  Finding appropriate interatomic potentials which can accurately describe the
crystal structure of material is one of important topics in material science.
In this paper, several interatomic potentials which comprise of Lennard-Jones
(LJ) potentials have been proposed for describing both the crystal structures
and the evolution of microstructure of the allotropes of carbon such as diamond
and graphite. The validity of these LJ potentials can be checked by molecular
dynamics (MD) simulation. For the lattice identification of simulated systems,
we have calculated the distribution functions of the angles between one atom
and its nearest neighbors and the distances between atoms and checked the
atomic arrangements. Our simulated results have clearly demonstrated that we
have successfully produced diamond and graphite structures by MD simulations
and with the above LJ potentials.
