Unit cell fluorite lattice

Make a simple estimate of the energy of defect formation in the fluorite structure (a) describe the coordination by nearest neighbours and next-nearest neighbours of an anion both for a normal lattice site and for an interstitial site at the centre of the unit cell shown in Figure 5.3(a). 

The fluorite structure has been described in terms of a face-centered-cubic unit cell containing four units of M02. Table I lists the lattice parameters for these substances. 

There are two main types of ionic oxides which are empirically formulated MOg. Where the metal ion is large (Th, 0.95 A Ce +, 0.92 A U, 0.89 A) the crystals are built up of fluorite-type unit cells with 8 4 co-ordination. But where the metal ion is smaller (Sn, 0.71 A Ti, 0.68 A) the structure is based on the rutile lattice with 6 3 co-ordination. Other examples of this structure are VOg, RuOg, PbOg and TeOg. The rutile lattice is slightly deformed in MoOg and WOg. 

The rare earths absorb hydrogen readily and form solid solutions and/or hydrides exothermally at temperatures of several hundred C. Their phase diagrams consist, in general, of three basic parts (a) the metallic solid solution, or a-phase, with the H atoms inserted in the tetrahedral interstices of the host-metal lattice (b) the equally metallic dihydride 3-phase, where the two H atoms occupy ideally the two available tetrahedral sites this phase crystallizes in the fee fluorite system (c) the insulating trihydride, or y-phase, which possesses an hep unit cell with both tetrahedral sites and the one octahedral site filled up. A schematic view is given in fig. 1. Exceptions are the divalent lanthanides Eu and Yb, whose dihydrides are already insulators and exhibit an orthorhombic structure, and Sc whose very small unit cell does not normally accept more than two H atoms. 

Fluorite, CaF2, shows a radius ratio of 0.96, which predicts that the calcium ions will occupy cubic holes formed by the fiuoride anions. Note in Figure 7.22a that the calcium ions do indeed occupy such sites. However, as required by stoichiometry (see Problem 7.39), half of the cubic holes must be unoccupied. (Note that the center of the unit cell is an unoccupied cubic hole formed by the fluoride ions.) The unit cell of the lattice therefore cannot be the simple cubic of fluorides with one calcium in the body. Rather, a larger unit cell of fee calcium ions with fluorides filling the tetrahedral holes is the more appropriate description. Note that the coordination number of the fluorides is 4, which is consistent with Equation (7.6). Table 7.11 indicates that there is a 90% correlation between the known crystal structure and the calculated radius ratio for compounds that assume the fluorite structure. 

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