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Using electron tomography in combination with spatially resolved electronenergy-loss spectroscopy at high energy resolution, we are able to map thevalency of the Ce ions in CeO$_{2-x}$ nanocrystals. Our three-dimensionalresults show a clear facet-dependent reduction shell at the surface of ceriananoparticles; {111} surface facets show a low surface reduction, whereas at{001} surface facets the cerium ions are more likely to be reduced over alarger surface shell. The novelty of this generic tomographic technique is thatit allows a full three dimensional datacube to be reconstructed, containing afull electron energy-loss spectrum in each voxel. The ability to extract anelectron energy-loss spectrum in each point of a reconstructed datacube,enables the three-dimensional investigation of a plethora of material-specificphysical properties such as valency, chemical composition, oxygen coordinationor bond lengths. These experiments will trigger the synthesis of nanomaterialswith improved properties and the design of nanostructures with novelfunctionalities.

Three dimensional valency mapping in CeO$_{2-x}$ nanocrystals