Fig. 3: Superstructure validation by calculations.
a–d Selected defect structures in Hf0.91N1.10 supercells with stochastic defect arrangements, mimicking HfN1.22 composition. e MLIP energies of a wide range of structures including the ones in (a–d). All supercells contain the same number of Hf98 and N (119) atoms on a 3 × 3 × 3 B1 lattice, and the snapshot is taken in the [001] zone axis. Note that the snapshots display four Hf0.91N1.10 supercell replicas. The two lowest-energy structures (a) and (b) are characterized by local agglomerations of cation vacancies (red spheres in upper part of supercell snapshots) decorated by N self-interstitials (blue spheres). Conversely, high-energy structures in (c) and (d) show a rather homogeneous distribution of defects over the entire supercell volume. A good reliability of the MLIP results was confirmed by re-relaxing the structures in (a–d) by DFT calculations (see Supplementary Section 5). f) Schematic of the 3-dimensional checkerboard superstructure with main <100> axes relating to the B1 NaCl lattice.
