Thermal stabilities Landscape of A$_2$BB$^{\prime}$O$_6$ compounds

Perovskite oxides have been extensively studied for their wide range of compositions and structures, as well as their valuable properties for various applications. Expanding from single perovskite ABO$_3$ to double perovskite $A_2BB^{\prime}$O$_6$ significantly enhances the ability to tailor specific physical and chemical properties. However, the vast number of potential compositions of $A_2BB^{\prime}$O$_6$ makes it impractical to explore them all experimentally. In this study, we conducted high-throughput calculations to systematically investigate the structures and stabilities of 4,900 $A_2BB^{\prime}$O$_6$ compositions (with $A$ = Ca, Sr, Ba, and La; $B$ and $B^{\prime}$ representing metal elements) through over 42,000 density functional theory (DFT) calculations. Our analysis lead to the discovery of more than 1,500 new synthesizable $A_2BB^{\prime}$O$_6$ compounds, with over 1,100 of them exhibiting double perovskite structures, predominantly in the $P2_1/c$ space group. By leveraging the high-throughput dataset, we developed machine learning models that achieved mean absolute errors of 0.0444 and 0.0330 eV/atom for formation energy and decomposition energy, respectively. Using these models, we identified 803 stable or metastable compositions beyond the chemical space covered in our initial calculations, with 612 of them having DFT-validated decomposition energies below 0.1 eV/atom, resulting in a success rate of 76.2 \%. This study delineates the stability landscape of $A_2BB^{\prime}$O$_6$ compounds and offers new insights for the exploration of these materials.