Extending the applicability of the Goldschmidt tolerance factor to arbitrary ionic compounds

Crystal structure determination is essential for characterizing materials and their properties, and can be facilitated by various tools and indicators. For instance, the Goldschmidt tolerance factor (T) for perovskite compounds is acknowledged for evaluating crystal structures in terms of the ionic packing. However, its applicability is limited to perovskite compounds. Here, we report on extending the applicability of T to ionic compounds with arbitrary ionic arrangements and compositions. By focussing on the occupancy of constituent spherical ions in the crystal structure, we define the ionic filling fraction (IFF), which is obtained from the volumes of crystal structure and constituent ions. Ionic compounds, including perovskites, are arranged linearly by the IFF, providing consistent results with T. The linearity guides towards finding suitable unit cell and composition, thus tackling the main obstacle for determining new crystal structures. We demonstrate the utility of the IFF by solving the structure of three hydrides with new crystal structures.