Fig. 11.27. Plots of the dependence of the four Flu(J) mode frequencies for K,C«, and RbjCj,, on dopant concentration x [11.93], This plot includes data of Rao et al. (open diamonds) [11.80], Martin et al. (open squares) [11.93], Kuzmany et al. (open circles) [11.77], and Fu et al. (pluses) [11.127], the percentage frequency change between x = 0 and x = 6. As the system cools below the phase transition, phase separation effects are observed in the infrared spectra [11.121,135-137] for Na,C60, K^Q,,, and RbjC^. Additional lines in the infrared spectra are identified with the breakdown of inversion symmetry in the dimer low-temperature quenched phase, as indicated in the inset of Fig. 11.25 [11.121], Other experiments showing this phase transition include electron spin resonance (ESR) [11.138] and differential scanning calorimetry [11.119]. Crystallographic studies [11.139] have shown that the low-temperature phase of Rb,C60 is orthorhombic with an unusually short separation of 9.1 A between the centers of C60 molecules along the crystallographic a direction (see §8.5.2).
11.6.3. Other Doping-Dependent Intramolecular Effects
High energy electron energy loss spectroscopy (HREELS) has also been used to explore the doping dependence of the vibrational spectrum of MXC60 [11.140]. EELS measurements done with a primary electron beam of 2.9 eV on Rb^Qo samples with nominal compositions x = 3,4, and 6 (although the near-surface composition may have been alkali metal deficient) show a strong attenuation in signal for the x — 3 stoichiometry for all the vibrational modes, and this attenuation was attributed to screening effects. Mode intensities for x — 4 and x = 6 are comparable to those for Qo, indicative of their semiconducting properties. Modes Flu(2) and FXu(4) could be followed as a function of alkali metal doping, while Flu(l) and Flu(3) could not be well resolved for x — 6, where the best EELS spectra for the doped samples were observed. The HREELS results are qualitatively similar to the infrared results summarized in §11.6.2, although significant quantitative differences between the IR and HREELS spectra have been reported [11.140].
A limited amount of information is now available through inelastic neutron scattering measurements on librations in the doped Qo compounds K3Qo [11.141], RbjQo, [11.72], Rb2.6K0.4C60 [11.55], and Na^Q, [11.142], using polycrystalline samples. Representative spectra for polycrystalline K3Qo for temperatures from 12 to 675 K are shown in Fig. 11.28, where the dashed lines show the librational contribution at low energy. In contrast to the corresponding observation in Qo, only a small mode softening and broadening is observed in K3C60 with increasing T over this wide temperature range, and these temperature-related effects are attributed to dispersion in the librational modes [11.55,141]. The measurements further show little change in librational mode frequency or linewidth as T is lowered below the superconducting transition Tc, although a small sharpening of the librational peak below Tc may indicate some small librational contribution to the electroñ-phonon interaction [11.141]. The persistence of the librational mode to 675 K in Fig. 11.28 indicates that the C60 molecules in K3Qo do not undergo rotational diffusion at high T, but rather continue to librate, consistent with the orientational alignment of the C60 molecules in K3C60. For a librational energy of 3.5 meV (or 28 ctn-1) at 300 K for CM molecules in K3Qo (see Fig. 11.28), the activation energy VA for rotational jumps is estimated as VA ~ 520 meV for 44.5° jumps in the rotational potential, which is in reasonable agreement with estimates for VA from other experiments. The observed temperature dependences of the librational modes for Rb2.6Ko.4C60 and K3C60 are similar with regard to mode frequency and
linewidth [11.55]. In contrast, the librational energy for Na2RbjC60 shows a strong temperature dependence [11.142], with a strong decrease in frequency and a strikmg increase in linewidth with increasing T, which is attributed to the Pa3 structure at low T for Na-containing compounds, in contrast to the fee structure for KjC^.
A comparison between the librational mode frequency and its temperature dependence for various alkali metal-doped C^ compounds has been used to show the dependence of the rotational potential on alkali metal
Fig. 11.29. Schematic dia-
gram showing the dependence g of the librational energy at low w temperature on the ionic radius of the alkali metal ions occupying the tetrahedral interstices, ~_
in MjQo fullerides: C^ [11.52], "3 ^60 ^C«, [11.141], Rb^Qo o 2 -[11.55], and Na2Rb1C60 [11.142], "¡a The dashed line at 1.12 A cor- ij responds to the size of the "" tetrahedral cavity in pristine C«, ol_
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