Disentangling small-polaron and Anderson-localization effects in ceria: Combined experimental and first-principles study

Abstract

By comparison of the electrical conductivity of ceria doped with penta- and hexavalent ions, we separate the total electron localization energy into the two contributions originating from the small polaron effects and the Coulomb interaction with the donor ions. The upper bound of the itinerant small polaron hopping energy is estimated at $66\ifmmode\pm\else\textpm\fi{}20$ meV. The binding energy of the ${\mathrm{Ce}}^{3+}--{M}^{5+/6+}$ defect complex increases from 121 meV for $M={\mathrm{Nb}}^{5+}/{\mathrm{Ta}}^{5+}$ to 243 meV for $M={\mathrm{W}}^{6+}/{\mathrm{U}}^{6+}$. The first-principles simulations are in qualitative agreement with the experimental findings. At low temperatures the $f$ electrons bound to the donor defects show dielectric relaxation with the lowest activation energy of 2.7 and 17 meV for Nb(Ta)- and W-doped ceria, respectively. Remarkably, these energies are significantly smaller than the hopping energy of the itinerant small polarons. While both the electron-lattice and the electron-defect interactions cause the $f$ electron localization in real-case ceria, the latter effects seem to be the dominant.