Distortion modes in halide perovskites: to twist or to stretch, a matter of tolerance and lone pairs

TL;DR

This study uses first-principles calculations to explore how different halide perovskites distort via rotations or off-centering, influenced by tolerance factors and lone-pair chemistry, revealing mutually exclusive distortion modes at equilibrium.

Contribution

It demonstrates the distinct distortion modes in halide perovskites are governed by tolerance factors and lone-pair effects, providing new insights into their structural behavior and stability.

Findings

CsBX₃ with B=Sn or Pb undergo octahedral rotations

Ge and Si compounds exhibit ferro-electric rhombohedral distortion

RbGeX₃ can distort via rotations or off-centering, with off-centering slightly more stable

Abstract

Using first-principles calculations, we show that CsBX$_3$ halides with B=Sn or Pb undergo octahedral rotation distortions, while for B=Ge and Si, they undergo a ferro-electric rhombohedral distortion accompanied by a rhombohedral stretching of the lattice. We show that these are mutually exclusive at their equilibrium volume although different distortions may occur as function of lattice expansion. The choice between the two distortion modes is in part governed by the Goldschmidt tolerance factor. However, another factor explaining the difference between Sn and Pb compared with Ge and Si is the stronger lone-pair character of Ge and Si when forced to be divalent as is the case in these structures. The lone-pair chemistry is related to the off-centering. While the Si-based compounds have not yet been synthesized, the Ge compounds have been established experimentally. As a final test of the importance of the tolerance factor we consider RbGeX$_3$, which has smaller tolerance factor than the corresponding CsGeX$_3$ because Rb is smaller than Cs. We find that it can lower its energy by both rotations or rhombohedral off-centering distortions but the latter lower the energy slightly more efficiently.