Solid State Chemistry and its Applications. Anthony R. West

slash StartRoot 2 EndRoot"/>. 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.

      1.17.2 Diamond

      This structure type, so important to the semiconductor industry, has already been described, as the zinc blende or sphalerite structure, Fig. 1.29 and Fig. 1.33. The diamond structure is obtained when the two elements in zinc blende are identical, as in diamond. It may therefore be described as a ccp array of carbon atoms, with one set of tetrahedral sites (either T₊ or T_–) occupied also by carbon atoms. It is, however, rather artificial to make a distinction between packing and interstitial atoms since structurally they are identical. Most Group IV elements crystallise with the diamond structure, Table 1.9.

       Table 1.11 Calculation of interatomic distances in some simple structures

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Structure type	Distance	Number of such distances	Magnitude of distance in terms of unit cell dimensions
Rock salt (cubic)	Na–Cl	6	a/2 = 0.5a
	Cl–Cl	12
	Na–Na	12
Zinc blende (cubic)	Zn–S	4
	Zn–Zn	12
	S–S	12
Fluorite (cubic)	Ca–F	8
	Ca–Ca	12
	F–F	6	a/2 = 0.5a
Wurtzite^a (hexagonal)	Zn–S	4
	Zn–Zn	12	a = 0.612c
	S–S	12	a = 0.612c
Nickel arsenide^a (hexagonal)	Ni–As	6
	As–As	12	a = 0.612c
	Ni–Ni	2	c/2 = 0.5c = 0.816a
	Ni–Ni	6	a = 0.612c
Caesium chloride (cubic)	Cs–Cl	8
	Cs–Cs	6	a