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M-Concentration (x)

M-Concentration (x)

Fig. 11.24. Dependence of the frequencies of the /lj(l), Ag(2), and Hs(l) modes on alkali metal concentration x in M,Cm, where M = Na, K, Rb, Cs. The frequency shifts of these Raman-active modes are plotted relative to the frequencies a>\Ag(l)] = 493 em-1, u>[Ag(2)] = 1469 cm-1, and <u[tfj(l)] = 270 cm~' for C«, at T = 300 K. A schematic of the displacements for the eigenvectors for the Ag(2) pentagonal pinch and Hg( 1) modes are shown. All the C atom displacements for the Ag(l) modes are radial and of equal magnitude. Data from Ref. [11.112] and Ref. [11.113] are artificially displaced to the left and right, respectively. The centered data are from Ref. [11.19], a study of the eleetron-phonon interaction shows strong electron coupling for the Hg(2), Hg(7), and Hg(8) Raman-active modes and enhanced coupling for Hg{ 1). For other modes the broadening is so great that the lines cannot be resolved in the M3Q0 spectrum [11.118].

The Raman spectra for RbjQo have been investigated by several groups [11.119,120] and the spectra show some unusual features, not present in the corresponding spectra for the other doped M^Qo compounds (see Fig. 11.25). These unusual features are related to the special structural phases of RbjQo (see §8.5.2). At 125°C, where R^Qo assumes a rock salt structure [11.119], the 10 Raman-active modes of Cro are clearly seen with little line broadening relative to the CM spectrum (see Fig. 11.25). If the sample is slowly cooled to 25° C, it is believed that a polymerized phase is

Fig. 11.25. Raman spectra of a RbjQo sample in its fee rock salt structure (bottom panel), its polymer state (middle), and its "quenched" state (top). The respective temperatures are indicated on the curves. The 10 Raman-active modes of pristine C«, and their identification are labeled in the bottom panel; the frequencies of modes activated by the reduction in symmetry are labeled for the quenched and polymer state spectra in the upper two panels. The inset sketches represent the dimer and polymer structures of the C«, molecules in the quenched and slow-cooled polymer states of Rb,^, respectively [11.121].

0 500 1000 1500

Raman shift (cm )

Fig. 11.25. Raman spectra of a RbjQo sample in its fee rock salt structure (bottom panel), its polymer state (middle), and its "quenched" state (top). The respective temperatures are indicated on the curves. The 10 Raman-active modes of pristine C«, and their identification are labeled in the bottom panel; the frequencies of modes activated by the reduction in symmetry are labeled for the quenched and polymer state spectra in the upper two panels. The inset sketches represent the dimer and polymer structures of the C«, molecules in the quenched and slow-cooled polymer states of Rb,^, respectively [11.121].

formed (see §8.5.2); the lower symmetry of this polymerized phase causes many more modes to become Raman-active, although the observed spectrum suggests that inversion symmetry is conserved in the 25° C spectrum (see Fig. 11.25). If instead, the Rb,C60 is rapidly quenched to -130°C, additional lines then appear in the Raman spectrum (see Fig. 11.25) and these additional lines are identified with the breakdown of inversion symmetry [11.121].

Resonant enhancement Raman effects have been observed using 6470 A laser excitation. The low-frequency modes are enhanced near the main in-

terband transitions: hu tlg at 2.6 eV and hg tlg at 3.5 eV (see §13.1.2). The low-frequency Raman lines show Fano lineshapes [11.19,118] indicative of an interaction with a Raman-active continuum, most likely associated with doping-induced electronic transitions.

11.6.2. Doping Dependence of the Flu-Derived Intramolecular Modes

As stated above, the four Flu symmetry, IR-active, intramolecular modes for C60 are observed [11.81] at a>x(Flu) = 527, cj2(FXu) = 576, w3(flu) = 1183 and w4(F1„) = 1429 cm-1 (see Table 11.1). When solid C60 is doped with alkali metals (K, Rb), several groups [11.77,93,119,122] have found that these modes persist in the infrared spectrum, exhibiting doping-induced shifts for three of the modes (io1( u>2, w4), whereas w3 is found to be largely insensitive to doping. Infrared spectra have been reported for x = 0,1,3,4,6 for RbjC so [11.93,121], and solid-state effects are found to be weak in these infrared spectra. Similar to results found for the Raman-active Ag and Hg symmetry intramolecular modes, the doping-induced changes in the IR activity or the frequencies of the Flu modes do not appear to depend on the size or mass of the alkali metal dopant; i.e., the important doping effects are simply related to the number of electrons transferred to the C60 molecule from the alkali metal dopants.

The FXu(j) mode-integrated oscillator strength S, is proportional to x2 and is given by [11.123]

where o-,(w) is the real part of the optical conductivity, N denotes the number of C60 molecules per unit volume, a is the contribution to the static electronic polarizability per added electron from the tlu tXg electric dipole transitions, A; is a dimensionless coupling constant, and = il; (C60, x = 0) is the unrenormalized mode frequency obtained by fitting the C60 spectrum. The phonon softening is linearly dependent on x and is given by

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