(0, a,0)












8(1)+ 8(2)

S(X -





Z(X -


(a, 1,0)



T(M -


(1,1, a)



samples were cooled from room temperature. Another report for frequencies of the Tu modes by IR spectroscopy [11.66] yielded values of 27 and 59 cm-1, which are not in good agreement with other IR measurements [11.56] or with the interpretation of the single-crystal neutron data [11.13].

As mentioned above, the zone center librations (Ag + Eg + 3Tg) are all Raman active, and various Raman studies of the low-frequency modes have been reported [11.44,57,67], Three low-frequency Raman lines were reported [11.44] at 56, 81, and 109 cm-1. Whereas the line at 56 cm-1 might be a disorder-induced scattering signature of the otherwise IR-active Tu mode observed by neutron and IR techniques near 55 cm-1, the remaining two peaks appear to exhibit much too high a frequency to be identified with any of the intermolecular phonon excitations. This view is also borne out by theoretical calculations [11.60], as discussed below.

Values for the zone center phonon frequencies, obtained from neutron scattering and IR spectroscopy, are collected together with selected theoretical values in Table 11.3. Symmetry assignments are made for all the zone center librational modes, assuming they appear on the experimental energy scale in the same order as calculated by Yildirim and Harris (see below) [11.10,11,61,63]. It is interesting to note that if the values for the T-point librational (gerade) frequencies of Yildirim and Harris are simply scaled by a factor of 2, they are then found in good overall agreement with the neutron scattering data of Pintschovius et al. [11.13]. Furthermore, since the dispersion calculations find the T-point mode frequencies of the Eg and Tg modes quite close in value, it is reasonable at this stage to make a tentative assignment of the neutron peak at 22 cm-1 (2.7 meV) at the T-point to an unresolved pair of Eg and Tg modes.

For comparison to the dispersion relations for the intermolecular modes obtained by analysis of the inelastic neutron scattering data, we show, for example, the theoretical dispersion curves of Yildirim and Harris (Fig. 11.9) calculated in the limit of complete decoupling between the librations and the translational phonons. Note that the librational branches [upper panel (a)] and translational branches [lower panel (b)] are plotted on two different frequency scales. Their calculations are based on a phenomenological point charge model [11.68], in which a negative point charge is placed on each of the double bonds of the C60 molecule and positive point charges (for charge neutrality) are placed on the C atoms. This model reproduces qualitatively the experimentally derived [11.48] orientational potential. Several variations [11.60,68-70] of this point charge model [11.68] have been used to calculate the phonon spectrum of C60 in which negative point charges are placed on the electron-rich double bonds, and the positive point charges, depending on the particular calculation, were positioned at various other locations on the molecule surface, i.e., either centered on

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