Stabilized bismuth oxides undergo a decay in conductivity when subjected to annealing at temperatures of <600 degrees C, because of the formation of an ordered superstructure, which is observed in transmission electron microscopy (TEM) diffraction patterns. Neutron-diffraction studies of the aged samples indicate that there is a displacement of almost all the anions, from the regular Sc sites to interstitial 32f sites. Based on the TEM patterns and the displacement of the oxygen ions, various structural models for the superstructure have been analyzed. From this work, it can be deduced that the observed decay in conductivity is due to the ordering of the oxygen sublattice, along with a possible concomitant ordering of cations.