Ag ® ^sltes = Ag + Tg, taking into account the larger unit cell for the Pa.3 structure (see §7.1.3).
Temperature-dependent infrared studies on single-crystal C60 have revealed splittings of each of the F,„(l), F,„(3), and F,„(4) spectral features into a quartet of lines below the first-order phase transition at T0l (261 K), as shown in Fig. 11.20 [11.106]. The development of the quartet structure occurs gradually with decreasing temperature, and not sharply at T0l. The authors [11.106] attributed the splittings to cubic crystal field effects associated with orientational ordering of the molecules below Tm and with increasing orientational ordering as T is decreased further. Group theoretical analysis indicates that the appearance of four inequivalent sites in the Pa3 structure below Tm results in a symmetry-lowering effect. If ^sltes — Ag + Tg describes the transformation properties of the four inequivalent sites, then the direct product Tu ® ,\'sltes is decomposed into the irreducible representations Au + Eu + 3Tu (in Th symmetry). Thus, if crystal field effects were responsible for the observed quartet of lines, we would expect each Flu mode to split into three infrared-active Tu modes, whose mode frequencies could be estimated by a zone-folding scheme applied to the phonon dispersion curves appropriate to the larger fee Brillouin zone. The authors [11.106] attributed the remaining line of the quartet to either the activation of a silent mode due to crystalline disorder or the splitting of one of the Tu
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