The Newman model for phase-change electrodes: physics-based hysteresis

Many modern, commercially relevant Li-ion batteries use insertion materials that exhibit lithiation-induced phase change (e.g. lithium iron phosphate, LFP). However, the standard physics-based model—the Newman model—uses a microscopic description of particle lithiation (based on diffusion) that is incapable of describing phase-change behavior and the physical origins of the voltage hysteresis exhibited by such phase-change electrodes. In this work a simple and rational model of hysteretic lithiation (in an electrode comprised of an ensemble of phase-change nanoparticles) is derived using an approach based on minimisation of the Gibbs energy. Voltage hysteresis arises naturally as a prediction of the model. Initially, equations that model the phase-change dynamics in a single particle of active material are considered. These are generalised to a model, termed the composite phase-change model, of a coupled ensemble of particles in a thin electrode. The composite phase-change model is then incorporated into the framework of a classical Newman model, allowing for the inclusion of transport effects in the electrolyte and electrode conductivity. The resulting modified Newman model is used to predict voltage hysteresis in a graphite/LFP cell. A simulation tool that allows readers to replicate, and extend, the results presented here is provided via the DandeLiion simulator at www.dandeliion.com.