So far, we have concerned ourselves with the molecular structure of C, i.e., the atom connectivity and molecular shape. However, it is also important to consider the solid-state structure, i.e., the way in which C molecules pack together in the bulk solid state. Bulk solid C is sometimes referred to as "fullerite" in analogy to graphite, and room-temperature X-ray powder diffraction has shown that fullerite adopts the face-centered cubic (fcc) close-packed structure with lattice constant a = 14.17 Å (Heiney, 1991).

As shown in Figure VII.A, an fcc close-packed structure can be constructed by placing close-packed layers on top of one another. The first layer consists of spheres in contact, with each sphere having six nearest neighbors in the plane. The second layer is formed by placing spheres in the dips of the first layer. The spheres of the third layer are placed above the gaps in the first layer. Thus the second layer covers half the holes in the first layer and the third layer lies above the remaining holes. This arrangement results in a ABCABC ... pattern and corresponds to a lattice with a face-centered cubic unit cell. Spheres sit at the eight corners and at the centers of the six sides of the cubic unit cell, which has an edge length ("lattice constant") of a. The distance between nearest neighbors (corner sphere to face sphere) is (2/2)a.

Figure VII.A: top) Layers of spheres in a face-centered cubic (fcc) packing arrangement. bottom left) Face-centered cubic unit cell. bottom right) Alternative view of fcc unit cell, showing the relationship between spheres in unit cell and spheres in fcc layers.

The energies of the Hückel -molecular orbitals for C have been calculated (Haddon, 1986, Vol.125). As shown in Figure VII.B.1, the triply-degenerate LUMO (t symmetry) is rather low-lying, suggesting that C should be relatively easy to reduce. In fact, treatment of C with three equivalents of alkali metal leads to the production of AC, which possesses a half-filled t electronic level, while treatment of C with six equivalents of alkali metal generates an AC phase with a filled t level (Haddon, 1991).

Figure VII.B.1: Energy-level diagram of Hückel -molecular orbitals for C.

The AC phase is a conductor at room temperature due to the partial filling of the t "conduction band". Electrons can move between C molecules through the radiating -orbitals. At low temperature, AC becomes super-conducting (vide infra). In contrast, the AC phase is an insulator due to the complete filling of the t orbitals.

The AC phase retains the basic face-centered cubic (fcc) structure that was discussed earlier for C itself (Stephens, 1991). The lattice constant increases slightly to accommodate the alkali metal cations. The reason that the fcc packing can be retained is that there are three "holes" per sphere in the fcc lattice, one octahedral hole and two tetrahedral holes. These holes are distributed as shown in Figure VII.B.2. The octahedral holes have local octahedral symmetry, i.e., they are surrounded by six nearest-neighbor spheres arranged octahedrally, while the tetrahedral holes have four nearest-neighbor spheres arranged tetrahedrally.

Figure VII.B.2: Location of octahedral holes (left) and tetrahedral holes (right) relative to lattice spheres in face-centered cubic unit cell. Note: The holes are gray and the lattice spheres are light blue in the unit cells above.

The AC phase contains twice as many A ions as there are holes in the fcc lattice. Therefore, it undergoes a total rearrangement of its packing pattern and adopts a body-centered cubic structure. This packing arrangement, which contains C molecules at the center and eight corners of a cubic unit cell, affords more room for the A ions (Zhou, 1991).