Isotope effect for diffusion of tin inβ−titanium-titanium

The isotope effect for diffusion of ${}_{}{}^{113}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sn}_{}^m{}_{}{}^{}$ in Ti has been measured at five temperatures in the bcc $\beta$ phase. Separation of the Sn isotopes was effected by $\beta$ spectroscopy on electroplated sources. The effect is small and highly temperature dependent, varying from 0.18 ± 0.03 at 972°C to 0.37 ± 0.03 at 1525°C. When corrected for the mass difference between the Sn tracers used and the Ti solvent, the magnitude of the effect seems to be consistent with a relaxed vacancy mechanism as observed in "normal" bcc metals. Between 1000 and 1200°C the isotope-effect parameter increases quite rapidly. The temperature variation seems to be inconsistent with the hypothesis that two competing mechanisms of bulk diffusion operate over the bcc temperature range. The data do seem to be consistent with three possible alternative mechanisms for diffusion: enhancement by dislocation networks which anneal out at higher temperatures, enhancement due to the presence of $\omega$ embryos at low temperatures, and diffusion by highly relaxed vacancies with a large coefficient of thermal expansion and specific heat of formation.