The predominant hydrogen-containing species in rutile were OH- ions, in which the oxygen occupied a regular oxygen ion site, and the O-H bond was perpendicular to the c-axis. It was proposed that diffusion of hydrogen parallel to the c axis proceeded by a proton jump from one O2- ion to another along the channel as represented by OH-···O2- → O2-···H+···O2- → O2-···HO-. It was also proposed that diffusion perpendicular to the c-axis proceeded by a rotation of the OH- bond to move the proton from one channel to an adjacent channel, followed by a proton jump to another O2-ion in the same channel. From a potential-energy model, which included a Morse function to represent the OH- bond, as well as electrostatic and repulsive terms, the activation energies for hydrogen and tritium diffusion parallel to the c-axis were calculated to be (including a zero-point energy correction) 0.60 and 0.69eV, respectively, in good agreement with the respective experimental values of 0.59 and 0.75eV. The calculated activation energy for diffusion perpendicular to the c-axis was 1.23eV (no zero-point energy correction), as compared to the experimental values of 1.28 and 1.11eV, respectively, for hydrogen and tritium. The calculated equilibrium orientation of the OH- ion in TiO2 and the calculated stretching frequency of this species were also in good agreement with the respective experimental results.

Mechanisms for Hydrogen Diffusion in TiO2. Bates, J.B., Wang, J.C., Perkins, R.A.: Physical Review B, 1979, 19[8], 4130-9