Cohesive properties and vibrational entropy of 3<i>d</i>transition-metal compounds:<i>MX</i>(NaCl) compounds (<i>X</i>=C, N, O, S), complex carbides, and nitrides

Abstract

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 (\ensuremath{\Omega}), 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 ${\mathrm{\ensuremath{\Delta}}}^{0}$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 ${E}_{\mathrm{coh}}$, \ensuremath{\Delta} $^{0}H$, 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 \ensuremath{\Delta} $^{0}H$ 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.