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.
We calculate entropies of formation for fully charged point defects, including the small polaron Ce'(Ce), in undoped fluorite-structured ceria by means of density functional theory in the GGA + U approximation. We discuss the behaviour of the entropy for the constant volume and the constant pressure case. Our results for constant pressure (p = 0) suggest that the change in volume, due to the formation of defects, dominates the entropy of formation. From the individual entropies of formation the entropies of Frenkel, anti-Frenkel and Schottky disorder as well as the entropy of reduction of ceria are obtained. At temperatures of about 1000 K the entropic contributions to the Gibbs energy are up to 0.9 eV per defect and thus are no longer negligible. For our calculated entropy of reduction of about 17 kB we find a remarkable agreement with experimental data from the literature.
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