Trends in elasticity and electronic structure of transition-metal nitrides and carbides from first principles

The elastic properties of selected transition-metal (TM) nitrides and carbides in B₁ structure are studied using the ab initio density-functional perturbation theory. We find that (1) the inequality B>G^'>G>0 holds for all these materials, where B=(C₁₁+2C₁₂)∕3, G^'=(C₁₁-C₁₂)∕2, and G=C₄₄ with Cᵢⱼ the elastic constants, and (2) G has large values when the number of electrons per unit cell ZV=8 or 9. The fitted curve of G vs. ZV predicts that rocksalt MoN is unstable, and TM carbonitrides (e.g., ZrCₓN_1-x) and di-TM carbides (e.g., HfₓTa_1-xC) have maximum G at ZV≈8.3.