Lattice-Constant Prediction and Effect of Vacancies in Aliovalently Doped Perovskites

Processing–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.