First-principles calculation of the effects of carbon on tetragonality and magnetic moment of BCC-Fe

The effects of carbon content on tetragonality and magnetic moment of bcc iron have been evaluated by first-principles calculation. Three kinds of supercells, Fe₅₄C₁, Fe₅₄C₂ and Fe₁₂₈C₁ (which correspond to Fe-0.40C, Fe-0.79 and Fe-0.17C mass%, respectively) are used for the calculation of tetragonality and magnetic moment of Fe-C system. Main results obtained are as follows. (1) The total energy and mechanical energy of the Fe-C system with carbon atom at the octahedral sites are smaller than those with carbon atom at the tetragonal sites. The carbon atom at octahedral site produces fairly large expansion in one direction. (2) Tetragonality of Fe-C system obtained by first-principles calculation increases linearly with increasing carbon content and agrees well with experimental results. The average magnetic moment of an Fe atom increases with increasing carbon content. (3) The magnetic moment of an Fe atom at the nearest neighbor of carbon atom is lower than that of pure iron and increases with increasing distance between the iron and carbon atoms. The projected density of states shows a hybridization with main contributions from Fe d and C p states which leads to the above mentioned decrease of the magnetic moment of an Fe atom. (4) In Fe₅₄C₂, tetragonality and magnetic moment of iron atom change with the distance between two carbon atoms. The value of tetragonality is either 0.981, 1.036 or 1.090. When the dumbbell structure which consists of the first carbon atom and its two nearest neighbor iron atoms is perpendicular to the second dumbbell structure which consists of the second carbon atom and its two nearest neighbor iron atoms, the tetragonality is 0.981 and does not agree with experimental value. The mechanical energy is relatively large. On the other hand, when the first dumbbell structure is parallel to the second dumbbell structure, the tetragonality is 1.036 which agrees well with experimental data. The mechanical energy is relatively small. When straight C-Fe-C pair is formed, tetragonality is 1.090. (5) In Fe₅₄C₂, formation enthalpy is relatively low when the calculated tetragonality is 1.036, and the existence probability under the assumption of Boltzmann distribution is high. In other cases, the existence probability is nearly zero. (6) The average magnetic moment of an Fe atom is proportional to volume, but not in a clear relation with tetragonality. It is considered that the increase of magnetic moment of an Fe atom by the addition of carbon atom is mainly due to the magneto-volume effect but not due to the tetragonality effect.