Assessing Thermodynamic Selectivity of Solid-State Reactions for the Predictive Synthesis of Inorganic Materials

Synthesis is a major challenge in the discovery of new inorganic materials. Currently, there is limited theoretical guidance for identifying optimal solid-state synthesis procedures. We introduce two selectivity metrics, primary and secondary competition, to assess the favorability of target/impurity phase formation in solid-state reactions. We used these metrics to analyze 3,520 solid-state reactions in the literature, ranking existing approaches to popular target materials. Additionally, we implemented these metrics in a data-driven synthesis planning workflow and demonstrated its application in the synthesis of barium titanate (BaTiO$_3$). Using an 18-element chemical reaction network with first-principles thermodynamic data from the Materials Project, we identified 82,985 possible BaTiO$_3$ synthesis reactions and selected nine for experimental testing. Characterization of reaction pathways via synchrotron powder X-ray diffraction reveals that our selectivity metrics correlate with observed target/impurity formation. We discovered two efficient reactions using unconventional precursors (BaS/BaCl$_2$ and Na$_2$TiO$_3$) that produce BaTiO$_3$ faster and with fewer impurities than conventional methods, highlighting the importance of considering complex chemistries with additional elements during precursor selection. Our framework provides a foundation for predictive inorganic synthesis, facilitating the optimization of existing recipes and the discovery of new materials, including those not easily attainable with conventional precursors.