Cohesive properties and vibrational entropy of 3dtransition-metal compounds:MX(NaCl) compounds (X=C, N, O, S), complex carbides, and nitrides

We let compounds between a 3d transition metal (M) and a nonmetal X (X=C,N,O,S) be characterized by three parameters: the average number of valence electrons per atom ($n_e$), the average volume per atom (Ω), and the logarithmically averaged atomic mass ($M_{\mathrm{eff})}$. Three quantities with the dimension of energy are then considered: the cohesive energy ${\mathit{E}}_{\mathrm{coh}}$ of the compound, its enthalpy of formation ${\mathrm{\Delta }}^0$H, and $FTHETA sub S— is a Debye temperature, properly defined to give the vibrational entropy at high temperatures. Remarkably accurate empirical relations are found between $n_e$ on one hand and $E_{\mathrm{coh}}$, Δ ${}_{}{}^0{}_{}{}^{}H$, and $E_S$. For compounds MX of the NaCl crystal structure one can understand the correlation from the electron band structure of (p-d)-bonded systems. We then extend the correlation to carbides and nitrides of more complex structure, for which not much is known about the electron states. The relation between $E_S$ and $n_e$ is of particular importance, since it allows an estimate of cohesive properties and the vibrational entropy in systems where there is no, or uncertain, experimental information. The correlations are applied to e.g., a study of the phase stability of the NaCl structure for large $n_e$ and to the estimation of the standard entropies ${}_{}{}^0{}_{}{}^{}\mathrm{S}$ and enthalpies of formation Δ ${}_{}{}^0{}_{}{}^{}H$ of various nitrides, carbides, and oxides. We also demonstrate how our method can be coupled with the so-called CALPHAD (‘‘calculation of phase diagrams’’) work.