Critical assessment and thermodynamic calculation of the binary system hafnium-carbon (Hf-C)

Based on an assessment of the available experimental thermochemical and phase diagram information, the phase equilibria involving the condensed phases of the Hf-C system were calculated. The Gibbs energies of the individual phases were described with thermodynamic models, The liquid 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 (CEM) with two sublattices. The parameters in the models were determined by computerized optimization using selected experimental data, The temperature dependence of the Gibbs energies of the metastable carbides HfC0.5 and HfC3, which are involved in the CEM for alpha Hf and beta Hf, were estimated using a method based on the regular behavior of the vibrational entropy of transition metal carbides. A thermodynamic description was obtained, which was used in the calculation of the Hf-C phase diagram, Detailed comparison is made between calculation and experimental data.