  According to defect chemistry, the experimental observations of enhanced
cation diffusion in a reducing atmosphere in zirconia, ceria and barium
titanate are in support of an interstitial mechanism. Yet previous
computational studies always found a much higher formation energy for cation
interstitials than for cation vacancies, which would rule out the interstitial
mechanism. The conundrum has been resolved via first-principles calculations
comparing migration of reduced cations and oxidized ones, in cubic ZrO2, CeO2
and BaTiO3. In nearly all cases, reduction alone lowers the migration barrier,
and pronounced lowering results if cation's electrostatic energy at the saddle
point decreases. The latter is most effectively realized when a Ti cation is
allowed to migrate via an empty Ba site thus being fully screened all the way
by neighboring anions. Since reduction creates oxygen vacancies as well, which
are highly mobile, we also studied their effect on cation migration, and found
it only marginally lowers the migration barrier. In several cases, however, a
large synergistic effect between cation reduction and oxygen vacancy is
revealed, causing an electron to localize in the saddle-point state at a much
lower energy than normal, signaling that the saddle point is a negative-U state
in which the soft environment enables a large electron-phonon interaction that
can over-compensate the on-site Coulomb repulsion. These general findings are
expected to be applicable to defect-mediated ion migration in most transitional
metal oxides.
