Carbon atoms in interstitial sites of the cementite crystal lattice: ab initio modelling

It was shown in previous works that iron sublattice in the structure of cementite Fe3C has four different types of interstitial sites that may potentially be occupied by carbon atoms, viz. ‘normal’ and ‘distorted’ prismatic (NP, DP) and ‘normal’ and ‘distorted’ octahedral (NO, DO) sites. Distances between their centres and the centres of z nearest-neighbour iron atoms are 1.99-2.04 Å (NP sites, z = 6); 1.80-1.87 Å (NO sites, z = 6); 1.62 Å (DP sites, z = 4) and 1.25 Å (DO sites, z = 2). It is usually believed that all carbon atoms are located in NP positions. In this work other possible variants are considered by ab initio calculations using FP-LAPW full-potential method as realized in WIEN2k program package and a cementite supercell containing 16 atoms (4 formula units). It is found that the structure containing all carbon atoms in NP positions has the lowest energy and volume. The structure with all carbon atoms in NO positions has the energy 0.267 eV/f.u. higher and the volume 9.20 % greater. If only one of the four carbon atoms in the supercell is shifted from NP to NO site the energy and volume increase by 0.233 eV/f.u. and 3.59 % correspondingly. The structure with one carbon atoms located in DP site and the other three in DO sites has the energy 0.452 eV and the volume 3.75 % higher than those of cementite with all carbon atoms in NP sites. The structures with all carbon atoms in DP sites and one or all carbon atoms in DO sites are mechanically unstable and transform spontaneously to conventional NP structure. Thermodynamic estimation based on these data shows that even at temperatures below 1000 K the fraction of carbon atoms that may move from NP sites to other ones may be as great as 20 %. Evaluation of the vacancy formation energy in cementite (supercell of 128 atoms containing 96 atoms of Fe and 32 atoms of C) resulted in the values of 0.50 eV for carbon vacancy and 1.34 (FeG) or 1.60 eV (FeS) for iron vacancy. In all these cases vacancy formation did not result in volume change of the system.