Correlations between transition temperature, tolerance factor and cohesive energy in 2+:4+ perovskites

Cohesive energies were calculated ab initio for a range of simple 2+:4+ perovskites (A(2+)B(4+)O(3)). Correlations were sought between the sets of lattice parameters, cohesive energies, cubic transition temperatures and Goldschmidt tolerance factors for these compounds. There is a noticeable correlation (R = -0.60) between the transition temperatures and the tolerance factors, but only weak relationships between the cohesive energy and the other parameters. However, for more than half the set of compounds, there is a strong correlation (R = 0.989), in the form of a simple linear trend between the tolerance factor and the ratio of cubic transition temperature to cohesive energy density. The remaining compounds form two distinct clusters and either retain cubicity down to 0 K or undergo transitions to lower symmetry at substantially lower temperatures than might be expected from the trend.