Researchers at University College London, UK, have reassessed the validity of the 'tolerance factor' (a decades-old indicator for the stability and distortion of crystal structures), used in predicting new hybrid perovskite structures. The results of their work may cast shadows on the optimism that surrounds perovskites' future uses.

Recent studies out of Cambridge University showed that the tolerance factor approach worked well at assigning radii to organic ions in a wide range of hybrid perovskites. They suggested that there could be more than 600 undiscovered hybrid perovskites. The UCL team was interested in whether the tolerance factor approach was still valid for halide perovskites suitable for solar cells. The chemical properties of the heavy iodide anions in these structures are very different to the hard atomic spheres assumed in tolerance factor calculations. The results suggested that ‘the tolerance factor simply doesn’t work for iodide perovskites.’

Although the researchers located a number of iodide compounds in the literature with the right atomic composition to be perovskites, the UCL team found that the tolerance factor couldn’t identify which ones formed stable perovskites. In this case, it's unlikely that this model could predict the stability of undiscovered compounds. The team identified two main problems with the tolerance factor approach. First, the ionic radii used in the calculations are based on metals bonded to hard, electronegative ions such as oxide and fluoride. They do not closely represent metal ions bonded to heavier anions such as iodide that show greater covalency.

Instead, the team adapted the tolerance factor approach to account for the chemical and physical differences of heavier halides. They calculated average metal–halide bond lengths for 17 metals from known structures in the Inorganic Crystal Structure Database, determining specific ionic radii for each metal ion when bonded to each halide anion.

The second problem is that iodide anions leave large octahedral spaces to fill in the crystal structure. ‘This normally isn’t a problem for small oxide and fluoride anions, but for very large iodide anions you need a large metal ion to fit into the octahedral hole.’ Smaller metal ions don’t form stable perovskites with the right electronic properties for solar cells.

By plotting the adapted tolerance factor for each perovskite structure against an octahedral factor that accounts for the required structural geometry of the metal ions, the team defined a stable zone for halide perovskites.

It seems that ‘Only a handful of metals are able to form iodide perovskites.’ This includes structures based on lead, whose toxicity is part of the reason for the search for new hybrid perovskites. Some others yield only very air-sensitive compounds. Instead of the vast number of ion combinations previously expected, there appears to be limited scope for discovering new halide perovskite materials for solar cells.

The Cambridge team responded that the UCL treatment ‘shows that it is necessary to assign smaller, anion-dependent radii when lead and other metals are combined with halides. The new sets of cation radii yield tolerance factors that account remarkably well for most of the known hybrid perovskite halides. As such, it is an important advance in this exciting field.’