Crystalline, electronic, and magnetic structures of θ-Fe3C, χ-Fe5C2, and η-Fe2C from first principle calculation

Abstract

First principle calculations have been performed to study the crystalline, electronic, and magnetic structures of three iron-carbide systems: $\theta \text{-}{\mathrm{Fe}}_3\mathrm{C}$ , $\chi \text{-}{\mathrm{Fe}}_5{\mathrm{C}}_2$ , and $\eta \text{-}{\mathrm{Fe}}_2\mathrm{C}$ . The Kohn-Sham equations were solved by applying the full-potential linearized augmented plane wave method. The generalized gradient approximation in the Perdew-Wang formalism was used to the exchange and correlation energy functional. The internal positions of atoms within the unit cell were optimized and the ground state properties such as lattice parameter and bulk modulus were calculated. The results are compared with experimental data when available. Comparison of the two metastable systems $\chi \text{-}{\mathrm{Fe}}_5{\mathrm{C}}_2$ and $\eta \text{-}{\mathrm{Fe}}_2\mathrm{C}$ shows that the last one has lower formation energy; this is corroborated by the formation sequence observed during tempering. The electronic structures of the three carbides were then studied and the magnetic moments calculated by means of electronic spin-resolved density of state calculations at their equilibrium lattice constants and optimized internal parameters.