Geometric Analysis and Formability of the Cubic A ₂ BX ₆ Vacancy-Ordered Double Perovskite Structure

A geometric analysis of the cubic A2BX6 structure commonly formed by metal halides is presented. Using the “hard-sphere” approximation, where the ions are represented by spheres of a fixed radius, we derive four limiting models that each constrain the distances between constituent ions in different ways. We compare the lattice parameters predicted by these four models with experimental data from the Inorganic Crystal Structure Database (ICSD). For the fluorides, the maintenance of the AX bond length at the sum of the A and X radii gives the best approximation of the lattice parameter, leading to structures with widely separated BX6 octahedra. For the heavier halides, a balance between forming an A-site cavity of the correct size and maintaining suitable anion–anion distances determines the lattice parameter. It is found that in many A2BX6 compounds of heavier halides, the neighboring octahedra show very significant anion–anion overlap. We use these models to predict a compound with A-site rattling and use density functional theory (DFT) to confirm this prediction. Finally, we use the geometric models to derive formability criteria for vacancy-ordered double perovskites.