Photon Energy cm17600 7800

Fig. 11.15. Photoluminescence (PL) spectra of Cm films exposed to 1802, top, and 1602, middle, at T = 4.2 K, and excited by 720 nm photons [11.14], The photon energy scale for the PL is shown on the top. On the bottom is a vibrational mode energy scale measured from the purely electronic principal transition, labeled El. The asterisks indicate the 02 vibrational mode replica of the strong electronic doublet. The bottom curve (NIS) is the inelastic neutron scattering data of Ref. [11.83].

Fig. 11.15. Photoluminescence (PL) spectra of Cm films exposed to 1802, top, and 1602, middle, at T = 4.2 K, and excited by 720 nm photons [11.14], The photon energy scale for the PL is shown on the top. On the bottom is a vibrational mode energy scale measured from the purely electronic principal transition, labeled El. The asterisks indicate the 02 vibrational mode replica of the strong electronic doublet. The bottom curve (NIS) is the inelastic neutron scattering data of Ref. [11.83].

Raman study further implied the presence of oxygen as 02, rather than as atomic oxygen bonded to the Qq molecules, which is directly confirmed by the singlet oxygen PL spectra (see Fig. 11.15). More important, the vi-bronic coupling between the 02 and Cm allows the molecular vibrational frequencies of Qq to appear as side bands on the T = 4.2 K luminescence emission spectra, as dioxygen returns to the triplet ground state (3£g) from the first excited singlet state ('As). The upper two PL spectra in Fig. 11.15 are from 1802 and 1602, respectively [11.14], whereas the bottom vibrational spectrum is obtained from inelastic neutron scattering studies of microcrys-talline Qo powders [11.83]. As can be seen from the figure, remarkably good agreement is obtained between the PL vibrational side bands and the more conventional inelastic neutron scattering probe. Furthermore, the higher-energy mode structure (> 700 cm-1) is much sharper in the PL data than in the inelastic neutron scattering data, thereby yielding more reliable values for the mode frequencies. Thirty-two of the 46 vibrational modes for Qo are seen in the PL spectra, many of which are unobservable in the first-order Raman or IR spectra due to symmetry selection rules.

11.5.8. Neutron Scattering

Inelastic neutron scattering provides an important technique for the study of intramolecular vibrations, because the technique is sensitive to modes of all symmetries, providing mode frequencies for Raman-active, infrared-active, silent modes, overtones, and combination modes. In addition, neutron scattering studies provide direct information on the overall phonon density of states. Because of its lower energy resolution than infrared or Raman spectroscopy, inelastic neutron scattering is most useful for the study of silent modes and the phonon dispersion relations, rather than the infrared- or Raman-active mode frequencies. Since the C60 vibrations extend to relatively high frequencies, pulsed neutron spallation sources are used for h<aq > 100 meV (800 cm-1), while reactor sources are available for vibrational mode studies for h(»q < 100 meV [11.54], Also, the limited size of C60 single crystals makes the study of phonon dispersion over the entire Brillouin zone possible at the present time only for the low-energy intermolecular branches (see §11.4).

A number of workers have measured the intramolecular mode frequencies for C60 by inelastic neutron scattering [11.83,84,86,99] and the results are summarized in Tables 11.5 and 11.6. In early neutron scattering work, the authors relied heavily upon experimental Raman and infrared spectroscopy as well as theoretical phonon mode calculations for their mode identifications. As seen in Table 11.5, good overall agreement is obtained between the mode frequencies studied by inelastic neutron scattering meth ods and by other methods. A plot of the inelastic neutron scattering intensity as a function of phonon energy (h<aq) is shown in Fig. 11.16 for the energy range ha)q < 110 meV and in Fig. 11.17 for 100 < h(oq < 220 meV [11.83].

Also shown in Fig. 11.16 are inelastic neutron scattering results for K3C6(I [11.86] and Rb3C 60 [11.100]. Although not shown in the figure, measurements on K3C60 have been made up through 200 meV, indicating higher neutron scattering intensity for K^Qo relative to C60 in the phonon energy range 130 < hwq < 200 meV [11.86]. Since all mode symmetries can be observed by the inelastic neutron scattering technique, it is significant that the peaks in K3C60 and Rb3C60 are in general broader than for pristine C60, but the mode broadening is not uniform, since certain spectral features appear to be broadened much more than others. In particular, the modes with Hg symmetry are broadened the most. Significant differences are reported in the 35 K spectrum for R^Qq above the superconducting transition temperature Tc (29 K) in comparison to the 22 K spectrum below Tc [11.100]. Significant changes in the scattering near 135 and 180 meV are observed, as well as the disappearance of the features at 54 and 60 meV below Tc, suggesting strong broadening of these modes, presumably due to the electron-phonon interaction.

Fig. 11.16. Inelastic neutron scattering intensity vs. energy transfer (phonon energy h<i)q) for (a) Cm. For comparison the corresponding spectra are shown in (b) for KjQo (summed data at 5 K and 30 K) [11.86] and in (c) RbjC«, (summed data at 22 K and 35 K). The C«, peaks at 54 and 66 meV are essentially absent in KjQo and RbjC^ [11.100]. Regarding units, note that 1 meV = 8.0668 cm-1.

Fig. 11.16. Inelastic neutron scattering intensity vs. energy transfer (phonon energy h<i)q) for (a) Cm. For comparison the corresponding spectra are shown in (b) for KjQo (summed data at 5 K and 30 K) [11.86] and in (c) RbjC«, (summed data at 22 K and 35 K). The C«, peaks at 54 and 66 meV are essentially absent in KjQo and RbjC^ [11.100]. Regarding units, note that 1 meV = 8.0668 cm-1.

20 40 60 80 100 120 Energy Transfer (meV)

Fig. 11.17. Inelastic neutron scattering spectrum for CM above 100 meV (807 cm-1) measured with a pulsed neutron source [11.83].

Energy Transfer (meV)

Fig. 11.17. Inelastic neutron scattering spectrum for CM above 100 meV (807 cm-1) measured with a pulsed neutron source [11.83].

11.5.9. HREELS Study of Vibrational Modes

Since the energy of the vibrational modes is generally very much smaller than the energies of electron beams used in electron energy loss spectroscopy (EELS), high-resolution detection of the energy of the electron beam is needed. Thus vibrational mode studies using EELS are normally carried out using the HREELS (high-resolution electron energy loss spectroscopy) version of this surface science technique (see §17.2).

If the sample surface is specular or nearly so, then LEED (low-energy electron diffraction) measurements can be carried out with the same electron beam to determine the crystal structure at the surface (see §17.2). In the EELS experiment, the inelastic scattering of electrons on the surface is used to measure the change in energy and momentum of the scattered electron beam relative to the incident beam. Two scattering mechanisms are possible for the scattered electron beam [11.91,101], In the impact scattering mode, the electron scattering is by the local atomic potentials of near-surface atoms, and the scattered electron beam is essentially isotropic, so that large momentum transfers can occur. In contrast, for the dipole scattering mechanism, the probe electron beam interacts with the electric field caused by a dipole in the near-surface region. Such a dipole field is associated with the excitation of infrared-active phonon modes with Flu symmetry. The long-range nature of the Coulomb interaction implies that the probing electrons interact primarily with long-wavelength excitations having small momentum q and a small angular aperture ip = h(oq/2Ep, where Ep is the energy of the primary probing electron beam, which is typ ically 3.7 eV for studies of the vibrational modes. The infrared-active modes are therefore expected to dominate the HREELS spectrum for scattering angles close to specular reflection, while the other vibrational modes are expected to be more prominent outside this angular scattering range.

Experimental studies of the vibrational spectra using HREELS have been carried out primarily on C60, using a variety of substrates, including Si (100) [11.87], GaSe (0001) [11.87], GeS (001) [11.87], Cu (111) [11.102], and Rh (111) [11.103]. Except for spectra taken to enhance the dipole scattering contribution, HREE'LS performed under the impact scattering mode provides an important method for observing silent modes, not seen in the IR or Raman spectra. The most intense of the 11 features that were reported in the HREELS spectra for C60 on Si (100) and GaSe (0001) is the peak near 66 meV (532 cm-1), which is near the two 527 cm-1 and 577 cnr1 infrared-active modes that cannot be resolved individually by HREELS. The resolution is ~10 meV on an Si (100) surface and ~7.5 meV on a GaSe (0001) substrate. The observed HREELS features identified with vibrational excitations, in general, are resolution limited [11.91,101].

By using a GaSe (0001) substrate, which is lattice matched to C60, good specular surfaces can be achieved for the adsorbed Qo film, leading to a clear resolution between the dipole scattering and impact scattering features. For C60 on GaSe (0001), the Flu(3) and Flu(4) infrared-active modes can also be seen by HREELS, and the feature at 66 meV has the expected linewidth of ha>q/eE0 & 10~2 radians (or 0.6°). An analysis of the relative intensities of the infrared-active lines in terms of Lorentz oscillators yield a ratio of the relative oscillator strengths of Flu(l):/rlu(2):F,u(3):Flu(4) = 100:29:6:5 [11.91],

11.5.10. Vibrational Modes as a Probe of Phase Transitions

The structural changes associated with the phase transition at T01 (see §7.1.3) result in changes in the Raman and infrared spectra, as reported by several groups [11.42,44,57,104,105]. Working with single-crystal samples, a hardening of six of the Raman-active modes for the fee sc (Fm3m Pa3) phase transition at T0l was identified [11.44], with magnitudes of the hardening ranging from 2 to 11 cm-1 as shown in Fig. 11.18. Since the Raman vibrational frequencies are large compared with the frequency of rotation, Raman spectroscopy takes a snapshot of the vibrating molecules showing the relative orientation of adjacent molecules. Above 701 the C60 molecules are randomly oriented with respect to each other, and below Tm there is some degree of orientational correlation between molecules. Certain Raman modes are sensitive to this local crystal site orientation effect. The mode frequency upshifts shown in Fig. 11.18 for the

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