Defect formation energy in pyrochlore: the effect of crystal size

Abstract

Defect formation energies of point defects of two pyrochlores Gd2Ti2O7 and Gd2Zr2O7 as a function of crystal size were calculated. Density functional theory with plane-wave basis sets and the projector-augmented wave method were used in the calculations. The results show that the defect formation energies of the two pyrochlores diverge as the size decreases to the nanometer range. For Gd2Ti2O7 pyrochlore, the defect formation energy is higher at nanometers with respect to that of the bulk, while it is lower for Gd2Zr2O7. The lowest defect formation energy for Gd2Zr2O7 is found at 15–20 Å. The different behaviors of the defect formation energies as a function of crystal size are caused by different structural adjustments around the defects as the size decreases. For both pyrochlore compositions at large sizes, the defect structures are similar to those of the bulk. As the size decreases, for Gd2Ti2O7, additional structure distortions appear at the surfaces, which cause the defect formation energy to increase. For Gd2Zr2O7, additional oxygen Frenkel pair defects are introduced, which reduce the defect formation energy. As the size further decreases, increased structure distortions occur at the surfaces, which cause the defect formation energy to increase. Based on a hypothesis that correlates the energetics of defect formation and radiation response for complex oxides, the calculated results suggest that at nanometer range Gd2Ti2O7 pyrochlore is expected to have a lower radiation tolerance, and those of Gd2Zr2O7 pyrochlore to have a higher radiation tolerance. The highest radiation tolerance for Gd2Zr2O7 pyrochlore is expected to be found at ∼2 nanometers.