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 B-1 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=(C-11+2C(12))/3, G'=(C-11-C-12)/2, and G=C-44 with C-ij the elastic constants, and (2) G has large values when the number of electrons per unit cell Z(V)=8 or 9. The fitted curve of G vs. Z(V) 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 Z(V)approximate to 8.3.