Simple Stochastic Model of Multiparticle Battery Electrodes Undergoing Phase Transformations

Incorporation of ions into battery electrodes can lead to phase transformations. When multiparticle phase-transforming electrodes charge or discharge, two processes must occur in each particle: the new phase must nucleate, and then grow until the particle is fully charged or discharged. A fundamental question is which of these two processes is rate limiting. Here we construct a simple stochastic model that shows how the relative rate of nucleation compared with growth determines the particle state-of-charge distributions in the electrode. We find that the number of particles that are partially charged at any time increases as the relative nucleation rate increases. The maximum number of particles that are actively charging occurs just before the time when the first particles are becoming completely charged. By comparing measured state-of-charge distributions with the model, we determine the relative rate of nucleation. We apply this procedure to measurements of the evolution of particles in LiFePO4 cathodes and show we can account for the particle state-of-charge distribution as a function of the electrode state of charge