Diamond lattice arrangements

Thomas and co-workers [8] discovered an entirely new morphology on examination of multiple-arm star block copolymers. For the right combinations of arm lengths and compositions, these materials organize themselves into a bicontinuous structure, with each phase fully interpenetrating the other in a diamond lattice arrangement. In these star molecules, the arms were diblock polymers a considerably wider range of structural variation is conceivable and even possible. 

Similar to the diamond lattice the B and N atoms are tetrahedrally coordinated. Every boron atom is surrounded by four nitrogen atoms and vice versa. In this arrangement boron and nitrogen atoms have sp3 hybridization. 

Figure 1.9 The lattice structure of hexagonal diamond. The arrangement of atoms in the horizontal crystal plane somewhat resembles a wavy graphite structure.

Figure 2 Molecular orbital energies arising from a linear combination of atomic p orbitals plotted against the relative number of electronic states with each energy. Data are for 64 carbon atoms arranged in a diamond lattice with periodic boundaries in each direction. Energies (in eV) are calculated from the tight binding Hamiltonian of Xu et al. (Ref. 33). 1 0 he experimental lattice constant for diamond, a is the lattice constant used in the calculations, and is the second moment of the density of states.

Figure 25.1. Spatial arrangement of carbon atoms in the diamond lattice (left) and graphite lattice (right).

The continuous reduction in size of a solid finally leads to a situation where the original solid state properties can be only partially observed or may be even completely lost, as these properties are exclusively the result of the cooperation between an infinite number of building blocks. Further reduction of size finally leads to typical molecular behavior. On the other hand, even here are structural relations to the bulk occasionally detectable. For instance, the arrangements of the sp hybridized carbon atoms in cyclohexane or in adamantane can easily be traced back to the diamond lattice, whereas benzene or phenanthrene represent derivatives of the graphite lattice. However, neither cyclohexane, benzene, nor phenanthrene have chemical properties which are comparable with those of the carbon modifications they originate from. The existence of the above mentioned Q, C]o or Ci4 units is otUy made possible by the saturation of the free valencies by hydrogen atoms. Comparable well known examples for other elements are numerous, for instance the elements boron, silicon, and phosphorous. Figure 1-1 illustrates some of the relations between elementary and molecular structures. 

Figure 1.3 Carbon crystallizing in two different modifications - as graphite and as diamond -having different lattice arrangements.

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