Electrochemical measurements and thermodynamic properties of alkali fullerides

Abstract

<p>The systems Na - C60 , K - C60 and Sr - Al were studied by the Electromotive force (EMF) technique using electrochemical cells which were composed of beta-alumina tubes glass-sealed to α-alumina lids. EMF measurements of Nax C60 at 599 K indicated solid solution regions at 1.7 < x < 3 and 3.3 < x < 12. (A sudden drop in EMF in the range of 3.3 < x < 3.7 allows the possibility of a nearly stoichiometric phase in this range). No compounds were observed in the composition range of 0 < x < 1.7. From EMF measurements, the Gibbs energies of mixing of [Special characters omitted.] Na3 C60 and [Special characters omitted.] Na6 C60 were determined as 85 and 81 kJ/mol, respectively. From EMF measurements of Kx C 60 at 572 K, the Gibbs energies of mixing of [Special characters omitted.] were found to be 83, 117, 120 and 121 kJ/mol, for x = 1, 3, 4 and 6, respectively. The ideal interstitial solution model of the Na - C 60 system indicates that tetrahedral sites are favored by Na. The difference between Nax C60 and Kx C60 seems to be related to the ionic size effects. EMF measurements of the Sr - Al system using a Sr beta-alumina solid electrolyte were unsuccessful. Thermodynamic consideration suggests that Sr beta-alumina is not compatible with pure Al or Sr. A model for the intermolecular interactions between C60 molecules, based on the effective Lennard-Jones interaction centers and local charge distribution, was proposed and tested for the Pa 3¯ structure of pure C60 by both regular solution and cluster variation methods. As the effective Lennard-Jones interaction centers move from carbon atoms to the centers of adjacent double bonds of the same molecule, the Pa 3¯ structure in which the pentagons of a molecule face double bonds of nearest molecules becomes more stable relative to the Pa 3¯ structure in which the hexagons face double bonds. By assigning charges to carbon atoms and to the centers of bonds, we can model the increase in activation energy for the jump between 22 and 82 degree orientations. External vibrational frequencies of simple cubic (sc ) C60 and M3 C60 (M = K, Rb) were computed by the harmonic approximation, using the model for the intermolecular interactions between C60 molecules. The computed frequencies of phonons are quite consistent with experiments. However, for librons there are some differences between computed and observed frequencies, which suggests that the harmonic approximation is not adequate for librons. By using group theory, the external vibrational modes of sc C60 at Γ, Σ, Δ and Λ are labeled and the corresponding symmetry adapted vectors are obtained. Thermodynamic properties of sc C60 were computed using the canonical partition function. The lattice energy and configurational entropy terms are estimated by the regular solution model. The dispersion curves were approximated by the Debye model for acoustic modes and the Einstein model for optical modes. The Debye characteristic temperature and optimum Grüneisen constant were determined as 54.14 K and 7.5, respectively. The contribution of the 82 degree orientation of the molecules to the constant volume heat capacity was found to be significant in the temperature range of 20 to 100 K.</p>