Fe4N is the most prominent iron nitride attracting attention as a product of various types of heat treatments of steel but also due to its ferromagnetic properties. In Fe4N, the Fe atoms show a face-centered cubic (fcc) arrangement with N occupying ¼ of the octahedral sites such that a cubic L12-like superstructure results . Unequivocal experimental evidence for an isostructural Fe4C, however, lacks. Frequent consideration of an L12-like Fe4C in the literature might have been motivated by a report  of an Fe4C compound with energetically unlikely  tetrahedral site occupation, which has the same unit cell size as the L12 structure as well as by evidence for L12-like C ordering in C-rich zones of tetragonal Fe-C martensite . This had led to many reports of DFT calculations of Fe4C with L12-like superstructure in the literature. Differences in the N–N and C–C interactions in short-ranged-ordered Fe-N/C austenite , however, suggest that differences should also exist in the ordering of Fe4N and Fe4C. Hence, we have now performed DFT calculations using the VASP software  on numerous fcc-based Fe4N and Fe4C superstructures, predicted as described in , to reveal the preferred state of ordering for either case.
These calculations reveal that for Fe4N the experimentally well-established L12-like superstructure is clearly the most stable one. However, for Fe4C this is not the case. Instead, several more stable C arrangements with C on the octahedral sites were encountered. Many of these structures experience a pronounced Bain distortion into the direction of a body-centred cubic arrangement of the Fe atoms. The structures of Fe4N and Fe4C and their energies are governed by interplay between strain-induced interactions and the ionic repulsion between the interstitial atoms. The stronger ionic interactions in the case of Fe4N appear to stabilise the L12-like superstructure, whereas for Fe4C with less electronegative C atoms, other superstructures come into play containing nearest-neighbour C–C pairs, which do not occur in the L12-like superstructure. Hence, if an fcc-based Fe4C would exist, it would be unlikely to show a L12-like superstructure.
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