Thermodynamic stability of β-phases in Zr-Nb alloys

We investigate the contribution of mixing enthalpy, configurational entropy, vibrational entropy, and electronic entropy towards the thermodynamic stability of beta-(Zr,Nb) phases, to explain discrepancies in experimental observation of irradiated Zr-Nb alloys. Mixing enthalpy, configurational entropy, and electronic free energy alone are insufficient to explain the relative stability of these phases. This emphasises the need for accurate determination of the vibrational free energy contributions, which we calculated using ab initio molecular dynamics. Including vibrational free energy contributions predicts beta-Zr decomposition in to HCP-Zr and beta-Nb at temperatures below similar to 880 K, in line with experimental observations. The relative energy difference between beta-Zr decomposition between 600 and 1200 K is small (<0.1 eV/atom) and may explain the wide range of apparently stable n phases observed in neutron and proton irradiated Zr-Nb alloys. Other factors that may contribute towards the stability of these phases are also discussed.