Number 6 Trigonal Prism

Periodic and uniform stacking sequences of trigonal-prism sandwiches 

Case Symbol of prism and number empty layers 

The sequences 2 and 3, as well as 6 and 7 of Table 1 can be transformed into each other by reflection at a plane parallel to the layers in other words, they are enantiomorphs. Types 1, 2, 4, 5 and 6 are known as 2H—Nbi HxSe2, rhombohedral M0S2, C7-type M0S2, NbS2 and 6R—Tai xS2 [30] resp. 

If we drop the uniformity condition, many more polytypes can be created. Brown and Beerntsen [27] list the sequences with three and four layers (Table 2). To our knowledge, only two of these possible polytypes have been detected, no. 10 in NbSe2 and TaSe2, and no. 18 in TaSe2. Wickman and Smith [29] also list the 16 five-layer and the 81 six-layer polytypes. 

Compounds crystallizing as trigonal-prismatic sandwiches seem to be especially well suited for intercalation of additional atoms or radicals within the empty octahedral layers. A large number of examples are known at present. 

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To make a calculation for three double bonds we need three more orbitals. These may be the three equatorial bonds of the trigonal prism with three caps that is, with 6 = 90° and = 60°, 180°, and 300° (the three other orbitals have 9 = 43.47° and 0 = 0°, 120°, and 240°). The axis for each of the three double bonds is placed midway between an equatorial orbital and one of the other orbitals. The double-bond axes lie at 6 = 63.73°, which corresponds to 101.85° for the bond angle for doubly bonded carbonyls in the M(CO)3 group (bond number n = 2). 

If one applies the same procedure to Figure 1.10B, an iron-sulfur cluster often used as a model for those in biological systems, the same magic number of 60 would be obtained. Cluster magic numbers would occur as 48 e for a triangular clusters, 60 e for tetrahedral, 72 e for trigonal bipyramidal, 74 e for square pyramidal, 86 e for octahedral, 90 e for trigonal prisms, and 120 e for cubic structures. 

A number of cage polysilanes with silicon architectures in the shapes of a cube, trigonal prism, and tetrahedron have also been prepared and crystallographically analyzed. These were synthesized prior to the years covered in this chapter, but as they were not mentioned in the previous organopolysilane chapter, their structures will be briefly noted here. 

Octacoordination is often encountered in lanthanide complexes. The preferred poly-hedra for eight coordination expected on the basis of interligand repulsivities are square antiprism (D ), dodecahedron with triangular faces (Z)2d), bicapped octahedron (D3(i), truncated octahedron (Z)2ft), 4,4-bicapped trigonal prism (C2v), distorted cube (C2v), and cube (0/,). The most commonly observed polyhedra for this coordination number are, however, the square antiprism and the dodecahedron. 

The lanthanide sulphides show pol5unorphism and contain mixed coordination polyhedra and coordination numbers. The sulphides of La—Dy M2S3) form orthorhombic (A-t5q)e) crystals, where there are two kinds of nonequivalent cations (229, 230), one is heptacoordinated (monocapped triangular prism), and the other is octacoordinated (bicapped trigonal prism). Monoclinic (D-type) sulphides are formed by Dy—Tm and Y (229, 231) and contain both hexacoordinated and heptacoordinated lanthanide ions. The rhombohedral (E-type) sulphides of Yb and Lu contain only hexacoordinated metal ions (229). 

For sodium the coordination number tends to be six, and three arrangements are found. In Nal (acetone) 3, which can be used to purify acetone, the arrangement is octahedral with Na—O = 2.46 A, (21), in Nal, (dimethyl-formamide) 3 the Na—O distance is 2.40 0.02 A, (22), and the arrangement is midway between trigonal prismatic and octahedral. (The trigonal prism is sometimes found with chelating ligands, see II. 1 and III. 3). 

It is clear then that the coordination number in both cases is 9 = 6 (trigonal prism) + 3 (caps) that in each case it is really 7 + 2 (cf. bond lengths) and that not only is the topology the same but the geometry almost identical too . P-K2SO4 is one of many compounds and structure types that may be accurately described as anion-stuffed C23 or C37. 

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