Thermodynamic modeling of the Ta–N–O system

In this work, we report the thermodynamic modeling of the Ta–N–O system using the Calphad approach combined with ab initio calculations and experiments. The formation enthalpies of stable and certain metastable compounds of the Ta–N and Ta–N–O systems were computed using the density functional theory (DFT) to serve as inputs for the Gibbs energy modeling. The DFT study has confirmed ${\mathrm{Ta}}_3{N}_5$ as an equilibrium phase. Hence, this phase is included as a stable phase in the Gibbs energy modeling of the Ta–N system. Wherever feasible, we have performed phonon calculations to estimate the heat capacities of compounds. The heat capacities of ${\mathrm{Ta}}_3{N}_5$ and TaON were measured using a differential scanning calorimeter. It is observed that $\theta$-TaN, a high-pressure polymorph of $\epsilon$-TaN, stabilizes at atmospheric pressure with oxygen substitution. The thermochemical data obtained in the present work are combined with carefully selected thermochemical and constitutional data from the literature to obtain the Gibbs energy descriptions of the Ta–N and Ta–N–O systems.