mb alignment of the electron-rich double bonds of one CgQ molecule opposite the centers of either the electron-poor pentagons or the electron-rich hexagons. As discussed in some detail in §7.1.3, these two states differ in energy by only 11.4 meV.

The hysteresis in the Cp(T) data in Fig. 14.16 suggests that on heating from below 165 K, the C60 molecules in the crystal phase remain in their low-temperature frozen state until a temperature of ~261 K is reached, where a first-order transition to the fee structural phase occurs [14.146]. On cooling, the C60 molecules gradually go from a rotating motion to a ratcheting motion, spending increasingly more time in one of the two stable states discussed above and in §7.1.3. The large magnitude of the anomaly in Cp(T) at 261 K on heating, in comparison to the two smaller anomalies at 261 K and 165 K on cooling, supports this interpretation [14.146], Below 165 K where the C60 molecules freeze, the Cp(T) behavior is the same upon heating and cooling. Associated with the specific heat anomaly at T02 = 165 K is an enthalpy change of 22.2 kJ/mol, a change in the heat capacity of 7 J/K mol, and a relaxation time of 4 x 10 "11 s associated with the two potential minima.

At low-temperatures, a change in the slope of the Cp(T) curve is observed at 50 K [14.145-148], with an excess specific heat that corresponds to an activation energy of 40 meV and is associated with the degrees of freedom for the intermolecular vibrations. A more detailed analysis of the low-temperature Einstein contribution yields 0E = 35 K (or 24 cm"1) [14.141], in good agreement with the neutron scattering value of 2.8 meV (21.6 cm"1) [14.151]. In the low-temperature regime, the C60 molecules should be considered as giant atoms of 720 atomic mass units which acquire rotational and translational macroscopic degrees of freedom (see §11.4). At very low T (below 8 K), a T3 dependence of Cp(T) is observed, yielding a Debye temperature 0D of 70 K [14.146] associated with the low-frequency intermolecular acoustic modes of this lattice of "giant atoms." More detailed studies at very low-temperature [14.141,148] in C60(85%)/C70(15%) compacts showed the low-T heat capacity to follow a

behavior. From the T3 term a Debye temperature SD = 80 K was obtained (Debye velocity of sound 2.4 x 105 cm/s), while the linear T contribution was attributed to low-temperature disorder, presumably associated with the merohedral disorder and having an excitation energy of 400 GHz (13.2 cm-1) [14.141], The magnitude of the linear term was found to be similar to that in amorphous SiOz and amorphous As2S3 [14.141],

14.8.2. Specific Heat for C1Q

We have already commented in §14.8.1 on the high-temperature behavior of Cp{T) for CgQ. From that discussion, it is expected that the intermediate temperature range would be of particular interest regarding thermal properties. For C70, two specific heat anomalies are observed at 337 K and 280 K, corresponding to enthalpy changes of 2.2 J/g and 3.2 J/g, respectively [14.144]. Structural studies [14.152-154] show a phase transition from an isotropic fee structure with nearly freely rotating C70 molecules to an anisotropic structure at 337 K where the fivefold axes of the C70 molecule become aligned (see §7.2). At ~276 K, structural studies indicate that rotations about the fivefold axes cease, as the molecules align in a monoclinic structure corresponding to a distorted hexagonal close-packed (hep) structure with c/a = 1.82.

An anomaly in the specific heat for C70 is observed at 50 K and is likely due to the onset of vibrational degrees of freedom of the C7U intermolecular normal mode. The low-temperature measurements (< 8 K) show a T3 law from which a Debye temperature of 70 K is estimated. The high value for the low-temperature Cp(T) in C70 is attributed [14.144] to a high density of librational modes for the whole C70 molecule [14.155,156], In addition, the 30 intramolecular modes associated with the 10 additional belt atoms tend to have relatively low vibrational frequencies. These additional intramolecular modes thus tend to contribute to the specific heat more effectively at lower temperatures, thus raising the Cp(T) of C70 per atom above that for C60, in agreement with experiment [14.146].

14.8.3. Specific Heat for K3Q,

Very few studies of the heat capacity for doped fulleride solids have thus far been reported. Using a conventional adiabatic heat pulse method and helium exchange gas for thermal contact [14.102], the low-temperature specific heat of K3C60 was measured. The resulting data shown in Fig. 14.18 were analyzed in terms of four contributions: (1) a contribution linear in T (and labeled TL) arising from structural disorder, (2) a cubic term identified with a Debye contribution (@D = 70 K determined by scaling the bulk moduli data for copper and M3C60) [14.102], (3) an Einstein term attributed to the librational mode at 34 K [14.157], and (4) a small electronic term associated with the specific heat jump near the superconducting transition temperature Tc. The results show that doping does not strongly affect the Debye and Einstein contributions to the specific heat. Most of the emphasis of this work [14.102] was given to estimating the electronic density of states and structure in the heat capacity associated with the superconducting phase transition.

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