"Experimental values reported for KxCflfl [11.125,126]. ''Values reported by Rice and Choi [11.123] and deduced from the IR transmission data of K^C^ [11.127], cSRd((Oj) is defined as the relative integrated intensity 5y(Rb3C60)/ 5y(Rb6C60) for the /th IR-active mode of C«, and is equal to 4 in the charged phonon model of Rice and Choi [11.123].

dThe F,.(l) mode in the metallic Rb3Cwl cannot be observed and therefore an experimental value for Sr^h),) cannot be obtained.

might be due to a coupling between the Flu modes and electronic transitions in the M-doped C60 compounds (i.e., transitions between filled tu-and empty tlg-derived orbitals). According to Rice and Choi, the electron-molecular vibration (EMV) coupling, in effect, allows for a transfer of oscillator strength from the electronic absorption band observed near ~1.2 eV, and identified in M6C60 [11.125,127-129] with tlu-tlg electronic absorption, to vibrational absorption bands identified with the otherwise weakly IR-active Flu modes. Thus, the EMV coupling can be viewed as if it contributes "charge" to the mode, enhancing the dipole moment or IR activity. For moderate EMV coupling, these modes are referred to as "charged" phonons [11.123]. In the limit of very weak EMV or electron-phonon coupling, the phonon or vibration is not termed "charged," but the EMV mechanism may still induce a"dynamic" dipole moment responsible for IR-mode activity, even though no static dipole exists in the unit cell (e.g., graphite) or in the C60 molecule [11.130]. Furthermore, as Rice and Choi point out, this phenomenon has been appreciated by physical chemists since 1958 [11.131] and has been applied successfully to explain the remarkable infrared activity in one-dimensional systems such as the linear chain organic semiconductors (MEM)(TCNQ)2 [11.132] and (TEA)(TCNQ)2 [11.133],

In their paper, Rice and Choi report the results of model calculations for the doping dependence of the Flu vibrational mode oscillator strength and frequency renormalization. Assuming icosahedral symmetry for the molecular ion, the EMV coupling between the tXu-tlg electronic transitions and the Flu(TXu) modes is symmetry allowed; i.e., the direct product T\u ® Tlg = Au + Tlu + Hu contains FXu(T{u) symmetry. For simplification, Rice and Choi neglect weak electronic and vibrational coupling between molecules in the M^Qo lattice and obtain, in the molecular limit and in the limit of weak EMV coupling, the results: (1) The Flu(j) mode oscillator strength Sj(x) is proportional to x2 [i.e., Sj(x) ~ Ay*2] where x denotes the charge transfer. (2) The frequency renormalization is linear in x or Aw ~ AjX, where A; is the EMV coupling constant for the mode j. In the molecular limit, x electrons occupy the lower-lying tlu orbital, which is full (with six electrons) at the saturation doping limit (x = 6). Furthermore, it is noted that the result S-(jc) ~ x2 ignores any intrinsic IR activity, that might be expected in the absence of an EMV effect. Such intrinsic IR activity might stem, for example, from a static interaction between the C^ ion electronic orbitals and the electric field from the M+ sublattice.

Since the original work on the saturated K- and Rb-doped compounds [11.127], several groups have carried out experiments to investigate the doping dependence of the -derived modes [Flu(i), i — 1,2,3,4], Kuzmany and co-workers [11.77,125,126,134] obtained qualitative information from reflectance studies of ~1 -/¿m-thick C60 films deposited on Si substrates;

the films were K doped in situ in a vacuum of 10~7 torr by repeated exposure to the vapors of the alkali metal. These sequential doping steps were continued until "spectroscopically clean" phases were obtained and equilibrated. Using this procedure, they reported the observation of spectra for the jc = 1,3,4,6 phases, the x = I cubic phase being stable only at elevated temperatures. Three of the four Flu modes were found to exhibit a mode-softening effect that is linear in x, consistent with the theory of Rice, whereas the (o3 mode exhibited little or no sensitivity to doping. No values for the oscillator strengths were obtained from the data, but the magnitude of the change AR in the reflectance associated with the Flu(2) and Flu(4) modes appears to indicate that a strong enhancement of the oscillator strength was observed for these modes, consistent with the charged-phonon model of Rice and Choi [11.123],

Since linear mode softening was also observed for some of the Hg (Raman-active) modes in MXC60 [11.19], linear mode softening, by itself, should not be considered as strong evidence for "charged phonons" in MjQo- Furthermore, a static, doping-induced expansion of the intramolecular C-C bonds could also contribute to the mode softening, similar to that observed for the Raman-active, pentagonal pinch Ag(2) mode, which in C60 is observed at 1469 cm-1.

Two recent optical transmission studies were carried out [11.80,93] on K- and Rb-doped films and these studies arrived at quantitative values for the oscillator strengths of the Flu modes. Martin et al. [11.93] carried out transmission experiments similar to the original experiments of Fu et al. [11.127], but as a continuous function of doping. Similar to Kuzmany and co-workers [11.77,134], Martin et al. [11.93] made an in situ observation of the four-point probe resistivity of their films. The spectra of Martin et al. [11.93] were taken with the substrate maintained at ~100°C, and as a result, their frequencies may exhibit a several wave number, temperature-induced, shift relative to data taken by others at room temperature. Since the doping dependence is much larger than the temperature dependence, the x dependence of the mode softening can still be obtained from their study. A series of spectra showing the evolution of the Flu modes as the film is doped with Rb in situ are presented in Fig. 11.26. The data are exhibited in two panels, a lower-frequency panel containing w, and w2 data and a higher-frequency panel containing a>3 and o»4 data. The spectrum labeled "min" corresponds to the dopant concentration where the four-point probe electrical resistivity was observed to be a minimum; presumably this trace corresponds to a value of x ~ 3. The frequency downshift and increased IR activity (oscillator strength) for the oj2 and a>4 modes are readily apparent in the figure, as is the lack of sensitivity of w3 to the Rb doping.

In the infrared studies by Rao et al. [11.80], the sample preparation was as follows. A three-layer Q0-M-C60 sandwich was vacuum-deposited onto

Fig. 11.26. Infrared transmission spectra showing the evolution of the Ftu modes as the C«, films are doped in situ with Rb. The left-hand panel shows the evolution of the lower-frequency a>i and a)2 modes while the right panel shows the evolution of the higher-frequency <o3 and a>, modes. The trace labeled "min" corresponds to the minimum-resistivity Rb concentration, presumably at x = 3 [11.93].

Fig. 11.26. Infrared transmission spectra showing the evolution of the Ftu modes as the C«, films are doped in situ with Rb. The left-hand panel shows the evolution of the lower-frequency a>i and a)2 modes while the right panel shows the evolution of the higher-frequency <o3 and a>, modes. The trace labeled "min" corresponds to the minimum-resistivity Rb concentration, presumably at x = 3 [11.93].

a salt substrate, which was removed from the deposition chamber under an Ar atmosphere and loaded immediately into a small, stainless steel IR cell, equipped with an ion pump. The samples were maintained thereafter at 10-5 torr during initial Raman experiments to determine the doping level and during subsequent detailed IR transmission studies. In this way, Rao et al. prepared x — 3 and x = 6 alkali metal-doped samples, as determined by the x dependence of the Ag(2) pentagonal pinch mode frequency (see Fig. 11.24). Both Rao et al. [11.80] and Martin et al. [11.93] obtained values for the oscillator strength Sj(x) by fitting a Lorentz oscillator dielectric function model to the optical transmission data (see Table 11.7). The <o2 and w4 modes exhibit oscillator strength enhancements proportional to x2, in reasonable agreement with the charged phonon model. The microscopic reasons why the oscillator strength for wi does not appear to follow an x2 dependence, or why w3 shows no x dependence in the M^C^ compounds, have not yet been clarified. Plots of Sj(x) vs. x do not exhibit any significant dependence on the particular alkali metal dopant (K or Rb), indicating that the C60 anions are only weakly coupled to the cations.

In Fig. 11.27 a summary of the currently available data [11.77,80,93] is displayed for the x dependence of the four Flu mode frequencies. The data for both Rb- and K-doped films are plotted on the same graphs, since the mode frequencies are insensitive to the particular dopant. In Fig. 11.27, a»!, &>2, and o>4 exhibit a linear frequency softening with increasing doping concentration x, whereas w3 appears insensitive to doping. The values of the slope [i.e., the wave number (cm-1) change in mode frequency per added electron to the C60 molecule] are given for each plot in terms of

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