Bond valences and anharmonicity in vacancy-ordered double perovskite halides

Anharmonic lattice dynamics are intimately linked with optical and electronic properties in perovskite halide semiconductors. Vacancy-ordered double perovskites are a subset of the perovskite halide family containing isolated octahedral units. The absence of polyhedral connectivity engenders the vacancy-ordered double perovskites with additional degrees of dynamic freedom, which presents an ideal structural framework to study dynamic-property relationships in perovskite halide semiconductors. In the present study, we examine the structure and bonding origins of anharmonicity in the vacancy-ordered double perovskites Cs 2 Sn 1− x Te x I 6 . While X-ray diffraction indicates that all members adopt the cubic vacancy-ordered double perovskite structure, the local coordination environment probed by X-ray pair distribution function (XPDF) analysis reveals asymmetry of the Cs-I/I-I pair correlation that smoothly decreases with increasing tellurium content. Temperature-dependent neutron total scattering suggests that this asymmetry in the PDF occurs due to anharmonic lattice dynamics arising from octahedral tilting and Cs + displacements, as supported by Reverse Monte Carlo simulations of the Cs 2 SnI 6 and Cs 2 TeI 6 end members. We further correlate the trends in asymmetry and anharmonicity with the bond valence sum of the Cs + ion, and find that the anharmonicity vanishes when the bonding preferences of the Cs + are satisfied by the size of the cuboctahedral void. This study presents a simple and effective approach for understanding the origin of anharmonicity in vacancy-ordered double perovskite materials. Anharmonicity is observed in vacancy-ordered double perovskites when the A-site cation is not optimally coordinated by the octahedral framework.