Theory of bonding in transition-metal carbides and nitrides

This paper deals with the bonding properties of 3d-, 4d-, and 5d-transition-metal carbides and nitrides. We consider NaCl-structure compounds, MC and MN, as well as carbides and nitrides with more complex crystal structures. The enthalpies of formation at zero temperature ${\mathrm{\Delta }}^0$H(0) of the MC and MN compounds are taken from previous ab initio linear-muffin-tin-oribtals calculations. We describe the structure as formed by a metal fcc lattice in which nonmetal atoms have been inserted at interstitial positions. ${\mathrm{\Delta }}^0$H(0) is divided into contributions from (i) formation of metallic fcc lattice, (ii) expansion of this lattice to the lattice spacing of the compound, and (iii) insertion of nonmetal atoms into the metal lattice. ${\mathrm{\Delta }}^0$H(0), plotted versus the position of M in the d series, shows a pronounced maximum for the Ti, Zr, and Hf carbides. In agreement with other work, we interpret this as due to the filling of bonding p-d hybridized states. The maximum in ${\mathrm{\Delta }}^0$H(0) is followed first by a decrease and then by an almost constant value. We interpret this as an effect of a gradual population of antibonding and nonbonding electronic states. Size effects, i.e., contribution (ii), are small for the 4d- and 5d-series compounds. ${\mathrm{\Delta }}^0$H(0) of MN is similar to that of MC, but the largest values occur for M=Sc,Y,La since N has one more valence electron than C. Bonding in the complex carbides and nitrides is given an analogous interpretation.