Effective Size of Vacancies in Aliovalently Doped SrTiO3 Perovskites

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Point defects like vacancies can have a profound effect on the structure of perovskite ceramics, but the exact mechanisms involved are still unclear. While a few theoretical models exist for some perovskites, none are particularly accurate or at all suited to the impure, doped, or otherwise defective ceramics which abound in commercial devices. A new empirical approach is presented here. A predictive model for the pseudocubic lattice constant of such perovskites, based solely on published ionic radii data, has been developed and adapted as a model for effective tolerance factor. This model shows that the average A-site size generally decreases with increasing vacancy concentration up to [V] = 22%, but not as much as would be expected if vacancies were truly zero-dimensional defects. Such vacancies have an effective size due to both bond relaxation and mutual repulsion of coordinating oxygen ions. At compositions corresponding to [V] < 1.5% this size is effectively negative, corresponding to the relaxation of oxygen ions towards the vacant site. For higher vacancy concentrations the size is positive, resulting from the electrostatic repulsion of the coordinating oxygen ions. These models more consistently predict both pseudocubic lattice constant, hence cell volume, and the tolerance factor for SrTiO3-based perovskites than existing methods and can potentially be expanded to other perovskite systems.