<p>CeNbO<sub>4+δ</sub>,
a family of oxygen hyperstoichiometry materials with varying oxygen contents
(CeNbO<sub>4</sub>, CeNbO<sub>4.08</sub>, CeNbO<sub>4.25</sub>, CeNbO<sub>4.33</sub>)
and showing mixed electronic and oxide ionic conduction, have been known for four
decades. However, the oxide ionic transport mechanism has remained unclear due
to the unknown atomic superstructures of CeNbO<sub>4.08</sub> and CeNbO<sub>4.33</sub>.
Here, we determinate the complex superstructures of CeNbO<sub>4.08 </sub>(89
unique atoms), <a>CeNbO<sub>4.25 </sub>(75 unique atoms)
and CeNbO<sub>4.33</sub> (19 unique atoms) by using recently developed
continuous rotation electron diffraction (cRED) technique from nano single
crystals. </a><a>The
Ce cationic size contraction upon oxidation in CeNbO<sub>4+δ</sub> allows not
only excess oxygen incorporation into the CeNbO<sub>4</sub> host lattice at the
interstitial site within the Ce cation chains (referred to as O<sub>i</sub>),
but also relaxation of the<sub> </sub>NbO<sub>n</sub> polyhedra in CeNbO<sub>4.08</sub>,
CeNbO<sub>4.25</sub>, CeNbO<sub>4.33</sub> being bridged through mixed
corner/edge-sharing in 3-dimentional directions. </a>Two kinds of oxide ion migration events are
identified in CeNbO<sub>4.08</sub> and CeNbO<sub>4.25</sub> phases by molecular
dynamic simulations, which form long-rang 3-dimensional migration pathway through
the interstitial sites O<sub>i</sub> via a synergic-cooperation knock-on mechanism involving continuous
breaking and reformation of Nb<sub>2</sub>O<sub>9</sub> units. However, the
excess oxygen in the CeNbO<sub>4.33</sub> phase hardly migrates because of
ordered distribution of high-concentration excess oxide ions. The relationship
between the structure and oxide ion migration for the whole series of CeNbO<sub>4+</sub><sub>d</sub> compounds elucidated
here provides a direction for the performance optimization of these compounds
and the development of oxygen hyperstoichiometric materials for wide variety of
applications.</p>