A Volume Averaged Approach to the Numerical Modeling of Phase-Transition Intercalation Electrodes Presented for Li_xC₆

An approach for the volume averaged numerical modeling of phase-transition intercalation electrodes is presented for lithiated graphite, Li x C 6 , in lithium-ion batteries. The proposed method directly treats phase formation and growth through a modified form of the Avrami equation enabling the physics-based mathematical model to capture the additional time constant observed in the two phase regions of lithiated graphite as well as a portion of the hysteresis commonly observed between charge and discharge voltage. The graphite phase diagram was taken to be composed of three stages, or phases, each with a Nernstian or ideal solution based equilibrium potential function. The behavior of the potential rise from a current pulse in the two-phase region is matched well with this methodology resulting in higher valued diffusion coefficients than found when only a single-phase approach is used. Simulated results for mesocarbon microbeads show the co-existence of all three phases within the electrode during higher rate discharges. Concentration dependent diffusion coefficients are found to be necessary to match experimental results at rates significantly higher than 1C. The model is shown to be capable of exhibiting core-shell behavior when fitted phase-transformation rate constants are sufficiently high in value, although not observed for MCMB.