Structure of rutile

Structure of rutile (a) connection of TiOg octahedra and the unit cell, (b) chains share vertices, viewed along the caxis. 

In the structure of rutile, the Ti atoms constitute deformed TiOe octahedra, in which the Ti-O distance are 194.85 pm (four) and 198.00 pm (two). The TiC 6 octahedra share edges to form chains, which further share vertices to yield a three-dimensional network, as shown in Fig. 10.2.6. 

The structure of rutile may also be described as a nearly hep of O atoms, with Ti atoms located in half of the octahedral interstices. 

Many tetravalent metal oxides and divalent metal fluorides adopt the rutile structure. Table 10.2.6 lists some compounds with the rutile structure and the parameters of their tetragonal unit cells. 

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The Rutile Structure.—A large number of compounds MX crystallize with the tetragonal structure of rutile, TiCfe. In this structure the position of the ion X is fixed only by the determination of a variable parameter by means of the intensity of reflection of x-rays from various crystal planes. In accordance with the discussion in a following section, we shall assume the parameter to have the value which causes the distances between X and the three ions M surrounding it to be constant. With this requirement the inter-atomic distance R and the edges a and c of the unit of structure are related by the equation R = (a/4 /2) [2 + (c/o)2]. In this way the inter-atomic distances in Table XII are obtained. In the case of magnesium fluoride the agreement is satisfactory. 

The elucidation of the factors determining the relative stability of alternative crystalline structures of a substance would be of the greatest significance in the development of the theory of the solid state. Why, for example, do some of the alkali halides crystallize with the sodium chloride structure and some with the cesium chloride structure Why does titanium dioxide under different conditions assume the different structures of rutile, brookite and anatase Why does aluminum fluosilicate, AljSiCV F2, crystallize with the structure of topaz and not with some other structure These questions are answered formally by the statement that in each case the structure with the minimum free energy is stable. This answer, however, is not satisfying what is desired in our atomistic and quantum theoretical era is the explanation of this minimum free energy in terms of atoms or ions and their properties. 

The structures of rutile and anatase, the two tetragonal forms of titanium dioxide, have been determined by rigorous methods (Figs. 1 and 2). They seem at first sight to have little in common beyond the fact... 

Fig. 1. The structure of rutile. Large circles represent the centers of titanium atoms, small circles those of oxygen atoms. One octahedron with oxygen atoms at its cornex and a titanium atom at its center is shown two of its edges, those indicated by arrows, are shared with adjoining octahedra.

The similarity of the structures of rutile, CaCl2 and marcasite also comes to light by comparison of their crystal structure data (Table 17.2). The space groups of CaCl2 and marcasite (both Pnnm) are subgroups of the space group of rutile. The tetragonal sym-... 

Different crystal forms of titanium dioxide are known rutile (tP6), anatase (til2) brookite (oP24). Rutile is the most common form (the others, metastable, transform into it on heating). The ideal structure of rutile can be described as ... 

Tossell J. A., Vaughan D. J. and Johnson K. H. (1974). The electronic structure of rutile, wustite and hematite from molecular orbital calculations. Amer. Mineral, 59 319-334. 

FIGURE 1.41 The crystal structure of rutile, T102. (a) Unit cell, (b) parts of two chains of linked [TiOe] octahedra, and (c) projection of structure on base... 

Titanium dioxide, TiOa (rutile), In the structures so far considered, all the atoms have occupied very special positions in the unit cell there were no continuously variable parameters to be determined. The structure of rutile, now to be considered, is a simple example of a structure in which there is one parameter. This structure has been described on p. 226, where it was introduced in connexion with the calculation of structure amplitudes. The general arrangement of the atoms was assumed, and the effect of the variation of the oxygen parameter on the structure amplitudes of the reflections was demonstrated (Fig. 123). Here we shall consider the evidence which leads to a knowledge of the general arrangement of the atoms. 

Fig. 174. Structure of rutile, Ti02. Arrangements in P4%jmnm (left) and P4znm (right).

Rutile Ceramic Pigments. Structurally, all rutile pigments are derived from the most stable titanium dioxide structure, ie, rutile. The crystal structure of rutile is very common for AX2-type compounds such as the oxides of four valent metals, eg, Ti, V, Nb, Mo, W, Mn, Ru, Ge, Sn, Pb, and Te as well as halides of divalent elements, eg, fluorides of Mg, Mn, Fe, Co, Ni, and Zn. 

Figure 5.30. The 2-2P01/2(t) structure of rutile (Ti02) (a) A perspective view of the cell showing the TiC>6 octahedra in the cell. The smaller atoms are Ti. (b) A perspective view of the rutile cell showing the octahedra around each Ti.

The existence of at least nine phases in the molybdenum-oxygen system is well established. Their crystal structures are briefly described and it is shown that they can be classified into four main families dependent on whether they possess a basic structure of rutile type, ReOs type, or MoOs type, or have complex structures where polygonal networks can be distinguished. The known tungsten and mixed molybdenum tungsten oxides fit into this scheme. Because of their complicated formulas many of these compounds may be termed "nonstoichiometric," but variance in composition has not been observed for any of them. 

As has been pointed out recently [10], bulk defects play a major role in a variety of surface phenomena where annealing to high temperature is necessary, e.g. during the encapsulation of Pt [11-13], in bulk-assisted re-oxidation [14,15], in restructuring and reconstruction processes [9,16], and in gas adsorption [17]. The relationship between crystal color, conductivity, bulk defects as characterized by EPR measurements, and surface structure of rutile (110) has been investigated systematically by Li et al. [10]. 

The expanding data base has made rutile the model system for metal oxides. Nevertheless, there are still many open questions concerning the crystal structure of rutile surfaces as pointed out throughout this Chapter. One interesting aspect is the advent of surface studies on anatase. From the recent... 

For more on the electronic structure of rutile and related compounds, see Burdett, J. K. ... 

Figure 7. Crystal structures of rutile (left) and anatase (right) Ti02.

Jones, P., and Hockey, J. A. (1971). Jnfra-red studies of rutile surfaces. 2. Hydroxylation, hydration and structure of rutile surfaces. Trans. Faraday Soc. 67, 2679-2685. 

Figure 17 shows the structures of rutile and a-PbOj, two structures based on an hep net of oxide ions in which half of the octahedral holes are filled by cations. In rutile straight... 

Figure 1.20 Distorted hexagonal close-packed structure of rutile...

FIGU RE 1.16 Structure of rutile white circles, black circles, TP+ large gray circles. O of adsorbed water small gray circles, H of adsorbed water. Lower-case letters denote various surface species. (Reprinted from Imanishi, A. et al., J. Am. Chem. Soc., 129. 11569, 2007. Copyright 2007 American Chemical Society. With permission.)... 

Fig. 8.05. Clinographic projection of the unit cell of the tetragonal structure of rutile, Ti02.

Fig. 8.06. Clinographic projection of the tetragonal structure of rutile, Ti02, showing the co-ordinating octahedra of anions round the cations and the way in which these octahedra are linked in bands by sharing horizontal edges.

Atomic co-ordinates are not, of course, always simple fractions of the cell translations. In the tetragonal structure of rutile (fig. 8.05, p. 148), for example, the co-ordinates of the atoms are... 

Structure of Rutile Surfaces Non-Stoichiometry and Oxygen Reactivity... 

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