Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 51

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 F, where relevant values for different coordination numbers and oxidation states are also given.

Consideration of atom arrangements in the three structure types described above shows that the concept of cp anions with cations in interstitial sites begins to break down in the fluorite structure. Thus, while the antifluorite structure of Na₂O may be regarded as containing ccp O^2– ions with Na⁺ ions in tetrahedral sites, in the fluorite structure of CaF₂, it is necessary to regard the Ca²⁺ ions as forming the ccp array with F^– ions in tetrahedral sites. In CaF₂ the Ca²⁺ ions have a eutactic ccp arrangement, but are well separated from each other; from Table 1.9 and Table 1.10, Ca–Ca = 3.86 Å, which is much larger than the diameter of a Ca²⁺ ion (depending on which table of ionic radii is consulted, the diameter of Ca²⁺ is in the range ~2.2–2.6 Å).

The F–F distance in CaF₂ is 2.73 Å, which indicates that the fluorines are approximately contacting . Although the array of F^– ions in CaF₂ is not cp but is primitive cubic, this is perhaps a more realistic way of describing the structure than as containing a eutactic ccp array of Ca²⁺ ions; nevertheless, both descriptions are used widely.