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 $AB{\mathrm{O}}_3\text{−}{A}^{\prime }{B}^{\prime }{\mathrm{O}}_3$ 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 $A^{\prime }{B}^{\prime }{\mathrm{O}}_3$ along the $\left[110\right]$ direction.

• Received 9 October 2015
• Revised 4 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.144205