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association 5(1)
1(2) takes the form TiO(5/1
1/2)
TiO 5.5 or Ti 2 O 11 .Itis
1
5
observed that the sequence of all the Ti
O radicals given in Table 8.3 is made up
of homological series with a general formula [Ti 2 O 12 2 n ] 2 2(8 2 n) , where n
0, 1, 2,
5
, 8. The most simple titano-oxygen motif is [TiO 6 ] 8 2 radical with all the six free
vertices. Instead of discussing each radical unit given in Table 8.3 , only a few selected
and most widespread radical groups are discussed here. The most popular among these
is the Ti
3,
...
O framework consisting of the basic structure related to perovskite-type
CaTiO 3 [68] . Similarly, it is interesting to consider perovskite-type framework in
ilmenite, pyrochlore, and spinel types; however, the most important association in the
crystal chemistry of titanates is the TiO 2 in three polymorphic modifications, of which
the rutile type is the most stable one, with linear columns of octahedra sharing the
edge. The most complex association is that where each oxygen atom is linked with
four Ti 4 1 octahedra and it is considered to be a highly unique structure since it indi-
cates an anomalously high supersaturation of the corresponding oxygen ligands with
Ti 4 1 . Such complex structures are formed in K(NbTi)O 5 ,Na 2 Ti 3 O 7 ,A 2 Ti 6 O 13 ,where
A
72] . Here, it is appropriate to discuss the
groups consisting of titanium coordination with five vertices, i.e., tetragonal pyramids
and trigonal pyramids. In this case also, it is possible to use the principle of character
association. With the help of simple and complex symbols, for Ti
5
Na, K, Rb, and similarly Na x Ti 4 O 8 [69
O polyhedra in the
discrete form, only tetragonal pyramids have been reported and such structures can be
expected in titanates, silicates, germanates, and rare earth titanates, RTiO 5 ,where
R 5 Y, La [73,74] . All the above-mentioned different motifs of Ti Ooctahedra—
either isolated or discrete pairs—are linked with each other to form chains, ribbons,
layers, etc., clearly indicating the ability of Ti 4 1 to decrease its coordination number
up to five and, thus, giving new motifs corresponding to Pauling's polyhedra.
Obviously, intercondensation of Ti
O polyhedra makes a part of their edges and ver-
tices remain free. This is attributed to the higher probability of the severely disturbed
charge balance, and it becomes important when the Ti
O distances in coordination
polyhedra fall from the normal values. Reduction in the coordination number of Ti 4 1
up to 5 can be considered due to the limited manifestation of the tendency of Ti 4 1
ions under the given conditions by giving out one of its ligands.
In summary, the above described crystal chemical elucidation of titanium, par-
ticularly Ti octahedra, undergo condensation, their varying associations, abundance
of the edge contacts between these polyhedra, an anomalous case of their faces
linked, reduction in the coordination number of Ti, the possibility of reaching a
complete charge compensation, etc., and justify a wide structural diversity, both in
natural and synthetic compounds.
In comparison with the other anion forming elements, Ti 4 1 stands close to Si 4 1
in several respects. Probably the main reason for such closeness is the repulsive
forces between the higher valent ions like Ti 4 1 and, in general, Ti 4 1 can form
complexes easily with the group IV elements of the periodic table. Since Ti 4 1 has
a higher coordination number, it is not as easy to understand the absence of analo-
gous phase, TiSiO 4 , in the system TiO 2 a
SiO 2 [75] . Out of 32 known titano-silicate
compounds in nature, 18 consist of one or the other groups of titanium octahedra.
Under these circumstances, it leads to an unexpected variation in their association,
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