Ab initio study of Kr in hcp Ti: Diffusion, formation and stability of small Kr–vacancy clusters

Ab initio electronic structure calculations have been performed to study the formation and migration of Kr impurities, and the stability of small Kr–vacancy clusters for clusters with up to four vacancies and four Kr atoms, in hcp Ti. Both the substitutional and the interstitial configurations of Kr are found to be stable. The octahedral configuration is however found to be more stable than the tetrahedral. Interstitial Kr atoms are shown to have attractive interactions and a low migration barrier, suggesting that, at low temperature, Kr bubble formation is possible, even in the absence of vacancies. We also find vacancy clusters to be stable. The binding energies of an interstitial Kr atom and a vacancy to a Kr–vacancy cluster are obtained from the calculated formation energies of the clusters. The stability of small-vacancy clusters is found to be dependent on Kr–vacancy ratio. The trends of the calculated binding energies are discussed in terms of providing further insights on the behaviour of Kr in implanted Ti.