γ-M₂₃C₆ carbide often forms at grain boundaries in creep-resistant steels and plays a crucial role in creep resistance by blocking microstructural changes at elevated temperatures. Given that the dislocations and stacking faults (SFs) in carbides may affect their stability, the observation of SF formation in γ-M₂₃C₆ using atomic-scale microscopy has implications for Cr-rich creep-resistant steels. Our analysis of SF energies (SFEs) derived from density functional theory calculations reveals that the SFEs are high, which suggests that the SF is not induced by external shear stress deformation but by lattice misfit between conjoined subgrains nucleated from the same austenite grain.

The effect of mixed partial occupation of metal sites on the phase stability of the γ-Cr_23-x Fe _x C₆ (x = 0-3) carbides is explored as function of composition and temperature. Ab initio calculations combined with statistical thermodynamics approaches reveal that the site occupation of the carbides may be incorrectly predicted when only the commonly used approach of full sublattice occupation is considered. We found that the γ-M₂₃C₆ structure can be understood as a familiar sodium chloride structure with positively charged rhombic dodecahedron (M^(4a) M₁₂ ^(48h)) and negatively charged cubo-octahedron (M₈ ^(32f) C₆ ^(24e)) super-ion clusters, together with interstitial metal atoms at the 8c sites. The stability of the partially occupied phase can be easily rationalized on the basis of a super-ion analysis of the carbide phase. This new understanding of γ-M₂₃C₆ carbides may facilitate further development of high-chromium heat-resistant steels.

Practical and reliable methods for theoretically determining the properties of B, C, N, and O in bcc iron have been explored by systematic DFT calculations. The energies of solution and migration, and the elastic strain fields due to the solute atom have been evaluated by supercell calculations under various conditions. By applying correction for spurious elastic interaction of the solute atom with its images in the periodic supercells, reasonable estimates of the solution energy have been obtained without employing very large supercells. The correction turned out unimportant for the migration energy, as it modifies the energies of the stable position and the saddle-point similarly. The lambda tensor, which uniquely characterizes the strain field induced by a solute atom, has been evaluated for the four species of various configurations, first through the force-dipole tensor obtained in zero-strain calculations, and second from changes in supercell dimensions in zero-stress calculations. The two procedures give similar results that typically differ by a few per cent from each other. The computed values for C and N in octahedral interstitial sites are comparable to experimental values. When experimental data become available for B and O, these evaluations will resolve the as-yet contentious location of these atomic species in bcc iron.