Rutile adaptive structures

Adaptive structures have a common structural principle. A large unit cell of the adaptive structure is built up from the ordered repetition of a set of basic sub-units, derived from the mother structure by systematic changes in site occupancy (see Section 1.4.11) or in stacking sequence, or by a shear operation. For example, the homologous compounds V O2 i (n = 3-9, see Section 2.2), which are derived from the mother compounds (rutile) by the shear operation (121)j[0il], are able to be a set of basic sub-units. 

Figure 1 has been constructed from Fig. 8.13 of [13], as modified by Fig. 2.8 of [14] to illustrate how this approach is applied to Ti02. The 3d, 4s, and 4p atomic states of Ti, and the 2s and the 2p atomic states of O, are used to construct a set of symmetry adapted linear combinations (SALC s) of atomic orbitals that are consistent with the Oh symmetry group of a regular, or undistorted octahedron as in an ideal cubic rutile structure. It is important to understand that other atomic states, e.g., the Hf 5f state symmetries can be introduced as well, and that the introduction of... 

Figure 7.19 The anion-centred polyhedron found in the hexagonal closest-packed structure (a) oriented with the hexagonal c-axis vertical (b) cation positions occupied in the ideal corundum, AI2O3, structure (c) cation positions filled in the idealised rutile, Ti()2, structure (d) cation positions occupied in the wurtzite, ZnS, structure, the central anion is omitted for clarity. Cations in tetrahedral sites are small and cations in octahedral sites are medium-sized. Adapted from E. W. Gorter, Int. Cong, for Pure and Applied Chemistry, Munich, 1959, Butterworths, London, 1960, p 303...

Figure 2. Crystalline structure of (A) anatase, (B) rutile and (C) brookite. (Adapted from Khataee and Kasiri [1] with permission from publisher, Elsevier. License Number ...

Fig. 2.4 Electronic band structure and density-of-states (DOS) of rutile Xi02. The black parts of the DOS indicate completely filled bands. Adapted from Hoffmann [6], pp. 31, copyright Wiley-VCH Verlag GmbH Co. KGaA. Reproduced with permission...

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