On the criteria of formation and lattice distortion of perovskite-type complex halides

Abstract

The famous Goldschmidt's tolerance factor t=(R A +R X )/ 2 (R B +R X ) gives us a necessary but not sufficient condition for the formation of perovskite-type compounds (ABX 3). In this work, computerized data analysis has been used to find some complementary criteria for the formation and lattice distortion of perovskite-type complex halides. It has been found that the radius ratio ( R A/ R X) and ( R B/ R X), affecting the stability of BX 6 octahedra and AX 12 cubo-octahedra (they are basic units of perovskite structure), are also dominating factors for the formation and lattice distortion of perovskite-type compounds. Besides, it has been found that the transition between the perovskite structure (with corner-sharing BX 6 octahedra) to BaNiO 3 structure (with face-sharing BX 6 octahedra) can be predicted by a criterion based on the relative magnitude of ionic radii and electronegativity. Based on multivariate data analysis, several complementary criteria for the formation and lattice distortion of perovskite-type complex halides have been obtained, and some empirical equations expressing the relationships between the ionic radii ( R A, R B, R X) and the lattice constants of perovskite-type complex halides have been found. The physical meaning of these empirical relationships has been discussed based on Pauling's rules of the crystal lattice stability of complex ionic compounds.