Structural, electronic, and magnetic properties of iron carbideFe7C3phases from first-principles theory

The iron carbide ${\text{Fe}}_{7}{\text{C}}_{3}$ exhibits two types of basic crystal structures, an orthorhombic $(o\text{\ensuremath{-}})$ form and a hexagonal $(h\text{\ensuremath{-}})$ one. First-principles calculations have been performed for the basic ${\text{Fe}}_{7}{\text{C}}_{3}$ forms and for the related $\ensuremath{\theta}{\text{-Fe}}_{3}\text{C}$ cementite phase. Accurate total-energy calculations show that the stability of ${\text{Fe}}_{7}{\text{C}}_{3}$ is comparable to that of $\ensuremath{\theta}{\text{-Fe}}_{3}\text{C}$. The $o{\text{-Fe}}_{7}{\text{C}}_{3}$ phase is more stable than the hexagonal one, in contrast to recent atomistic simulations. Furthermore, the calculations also show a rather low energy for a carbon vacancy in the $o$ structure, which implies possible C deficiency in the lattice. Both ${\text{Fe}}_{7}{\text{C}}_{3}$ phases are ferromagnetic metals. Electronic band-structure calculations show that all Fe atoms exhibit high-spin states with the majority of their $3d$ states being almost fully occupied. From an analysis of the structural and energetic properties, the formation of the $o$ phase in steel treatment processes and of $h$ form in carburization of ferrite is discussed.