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The antifluorite structure has ccp/fcc anions with cations in all (T₊ and T_–) tetrahedral sites. The difference between antifluorite and fluorite is that antifluorite refers to an anion array with tetrahedral cations, whereas fluorite has the inverse arrangement with a ccp cation array and tetrahedral anions. Since the cation:anion ratio is 2:1 in antifluorite and the cation coordination is 4, the anion coordination must be 8, Fig. 1.30.

The very different coordination environments of anions and cations leads to two entirely distinct descriptions of the structure in terms of a 3D network of either tetrahedra or cubes, Fig. 1.34; (a) corresponds to the arrangement shown in Fig. 1.29(c) and the tetrahedra are highlighted; (b) corresponds to the arrangement in Fig. 1.30(b) in which the cubic coordination arrangement is highlighted. A more extended network of corner‐and edge‐sharing cubes is shown in Fig. 1.34(c). This must surely rate as one of the world's largest models of the antifluorite structure!

The antifluorite structure is shown by a large number of oxides and other chalcogenides of the alkali metals (Table 1.10), i.e. compounds of general formula . A group of fluorides of large, divalent cations and oxides of large tetravalent cations have the inverse, fluorite, structure, i.e. M²⁺F₂ and M⁴⁺O₂.

From Fig. 1.34(b) and (c), an alternative way of describing the fluorite structure is as a primitive cubic array of anions in which the eight‐coordinate sites at the cube body centres are alternately empty and occupied by a cation. It should be stressed that the true lattice type of fluorite is fcc and not primitive cubic, since the primitive cubes represent only a small part (one‐eighth) of the fcc unit cell. Description of fluorite as a primitive cubic array of anions with alternate cube body centres occupied by cations shows a similarity to the CsCl structure (see later). This also has a primitive cubic array of anions, but, instead, cations occupy all the body centre sites.

Table 1.9 Some compounds with the zinc blende (sphalerite) structure, a/Å

CuF	4.255	BeS	4.8624	β‐CdS	5.818	BN	3.616	GaP	5.448
CuCl	5.416	BeSe	5.07	CdSe	6.077	BP	4.538	GaAs	5.6534
γ‐CuBr	5.6905	BeTe	5.54	CdTe	6.481	BAs	4.777	GaSb	6.095
γ‐CuI	6.051	β‐ZnS	5.4060	HgS	5.8517	AlP	5.451	InP	5.869
γ‐AgI	6.495	ZnSe	5.667	HgSe	6.085	AlAs	5.662	InAs	6.058
β‐MnS, red	5.600	β‐SiC	4.358	HgTe	6.453	AlSb	6.1347	InSb	6.4782
C a	3.5667	Si	5.4307	Ge	5.6574	α‐Sn (grey)	6.4912

^a Diamond structure.

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

	Fluorite structure			Antifluorite structure
CaF2	5.4626	PbO2	5.349	Li2O	4.6114	K2O	6.449
SrF2	5.800	CeO2	5.4110	Li2S	5.710	K2S	7.406
SrCl2	6.9767	PrO2	5.392	Li2Se	6.002	K2Se	7.692
BaF2	6.2001	ThO2	5.600	Li2Te	6.517	K2Te	8.168
CdF2	5.3895	UO2	5.372	Na2O	5.55	Rb2O	6.74
β‐PbF2	5.940	NpO2	5.4334	Na2S	6.539	Rb2S	7.65