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The fluorite structure of CaF₂ can be described as eutactic ccp Ca²⁺ ions with F^– ions occupying all tetrahedral sites, Fig. 1.29. A number of more complex fluorite‐related structures occur with an excess or deficiency of anions or with cation ordering.

A remarkable anion‐excess fluorite is LaH₃; 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 LaH_1.9 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 UO_2+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 UO_2+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 O^2– 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 Bi₂Ru₂O_7‐δ is metallic and Cd₂Re₂O₇ is a low temperature superconductor. (Gd_1.9Ca_0.1) Ti₂O_6.9 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.

Figure 1.48 The pyrochlore structure, which may be regarded as a distorted, 2 × 2 × 2 superstructure of a cation‐ordered, anion‐deficient fluorite. Anions in eightfold positions, e.g. in fluorite split into two groups in pyrochlore, with one group, X, in 48‐fold positions at e.g. (x, 1/8, 1/8). (b) Temperature‐dependent polymorphism of the rare earth sesquioxides.

G. Adachi and N. Imanaka, Chem. Rev. 98, 1479 (1998).

(c) part of the C-type La2O3 crystal structure showing 7-coordinate La.

A range of complex oxides have weberite structures, in compositional families such as Ln₃NbO₇, better written more informatively as Ln₂(Ln, Nb)O₇: Ln = La, Nd, Gd, Dy; Ln₂B₂O₇: LnB = NdZr, SmTi; A₂Sb₂O₇: A = Ca, Sr, Pb and Ca₂(Ta, Nb)₂O₇ (see L Cai and JC Nino, Acta Cryst B 65, 269 (2009) for more details). Weberite oxides are of interest, showing a diverse range of electrical properties. Various weberite fluorides are known, with Na or Ag as the A-cations and different divalent, trivalent B cation combinations such as B²⁺: Mg, Mn, Fe, Co, Ni, Cu, Zn and B′³⁺: Sc, V, Cr, Fe, Al, Ga, In, Tl; most interest is in the magnetic interactions associated with the different transition metal combinations in the B sites within the Kagome A sublattice.