Crystal structures of Fe4C vs. Fe4N analysed by DFT calculations: Fcc-based interstitial superstructures explored

Abstract

Knowledge of the thermodynamic and structural properties of iron carbide and nitride phases is crucial for understanding phase transformations and related microstructure formation in steels. While the existence and crystal structure of the primitive cubic fcc-based γ′-Fe₄N_1-z phase is experimentally well-established, there is no consensus in contemporary literature about an analogous γ′-Fe₄C compound. Here, we present DFT calculations for all fcc-like Fe₄C and Fe₄N superstructures with up to two formula units per primitive unit cell, providing energy values and the relaxed atomic structures, which were analysed mathematically and by visual inspection of the atomic arrangement. Notably, all considered Fe₄C and Fe₄N superstructures are metastable with respect to α-Fe and cementite-Fe₃C/ε-Fe₃N. Unsurprisingly, we find the well-known γ′ compound's crystal structure to be most favourable among these metastable Fe₄N superstructures. However, we find the equivalent superstructure to be quite unfavourable in Fe₄C. The most favourable among these metastable Fe₄C structures are stabilised by a partial Bain-like distortion into the direction of a body-centred cubic arrangement of Fe atoms. This makes the particular C-ordering interesting for comparison with the short-range order in Fe-C martensites. However, even the lowest-energy Fe₄C structure releases about 0.056 eV/atom upon decomposition into α + Fe₃C, much more than it is the case for Fe₄N (0.019 eV/atom). That energy difference is difficult to overcome even at T > 0 K, in agreement with the lack of clear experimental evidence for existence of a Fe₄C phase.