Explain the structures of diamond and graphite.

(N/A) Diamond has a crystalline lattice. In diamond, each carbon atom undergoes $sp^{3}$ hybridisation and is linked to four other carbon atoms using hybridised orbitals in a tetrahedral fashion.
The $C-C$ bond length is $154 \ pm$. The structure extends in space and produces a rigid three-dimensional network of carbon atoms.
In this structure, directional covalent bonds are present throughout the lattice. It is very difficult to break this extended covalent bonding, and therefore, diamond is the hardest substance on Earth.
Uses: It is used as an abrasive for sharpening hard tools, in making dies, and in the manufacture of tungsten filaments for electric light bulbs.
Graphite has a layered structure.
Layers are held by van der Waals forces, and the distance between two layers is $340 \ pm$.
Each layer is composed of planar hexagonal rings of carbon atoms. The $C-C$ bond length within the layer is $141.5 \ pm$.
Each carbon atom in the hexagonal ring undergoes $sp^{2}$ hybridisation and makes three sigma bonds with three neighbouring carbon atoms.
The fourth electron forms a $\pi$-bond. The electrons are delocalised over the whole sheet. These electrons are mobile, and therefore, graphite conducts electricity along the sheet.
Graphite cleaves easily between the layers, and therefore, it is very soft and slippery. For this reason, graphite is used as a dry lubricant in machines running at high temperatures, where oil cannot be used as a lubricant.