Anisotropic chemical strain in cubic ceria due to oxygen-vacancy-induced elastic dipoles

Accurate characterization of chemical strain is required to study a broad range of chemical–mechanical coupling phenomena. One of the most studied mechano-chemically active oxides, nonstoichiometric ceria (CeO2−δ), has only been described by a scalar chemical strain assuming isotropic deformation. However, combined density functional theory (DFT) calculations and elastic dipole tensor theory reveal that both the short-range bond distortions surrounding an oxygen-vacancy and the long-range chemical strain are anisotropic in cubic CeO2−δ. The origin of this anisotropy is the charge disproportionation between the four cerium atoms around each oxygen-vacancy (two become Ce3+ and two become Ce4+) when a neutral oxygen-vacancy is formed. Around the oxygen-vacancy, six of the Ce3+–O bonds elongate, one of the Ce3+–O bond shorten, and all seven of the Ce4+–O bonds shorten. Further, the average and maximum chemical strain values obtained through tensor analysis successfully bound the various experimental data. Lastly, the anisotropic, oxygen-vacancy-elastic-dipole induced chemical strain is polarizable, which provides a physical model for the giant electrostriction recently discovered in doped and non-doped CeO2−δ. Together, this work highlights the need to consider anisotropic tensors when calculating the chemical strain induced by dilute point defects in all materials, regardless of their symmetry.