Figure 1.26 (a) hcp arrangement of Br atoms in crystalline Al2Br6; (b) Al atoms occupy T+ and T– sites. Dashed circles are below the plane of the paper.
1.15.6 Fullerenes and fullerides
The simplest, best known and symmetrical fullerene is C60 whose discovery led to the 1996 Nobel Prize in Chemistry awarded to Kroto, Curl and Smalley. It is a hollow, spherical cage of diameter 7.1 Å formed from 3‐coordinate (approximately sp 2 hybridised) C atoms which link to form a network of 12 pentagons and 20 hexagons, Fig. 1.27(a), that match exactly the pattern on a soccer ball (hence the alternative, colloquial, American name ‘buckyball’; the name ‘fullerene’ is in honour of Buckminster Fuller, who designed the geodesic dome that has the same network structure as C60).
Not surprisingly, in crystalline C60, the C60 molecules arrange themselves according to the principles of close packing. At room temperature, crystalline C60 is face centred cubic, Z = 4 (C60), a = 14.17 Å, and the C60 molecules are orientationally disordered. The separation of adjacent C60 molecules can be calculated with the aid of Fig. 1.22(a); a cube face diagonal corresponds to a cp direction from which we calculate that the centres of adjacent molecules are separated by 10.0 Å. The ‘hard diameter’ of a C60 molecule is calculated to be 7.1 Å which leaves a gap of 2.9 Å between adjacent molecules for van der Waals bonding.
Figure 1.27 (a) The C60 molecule; one pentagon surrounded by five hexagons is shown in bold. (b) Parts of two C60 molecules in the region of closest contact showing a short C–C bond separating two hexagons in one molecule pointing towards the middle of a pentagon in an adjacent molecule.
Adapted from W. I. R. David et al., Nature 353, 147 (1991).
Because the C60 molecules are not perfectly spherical, Fig. 1.27(a), they settle into an ordered arrangement below 249 K. The driving force for this ordering is optimisation of the bonding between adjacent C60 molecules. In particular, in a given [110] cp direction, the short electron‐rich C–C bond that links two hexagons in one C60 molecule points directly at the centre of an electron‐deficient pentagon, on an adjacent C60 molecule, as shown for two ring fragments in Fig. 1.27(b).
This arrangement minimises direct C–C overlap but maximises donor–acceptor electronic interactions between adjacent molecules. The C–C bonds in fullerene fall into two groups, 1.40 Å for C–C bonds linking two hexagons and 1.45 Å for bonds linking one hexagon and one pentagon; pentagons are isolated in C60. Comparing these with typical single and double bond lengths in organic compounds, 1.54 and 1.33 Å, respectively, we can see that the C–C bonds in C60 are of intermediate bond order.
Some other fullerenes, such as C70, also form cp structures, even though the molecules are not spherical. Thus, the C70 molecule is an ellipsoid (shaped like a rugby ball with a long axis of 8.34 Å and a short axis of 7.66 Å), but in crystalline C70 at room temperature the ellipsoids are able to rotate freely to give quasispherical molecules on a time average which form an fcc structure, a = 15.01 Å.
cp structures have, of course, tetrahedral and octahedral interstitial sites and in C60 these may be occupied by a range of large alkali metal cations to give materials known as fullerides. The most studied C60 fullerides have general formula A3C60 as in Rb3C60 or K2RbC60, in which all T+, T– and O sites are occupied. These materials are metallic since the alkali metals ionise and donate their electrons to the conduction band of the C60 network, which is half full in A3C60. At low temperatures, many of these fullerides become superconducting. The highest T c (the temperature at which the metal–superconductor transition occurs on cooling, Chapter 8) to date in the fullerides is 45 K in Tl2RbC60.
Other fullerides exist with different patterns of occupancy of interstitial sites, e.g. rock salt or zinc blende analogues in AC60 and fluorite analogues in A2C60. It is also possible to increase the number of A ions per C60 beyond 3; in A4C60 (A = Na), A4 clusters form in the octahedral sites. In A6C60, the packing arrangement of the C60 molecules changes from ccp to bcc; the bcc structure has a large number of interstitial sites, e.g. twelve distorted tetrahedral sites, distributed over the cube faces in the bcc array of anions (discussed in Chapter 8, for α‐AgI, Fig. 8.28). This wide range of formulae arises because the C60 molecule can accept a number of electrons to give anions
1.16 Structures Built of Space‐Filling Polyhedra
This approach to describing crystal structures emphasises the coordination number of cations. Structures are regarded as built of polyhedra, formed by the cations with their immediate anionic neighbours, which link by sharing corners, edges or faces. For example, in NaCl each Na has six Cl nearest neighbours arranged octahedrally; this is represented as an octahedron with Cl at the corners and Na at the centre. A 3D overview of the structure is obtained by looking at how neighbouring octahedra link to each other. In NaCl, each octahedron edge is shared between two octahedra (Fig. 1.31, see later), resulting in an infinite framework of edge‐sharing octahedra. In perovskite, SrTiO3, TiO6 octahedra link by corner‐sharing to form a 3D framework (Fig. 1.41, see later). These are just two examples; there are very many others, involving mainly tetrahedra and octahedra, leading to a wide diversity of structures. Some are listed in Table 1.5.
Table 1.5 Some structures built of space‐filling polyhedra
| Structure | Example |
|---|---|
| Octahedra only | |
| 12 edges shared | NaCl |
| 6 corners shared | ReO3 |
| 3 edges shared | CrCl3, BiI3 |
|
2 edges and 6
| |