Stability, Magnetism and Hardness of Iron Carbides from First-Principles Calculations

Abstract

The stability, electronic structure, magnetism and hardness of iron carbides in eight different space groups were investigated by the first-principles calculations. The electron-ion interactions were modelled using the Vanderbilt ultra-soft pseudopotentials (USPP) and norm-conserving pseudopotentials (NCPP). Generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) formulation was used to describe the exchange-correlation energy. The calculated lattice parameters for USPP were in good agreement with experimental results. The formation enthalpy, cohesive energy and elastic constants revealed that with the exception of hex-Fe2C, all Fe-C compounds were both thermodynamically and mechanically stable. Meanwhile, the iron carbides’ bulk and shear moduli were also calculated and compared. Furthermore, magnetic properties were studied and it was found that the average magnetic moment of Fe23 C 6 (2.123 μ B) was the largest among these compounds, with a value close to that of pure α-Fe (2.24 μ B μ. As expected, hex-Fe2C is a paramagnetic metal based on the obtained densities of states and partial densities of states. Furthermore, the magnetic behaviour of iron carbides with polymorphic transformation was almost identical. Finally, several semi-empirical methods were used for estimating the hardness of the iron carbides.