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Diamond and graphite are the two allotropes of carbon, that is they are different forms of the same element carbon having different physical properties but similar chemical properties.
Diamond is the hardest substance known where each carbon atom is joined to four other carbon atoms by the covalent bond in a tetrahedral structure. The carbon atoms have a regular crystal lattice arrangement. As all the valency of carbon is satisfied in the tetrahedral structure of diamond there are no free electrons in the structure.
Graphite on the contrary is soft having a giant covalent structure. Each atom is joined to three other carbon atoms by a covalent bond. In graphite molecules, the carbon atoms form layers with a hexagonal arrangement of atoms and the layers have weak Vander Waal forces existing between them. Each carbon atom has one non-bonded outer electron, which is responsible for making graphite a good conductor of electricity.