This paper has constructed two kinds of atomic and electronic models for hexagonal β-Mo2C and orthorhombic α-Mo2C. The optimized lattice parameters, elastic constant matrixes and overlap population for Mo2C crystal cells have been obtained to realize the characterization of the hardness and melting point of the two structures by the first-principles plane wave pseudo potential method based on the density functional theory. The results reveal that the calculated lattice parameters of the Mo2C crystal cells agree with the experimental and other calculated data. The calculated melting point/hardness are 2715 K/11.38 GPa for β-Mo2C and 2699 K/10.57～12.67 GPa for α-Mo2C, respectively. The calculated results from the density of states (DOS) demonstrate that the hybridization effect between Mo-3d and C-2p states in α-Mo2C crystal cell is much stronger than that in β-Mo2C one.
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