Coordination lattice eight

Fluorite is calcium fluoride, Cap2, with a cubic face-centered lattice, while each fluorine ion is at the center of one of the smaller cubes obtained by dividing the unit cube into eight parts. Each Ca is coordinated by eight F ions and each F is surrounded by four Ca ions arranged at the corners of a regular tetrahedron. 

The distance along any side of the body-centred cubic lattice as shown in Figure 7.1(a) is equal to twice the metallic radius of the atom, 2rM. The distance between the centre of the atom in the centre of the unit cell and the centre of any atom at the cube corner is 31/3/ m. The distance between the centres of two atoms at the centres of adjacent cubes is 2rM. This means that any atom in the body- centred cubic arrangement is coordinated by eight atoms at the 1 cube corners with a distance 3l/3rM, and six more atoms in the centres of the six adjacent cubes with a distance 2rM. The extra six atoms contributing to the coordination number of body-centred atoms are 100 x (2rM - 3,/3rM)/(3I/3rM) = 15.5% further away from the central atom than the eight nearest neighbours. 

The sodium chloride structure. Sodium chloride crystallizes in a face-centered cubic structure (Fig. 4.1a). To visualize the face-centered arrangement, consider only the sodium ions or the chloride ions (this will require extensions of the sketch of the lattice). Eight sodium ions form the comers of a cube and six more are centered on the faces of the cube. The chloride ions are similarly arranged, so that the sodium chloride lattice consists of two interpenetrating face-centered cubic lattices. The coordination number (C.N.) of both ions in the sodium chloride lattice is 6. that is, there are six chloride ions about each sodium ion and six sodium ions about each chloride ion. 

If we consider the fluorides, for example, which form pure coordination lattices (p. 33), then those from the alkaline earth metals with the exception of magnesium and beryllium crystallize in the fluorite structure, in which the cation is surrounded by eight fluorine ions for CaF2 and CdF2, which have the same structure, r+/r is 0.71 and 0.69 respectively just at the limit V 3— 1 — 0.73. The fluorides of other divalent ions, such as Mn, Fe, Co and Ni and also Mg, crystallize in a structure with coordination number six (rutile type). It is only for BeF2 that the ratio r+/r = 0.23 lies below the limit of this coordination number and it has a structure similar to that of cristobalite (Si02) with four neighbours (see also p. 66). 

UO2 has the fluorite structure it is a face centered cubic based structure with each uranium ion coordinated to eight oxygen ions (Figure 13.2). The fact that there are vacant coordination positions in the lattice is critical for the catalytic, and other, properties of the oxide. This is because ion exchange is more efficient by... 

Spinels have anion lattices with tetrahedral and octahedral sites for transition metal dopants. Garnets have three types of cation lattice sites. Some cation sites are coordinated by eight oxide ions on the corners of a distorted cube around the cation, four-coordinated (tetrahedral), and six-coordinated (octahedral) lattice sites. By substituting the right transition metal or lanthanide ions in these sites the color and optical activity of garnet pigments can be controlled. 

We shall restrict discussion to the case of B2-structure alloys, where a sites are at the corners and p sites at the centers of the cubic lattice cells, each a (resp. ff) site being coordinated to eight (resp. a) sites. One then h sN = N =l/2, and... 

In Th02, however, they were situated at considerably lower energy than in Zr02, e.g. Tb4+ in Th02 at 20.3 kK and in Zr02 at 28.6 kK. These c. t. bands have been studied in more detail by Hoefdraad (5). He introduced Ce +, Pr + and Tb4+ in a number of oxidic host lattices where the coordination of the Ln + ions would be fixed, viz. either six- or eight-coordination. His results are as follows ... 

The c.t. transitions of Ln + ions in eight-coordination are ascribed to the transition 2tig- -f. Note that there are two ligand m.o s of t g symmetry. These are perturbed by the i2g(Sd) metal ion orbital. As a consequence the position of the 2t2g level depends on the energetic position and the extent of delocalization of the eight-coordination on the choice of the host lattice. 

Figure 7.1(a) is the body-centred cubic lattice in which the coordination number of each atom is eight. There are six next nearest neighbours in the centres of the adjacent cubes only 15% further away, so that the coordination number may be considered to be 14. 

The cubic closest-packed lattice is shown in Figure 7.1(b), and can also be described as a face-centred cubic arrangement in which there is an atom at the centre of each of the six faces of the basic cubic of eight atoms. The coordination number of any particular atom in a cubic closest packed lattice is 12. Considering an atom in one of the face centres of the diagram in Figure 7.1(b), there are four atoms at the corners of... 

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