A Bayesian method for selecting data points for thermodynamic modeling of off-stoichiometric metal oxides

Abstract

Thermodynamic characterization of metal oxide reduction/re-oxidation plays a vital role in material identification and optimization of many chemical processes. However, this characterization generally requires significant data collection (spanning several hundred T, pO₂, and composition (X) combinations) to appropriately sample phase space and identify key inflection zones that are not known a priori and are missed without sampling on a fine mesh grid of T, pO₂, and X combinations. Here we have coupled our previously reported CrossFit compound energy formalism algorithm for reduction/re-oxidation thermodynamic model fitting with Bayesian Inference techniques to build an optimized data selection scheme. Using the Ba_xSr_1−xFeO_3−δ system as a proof of concept, we show that our Bayesian data selection technique required less than half (44) data points to achieve the same accuracy as a mesh grid of 100 T, pO₂, and X point combinations. Our method has errors of <2 kJ mol⁻¹ in reduction enthalpy and <3 J (mol⁻¹ K⁻¹) difference in reduction entropy compared to the full data set. Further, 20 instances of a set of 44 randomly selected T, pO₂ and X data points only reproduced the ground truth model 5% of the time, demonstrating the power of our approach. Our method offers a human free, physically informed, data collection approach and paves the way for a high-throughput active data selection process for metal oxide reduction/re-oxidation thermodynamics.