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a b s t r a c tProcessing-structure relationships are at the heart of materials science, and predictive tools are essential for modern technological industries insofar as structure dictates properties. Point defects can have a profound effect on structure and consequently properties, but their effect on crystal chemistry is still not generally known or understood. None of the very few theoretical models which exist for perovskites are suited to the doped and defective ceramics most commonly used in commercial devices; therefore, a new empirical approach is presented here. A predictive model for the effective size of anions as well as cation vacancies and ultimately the pseudocubic lattice constant of such perovskites, based solely on published ionic radii data, has been developed here. The model can also be used to derive ionic radii of cations in twelvefold coordination. Vacancies have an effective size due to both bond relaxation and mutual repulsion of coordinating anions, and as expected this size scales with the host cation radius, but not in a straightforward way. The model is able to predict pseudocubic lattice constants, calculate the effective size of anions and cation vacancies, and identify the effects of both cation ordering and second-order Jahn Teller distortions. A lower limit on the tolerance factor of stable oxide perovskites is proposed.

Engineering defective structures in an attempt to modify properties is an established technique in materials chemistry, yet, no models exist which can predict the structure of perovskite compounds containing extrinsic point defects such as vacancies. An empirically derived predictive model, based solely on chemical composition and published ionic radii has been developed. Effective vacancy sizes were derived both empirically from an existing model for pseudocubic lattice-constants, as well as experimentally, from average bond lengths calculated from neutron diffraction data. Compounds of lanthanum-doped barium titanate and strontium-doped magnesium titanate were synthesized with vacancies engineered on the A-and B-sites. Effective vacancy sizes were then used in empirical models to predict changes in lattice constants. Experimentally refined bond lengths used in the derivation of an effective vacancy size seemed to overestimate the effect of the point defects. Conversely, using calculated vacancy sizes, derived from a previously reported predictive model, showed significant improvements in the prediction of the pseudocubic perovskite lattice.

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