Reduced CeO2(111) ordered phases as bulk terminations: Introducing the structure of Ce3O5

Reduced ceria (${\mathrm{CeO}}_{2\ensuremath{-}x}$) has a rich phase diagram comprising a variety of bulk phases with stoichiometries ranging from ${\mathrm{CeO}}_{2}$ to ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ as the reduction conditions are increased. Some observed reduced ceria (111) surface reconstructions are terminations of stable bulk phases, such as $\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$, whereas others are not associated with any known stable phases, namely, $\sqrt{7}\ifmmode\times\else\texttimes\fi{}3,\phantom{\rule{0.28em}{0ex}}3\ifmmode\times\else\texttimes\fi{}3$, and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$. In this paper, we analyze different periodic reconstructions of reduced ceria (111) surfaces within a theoretical framework. We describe the surfaces of stable bulk phases and elucidate the structure of the observed periodicities not corresponding to terminations of known stable bulk phases. Extending the $3\ifmmode\times\else\texttimes\fi{}3$ and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ terminations into a bulk structure, we find a new quasistable ${\mathrm{Ce}}_{3}{\mathrm{O}}_{5}$ bulk phase, which explains both periodicities. On the contrary, the $\sqrt{7}\ifmmode\times\else\texttimes\fi{}3$ surface structure cannot be extended into a bulk but stabilizes as a very thin overlayer. We also analyze other reported bulk structures with stoichiometry close to the ${\mathrm{Ce}}_{3}{\mathrm{O}}_{5}$ one, namely, the $C$-type ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3+\ensuremath{\delta}}$ bulk phase, which cannot describe the observed terminations. Our goal is to provide a unified picture to describe the road map of ${\mathrm{CeO}}_{2\ensuremath{-}\ensuremath{\delta}}(111)$ surface reconstructions and, when possible, their relationship to reduced ceria bulk phases.