Ab initio calculation of the attempt frequency of oxygen diffusion in pure and samarium doped ceria

The rate of oxygen ion jumps in a solid oxide depends not only on the activation energy but also on the pre-exponential factor of diffusion. In order to allow a fully ab initio prediction of the oxygen ion conductivity in pure and samarium doped ceria, we calculated the attempt frequency for an oxygen ion jump from first principles combining DFT+U, the NEB method, phonon calculations and the transition state theory. Different definitions of the jump attempt frequency are presented. The equivalence of the Eyring and the Vineyard method is shown without restriction to the Gamma point. Convergence checks of the phonon mesh reveal that the common reduction to the Gamma point is not sufficient to calculate the attempt frequency. Calculations of Sm doped ceria revealed an increase of the prefactor. The attempt frequency for the constant pressure case in quasi-harmonic approximation is larger than the attempt frequency at constant volume in harmonic approximation. The calculated electronic energies, enthalpies and entropies of migration are in agreement with the experimental diffusion coefficients and activation energies.