Atomistic calculation of association energy in doped ceria

Atomistic simulation based on energy minimization techniques was carried out to study the association energies of more than 300 defect structures of ceria doped with Lu₂O₃, Yb₂O₃, Er₂O₃, Y₂O₃, Gd₂O₃, Eu₂O₃, Sm₂O₃, Nd₂O₃ and La₂O₃. The calculation ensemble includes all the possible defect structures in 6.25 mol% doped ceria. It is revealed that a clear preference for vacancy-dopant association occurs energetically for small dopant cations and vacancy-Ce⁴⁺ association for large dopant cations, with the crossover at Gd³⁺. The defect structures with the maximum association effect for different trivalent cations were determined. For Gd³⁺ doped ceria which presents the lowest association effect in the trivalent doped ceria, the association energies of four different defect structures are extremely close, which agrees well with a recent EXAFS investigation, that is, Gd³⁺ is distributed randomly in the ceria lattice. This work provides insight for the understanding of ionic conductivity in doped ceria.