric iron oxide (Fei xO), which shows the rock-salt type face center cubic structure (fee). The unit cell of Fei xO are constituted from four Fei xO molecules, where there are eight tetrahedral interspaces A site) and four octahedral interspaces B sites) with 0 closely packing onto NaCl-type cubic lattices. 

In eq. 48 we have used the fact that in a face-centered-cubic structure there is one octahedral interstitial site per metal atom (thus s=l in eq. 24). 

Pentlandite, (Fe,Ni,Co)9Sg, has a face-centered cubic structure with iron and other metal atoms such as Ni and Co distributed among tetrahedral and octahedral sites. At RT the Mossbauer spectrum appears as an asymmetric doublet consisting of a quadrupole doublet with <5pe = 0.36 and A = 0.30-0.37 mm/s and an additional singlet with (5pe 0-6 mm/s, which is responsible for the asymmetry [155, 156]. 

The alkali metal fullerides, M3C60 (M = Na, K, Rb, and Cs), are a little different. The absence of the sign indicates that these are not endohedral fullerenes. Take K3C6O a representative example. It is prepared from stoichiometric amounts of solid C o potassium vapor. The three potassium atoms transfer their valence electrons to the fuUerene so that K3C60 more accurately written as (K )3(C o ) This special compound becomes a superconductor below the critical temperature, 7, of 19.3 K. (Below the 7, a superconductor is perfectly conducting—that is, it has zero resistance.) It has a face-centered cubic structure of C o anions with potassium cations in both the octahedral and tetrahedral holes as shown in Figure 15.9. (See p. 173 for more details on the positions and numbers of these holes.)... 

Fig. 2. Structures for the solid (a) fee Cco, (b) fee MCco, (c) fee M2C60 (d) fee MsCeo, (e) hypothetical bee Ceo, (0 bet M4C60, and two structures for MeCeo (g) bee MeCeo for (M= K, Rb, Cs), and (h) fee MeCeo which is appropriate for M = Na, using the notation of Ref [42]. The notation fee, bee, and bet refer, respectively, to face centered cubic, body centered cubic, and body centered tetragonal structures. The large spheres denote Ceo molecules and the small spheres denote alkali metal ions. For fee M3C60, which has four Ceo molecules per cubic unit cell, the M atoms can either be on octahedral or tetrahedral symmetry sites. Undoped solid Ceo also exhibits the fee crystal structure, but in this case all tetrahedral and octahedral sites are unoccupied. For (g) bcc MeCeo all the M atoms are on distorted tetrahedral sites. For (f) bet M4Ceo, the dopant is also found on distorted tetrahedral sites. For (c) pertaining to small alkali metal ions such as Na, only the tetrahedral sites are occupied. For (h) we see that four Na ions can occupy an octahedral site of this fee lattice.

In an ionic solid, the coordination number means the number of ions of opposite charge immediately surrounding a specific ion. In the rock-salt structure, the coordination numbers of the cations and the anions are both 6, and the structure overall is described as having (6,6)-coordination. In this notation, the first number is the cation coordination number and the second is that of the anion. The rock-salt structure is found for a number of other minerals having ions of the same charge number, including KBr, Rbl, MgO, CaO, and AgCl. It is common whenever the cations and anions have very different radii, in which case the smaller cations can fit into the octahedral holes in a face-centered cubic array of anions. The radius ratio, p (rho), which is defined as... 

Figure 5.18.1 The NaCl crystal structure consisting of two interpenetrating face-centered cubic lattices. The face-centered cubic arrangement of sodium cations (the smaller spheres) is readily apparent with the larger spheres (representing chloride anions) filling what are known as the octahedral holes of the lattice. Calcium oxide also crystallizes in the sodium chloride structure.

Spinels have a crystal structure in which there is a face-centered cubic arrangement of O2 ions. There are two types of structures in which cations have octahedral or tetrahedral arrangements of anions surrounding them. In the spinel structure, it is found that the +3 ions are located in octahedral holes and the tetrahedral holes are occupied by the +2 ions. A different structure is possible for these ions. That structure has half of the +3 metal ions located in the tetrahedral holes while the other half of these ions and the +2 ions are located in the octahedral holes. In order to indicate the population of the two types of lattice sites, the formula for the compound is grouped with the tetrahedral hole population indicated first (the position normally occupied by the +2 ion, A) followed by the groups populating the octahedral holes. Thus, the formula AB204 becomes B(AB)04 in order to correctly... 

The same atom-centered polyhedra can be used to describe interstitial diffusion in all the many metal structures derived from both face-centered cubic and hexagonal closest packing of atoms. In these cases the polyhedra are centered upon a metal atom and all the tetrahedral and octahedral interstitial sites are empty. The hardening of metals by incorporation of nitrogen or carbon into the surface layers of the material via interstitial diffusion will use these pathways. 

Where the lithium ions fit best will be determined by their size relative to the iodide ions. Note from above that there are two types of interstices in a closest packed structure. These represent tetrahedral (f) and octahedral (o) holes because the coordination of a small ion fitted into them is either tetrahedral or octahedral (see Fig. 4.12). The octahedral holes are considerably larger than the tetrahedral holes and can accommodate larger cations without severe distortion of the structure. In lithium iodide the lithium ions fit into the octahedral holes in a cubic closest packed lattice of iodide ions. The resulting structure is the same as found in sodium chloride and is face-centered (note that face-centered cubic and cubic closest packed describe the same lattice). 

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