both a high density of defect states associated with the merohedral disorder (see §14.2.1) and a low Debye temperature (©D = 70 K) in C60 compared to graphite (©D = 2500 K) [14.175].
To model the observed temperature dependence of k(T), two nearly degenerate molecular orientations are considered (differing by ~12 meV in energy), and separated by an energy barrier of ~290 meV (see §7.1.3). One interpretation of this result, consistent with specific heat measurements (see §14.8.1) and structural measurements (see §7.1.3), suggests that the energy difference of 11.4 meV may relate to the energy difference between the orientation of the double bonds opposite pentagonal faces relative to hexagonal faces, and the larger energy of ~290 meV may correspond to the energy barrier that must be overcome in making the transition from the higher-lying hexagonal face orientation to the lower-energy pentagonal face orientation opposite the double bond in the adjacent C60 molecule (see §7.1.3 and §14.8.1).
A thermal conductivity study of a C60(85%)/C70(15%) compacted sample going down to ~0.04 K shows an approximately T2 dependence below ~1 K and an almost temperature-independent k(T) above ~10 K. A comparison of the measured k(T) (points) with an Einstein model with &E = 35 K and no adjustable parameters (dashed curve) is shown in Fig. 14.22(a), where the Einstein contribution to the thermal conductivity is
in which nv is the number density of C60 molecules and x = 0£/7. In Fig. 14.22(b)
are shown results for single-crystal samples of diamond, C60, and graphite for heat flow in-plane and along the c-axis. For T < 10 K, solids such as Si02 and As2S3 [14.141] also show a T2 dependence for k(T) below 1 K [see Fig. 14.22(a)]. Sundqvist has modeled 1 /k(T) vs. T in terms of phonon-phonon and phonon-defect scattering and finds that the k(T) data for C60 can be explained by standard theories [14.176],
The Seebeck coefficient or thermoelectric power 5 is defined as the electric field E produced by a temperature gradient VT under the condition of no current flow, S(E) = E/VT, where 5 represents the amount of heat per electric charge carried by the carriers as they move from a hot to a cold junction. At the hot junction there are relatively more energetic carriers than at the cold junction, thereby giving rise to a redistribution of carriers. This charge redistribution causes a small pileup of negative charge at the cold junction and of positive charge at the hot junction, thereby causing a voltage (or an electric field) to develop, which impedes further diffusion of
1 10 Temperatur* (K)
Fig. 14.22. Thermal conductivity of (a) polycrystalline Cm/C10 compacts (filled circles and squares) compared with that of amorphous Si02 (open circles) and amorphous As2S3 (asterisks) and a T2 dependence (dashed line), (b) Carbon in its three phases: diamond (open diamonds), single-crystal Cm (solid line), and single-crystal graphite, heat flow in the ab-plane (filled stars) and parallel to c-axis (open stars). The dashed line corresponds to the thermal conductivity based on the Einstein model (Eq. 14.17). [14.141],
Was this article helpful?