Rutile shear structure

Next, the rutile (TiO2) based shear structure is discussed. In the rutile-type structure (tetragonal), the metal and oxygen occupy the following positions as shown in Fig. 2.8 ... 

On the other hand, two types of shear structure based on rutile appear in the TijOj-TiOj, (>20,1102, and systems. For the... 

Fig. 2.112 Reciprocal lattice plane of rutile-typc structure with [111] zone axis. The (s, t) series of shear planes are indicated by dashed lines (see text). White circles are the possible shear planes for this system.

The simplest member of a shear structure derived from rutile is that found for Tis09 where n = 5. A block of the structure is shown in Figure 15. Here, edge and comer-sharing TiOe blocks of the ratile type, five octahedra thick, are joined by face sharing to similar five unit blocks. As the level of reduction decreases, the size of the ratile block increases but the crystallographic shear remains the same. 

Operation (7) The mother structure (for example, TiO2 (rutile)) is divided into blocks with the dimension of a = x (n is an integer), where is a shear plane with plane indices (hkl) and is the plane spacing of H. (Fig. 2.2(a)). 

The homologous compounds V O2 -1 are derived by the shear operation (121) [0i 1] on rutile. As mentioned above, the arrangement of atomic planes parallel to (121) is. .. ABABAB. .., where A = O and B = MO. After the elimination of an oxygen-only plane A in every n B plane, the arrangement of the atomic planes gives compounds generally expressed as M O2 -1 ( = (n — 1)A + nB). As a typical example. Fig. 2.12 shows an ideal structure of VgOi 1 (n = 6). The structure has been confirmed by X-ray diffraction. In Table 2.1, the shear compounds of the transition metal oxides are summarized. ... 

Fig. 2.12 Ideal structure of VgOjj viewed along the a-axis of rutile, derived by the shear operation (121) [0il] on rutile. The marks and show the metals at x = 0 and leading to face-sharing of adjacent octahedra, similar to a Corundum-type structure.

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 2 Section through rutile structure idealized) containing (132) shear planes...

Shear Plane-Point Defect Equilibria.—The question of the existence of point defects in compounds where extended defects are known to occur has been controversial. Indeed, it has occasionally been claimed that point defects cannot form in such phases and that they will always be eliminated with the formation of extended structures. We reject these latter arguments as thermodynamically unsound. From a thermodynamic standpoint, the formation of extended defects can be viewed as a special mode of point defect aggregation as such, shear planes will be in equilibrium with point defects, with the position of the equilibrium depending on both temperature and the extent of the deviation from stoicheiometry. Thus, if we assume, as is suggested by our calculations, that anion vacancies are the predominant point defects in reduced rutile (a further point of controversy as mentioned above) then there will exist an equilibrium of the type... 

Crystallographic Shear (C5) Phases.—The CS phases are the best-known group of materials which appear to be intolerant of point-defect populations. There are three major families those based upon tungsten trioxide, WO3, upon rutile, Ti02, and upon niobium pentoxide, Nb205. These and other less studied systems have been described in some considerable detail in two previous review articles in this series and elsewhere and the fundamental principles underlying their structures will not be repeated here. In this section some of the results found in the tungsten trioxide and rutile-related systems will be outlined. Older results, covered in the earlier reviews, will merely be sketched in where relevant, and emphasis will be upon newer data or else on a re-examination of earlier results from the point of view of this article. 

Further reduction with H2, C or CO produces a series of discrete chemical-shear phases (Magn61i phases) of general formula 02 i based on a rutile structure with periodic defects (p. 961), before the black, refractory sesquioxide 203 is reached. Examples are 407, 509, 60u, 7013 and gOi5. The oxides 0, 203 and 30.5 also conform to the general formula V 02 i, but this is a purely formal relation and their structures are not related by chemical-shear to those of the Magneli phases. 

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