Trigonal packing

When the ratio r/R is different from 1 the form of the chains may be approximated by a cylinder in which hollows and bulges are periodically repeated that is, the chains have an outside envelope similar to a screw [1] (Fig. 2.11a). If the ratio r/R is very small, close to 0.1-0.2, such as for chains in threefold helical conformation, a trigonal packing of enantiomorphous chains may arise. Each 3i right-handed chain is surrounded by three left-handed isoclined or anticlined chains, and vice versa (space group R3c or R3, respectively), such as in iPS (Fig. 2.12a) [40], form I of iPB (Fig. 2.12b) [45], poly (vinyl methyl ether) [83], isotactic l,2-poly(l,3-butadiene) [84], and isotactic poly(o-fluorostyrene) [8. ... 

Fig. 35. (continued)—(b) Antiparallel packing arrangement of two double helices, drawn in open and filled bonds, in the trigonal unit-cell projected along the c-axis. 

Fig. 37. (continued)—(b) An axial view projected along the r-axis shows the packing arrangement of three welan double helices in the trigonal unit cell. The helix drawn in solid bonds is antiparallel to the remaining helices (open bonds). Note that calcium ions are positioned between the helices and each water molecule (large open circle) shown here is connected to all three surrounding helices. The interstitial space is occupied by several other ordered water molecules (not shown). 

Nickel atoms in BajNi B form distorted, puckered 3.6.3.6-kagome nets stacked in six layers perpendicular to the c axis. The densely packed framework of trigonal-Ni prisms again result in boron-pair formation, although Ba atoms are too large to be sandwiched between two Ni layers, and only four Ba can be accommodated within six Ni layers. Superconductivity is found for ( a, Sr, Ba)2pt9Bg borides with a structure related to Ba2Ni9Bfi and e o,B2 however, with respect to crystal chemistry and boron coordination, only the subcell is derived so far. 

In the WC type the metal atoms do not have a closest-packing, but a hexagonal-primitive packing the metal atoms form trigonal prisms that are occupied by the C atoms. 

For AX molecules with no lone pairs in the valence shell of A, both the VSEPR model and the LCP model predict the same geometries, namely AX2 linear, AX3 equilateral triangular, AX4 tetrahedral, AX5 trigonal bipyramidal, and AX octahedral. Indeed Bent s tangent sphere model can be used equally as a model of the packing of spherical electron pair domains and as a model of the close packing of spherical ligands around the core of the central atom. 

---