Anthony R. West - Solid State Chemistry and its Applications

This structure is related to fluorite, CaF 2but 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 3 d 10and may be rationalised in terms of sp hybridisation giving two Cu sp hybrid orbitals, arranged linearly.

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 Na 2O may be regarded as containing ccp O 2–ions with Na +ions in tetrahedral sites, in the fluorite structure of CaF 2, it is necessary to regard the Ca 2+ions as forming the ccp array with F –ions in tetrahedral sites. In CaF 2the Ca 2+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 Ca 2+ion (depending on which table of ionic radii is consulted, the diameter of Ca 2+is in the range ~2.2–2.6 Å).

The F–F distance in CaF 2is 2.73 Å, which indicates that the fluorines are approximately contacting . Although the array of F –ions in CaF 2is 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 Ca 2+ions; nevertheless, both descriptions are used widely.

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

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

a These formulae do not necessarily apply when c/a is different from the ideal value of 1.633.