Assessing the high concentration of vacancies in refractory high entropy alloys

Accurate determination of monovacancy formation enthalpy is vital for work on diffusion, melting point determination of high temperature materials, radiation damage, and thermophysical stability of alloys. These enthalpies take on a single value in pure metals but is made more complex in concentrated solid solutions due to the local chemical environments possible around each vacancy. Herein, using first-principles density functional theory, we report the distributions of vacancy formation enthalpies in 21 equiatomic 5-component solid-solution alloys from the Hf-Mo-Nb-Ta-Ti-W-Zr system. Chemical disorder is treated using the special quasi-random structure method, and the chemical potential of vacant element is treated by approximating it to its total energy in its standard state. We find that the highest vacancy formation enthalpies belong to the MoNbTaTiW alloy (which incidentally is the most reported in literature) and the lowest belongs to HfNbTaTiZr, with other alloys in-between. We use the whole distribution of formation enthalpies to estimate the equilibrium concentration of vacancies as a function of temperature.