Stability and amphotericity analysis in rhombohedral ABO<inf>3</inf> perovskites

Perovskite structures (ABO3) exhibit several desirable physical properties. These properties relate closely to composition and structure. For instance, structural distortions such as off-centering of B-site cation and/or tilting of BO6 polyhedra allow tuning of properties. Notably, the tilting of BO6 polyhedra yields a rhombohedral structure. This structure is increasingly relevant for functional perovskites. However, there exists no predictive approach thus far that allows for stability analysis in rhombohedral perovskites, and the determination of amphotericity domains for dopants. Here, we derive a tolerance factor equation (tR) that works well for the rhombohedral ABO3 perovskites. The predictive capability of the equation is benchmarked using sodium bismuth titanate (NBT), as a case in point. Using tR, we determined the following rare-earth doping trends in NBT: La to Nd occupy A-site; Tm to Lu go to B-site; and intermediate ions (Sm to Er) occupy both the sites (i.e., show amphotericity). The approach is consistent with experimental literature and hence benchmarked duly. The tolerance factor based analysis described here is hence plausibly relevant for the broader category of rhombohedral perovskites. In fact, it would be useful for accelerated prediction and determination of (a) stable rhombohedral structures, and (b) amphoteric dopants.