Coordination numbers rutile

The room temperature transformation of the columbite phase to baddeleyite commences at 13-17 GPa 6, with transition pressure increasing linearly with temperature Direct transition from rutile to baddeleyite phase at room temperature and 12 GPa has also been reported 7. The baddeleyite phase undergoes further transition to an as yet undefined high-symmetry structure at 70-80 GPa. The most likely candidate for the high-pressure phase is fluorite, which is consistent with the general pattern of increasing Ti coordination number from 6 in rutile, to 7 in baddeleyite (a distorted fluorite structure), and to 8 in fluorite. 

The Fe—O distances in hematite are 1.99 and 2.06 A. The (Mn,Fe)—O distances in bixbyite are expected to be the same in case that (Mn, Fe) has the coordination number 6, and slightly smaller, perhaps 1.90 A, for coordination number 4. The radius of 0= is 1.40 A, and the average O—O distance in oxide crystals has about twice this value. When coordinated polyhedra share edges the O—O distance is decreased to a minimum value of 2.50 A, shown by shared edges in rutile, anatase, brookite, corundum, hydrargillite, mica, chlorite, and other crystals. Our experience with complex ionic crystals leads us to believe that we may... 

Several additional, more complicated structure types are known for ionic compounds. For example, according to the radius ratio, one could expect the rutile type for strontium iodide (rSr2+ /i = 0.54). In fact, the structure consists of Sr2+ ions with a coordination number of 7 and anions having two different coordination numbers, 3 and 4. 

The surface chemistry of coesite and stishovite was studied by Stiiber (296). The packing density of hydroxyl groups was estimated from the water vapor adsorption. More adsorption sites per unit surface area were found with silica of higher density. Stishovite is especially interesting since it is not attacked by hydrofluoric acid. Coesite is dissolved slowly. The resistance of stishovite is ascribed to the fact that silicon already has a coordination number of six. Dissolution of silica to HaSiFg by hydrogen fluoride is a nucleophilic attack. It is not possible when the coordination sphere of silicon is filled completely. In contrast, stishovite dissolves with an appreciable rate in water buffered to pH 8.2. The surface chemistry of. stishovite should be similar to that of its analog, rutile. 

AB2 structures. Fluorides and oxides of the formula AB2, which are distinctly ionic, crystallize in structures determined by size considerations. As in the case of AB structures, it is the coordination geometry of anions around the cation that determines the structural arrangement. The coordination may be 8-, 6-, or 4-fold, fixing the corresponding anion coordination numbers to 4,3 or 2. We thus have the following structures for ionic AB2 compounds fluorite (8 4), rutile (6 3) and silica (4 2) and these structures are shown in Fig. 1.7. 

Rutile structure (Fig. 4-15). Titanium dioxide occurs naturally as ana-tase, brookite, and rutile, all of which contain octahedral TiC>68 units. The coordination number of the central Ti4+ is very obviously six, and a little thought confirms that the same is true of the Ti4+ ions at the corners. That the coordination number of the O2- ions is three is seen from the nearest... 

The rutile structure. Titanium dioxide crystallizes tn three crystal forms at utmospheric pressure anatase, brookite, and rutile (Fig. 4.4a). Only the last (tetragonal P42/mnin) will be considered here. The coordination numbers are 6 for the cation (six oxide anions arranged approximately octahedrally about the titanium ions) and 3 for the anion (three tiianium ions trigonally about the oxide ions). The rutile structure is also found in the dioxides of Cr, Mn, Ge, Ru, Rh, Sn, Os. Ir, Pt. and Pb. 

Another simplification consists in the fact that among the various structural types of fluorides, the involved d-transition elements generally possess the coordination number 6. The crystallographic features can be deduced from the arrangement of (MF6) octahedra5,6. Besides in three-dimensional (3-D) networks such as found in perovskite, rutile or pyrochlore types for instance, fluorides crystallyze in two-dimensional (2-D) layer structures, one-dimensional (1-D) chain structures and isolated unit arrangements. 

If we consider the fluorides, for example, which form pure coordination lattices (p. 33), then those from the alkaline earth metals with the exception of magnesium and beryllium crystallize in the fluorite structure, in which the cation is surrounded by eight fluorine ions for CaF2 and CdF2, which have the same structure, r+/r is 0.71 and 0.69 respectively just at the limit V 3— 1 — 0.73. The fluorides of other divalent ions, such as Mn, Fe, Co and Ni and also Mg, crystallize in a structure with coordination number six (rutile type). It is only for BeF2 that the ratio r+/r = 0.23 lies below the limit of this coordination number and it has a structure similar to that of cristobalite (Si02) with four neighbours (see also p. 66). 

Rutile, and many other transition-metal compound structures, arc characterized by dense packing and high coordination numbers (numbers of nearest neighbors). Their bonding properties arc those of ionic solids, and many of the structures have been rationalized in terms of ionic radii and Madelung energies. 

An important use of high mechanical pressiues is to force solids to assume crystal structures and coordination numbers in which they are normally unstable. Thus, four-coordinate Si in Si02, typified by quartz or try dimite, can be forced to assume the six-coordinate rutile stracture under very high pressures. Once formed, these structures are kinetically stable. The high-pressure polymorph of silica, called stishovite is found terrestrially as the result of meteor impact. 

Germanium oxide, GeOg differs from Si02 in that in addition to a quartz type structure in which the coordination numbers of germanium and oxygen are respectively 4 and 2, there exists a second modification with a rutile structure (coordination numbers respectively 6 and 3). The reason for the formation of the second structure is not clear, but it may be due to an increased contribution from the ionic form of the GeO bond. 

Fig. 7.1 Side view of the unreconstructed (bulk terminated) rutile TiO surfaces. The black spheres represent Ti atoms, and the gray spheres are O atoms. The coordination number (CN) for the Ti atoms is five for the (110) and (100) and four for the (001) structure...

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