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Question should be:     Why Diamond DOES NOT HAVE zero enthalphy.....

Diamond has an enthalpy of formation = 1.88 kJ/mol 
Graphite                                                = 0 kJ/mol

Reason is that diamond is not the most stable allotrope of carbon and graphite is.


Enthalpy of formation is defined as the change in enthalpy when a compound is formed from its constituent elements.  Chemical elements in their most stable form have an enthalpy of formation = 0.  So Graphite has an enthalpy = 0.

Diamond has the same Chemical formula C (carbon) as graphite. Diamond and Graphite are allotropes of Carbon⁴.  Diamond is a little less stable than graphite. They have different forms or crystalline structures.  

Diamond has a tetrahedral lattice arrangement of carbon atoms.  Graphite has a hexagonal lattice structure.  So the enthalpy formation of diamond is the change in enthalpy for the tetrahedral lattice structure from hexagonal lattice.  Energy in the bonds in the crystalline forms are different. So work is to be done to form the new structure.  This is the reason for diamond to have a positive enthalpy of formation.