First-Principles Calculation of the Effects of Carbon on Tetragonality and Magnetic Moment of BCC-Fe

Abstract

Theeffectsofcarboncontentontetragonalityandmagneticmomentofbccironhavebeenevaluatedbyfirst-principlescalculation.Three kinds of supercells, Fe 54 C 1 , Fe 54 C 2 and Fe 128 C 1 (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 atomatoctahedralsiteproducesfairlylargeexpansioninonedirection.(2)TetragonalityofFe-Csystemobtainedbyfirst-principlescalculation 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 Fe 54 C 2 , tetragonality and magnetic moment of iron atom change with the distance between two carbon atoms. The value of tetragonality iseither0.981,1.036or1.090.Whenthedumbbellstructurewhichconsistsofthefirstcarbonatomanditstwonearestneighborironatoms is perpendicular to the second dumbbell structure which consists of the second carbon atom and its two nearest neighbor iron atoms, the te-tragonalityis0.981anddoesnotagreewithexperimentalvalue.Themechanicalenergyisrelativelylarge.Ontheotherhand,whenthefirst 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 Fe 54 C 2 , 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.

Recent Studies on the Nature and State of Carbon Atoms in Iron

“…6) This agreement between calculation and experimental data is reported in some papers. 2,6,8,51) Considering the calculation data by Ohtsuka et al, if all carbon atoms exist at single variant O site and carbon is ordered, the tetragonality value should be on the line shown in Fig. 2(c).…”

“…The solution energy for Fe-C system has been evaluated by first principles calculation in many papers. [2][3][4][5][6][7][8][9] The solution energy, ΔE, is also dubbed as solution enthalpy or formation enthalpy and ΔE for Fe-C system which consists of n iron atoms and 1 carbon atom is expressed as…”

“…gives some information of energy, bonding state and magnetization. Domain et al, 3) Fors and Wahnström, 4) Baik et al, 5) Nguyen et al 9) and Ohtsuka et al 6) calculated DOS of Fe-C system. In all of the above calculations, it is shown that a strong hybridization between carbon p orbital and iron d orbital is observed at around − 6 eV.…”

“…Ohtsuka et al showed that the magnetization of iron atom at the first nearest neighbor of carbon atom is reduced and the magnetization of iron increases, decreases and increases again with increasing distance between carbon and iron atom. 6) Domain et al 3) calculated the charge density distribution for Fe-C and Fe-N systems and found that the area of charge transfer is narrower around the carbon atom. Baik et al 5) calculated the Partial Density of States (PDOS: DOS decomposed into contributions of fragment molecular orbitals.)…”

“…Recently many papers report that energy of Fe-C system with carbon atom at O site and T site is evaluated by the first principles calculation, and it is found that O site has a lower energy and is a stable site for carbon atoms in the case of relatively low carbon content. [2][3][4][5][6][7][8][9]25) (Ruda et al 46) showed that T site has a lower energy than O site with EAM potential, but made a correction later, 47) which will be explained in detail at section 6 later.). However some issues are not solved yet.…”