On phase stability of Mo-Nb-Ta-W refractory high entropy alloys

Refractory high entropy alloys (RHEAs) emerge as promising candidate materials for ultrahigh-temperature applications. Accurate phase stability is the prerequisite for design of high-performance RHEAs, but still missing in the literature due to the big challenge in experiments. In this paper, the reliable 3rd-generation Gibbs energy expressions for pure Mo, Nb, Ta and W were firstly evaluated by integrating the physical based Segmented Regression model with thermal vacancy description from 0 K to high temperatures. The thermodynamic database of the Mo-Nb-Ta-W quaternary system was then developed by combining the established 3rd-generation Gibbs energies with the phase equilibrium and thermodynamic data by using the CALPHAD (CALculation of PHAse Diagram) approach. The calculated phase equilibria, thermodynamic properties as well as the A2/B2 ordering transition behaviors show good agreement with those from experimental determination and theoretical calculation. The phase constitutes and elemental distributions in an equiatomic MoNbTaW as-cast alloy were experimentally investigated and compared with the non-equilibrium solidification simulations to further verify the database reliability. The high-throughput mapping of phase stability within the composition-temperature space in various Mo-Nb-Ta-W alloys was then constructed by applying thermodynamic calculations. The alloying effects on the formation of B2 phase were systematically analyzed. The Mo-Nb-Ta-W alloys have a wide temperature region with a single A2 phase, while the A2 + B2 phase regions exist at very low temperatures. It is highly anticipated that the present accurate 3rd-generation thermodynamic database provides an important basis for efficient design and development of novel Mo-Nb-Ta-W RHEAs.