Solid State Chemistry and its Applications. Anthony R. West

       Figure 1.34 The antifluorite structure of Na2O showing the unit cell in terms of (a) NaO4 tetrahedra and (b) ONa8 cubes. A more extended array of cubes is shown in (c); this model resides on a roundabout in Mexico City.

Most fluorite structures are eutactic in terms of descriptions as both a primitive cubic array of anions and an fcc array of cations. Thus, the anions are usually too large to occupy tetrahedral holes in a fully dense ccp cation array and, conversely, cations are too large to occupy eight‐coordinate sites in a fully dense primitive cubic anion array. A compound that approaches maximum density is Li₂Te containing the smallest alkali metal and largest chalcogen and for which the Te–Te distance, 4.6 Å, is only slightly greater than the diameter of the Te²⁺ ion, 4.4 Å.

      In this section, we have described the ideal cubic fluorite structure, A₂X. A number of closely related structures with a range of formulae, including the pyrochlore structure, is described in Section 1.17.12.

       Table 1.10 Some compounds with fluorite or antifluorite structure, a/Å

       1.17.1.4 Cuprite structure, Cu2O

      This structure is related to fluorite, CaF₂ but only 1/4 of the tetrahedral positions are occupied by anions. Cu forms an fcc array; two tetrahedral sites, at 1/4, 1/4, 1/4 and 3/4, 3/4, 3/4, are occupied by O. Consequently, the CN of Cu is twofold linear, rather than 8‐fold for Ca in fluorite and 4‐fold for Zn in sphalerite. Another way to view the structure is as two interpenetrating lattices, fcc Cu and bcc O, giving a structure that, overall, is primitive cubic, a = 4.267 Å. The linear, or ‘dumbell’ coordination of 2 is unusual for a reasonably sized cation but is a common feature in structures of monovalent Cu 3d ¹⁰ and may be rationalised in terms of sp hybridisation giving two Cu sp hybrid orbitals, arranged linearly.

       1.17.1.5 Bond length calculations

      It is very often desirable to be able to calculate interatomic distances in crystal structures. This is usually straightforward for crystals which have orthogonal unit cells (i.e. α = β = γ = 90°), and involves simple trigonometric calculations. For example, in the rock salt structure, the anion‐cation distance is a/2 and the anion–anion distance is . The main interatomic distances involving cations in T/O sites in an fcc/ccp anion array are shown in Fig. 1.25(c) and are summarised in Table 1.11 for the important structure types. These may be used together with the tables of unit cell dimensions, Table 1.9, etc., for calculations on specific compounds. Typical values of bond distances (to oxygen and fluorine) for all the elements are given in Appendix

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