LaH2 forms the basic fluorite structure and extra hydrogens occupy fully the octahedral sites. The structure therefore has all tetrahedral and octahedral sites occupied by H within a ccp La array, Fig. 1.24. A similar structure is observed in intermetallics such as Li3Bi and Fe3Al. These structures represent an extreme with full occupancy of all tetrahedral and octahedral sites. Partial tetrahedral site occupancies occur in the lanthanum hydrides which form a continuous solid solution between LaH1.9 and LaH3.
Figure 1.46 Crystal structures of (a) corundum, (b) ilmenite and (c, d) LiNbO3.
Table 1.24 Some compounds with corundum‐related structures
| Corundum | M2O3: M = Al, Cr, Fe (hematite), Ti, V, Ga, Rh |
| (α‐alumina) | Al2O3: with Cr dopant (ruby) Al2O3: with Ti dopant (sapphire) |
| Ilmenite | MTiO3: M = Mg, Mn, Fe, Co, Ni, Zn, Cd MgSnO3, CdSnO3 NiMnO3 NaSbO3 |
| LiNbO3, LiTaO3 |
Oxygen‐excess fluorites occur in UO2+x (see Fig. 2.10); the structure is distorted locally and the extra oxide ions are displaced off cube body centres. This has a knock‐on effect in which some of the corner oxide ions are displaced onto interstitial sites. The UO2+x system has been studied in considerable detail because of its importance in the nuclear industry as a fuel in nuclear reactors.
Mixed anion oxyfluorides such as LaOF and SmOF form the fluorite structure in which similarly sized O2– and F– ions are disordered over the tetrahedral sites. Various examples of mixed‐cation fluorites are known in which two different cations are ordered, as shown for several examples in Fig. 1.47. These structures are rather idealised, however, since the anions are displaced off the centres of the tetrahedral sites in various ways to give, for instance, a distorted tetrahedral environment for Cr2+ in SrCrF4 and distorted octahedral coordination for both Ti and Te in TiTe3O8.
Li2O has the antifluorite structure and various Li‐deficient antifluorites are good Li+ ion conductors; for instance, Li9N2Cl3 has 10% of the Li+ sites vacant, giving rise to high Li+ ion mobility.
The pyrochlore structure may be regarded as a distorted, anion‐deficient fluorite with two different‐sized cations A and B. Its formula is written as either A2B2X7 or A2B2X6X′. The unit cell is cubic with a ~11 Å and contains eight formula units. In principle, the structure is simple since, ideally, it is a fluorite with one‐eighth of the tetrahedral anion sites empty. Also, there is only one variable positional parameter, the x fractional coordinate of the 48 X atoms in the position (x, 1/8, 1/8), etc., Fig. 1.48. Various compounds form the pyrochlore structure and their differences depend on the value of x, which is usually in the range 0.31–0.36. In the extreme case that x = 0.375, the structure is derived from an undistorted fluorite with 8‐coordinate A cations, as in fluorite, but grossly distorted BX6 octahedra. As x decreases, the 48 X atoms move off their regular tetrahedral sites and the cubic coordination of A becomes distorted: six X neighbours form a puckered hexagon and two X′ atoms are at a different distance, in apical positions, on either side of the puckered hexagon.
At x = 0.3125, the B coordination becomes undistorted octahedral and the BX6 octahedra link by sharing corners to form a 3D network. The A coordination may be described as 2X′ + 6X, with short A–X′ bonds. These A–X′ bonds form a 3D network, A2X′, that interpenetrates the network of BX6 octahedra, of stoichiometry B2X6. The A2X′ net, with linear X′–A–X units and X′A4 tetrahedra, is similar to that in cuprite, Cu2O. The B2X6 and A2X′ networks, that together form the pyrochlore structure, are shown separately in Fig. 1.48.
Pyrochlore‐based oxides have a range of interesting properties and applications. La2Zr2O7 is an electronic insulator whereas Bi2Ru2O7‐δ is metallic and Cd2Re2O7 is a low temperature superconductor. (Gd1.9Ca0.1) Ti2O6.9 is an oxide ion conductor and Y2Mo2O7 is a spin glass. As indicated in some of the above examples, the anion content is not always 7 and indeed the amount of X′ in the general formula can have values between 0 and 1 in different pyrochlores.
Figure 1.47 Some cation‐ordered fluorites showing cation positions relative to those in fcc fluorite.
A. F. Wells, Structural Inorganic Chemistry, Oxford University Press (2012).
The rare earth oxides RE2O3 have structures derived from oxygen‐deficient fluorite in which the rare earth CN is reduced to 7 or 6. There are three structure types stable below 2000 °C: hexagonal A, monoclinic B and cubic C (or bixbyite) with A favoured by larger cations La to Pm, C by the smaller cations Gd to Lu and B by those of intermediate size. Some oxides are polymorphic and transform in the sequence C to B to A with increasing temperature, although most do not form all three polymorphs. Structure types and polymorphisms are summarised in Fig. 1.48(b) with part of the structure of A‐type La2O3 in (c) showing 7‐fold coordination of La in the form of a distorted cube with one corner missing. The B structure is a monoclinic distortion of A giving rise to a mixture of 6‐ and 7‐coordinate RE cations whereas the C structure has 6‐coordinate cations. The mineral name of the C structure is bixbyite, (Fe,Mn)2O3 and it is essentially cubic fluorite with ¼ of the oxygens missing.
The weberite structure, Na2MgAlF7, is another anion-deficient fluorite superstructure, closely related to pyrochlore that is shown by a range of fluorides and oxides of general formula A2B2X7. The ideal symmetry of weberite is orthorhombic, space group Imma, but several structurally-related polymorphs occur, depending on composition. The anion-deficiency relative to fluorite leads to an overall reduction in cation coordination number with two types of distorted AX8 polyhedra and two sets of BX6 octahedra. It may be regarded as a 3D network of corner-sharing BX6 octahedra, but also as a complex interpenetrating network of corner- and edge-sharing AO8 polyhedra within which the anions occupy three sets of crystallographically-distinct tetrahedral sites. The cations in isolation form ccp layers, equivalent to those in the (111) orientation in fluorite and pyrochlore, but have two stoichiometries, A3B and AB3, that alternate. The A components of these layers also form a so-called Kagome network of interlinked hexagons and triangles which may be regarded as cp layers with ¼ of the packing atoms absent.
