First-principles calculations of energetics of sigma phase formation and thermodynamic modelling in the Cr–Fe–W system

Ab initio total energies of the alloy sigma phase in Cr–W and Fe–W systems were calculated by means of the linear muffin-tin orbital method in the atomic sphere approximation. Total energies of the pure constituents in the sigma phase and standard element reference (SER) states were evaluated using the full-potential linear augmented plane wave method. The combination of these results was used for the prediction of the energy of formation of the sigma phase with respect to both sigma phase of pure constituents and SER states at equilibrium structure parameters. We have also provided a novel physical approach to the thermodynamic modelling of the sigma phase and a reliable construction of the phase diagram of the Cr–Fe–W system, using ab initio calculated total energy differences in the calculation of phase diagram (CALPHAD) approach.