A model to determine the chemical expansion in non-stoichiometric oxides based on the elastic force dipole

In this work a novel continuum model informed by density functional theory (DFT) simulations is presented and used to predict the chemical expansion observed in non-stoichiometric oxides. We introduce an elastic dipole tensor that describes the long-range elastic fields created upon formation of oxygen vacancies. We show that this tensor, which can be accurately determined through first-principle DFT calculations, can be used to predict the chemical expansion of ceria and in general other non-stoichiometric oxides. Compared to previous work where expansivity was obtained with empirical potentials, our work provides an efficient way of computing it directly by DFT calculations. Furthermore, we discuss how the elastic dipole tensor can predict the O2 partial pressure vs O/Ce ratios in strained systems and show that CeO2 can be reduced more easily in the presence of tensile strains. More generally, the elastic dipoles can be used in continuum models to predict the distribution of vacancies near nanocrystal surfaces, grain boundaries and extended defects such as dislocations and hence provide information on how these structures and defects influence the overall reducibility of the material.