J

Fig. 17.8. Carbon Is core level excitation spectra of various fullerenes as observed by the EELS technique on transmission [17.23].

282 284 286 288 290 292 ENERGY (eV)

T-'-1---r to another [17.23,25]. This shift is identified with the lower curvature of the larger fullerenes as they become closer to the core level spectra for graphite. Comparisons have been made between core level spectra in the solid state to molecular spectra [17.58,59] and between experiments and theory [17.60],

17.2.4. Plasmon Studies

Because of the differences in selection rules, the EELS technique is able to detect electron energy loss due to longitudinal excitations, such as plasmon excitations, which are not generally accessible by optical techniques. Typically, in an EELS experiment (see Fig. 17.9), the frequency dependence of the electron energy loss function Im[—l/e(w)] is measured at a fixed electron momentum transfer (see §17.2). From a Kramers-Kronig analysis of the loss function in conjunction with optical data or by using a sum rule, e,(w), e2(w), and the complex conductivity cr(a)) are obtained [17.16] for

Fig. 17.9. Analysis of EELS measurements for C76 to yield the frequency-dependent: (a) Im[-l/e(«)], (b) 6,(o)), (c) «,(«), and (d) the optical conductivity a(<u). A momentum transfer of 0.1 A"1 was used to take these data [17.23].

Fig. 17.9. Analysis of EELS measurements for C76 to yield the frequency-dependent: (a) Im[-l/e(«)], (b) 6,(o)), (c) «,(«), and (d) the optical conductivity a(<u). A momentum transfer of 0.1 A"1 was used to take these data [17.23].

that fixed momentum transfer value. Use of a sum rule leads to 6,(0) = 3.6 for C60 and 4.4 for C76 [17.23]. Reasonable agreement is obtained between the value of e,(0) from EELS and values for 6,(0) for C60 using optical (3.9) and low-frequency (4.4) measurement techniques (see §13.3.3).

Referring to Fig. 17.9(a) we see two dominant peaks in the frequency dependence of the loss function Im[-l/e(w)] for C76, the lower peak occurring at ~6 eV for the it plasmon and an even more prominent peak occurring at ~25 eV for the (tt + cr) plasmon. These peaks in Im[—l/e(w)] are typical of the spectra for the tt and (tt 4- a) plasmons in fullerenes and are identified with the tt plasmon and (tt + a) plasmon frequencies con and ojv+(T. Also shown in this figure are e,(w) and e2(co) for C76, which were used to determine Im[-l/e(w)], and the optical conductivity a(w), which is derived from e2(w). Several groups have reported values for the frequencies (oa+7T for C60 [17.11,16,23,56,61-66] and a few values have also been reported for (on and oj7r+(T for the higher-mass fullerenes C70, C76, and C84 [17.16,23,25,61,62,67,68], The results summarized in Table 17.1 show that wn and <ov+a. have only a weak dependence on nc and are also close to the corresponding values reported for graphite (see Table 17.1). Although the variations of these plasma frequencies with nc are bracketed by the range of values reported by the various groups for C60 alone, trends in the dependence of wn and u>n+IT on nc can be inferred by comparing results using the same experimental technique and method of analysis. This approach (see Fig. 17.10) suggests that a)v may shift to lower energy as the fullerene mass increases, whereas w1T+0. for the various fullerenes shifts to higher energies. The spectra in Fig. 17.10 further show well-resolved peaks in the tt plasmon of C60 which are attributed to the multiple narrow energy bands in C60 associated with tt-tt* transitions. These transitions are not so well resolved in the EELS spectrum for the higher-mass fullerenes. Figure 17.10 also shows that the onset of the EELS loss function decreases from 1.8 eV for C60 to 1.2 eV for C84, consistent with a smaller

Table 17.1

Plasmon parameters for various fullerenes and for graphite.

Table 17.1

Plasmon parameters for various fullerenes and for graphite.

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