Covalent and molecular solids

A covalent solid consists of atoms held together by covalent bonds, creating a network that extends throughout the crystal, while a molecular solid is formed when molecules are held together by van der Waals forces, hydrogen bonds, or a combination of the two types of intermolecular forces.

Diamond is an example of a covalent solid with a structure similar to that of zinc blende. The structure involves carbon atoms (orange in diagram above) occupying four tetrahedral holes within a face-centred cubic structure formed by carbon atoms (blue). Like zinc blende, the unit cell of diamond is face-centred cubic. Other elements, such as silicon and germanium in group 14, also have the same structure.

An example of a molecular solid is ice. Water molecules, when cooled below 273.15 K at standard atmospheric pressure, are held together in a chair configuration (see diagram I above) by hydrogen bonds. When viewed from the top, hexagonal rings extend throughout the crystal, with the unit cell being hexagonal (demarcated by red lines in diagram II).

The structure of graphite, on the other hand, features characteristics of both a covalent solid and a molecular solid. The diagram above shows carbon atoms covalently bonded to form giant planar sheets of hexagonal rings that are stacked in an XYXY… manner. Each sheet is called graphene. Every carbon in graphite is sp2 hybridised, leaving an electron in the orbital that is free to form a π-bond with one of three neighbouring orbitals. One may expect alternating single and double bonds throughout each sheet. However, x-ray diffraction data show that all covalent bonds in the sheets have a similar length of 0.141 nm, implying that the orbitals overlap to form a conjugated -electron system where the electrons are delocalised. This is the reason why graphite conducts electricity. Experiments also show that graphite is only electrically conductive in the direction parallel to the sheets, but not perpendicular to them, suggesting that the sheets are not held together by the overlap of pz orbitals in the perpendicular direction. Layers of graphene are instead loosely stabilised by van der Waals forces and can slide against each other, making graphite a good lubricant. The thermodynamically stable form of graphite, as shown in the diagram above, has a hexagonal unit cell containing four carbon atoms.

 

Question

Why does the unit cell of graphite contain four carbon atoms?

Answer

The edges of the hexagonal unit cell of graphite extend through three layers of graphene (see above diagram). The top sheet has four corner atoms, each being shared by six unit cells, and one other atom shared by two unit cells \left ( \frac{4}{6}+\frac{1}{2} \right ). The same occurs for the bottom layer. For the middle layer of graphene, four peripheral atoms are shared by six unit cells but one atom remains entirely within the unit cell \left ( \frac{4}{6}+1\right ). Therefore, there are a total of four atoms in a single hexagonal unit cell of graphite.

 

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