  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.
