Effect of vacancies on the mechanical properties of zirconium: An ab   initio investigation
  It is well known that the irradiation-induced defects strongly influence the mechanical properties of zirconium (Zr) or its alloys in nuclear reactors. However, how the point defect changes the mechanical properties has been rarely studied. Here, we systematically investigated the effect of vacancies on the mechanical properties of alpha-Zr based on density functional theory (DFT). Both uniformly distributed vacancies and vacancy clusters were considered. Our results reveal that the existence of vacancy will reduce the bulk modulus, while enhance the shear and Young's moduli. Based on these moduli, the ductility and hardness were further calculated. With the introduction of vacancy, the ductility decreases, but the hardness increases. However, when the vacancy concentration is larger than a critical value, a rise in the ductility and a reduction in the hardness occur, which indicates the degeneration of the material. Moreover, it was found that the vacancies lead to a more isotropic distribution of Young's modulus in 3D space. To further investigate how the clustering of vacancies influences the mechanical properties, the most stable configurations of di- and trivacancy clusters have been predicted, which correspond to the most compact distribution of vacancies. Compared with the uniform distribution of vacancies, clustering of vacancies will strengthen the above changes of elastic moduli, ductility and hardness. Our results indicate that the increase of the vacancy concentration may be the basic cause for the changes of the mechanical properties under irradiation, while the formation of vacancy clusters intensifies these changes. 
Xueyan Zhu, Xingyu Gao, Haifeng Song, Guomin Han, and De-Ye Lin
cond-mat.mtrl-sci