Infrared spectral properties of hydrogen, deuterium, and tritium in TiO2

Infrared spectra of Ti${\mathrm{O}}_2$ single crystals containing either hydrogen, deuterium, or tritium were measured at 300, 77, and 8 K. Bands observed at 3276, 2437, and 2065 ${\mathrm{cm}}^{-1\mathrm{}}$ near 300 K are, respectively, assigned to O${\mathrm{H}}^{-}$, O${\mathrm{D}}^{-}$, and O${\mathrm{T}}^{-}$ based on a two-term anharmonic-oscillator model of the hydrogenic species. The frequencies were also analyzed by using a linear hydrogen-bonded model with harmonic forces, but the correlation between frequencies and bandwidths was at variance with that of known H-bonded systems. The absorption strength per ion of O${\mathrm{T}}^{-}$ was calculated at several levels of approximation, and the best value determined was $a_{\mathrm{T}}=9.24\mathrm{}\times {10}^{-18\mathrm{}}$ cm. The harmonic and anharmonic mean-square displacements of O${\mathrm{H}}^{-}$, O${\mathrm{D}}^{-}$, and O${\mathrm{T}}^{-}$ were calculated, and the differences between these quantities reflect the changes in the infrared bandwidths with reduced mass.