Modeling the Effective Size of Charge-Balancing Vacancies in the Structure of Rare Earth Doped Perovskites.
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 vacancies are not zero-dimensional defects but have an effective size due to both bond relaxation and mutual repulsion of coordinating oxygen ions. For some compositions this size can be effectively negative, corresponding to the relaxation of oxygen ions towards the vacant site. For other compositions 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 [(Ca,Sr,Pb)1-3xLn2x]TiO3 (Ln = Y, La, Ce, Nd) perovskites than existing methods.