Thermodynamic analysis of the phase equilibria in the Fe-Zr-B system

A thermodynamic analysis of the Fe-Zr-B ternary system has been carried out using the CALPHAD method. Among the three binary systems present in the ternary phase diagram, the thermodynamic descriptions of the Fe-Zr and Fe-B binary systems were taken from reported results and from our previous study, respectively. The thermodynamic parameters of the Zr-B binary system were evaluated using the thermochemical properties from our first-principles calculations, as well as available experimental data. In this modelling, the Gibbs energy of ZrB₂ with an AlB₂-type structure was represented using the two-sublattice model, in which vacancies were introduced into both the Zr and the B sublattices, following the recent data obtained from neutron diffraction experiments on NbB₂ with the same structure as that of ZrB₂. The optimized thermodynamic parameters of the Zr-B system enabled us to obtain reproducible calculations of the experimental data on phase boundaries and formation enthalpies obtained from first-principles calculations. The ternary parameters were determined using the experimental data on phase boundaries. The calculated results have nicely reproduced the experimental Fe-Zr-B ternary phase diagrams.