The maximum predicted content of cation vacancies in inorganic and organic-inorganic perovskites: the role of the tolerance factor.

The maximum content of cation vacancies in perovskites determines the maximum adjustment to the physical properties. By using the classical criterion of the tolerance factor, we put forward a new method to obtain the maximum content of cation vacancies in perovskites. The effective ionic radius was calculated using the weighted average method, and the limit of tolerance factors was used to determine the maximum value of the cation vacancies. The calculated results of the La1-xMnO3 and La0.75Sr0.25Mn1-yO3 materials coincide with experimental results. For application, [(A(1))(1-x)(A(2)) (x)] (1-z1) (B1B2) X-3 or [(A(1))(1-x)(A(2)) x](B1B2) (1-z2) X-3 (X = O, F, Cl, Br, I) inorganic and hybrid organic-inorganic perovskite materials with vacancies at the A or B sites were predicted successfully, which provides a new method to improve the physical properties of perovskite materials.