Stability Trend of Tilted Perovskites

Halide perovskites, with prototype cubic phase ABX(3), undergo various phase transitions accompanied by rigid rotations of corner-sharing BX6 octahedra. Using first-principles density functional theory calculations, we have performed a comprehensive investigation of all of the possible octahedral tilting in 18 halide perovskites ABX(3) (A = Cs, Rb, and K; B = Pb and Sn; and X = I, Br, and Cl) and found that the stabilization energies, i.e., energy differences between cubic and the most stable tilted phases, are linearly correlated with the tolerance factor t. Moreover, the tilt energies, i.e., energy differences between cubic and various tilted phases, are linearly correlated with the change of atomic packing fractions (Delta eta), indicating the importance of the atomic packing fraction on the stabilities of distorted perovskites. This work may provide guidance for searching proper perovskite ABX(3) to extend distorted perovskite for wide applications, such as Stability AED(meV/atom) thermochromics.