Strain Dependence of Energetics and Kinetics of Vacancy in Tungsten.

We investigate the influence of hydrostatic/biaxial strain on the formation, migration, and clustering of vacancy in tungsten (W) using a first-principles method, and show that the vacancy behaviors are strongly dependent on the strain. Both a monovacancy formation energy and a divacancy binding energy decrease with the increasing of compressive hydrostatic/biaxial strain, but increase with the increasing of tensile strain. Specifically, the binding energy of divacancy changes from negative to positive when the hydrostatic (biaxial) tensile strain is larger than 1.5% (2%). These results indicate that the compressive strain will facilitate the formation of monovacancy in W, while the tensile strain will enhance the attraction between vacancies. This can be attributed to the redistribution of electronic states of W atoms surrounding vacancy. Furthermore, although the migration energy of the monovacancy also exhibits a monotonic linear dependence on the hydrostatic strain, it shows a parabola with an opening down under the biaxial strain. Namely, the vacancy mobility will always be promoted by biaxial strain in W, almost independent of the sign of strain. Such unexpected anisotropic strain-enhanced vacancy mobility originates from the Poisson effect. On the basis of the first-principles results, the nucleation of vacancy clusters in strained W is further determined with the object kinetic Monte Carlo simulations. It is found that the formation time of tri-vacancy decrease significantly with the increasing of tensile strain, while the vacancy clusters are not observed in compressively strained W, indicating that the tensile strain can enhance the formation of voids. Our results provide a good reference for understanding the vacancy behaviors in W.