Cs_1–<i>x</i>Rb_<i>x</i>PbCl₃ and Cs_1–<i>x</i>Rb_<i>x</i>PbBr₃ Solid Solutions: Understanding Octahedral Tilting in Lead Halide Perovskites

The structures of the lead halide perovskites CsPbCl₃ and CsPbBr₃ have been determined from X-ray powder diffraction data to be orthorhombic with <i>Pnma</i> space group symmetry. Their structures are distorted from the cubic structure of their hybrid analogs, CH₃NH₃PbX₃ (X = Cl, Br), by tilts of the octahedra (Glazer tilt system <i>a</i>^–<i>b</i>⁺<i>a</i>^–). Substitution of the smaller Rb⁺ for Cs⁺ increases the octahedral tilting distortion and eventually destabilizes the perovskite structure altogether. To understand this behavior, bond valence parameters appropriate for use in chloride and bromide perovskites have been determined for Cs⁺, Rb⁺, and Pb²⁺. As the tolerance factor decreases, the band gap increases, by 0.15 eV in Cs_1–<i>x</i>Rb_<i>x</i>PbCl₃ and 0.20 eV in Cs_1–<i>x</i>Rb_<i>x</i>PbBr₃, upon going from <i>x</i> = 0 to <i>x</i> = 0.6. The band gap shows a linear dependence on tolerance factor, particularly for the Cs_1–<i>x</i>Rb_<i>x</i>PbBr₃ system. Comparison with the cubic perovskites CH₃NH₃PbCl₃ and CH₃NH₃PbBr₃ shows that the band gaps of the methylammonium perovskites are anomalously large for APbX₃ perovskites with a cubic structure. This comparison suggests that the local symmetry of CH₃NH₃PbCl₃ and CH₃NH₃PbBr₃ deviate significantly from the cubic symmetry of the average structure