Fig. 1: Schematic representation of approach for predicting aqueous-solution-based synthesis conditions.

a, Generation of the hypothesis: conditions where the target phase experiences minimum thermodynamic competition from other phases are favoured for synthesis. Upper: the 2D plot depicts this general concept. The different coloured lines represent the energy of various phases. The green line represents the desired target phase; the other lines depict the energies of competing phases. Double-headed arrows between the lines illustrate the difference in free energy between the desired target phase and the minimum free energy among all competing phases, which is the thermodynamic competition denoted as ΔΦ. The solid arrow indicates the MTC, and stars denote the conditions at which MTC is achieved. The projection of the phases with the lowest energy under different conditions forms the thermodynamic phase diagram, with the stability regions of phases indicated by blocks of corresponding colours. Lower: the 3D plot represents the energy landscape of thermodynamic competition in a multidimensional Pourbaix system. The dotted line axes represent the high-dimensional aspect for the other conditions. b, Predictive synthesis: minimizing thermodynamic competition to predict synthesis conditions. E, redox potential. c, Hypothesis testing: large-scale analysis based on the text-mined dataset and detailed investigation of LiIn(IO₃)₄ and LiFePO₄.