First-principles computational study of defect clustering in solid solutions of ThO₂ with trivalent oxides

The energetics of mixing and defect ordering in solid solutions of fluorite-structured ThO₂ with oxides of trivalent cations (Sc, In, Y, Nd, and La) are investigated by electronic density-functional theory (DFT). Through DFT calculations of structures enumerated by lattice-algebra techniques, we identify the lowest energy patterns for defect clustering for four separate dopant concentrations. The most stable structures are characterized by a repulsive interaction between nearest-neighbor vacancies on the oxygen sublattice. The enthalpies of formation with respect to constituent oxides are positive for all dopants considered, and show a tendency to decrease in magnitude as the size and electronegativity of the trivalent dopant decrease. Due to the small positive formation enthalpies and low oxygen-vacancy binding energy with La dopants, La₂ O₃ -ThO₂ solid solutions are predicted to have relatively high ionic conductivities relative to those for the other aliovalent dopants considered. Our results are compared with those for the more widely studied ZrO₂ and CeO₂ fluorite-structured solid solutions with trivalent cations.