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

Solid State Chemistry and its Applications - Anthony R. West


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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.

Schematic illustration of some cation-ordered fluorites showing cation positions relative to those in fcc fluorite.

       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).

      Schematic illustration of the pyrochlore structure, which may be regarded as a distorted, 2 times 2 times 2 superstructure of a cation-ordered, anion-deficient fluorite. Schematic illustration 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

Schematic illustration of the garnet crystal structure.

       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+.


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