Distortion modes in inorganic halide perovskites: to twist or to stretch

While the hybrid organic metal halide perovskites have shown promise for solar cell and other applications, an issue in this family of materials is structural stability and the distortions of the structure. In this work, the structural stability of CsBX₃ compounds with B from group IV elements and X=I,Br,Cl are studied using first-principles calculations with the full-potential linearized muffin-tin orbital method. It is shown that CsBX₃ halides with B=Sn or Pb undergo octahedral rotation distortions, while B=Ge or Si undergo a ferro-electric off-centering distortion along the [111] cubic axis along with rhombohedral stretching of the lattice. Specifically, we study the rotation about one cubic axis leading to the cubic to tetragonal phase transition. It is also shown that the preference for rotation or ferro-electric distrortion are mutually exclusive at their equilibrium volume. In other words, Ge and Si do not lead to rotations while Sn and Pb do not lower their energy under ferroelectric distortions. However the rotating structures, under thermal expansion supresses the rotation and encourages ferroelectric distortion. This behavior has been observed before in CsSnBr3 but is here extended to the other compounds and related to lone-pair induced anisotropic bonding.