Learning Heterogeneous Reaction Kinetics from Images of Li-Ion Battery Nanoparticles

<br/>Nanoscale heterogeneity, which often controls the overall rate of electrochemical reactions, is notoriously difficult to measure or model. Here, we show that reaction kinetics and surface heterogeneity can be learned from operando scanning transmission X-ray microscopy (STXM) images of lithium iron phosphate (LFP) nanoparticles undergoing driven phase transformations in Li-ion batteries. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, PDE-constrained optimization, and uncertainty quantification, we extract the LFP free energy and local reaction rate, and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which we find closely matches the carbon-coating thickness profiles obtained through auger electron microscopy. The chemo-mechanical model is validated by ex-situ STXM and X-ray ptychography images. The 6.8% error between the learned model and over 180,000 pixels of image data is close to the experimental noise. Our results unlock the potential of learning nonequilibrium properties from image data that are difficult to measure in traditional electrochemical methods and offers a new non-destructive method of characterizing reactive surface heterogeneity.