Generalized trends in the formation energies of perovskite oxides

Generalized trends in the formation energies of several families of perovskite oxides (ABO3) and plausible explanations to their existence are provided in this study through a combination of DFT calculations, solid-state physics analyses and simple physical/chemical descriptors. The studied elements at the A site of perovskites comprise rare-earth, alkaline-earth and alkaline metals, whereas 3d and 5d metals were studied at the B site. We also include ReO3-type compounds, which have the same crystal structure of cubic ABO3 perovskites except without A-site elements. From the observations we extract the following four conclusions for the perovskites studied in the present paper: for a given cation at the B site, (I) perovskites with cations of identical oxidation state at the A site possess close formation energies; and (II) perovskites with cations of different oxidation states at the A site usually have quite different but ordered formation energies. On the other hand, for a given A-site cation, (III) the formation energies of perovskites vary linearly with respect to the atomic number of the elements at the B site within the same period of the periodic table, and the slopes depend systematically on the oxidation state of the A-site cation; and (IV) the trends in formation energies of perovskites with elements from different periods at the B site depend on the oxidation state of A-site cations. Since the energetics of perovskites is shown to be the superposition of the individual contributions of their constituent oxides, the trends can be rationalized in terms of A-O and B-O interactions in the ionic crystal. These findings reveal the existence of general systematic trends in the formation energies of perovskites and provide further insight into the role of ion-ion interactions in the properties of ternary compounds.