COHESIVE PROPERTIES AND VIBRATIONAL ENTROPY OF 3D-TRANSITION METAL CARBIDES

We make an extensive study of cohesive properties such as the enthalpy of formation DELTA-H-0 and the standard vibrational entropy 0S at 298.15 K of metal carbides MeC, Me3C2, Me2C, Me7C3, Me5C2, Me3C and Me23C6, with Me being a 3d-transition metal, Sc, Ti, V, Cr, Mn, Fe, Co and Ni. Direct and indirect experimental information is used. For systems where experimental data are lacking, we rely on interpolation and extrapolation procedures, assuming that the bonding properties vary smoothly as a function of the average number of valence electrons per atom in the compound, n(e). In 0S the atomic masses enter in such a way that they can be taken into consideration exactly, and only an appropriate averaged interatomic force constant k(s) needs to be estimated. The systematic variations with n(e) were previously noted by us in 3d-transition metal carbides and nitrides (Fernandez Guillermet and Grimvall, Phys. Rev. B 40, 10,582 (1989)), and can be theoretically understood through an electron-band filling argument. That approach is considerably extended in the present work. Many of the compounds studied are metastable, i.e. the phase does not appear in the stable metal-carbon phase diagram. This fact is used as important indirect information which, together with our estimated entropy, gives limits to DELTA-H-0 of metastable carbides through CALPHAD calculations of phase diagrams. Our results are summarized in tables of the room-temperature enthalpy of formation DELTA-H-0, the entropy Debye temperature theta(s), the corresponding average interatomic force constant k(s) and the standard vibrational entropy 0S(298.15). DELTA-H-0 is in good general agreement with predictions from Miedema's formula, with some small but significant differences. The general picture of the cohesion in the carbides suggests important p-d bonding for Sc, Ti and V compounds, with a maximum strength for TiC, and weaker and more metallic bonding in Cr, Mn, Fe, Co and Ni carbides.