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    Section VII
    Solid-State Structure of Cand A C

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* Index *

    * Fullerite Structure <#Structure>
    * Synthesis and Structure of A C
      <#Synthesis>
    * <#Synthesis>Problem VII.A <#Problem7a>
    * Problem VII.B <#Problem7b>

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   1. Fullerite Structure

      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.

      <full_prob7a.html>

      Index <#index>

   2. Synthesis and Structure of AC

      The energies of the H�ckel -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 H�ckel -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).

      <full_prob7b.html>

Index <#index>

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