Solid State Chemistry and its Applications. Anthony R. WestЧитать онлайн книгу.

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.

Schematic illustration of the antifluorite structure of Na2O showing the unit cell in terms of (a) NaO4 tetrahedra and (b) ONa8 cubes.

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

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 Скачать книгу