Analysis of electrostatic stability and ordering in quaternary perovskite solid solutions

There are three distinct classes of perovskite structured metal oxides, defined by the charge states of the cations: ${A}^{\text{I}}{B}^{\text{V}}{\mathrm{O}}₃,{A}^{\text{II}}{B}^{\text{IV}}{\mathrm{O}}₃$, and ${A}^{\text{III}}{B}^{\text{III}}{\mathrm{O}}₃$. We investigated the stability of cubic quaternary solid solutions $AB{\mathrm{O}}₃\text{\ensuremath{-}}{A}^{\ensuremath{'}}{B}^{\ensuremath{'}}{\mathrm{O}}₃$ using a model of point-charge lattices. The mixing enthalpies were calculated and compared for the three possible types of combinations of the compounds, both for the random alloys and the ground-state-ordered configurations. The mixing enthalpy of the (I,V)${\mathrm{O}}₃$-(III,III)${\mathrm{O}}₃$ alloy is always larger than the other alloys. We found that, different from homovalent alloys, for these heterovalent alloys a lattice constant mismatch between the constituent compounds could contribute to stabilize the alloy. At low temperatures, the alloys present a tendency to spontaneous ordering, forming superlattices consisting of alternated layers of ${AB\text{O}}₃$ and ${A}^{\ensuremath{'}}{B}^{\ensuremath{'}}{\mathrm{O}}₃$ along the $[110]$ direction.