Cohesive properties and vibrational entropy of 3 d transition-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 (nₑ), the average volume per atom ({Ω}), and the logarithmically averaged atomic mass (Meff). Three quantities with the dimension of energy are then considered: the cohesive energy Ecoh of the compound, its enthalpy of formation Δ⁰H, 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 ${E}coh, Δ⁰H$, 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 ES and nₑ 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 nₑ and to the estimation of the standard entropies ⁰S and enthalpies of formation {Δ} ⁰H 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.