Thermodynamic modelling of the Ni–Zr system
A. Jana, S. Sridar, S. G. Fries, T. Hammerschmidt, H. K. C. Kumar.
In this work, we report the thermodynamic modelling of the Ni–Zr system using the Calphad method combined with ab initio calculations. Density functional theory (DFT) is employed to calculate the enthalpy of formation of the intermediate phases. The calculated enthalpies of formation are in close agreement with the experimental data. An approach based on special quasirandom structures (SQS) was used for calculating the enthalpy of mixing of the fcc solid solution. The vibrational contribution to the heat capacities of NiZr, NiZr2, Ni3Zr and Ni7Zr2 phases were calculated using the quasiharmonic approximation (QHA) and the corresponding electronic contribution was obtained using an approach based on Mermin statistics. The total heat capacities for these phases were fitted to appropriate expressions and integrated to obtain the Gibbs energy functions valid down to 0 K. The calculated thermochemical properties along with critically selected experimental constitutional and thermochemical data served as input for the thermodynamic optimisation of the system. The calculated phase equilibria and the thermodynamic properties using the optimised Gibbs energy functions are in good agreement with the input data. The calculated congruent melting points of NiZr and NiZr2 phases are close to the recent experimental data. The Ni10Z7 phase forms by a peritectic reaction, which is also in agreement with the experimental data.
Phase equilibrium in the Ni-Zr system obtained by thermodynamic modelling using experimental data and ab initio calculations.