Thermodynamic analysis of phase equilibria in the Fe-Nb-P ternary system

A thermodynamic analysis of the Fe-Nb-P ternary system has been carried out using the CALPHAD method. Among the three binary systems present in this ternary phase diagram, the phase equilibria in the Nb-P binary system, on which very few studies have been reported, were thermodynamically analysed. The thermodynamic properties of various phosphides and of a bcc solid solution obtained from first-principles calculations were utilized in this analysis to compensate for the lack of available experimental data. By applying these procedures, a highly plausible Nb-P binary phase diagram was established over the entire composition range. The thermodynamic descriptions of the Fe-Nb and Fe-P binary systems were taken from previous studies. The thermodynamic parameters of the Fe-Nb-P ternary system were evaluated based on experimental data for the phase boundaries and estimated thermodynamic properties of the ternary phosphides obtained using first-principles calculations. The calculated phase equilibria were in good agreement with the available experimental data. From the calculated results, we confirmed that the ternary phosphide, FeNbP, took part in equilibria with most of the binary phosphides.