Uncertainty Quantification of First Principles Computational Phase Diagram Predictions of Li-Si System Via Bayesian Sampling

Abstract

In this work, an assessment of the CALPHAD method trained on only density functional theory (DFT) data is performed for the Li-Si binary system, as a case study. Using a parameter sampling approach based on the Bayesian Error Estimation Functional (BEEF-vdW) exchange-correlation potential. By using built-in ensemble of functionals from BEEF-vdW, the uncertainties of the Gibbs Free Energy fitting parameters are obtained and can be propagated to the resulting phase diagram. To find the best fitting form of the CALPHAD model, we implement a model selection step using the Bayesian information criterion (BIC). Applying the best selected CALPHAD model from the DFT calculation, to other sampled BEEF functionals, an ensemble of CALPHAD models is generated leading to an ensemble of phase diagram predictions. The resulting phase diagrams are then compiled into a single-phase diagram representing the most probable phase predicted as well as a quantitative metric of confidence for the prediction. This treatment of uncertainty resulting from DFT provides a rigorous way to ensure the correlated errors of DFT is accounted for in the estimation of uncertainty. From the phase diagram, we have determined intercalation voltages for lithiated silicon. In combination, we can generate a better understanding of the phase transitions and voltage profile to make a more analysis-informed prediction for experiments and the performance of Si-anodes within batteries.