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

Abstract

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.

The ionic conductivity of Sm‐doped ceria

“…The experimental attempt frequency and activation enthalpy extracted from the Arrhenius behavior of the ionic conductivity according to an earlier work is shown in Figure 6. Several trends similar to other experiments can be observed: A decrease and subsequent increase of the activation enthalpy with increasing dopant fraction with a minimum at low dopant fractions can be found. However, the minimum in activation enthalpy of the bulk contribution at x = 0.025 appears at significantly lower dopant fractions compared to the maximum in ionic conductivity.…”

“…As our migration energy model in the KMC simulations should be best for pure ceria and small Sm dopant fractions, the discrepancy in conductivity may point out a fundamental difference between calculations and experiments. In fact, it is well known that in the experiments nominally pure ceria samples always contain small impurity amounts, which lead to higher oxygen vacancy concentrations than intrinsic defects (anti‐Frenkel) or defects caused by reduction at for temperatures below 800°C . Although often in literature no defect interactions for small dopant concentrations are expected, experiments show a significant influence of the impurity level on the conductivity and activation enthalpy .…”

“…In fact, it is well known that in the experiments nominally pure ceria samples always contain small impurity amounts, which lead to higher oxygen vacancy concentrations than intrinsic defects (anti‐Frenkel) or defects caused by reduction at for temperatures below 800°C . Although often in literature no defect interactions for small dopant concentrations are expected, experiments show a significant influence of the impurity level on the conductivity and activation enthalpy . If these impurities are considered in the KMC simulations and are assumed to have a strong trapping effect, for example, small amounts of Sc with a trapping energy of −0.65 eV as discussed in our earlier work, the simulated ionic conductivity of nominally pure ceria decreases significantly.…”

Coordination Numbers in Sm-Doped Ceria Using X-ray Absorption Spectroscopy

“…2,22 For Sm doped ceria, defect interactions are small compared to other rare-earth dopants resulting in the high oxygen ion conductivity as found in experiments 3140 and our earlier simulations. 2,26,28 In our simulations, we predicted ionic conductivity using Kinetic Monte Carlo (KMC) simulations 41 based on density functional theory (DFT) calculations, which are in excellent agreement with experiments. 2,42 For an experimental proof and a better understanding of the weak defect interactions in Sm doped ceria, the average coordination number for the rst shells around cerium ions, which contain oxygen ions, can be studied.…”

A review of defect structure and chemistry in ceria and its solid solutions

“…The decreasing Ce-O distances (with x) were used in combination with known Shannon ionic radii for N = 8 and N = 6 to derive a decreasing (with x) set of coordination numbers. A comparison to coordination numbers derived using XRD and prior simulations data 163 suggested that the vacancy distribution in Sm-doped ceria is close to random, namely there is no preference for Sm-V O over Ce-V O association. In summary, the models proposed above link the decrease in average coordination number around Ce or Do with x to the decrease in Cat-O distances.…”