Improved Tolerance Factor for Classifying the Formability of Perovskite Oxides and Halides

The Goldschmidt tolerance factor (t) has been used for decades to predict whether ABX₃ solids are likely to crystallize into perovskite or nonperovskite structures. We find that t correctly classifies only 80% of 555 experimentally characterized ABX₃ solids (X = O, F, Cl, Br, I) using a decision tree model fit to all examples to identify the optimal range for t. Higher structure classification accuracy is desired for the high-throughput screening of perovskite formability, especially for perovskite halides, which are generally predicted less accurately than perovskite oxides using t. In this work, Sure Independence Screening and Sparsifying Operator (SISSO) is used to identify the highest performing 2D descriptors among ~10¹¹ candidate features derived from basic elemental and atomic properties (e.g., radii, mass, electronegativity, etc. of each A, B and X element). The result is an interpretable and linear descriptor that correctly classifies 93% of the 555 oxides and halides, including 95% on an excluded test set of 111 compounds. This descriptor is implemented on ~8,000 ABX₃ compositions to construct a map of perovskite formability with respect to each of the elements, A, B, and X, and identify new chemical spaces that are likely to form perovskite structures.