Point defect properties in hcp and bcc Zr with trace solute Nb revealed by ab initio calculations

The properties of simple point defect (i.e. vacancy, self and foreign interstitial atoms) in the hcp (alpha) and bcc (beta) Zr with trace solute Nb have been studied by ab initio calculations with VASP codes. The calculations indicate that the formation energies of vacancy and substitutional Nb atom are 1.94 eV and 0.68 eV in alpha Zr and 0.36 eV and 0.07 eV in beta Zr, respectively, while the binding energies of the nearest neighbor vacancy–substitutional Nb pair and the nearest neighbor substitutional Nb–Nb pair are 0.09 eV and 0.03 eV in alpha Zr and 2.78 eV and 0.72 eV in beta Zr, respectively. These results suggest that the Nb atoms are more likely to agglomerate and form precipitates in the beta Zr than in the alpha Zr. Thus, the α-Zr–β-Zr–β-Nb transition mechanism through in situ α to β transformation of Zr and the vacancy-assisted Nb diffusion for Nb conglomeration in beta Zr under irradiation is proposed to explain the existence of beta Nb and Zr precipitate mixtures observed in the experiments for the Zr–Nb alloy. In addition, the defect formation energies in bcc Nb are also presented.