Valence electron concentration as an indicator for mechanical properties in rocksalt structure nitrides, carbides and carbonitrides

First-principles calculations are employed to determine the mechanical properties of rock-salt structure binary and ternary transition metal nitrides, carbides, and carbonitrides from groups 4 to 12, predicting a unified indicator for mechanical properties: the valence electron concentration (VEC). Pugh's and Poisson's ratios indicate an increasing ductility with increasing VEC, with a brittle-to-ductile transition at a critical VEC = 10. The calculated C44 of carbonitrides and ternary nitrides monotonically decreases from 164 ± 12 GPa at VEC = 8 to −39 ± 46 GPa at VEC = 11, indicating a transition to mechanical instability at VEC = 10.6. Similarly, the average isotropic elastic modulus decreases slightly from 420 GPa for VEC = 8 to 388 GPa for VEC = 10, but then steeply to −98 GPa for VEC = 11, while the corresponding hardness decreases from 25 to 12 to 2 GPa. The overall softening with increasing VEC is attributed to the increasing electron density in d–t2g orbitals, which overlap upon shear and cause a decrease in C44. Phonon dispersion curves, calculated at 0 K for binary nitrides and carbides, exhibit imaginary frequencies for VEC ≥10, indicating a dynamical stability-to-instability transition between VEC = 9 and 10, which is smaller than the critical VEC = 10.6 for the mechanical stability-instability transition. In addition, mechanical stability is increased by magnetic ordering but decreased when accounting for on-site Coulomb repulsion, while temperature and vacancies cause a reduction in the magnitude of C44 for both stable and unstable compounds, likely leading to an increase in the critical VEC for the stability-instability transition. The overall results indicate a narrow region between VEC = 9 and 10 where rocksalt carbonitrides are ductile but also exhibit a high hardness, mechanical and dynamical stability, and therefore are expected to exhibit the highest toughness.