A

u+Eu

A + T

Au + T„

2AU+EU+ATU

Hu

+ 2 Eu

E + T

Eu + Tu

A,„ + 2 Eu + 5 Tu

Tg modes only for the ||, J_ geometry, where the two indicated orientations refer to the polarizations of the incident and scattered light.

At low temperature (as discussed in §7.1.3), the appropriate space group crystal structure is or Pa3, as has been determined by x-ray, neutron, and electron diffraction experiments. In the low-temperature phase, there are four distinct C60 molecules per cubic unit cell. The Th point group symmetry is maintained for the t point in the Brillouin zone by virtue of the four molecules interchanging places under the point group symmetry operations (see Table 7.6).

Table 7.7 gives the site symmetries for the low-temperature space group. The four C60 molecules per unit cell are located on the a sites listed in Table 7.7, which has 3 site symmetry. As a result of the lower site symmetry of the C60 molecules in fa3 relative to the Fm3 space group, the number of inequivalent sites for the carbon atoms of the C60 molecule in Pa3 increases to 10, as shown in Fig. 7.4. It is shown in Table 7.8 that dopants can occupy all the b sites, or all the c sites, or all the d sites of space group Pa3 without lowering the space group symmetry. The sites for common dopants in fullerene solids are discussed in §8.6 and §8.7.

The four fullerene molecules per unit cell in the Pa3 structure transform into one another according to the irreducible representations of the equivalence transformation (Ag + Tg) as shown in Table 7.8 [7.51]. The irreducible representations for the equivalence transformation s for dopants on other sites of the space group (Pa3) are given in Table 7.8. The character table for the point group S6(3) is given in Table 7.9. The irreducible

Table 7.7

Site symmetries for the simple cubic space group T® (or Pah) [7.49],

Site coordinates"

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