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Magnetic Field [T]

essentially unchanged in amplitude until the temperature is increased to

Tcf where D is the electron diffusion constant D = 5 x 10~3 m2/s [19.134] and L is the tubule length. As T increases above TCF the system averages over contributions from many uncorrelated patterns, thereby attenuating the signal due to conductance fluctuations.

19.6.4. Magnetic Susceptibility Studies

Closely related to the magnetoresistance study on a single tubule bundle are magnetization and magnetic susceptibility measurements carried out on samples containing multiple tubule bundles [19.122,123]. In these studies, measurements were made on samples containing a distribution of tubule diameters with some variation in the orientation of the individual tubules, although attempts were made [19.123] to orient the magnetic field parallel or perpendicular to the axis of the tubule bundle. Because of the three orders of magnitude difference in the calculated susceptibility for H parallel or perpendicular to the tubule axis of a single-wall tubule [19.119], small misalignments of the field are expected to have an enormous effect on the measured x f°r magnetic field directions close to the tubule axis. It may well be that the measurements shown in Fig. 19.45(f) labeled H || tubule axis [19.123] are in fact dominated by contributions from H 1 tubule axis, even for small misalignment angles. On the other hand, with increasing tubule diameter, the susceptibility of the tubules should become more like that of graphite, which exhibits a large anisotropy in x with Xc = 22.0 x 10 6 emu/g and Xab = 0-5 x 10~6 emu/g [19.140],

These measurements nevertheless show that x for carbon tubules is large and diamagnetic, being roughly half of the value for graphite with H || c-axis [19.122,123], as shown in Fig. 19.45, where the room temperature * for the tubules is compared with that for other carbons, including graphite (both H || c-axis and H ± c-axis), C60 powder, polycrystalline graphite anode material, and the gray-shell anode material [19.123]. The weak field dependence of * in the 0.1 to 0.5 tesla field range (Fig. 19.45) is clarified by the plots of the low-temperature (5 K) magnetization and susceptibility shown in Fig. 19.46 over a wider field range [19.122].

Three magnetic field regimes for x are identified in Fig. 19.46: the low-field regime, where x rapidly becomes more diamagnetic with increasing field; the intermediate-field regime, where the diamagnetic susceptibility effect is largest and where x is almost independent of field; and finally

Fig. 19.45. Magnetic field dependence of the susceptibility measured up to 0.5 tesla at T = 300 K for (a) graphite with H perpendicular to the c-axis, (b) Cw powder, (c) polycrystalline graphite anode material, (d) gray-shell anode material, (e) a bundle of carbon nanotubes with H approximately X to the tubule axis, (f) a bundle of carbon nanotubes with H approximately || to the tubule axis, and (g) graphite with H parallel to the c-axis [19.123].

Fig. 19.45. Magnetic field dependence of the susceptibility measured up to 0.5 tesla at T = 300 K for (a) graphite with H perpendicular to the c-axis, (b) Cw powder, (c) polycrystalline graphite anode material, (d) gray-shell anode material, (e) a bundle of carbon nanotubes with H approximately X to the tubule axis, (f) a bundle of carbon nanotubes with H approximately || to the tubule axis, and (g) graphite with H parallel to the c-axis [19.123].

the high-field regime, where x becomes less diamagnetic with increasing magnetic field [19.122], The behavior of the low-field regime may be due to the fact that the samples used for these measurements contain both metallic and semiconducting components. At the lowest magnetic fields, only the metallic constituents of the sample contribute to x- But as the field is increased, the contribution from the semiconducting constituents increases until region II is reached, where the whole sample contributes to X. If we identify the onset of region III with a regime where the magnetic radius rL—i — (hc/eH)1/2 becomes comparable to the tubule radius, then the carriers are not much affected by the curvature of the tubule and the carriers then start to behave like the carriers in graphite, thereby explaining the decrease in the diamagnetism with increasing field, which is about the same percentage decrease as is observed for x in graphite (H || c-axis). A detailed analysis of the results in Fig. 19.46 is not yet available.

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