Atomic positions and diffusion paths of h and he in the $\alpha$-Ti lattice

The solution energy of H and He in various interstitial and substitution positions in the hcp lattice of $\alpha$-Ti has been calculated based on the method of electron density functional. The lowest solution energy of He corresponds to the basal octahedral position and that of H corresponds to the octahedral position (next in energy is the tetrahedral position). The calculated vibration frequencies of H in various positions are used for identification of lines in the vibration spectrum obtained by the method of neutron inelastic scattering. Taking into account these spectra, it can be concluded that hydrogen atoms occupy in the hcp lattice of Ti both the octahedral and tetrahedral positions even at 600 K. The available experimental data do not contradict the conclusion that the octahedral position is more preferable in $\alpha$-Ti. The energy barriers are estimated for various diffusion paths of H and He.