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., ZrCxN1-x) and di-TM carbides (e.g., HfxTa1-xC) have maximum G at ZV∼8.3.