of the pyrochlore structure, which may be regarded as a distorted, 2 times 2 times 2 superstructure of a cation-ordered, anion-deficient fluorite."/>
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.
1.17.13 Garnet
The garnets are a large family of complex oxides, including both minerals and synthetic materials, some of which are important ferromagnetic materials; yttrium aluminium garnet (YAG) is used as a synthetic gemstone and when doped with neodymium is the key component in YAG lasers; more recently, garnets with high Li+ ion conductivity have been synthesised; garnets have hardness 6.5–7.5 on the Mho scale and are used industrially as an abrasive on sandpaper. They have the general formula A3B2X3O12: A = Ca, Mg, Fe, etc.; B = Al, Cr, Fe, etc.; X = Si, Ge, As, V, etc. A is a large ion with a radius of ~ 1 Å and has a coordination number of eight in a distorted cubic environment. B and X are smaller ions which occupy octahedral and tetrahedral sites, respectively. Garnets with A = Y or a rare earth: Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb or Lu and B, X = Fe3+ have interesting magnetic properties. One of the most important is yttrium iron garnet (YIG), Y3Fe5O12, the structure of which is shown in Fig. 1.49. Many other A, B, X combinations are possible, such as those in Table 1.25.
Figure 1.49 The garnet crystal structure.
The unit cell of garnet is body centred cubic, a ≈ 12.4 Å, and contains eight formula units. The structure may be regarded as a framework built of corner‐sharing BO6 octahedra and XO4 tetrahedra. The larger A ions occupy eight‐coordinate cavities within this framework. In YIG and the rare earth garnets, the B and X ions are the same, Fe3+.
1.17.14 Perovskite‐rock salt intergrowth structures: K2NiF4, Ruddlesden–Popper, Aurivillius and Dion Jacobsen phases and layered cuprate superconductors
The K2NiF4 structure is the simplest structure of a large family of related materials that has attracted much attention in recent years because several of them are superconductors. The structure may be regarded as alternating layers of perovskite and rock salt structures, as shown in Fig. 1.50. The formula K2NiF4 could be written in expanded form as KNiF3.KF to indicate the perovskite and rock salt components. The structure is body centred tetragonal with perovskite‐like layers of octahedra centred at c = 0 and
Table 1.25 Examples of A, B, X combinations in garnets
| Garnet | A | B | X | O |
|---|---|---|---|---|
| Grossular | Ca3 | Al2 | Si3 | O12 |
| Uvarovite | Ca3 | Cr2 | Si3 | O12 |
| Andradite | Ca3 | Fe2 | Si3 | O12 |
| Pyrope | Mg3 | Al2 | Si3 | O12 |
| Almandine | Fe3 | Al2 | Si3 | O12 |
| Spessartine | Mn3 | Al2 | Si3 | O12 |
| Ca3 | CaZr | Ge3 | O12 | |
| Ca3 | Te2 | Zn3 | O12 | |
| Na2Ca | Ti2 | Ge3 | O12 | |
| NaCa2 | Zn2 | V3 | O12 |
A‐site
