The oxygen atoms of cubic ZrO2 form a primitive cubic (pc) lattice. Two pos
itions of the pc lattice are occupied by metal atoms in the perovskite-rela
ted structures (PER group) of superconducting oxides. Many ZrO2-related str
uctures with ordered oxygen defects square like Zr(3)Sc(4)square(2)O(12) or
Cu2O square(3) and most superconducting oxides can be characterized by the
ordering of the defects and oxygen atoms. The structures are analyzed by t
he self-coordination numbers T-i of the oxygen atoms with other oxygen atom
s in the i=1-3 coordination shell and the T-1, T-2 values plotted in struct
ure maps. The T-i values can be correlated with attractive or repulsive int
eractions and the mobility of oxygen atoms. The different structures can be
classified in about 20 structure families like the Ruddlesden-Popper phase
s. The characterization by sequences of structural units or sequences of co
ordination numbers allows the search for new compounds with high oxygen mob
ility. (C) 2000 Elsevier Science B.V. All rights reserved.