Density-functional calculations of prefactors and activation energies for H diffusion inBaZrO3

Density-functional calculations are used to investigate hydrogen diffusion in the solid-state proton conductor $\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_{3}$. Activation energies and prefactors for the rate of proton transfer and reorientation are evaluated for a defect-free region of this simple cubic perovskite-structured oxide. Both semiclassical over-barrier jumps and phonon-assisted tunneling transitions between sites are considered. It is found that the classical barriers for the elementary transfer and reorientation steps are both of the order of $0.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The quantum-mechanical zero-point motion effects are found to be sizable, to effectively reduce the barrier heights, and to make the prefactors similar for the transfer and reorientation steps. The Flynn-Stoneham model [Phys. Rev. B 1, 3966 (1970)] of phonon-assisted tunneling yields an activation energy of around $0.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and a very small prefactor for proton transfer, whereas the corresponding adiabatic model gives a similar activation energy but a much larger prefactor. It is suggested that the effect of other defects such as dopants has to be included for a proper description of hydrogen diffusion in this material.