H. Bittermann et P. Rogl, CRITICAL-ASSESSMENT AND THERMODYNAMIC CALCULATION OF THE BINARY-SYSTEM HAFNIUM-CARBON (HF-C), Journal of phase equilibria, 18(4), 1997, pp. 344-356
Based on an assessment of the available experimental thermochemical an
d phase diagram information, the phase equilibria involving the conden
sed phases of the Hf-C system were calculated. The Gibbs energies of t
he individual phases were described with thermodynamic models, The liq
uid phase was described as a substitutional solution using the Redlich
-Kister formalism for the excess Gibbs energy. Graphite was treated as
a stoichiometric phase, The solid solutions of carbon in alpha Hf and
beta Hf as well as the nonstoichiometric phase HfC1-x were described
as interstitial solid solutions employing the compound energy model (C
EM) with two sublattices. The parameters in the models were determined
by computerized optimization using selected experimental data, The te
mperature dependence of the Gibbs energies of the metastable carbides
HfC0.5 and HfC3, which are involved in the CEM for alpha Hf and beta H
f, were estimated using a method based on the regular behavior of the
vibrational entropy of transition metal carbides. A thermodynamic desc
ription was obtained, which was used in the calculation of the Hf-C ph
ase diagram, Detailed comparison is made between calculation and exper
imental data.