Page 125 - Carbon Nanotubes

Properties of buckytubes and derivatives 115
tronic properties are close to those of a graphite plane. The above discussion ignores all paramagnetic ef-
The study of electron energy loss spectra (EELS) sup- fects including band paramagnetism. Evidence for a
ports this model[19]. We can identify three relevant Curie-like contribution is seen at low temperatures in
energy scales. First, the quantizing effect of the cylin- some of the curves displayed in Fig. 5 and could arise,
drical geometry involves an energy AE = h2/2mR2 = in part, from paramagnetic impurities (see below).
0.7 x lop2 eV. Second, there is the Fermi energy Ei, The anisotropic susceptibility of buckytubes is gov-
which is 1.2 x lop2 eV. Third, there is the thermal en- erned by various geometrical and structural factors
ergy, which at room temperature (the highest temper- (such as the aspect ratio and degree of perfection of
ature studied) is about 2.5 x eV. We see that all its structure). In the direction perpendicular to the
three of these energy scales are of the same order. If buckybundle axis, we do not expect xi to be larger
we consider a higher temperature, where the carriers than 0.5 x:. However, in the direction parallel to the
are Boltzmann particles (with a small inelastic mean buckybundle axis x: might be much larger for a high-
free path !,)> and the magnetic field (-tesla) is a quality sample of buckytubes, as discussed above. The
small perturbation on the particle motion, the mag- measured anisotropy factor in this work (approxi-
neric susceptibility would be due to small quantum mately 1.1 at room temperature and increasing with
corrections to the energy of the system. For this quasi- falling temperature) likely represents a value smaller
classical case., the quantizing action of the geometry than that achievable with a highly ordered structure.
is not important; the response of the system to the per- The small value may be caused by imperfectly aligned
turbation may be considered as a sum over small pla- buckytubes in the buckybundle.
quettes of the size I,. (This additivity is hidden by the The magnetic susceptibility data for buckytubes,
effect of a non-gauge-invariant formalism[35]; never- amorphous graphite, crystalline graphite, the gray-
theless, it is a general physical property, and the in- shell material, and C,, as a function of temperatures
elastic mean free path is the correlation radius of a are shown in Fig. 5. Paramagnetic upturns were ob-
local magnetization.) Therefore, at high temperatures served (for all of the curves) at temperatures lower
a buckytube with R > I, may be considered as a than 10 K. Amorphous graphite and C,, show no ob-
rolied-up graphitic sheet (or concentric tubes). We use servable temperature dependence at temperatures
this model to calculate the susceptibility, xk, for the ranging from 10 K to 300 K, whereas the buckytube
field perpendicular to the buckybundle axis. We write sample exhibits a large increase in diamagnetic suscep-
the susceptibility tensor of single crystal graphite as tibility with falling temperature.
A plot of xpl vs T for C6, was used to estimate a
Curie constant of 8.6 x lO-’/mole, which corre-
sponds to 1.7 x lo-* electron spins per carbon atom
in C,,. It is possible that the paramagnetic upturn is
caused by a small amount of 0, within the sample.
To examine this point, we sealed a Cs0 sample under
a vacuum of 2 x lo-’ Torr in a chamber located at
To obtain the magnetic susceptibility of a buckytube
for the magnetic field perpendicular to the buckybun-
dle axis, xk, we have to average the magnetic energy
E = 0.5 xjJ H, Hj over the cylindrical geometry of the
buckytube (over a plane containing the a and c axes):
dE = 0.5[~& H2 cos2 a + (6 H2 sin2 a] da (2)

or

E = O.5H2[x& cos2 a + x& sin2 a] da

= 0.5H2(0.5x& + 0.5xk); (3)
Thus

Because x& = 41x&, this argument predicts
Temperature (K)
xg 0.5~; (5)
Fig. 5. Temperature dependence of the magnetic suscepti-
bilities measured in a magnetic field of 2 T: (a) C,, powder,
This is consistent with our experimental results, which (b) polycrystalline graphite anode, (c) gray-shell material, (d)
strongly Suggest the existence of delocalized buckybundle: axis perpendicular to H, and (e) buckybundle:
Discussion of (L can be found in reference[36]. axis parallel to H.