Tell us about the difference in the structure of the crystal lattices of diamond and graphite.

At the nodes of the crystal lattices of diamond and graphite are carbon atoms. But since diamond and graphite have different structures, they differ in physical properties.
The crystal lattice of diamond has a pitch of a tetrahedron, in which each carbon atom is circled by 4 more atoms and is the vertex of the neighboring tetrahedron, forming an infinite number of atoms with strong covalent bonds.
In graphite, carbon atoms are arranged in layers, inside of which the combination of carbon atoms looks like a honeycomb. These layers are connected to each other much weaker than the carbon atoms in each layer. Therefore, graphite easily exfoliates into flakes, and you can write with it.