## Decahedra

The decahedron (a model of which is shown in Fig. 12) consists of five subunits. The deformation can be performed in two different ways. Figure 13 a shows a deformed tetrahedral subunit consisting of six edges: one x1, four x2, and one x3.

Case a: x2 = x3, x1 is larger by 5% than the other five edges x2, x3.

Case b: x1 = x2, x3 is larger by 1.8% than the other five edges x1, x2.

In the latter case (b), five edges for the five subunits have to be deformed, whereas in case a, only one common edge has to be deformed. In both cases the decahedra consist of 10

Figure 7. Computer simulation (top) of a hcp structure and electron Figure 9. Computer simulation (top) of a hcp structure and electron micrograph (bottom) of CdS and the PS on the right-hand side in the micrograph (bottom) of CdS and the PS on the right-hand side in the [011] orientation. The simulation consists of seven shells, 2037 atoms. [211] orientation. The simulation consists of seven shells, 2037 atoms.

Figure 7. Computer simulation (top) of a hcp structure and electron Figure 9. Computer simulation (top) of a hcp structure and electron micrograph (bottom) of CdS and the PS on the right-hand side in the micrograph (bottom) of CdS and the PS on the right-hand side in the [011] orientation. The simulation consists of seven shells, 2037 atoms. [211] orientation. The simulation consists of seven shells, 2037 atoms.

Figure 10. Flat triangular CdS cluster with hexagonal structure in the [001] orientation. (A) Overview image. (B) HRTEM image. (C) PS. Reprinted with permission from [16], N. Pinna et al., Adv. Mater. 13, 261 (2001). © 2001, Wiley-VCH.

dm = a*3 cos p, d200 = ax3/(2tgp), the normalising factor is a = a /42

Case a: x1 = x2y 4 sin2 p — 1/ sin p, x2 = x3 = 1 Case b: x3 = x^V3 sin x1 = x2 = 1

Figure 10. Flat triangular CdS cluster with hexagonal structure in the [001] orientation. (A) Overview image. (B) HRTEM image. (C) PS. Reprinted with permission from [16], N. Pinna et al., Adv. Mater. 13, 261 (2001). © 2001, Wiley-VCH.

(111)-planes at the surface. Sometimes (cf. examples below) truncated decahedra (or decahedra with additional intermediate planes) are also discussed. These consist of five additional rectangular (100)-planes. The magic numbers of the nontruncated decahedron are 7, 54, 181, 428, 835____ Dec-

ahedra do not have a central atom. The tetrahedral angle 2p = 72°. In terms of the normalized edges x1... x3 netplane distances can be expressed as follows for the two cases:

dm = a*3 cos p, d200 = ax3/(2tgp), the normalising factor is a = a /42

Case a: x1 = x2y 4 sin2 p — 1/ sin p, x2 = x3 = 1 Case b: x3 = x^V3 sin x1 = x2 = 1

a is again the lattice parameter of the cubic bulk lattice.

Figure 14 shows a computer simulation and an experimental image together with the PS from top to bottom of a Cu decahedron viewed along the 5-fold axis.

## Post a comment