Allotropes are different forms of an element in the same physical state. Diamond and graphite are allotropes of carbon. They both consist of giant covalent structures in which very many carbon atoms are joined together by covalent bonds. However, their detailed structures and bonding differ, so their physical properties are different.
Diamond is a giant covalent substance in which:
The three-dimensional arrangement of carbon atoms, held together by strong covalent bonds, makes diamond very hard. This makes it useful for cutting tools, such as diamond-tipped glass cutters and oil rig drills.
Diamond has a very high melting point because a large amount of energy is needed to overcome the many strong covalent bonds. There are no electrons or other charged particles that are free to move so diamond does not conduct electricity.
Graphite is a giant covalent substance in which:
The layers in graphite can slide over each other because the forces between them are weak. This makes graphite slippery, so it is useful as a lubricant.
Graphite is used to make the core or 'lead' in pencils because it is soft. The layers are easily rubbed off to leave a mark on paper.