Charge distribution near bulk oxygen vacancies in cerium oxides

Understanding the electronic charge distribution around oxygen vacancies in transition metal and rare earth oxides is a scientific challenge of considerable technological importance. We show how significant information about the charge distribution around vacancies in cerium oxide can be gained from a study of high resolution crystal structures of higher order oxides which exhibit ordering of oxygen vacancies. Specifically, we consider the implications of a bond valence sum analysis of Ce₇O₁₂ and Ce₁₁O₂₀. To illuminate our analysis we show alternative representations of the crystal structures in terms of orderly arrays of coordination defects and in terms of fluorite-type modules. We found that in Ce₇O₁₂, the excess charge resulting from removal of an oxygen atom delocalizes among all three triclinic Ce sites closest to the O vacancy. In Ce₁₁O₂₀, the charge localizes on the next nearest neighbour Ce atoms. Our main result is that the charge prefers to distribute itself so that it is farthest away from the O vacancies. This contradicts the standard picture of charge localization which assumes that each of the two excess electrons localizes on one of the cerium ions nearest to the vacancy. This standard picture is assumed in most calculations based on density functional theory (DFT). Based on the known crystal structure of Pr₆O₁₁, we also predict that the charge in Ce₆O₁₁ will be found in the second coordination shell of the O vacancy. We also extend the analysis to the Magnéli phases of titanium and vanadium oxides (M(n)O(₂n₋₁), where M = Ti, V) and consider the problem of metal-insulator transitions (MIT) in these oxides. We found that the bond valence analysis may provide a useful predictive tool in structures where the MIT is accompanied by significant changes in the metal-oxygen bond lengths. Although this review focuses mainly on bulk cerium oxides with some extension to the Magnéli phases of titanium and vanadium, our approach to characterizing electronic properties of oxygen vacancies and the physical insights gained should also be relevant to surface defects and to other rare earth and transition metal oxides.