First principles study on the elastic properties and electronic structures of (Fe, Cr)₃C

First principles calculations are performed to investigate the elastic properties and electronic structures of Cr doped Fe₃C carbides, the obtained results are compared with Cr₃C and Fe₃C. The calculated bulk modulus of Fe₁₁CrC₄ and Fe₁₀Cr₂C₄ is 260GPa and 270GPa, respectively, larger than Fe₃C. So the hardness of Fe₃C phase can be enhanced by doped with an appropriate amount of Cr, however, the calculated formation enthalpy and defect formation enthalpy of Fe₁₁CrC₄ and Fe₁₀Cr₂C₄ are positive. On the other hand, the electronic calculations reveal that the ground states of Fe₁₁CrC₄ and Fe₁₀Cr₂C₄ are ferromagnetic. The evaluated local magnetic moments of Fe at 4c sites are larger than that of 8d sites, which is analogous to Fe₃C. Milliken population results indicate that the stabilities of Fe₁₁CrC₄ and Fe₁₀Cr₂C₄ are reduced mainly due to the strong repulsive bonds among metal atoms.