First principles calculations on CeO2 doped with Tb3+ ions

Abstract The atomic and electronic structure of CeO2 doped with Tb has been calculated from first principles with inclusion of strong correlation effects on the basis of Hubbard model (DFT + U). The two values of Hubbard U-parameter were applied separately on Ce and Tb ions, in order to treat correctly two oxidation states of Tb (3 + and 4+). Crystal structure distortion is also discussed for Tb3+ ions in ceria without oxygen vacancies. The corresponding total energy difference between the 3 + and 4 + states is very small and, thus, these states can co-exist without oxygen vacancy formation (unlike Gd doping). Multiple configurations have been obtained with localization of electrons on different number of cations, if the Tb ion has an oxygen vacancy nearby. A site symmetry approach has been successfully applied to identify the ground state configuration. Gibbs formation energy of oxygen vacancy due to Tb doping is reduced by almost a factor of four, in comparison with the pure CeO2. The dependence of Gibbs formation energy on the temperature and oxygen partial pressure is discussed. It has been also shown that the lowest formation energy for the small polaron occurs when the Ce3+ and Tb3+ ions are located as nearest neighbors to oxygen vacancy. The results obtained are compared with the existing literature data from the electrical conductivity and optical measurements.