Fig. 2: Battery modeling and phase transitions.
From: Accelerating the transition to cobalt-free batteries: a hybrid model for LiFePO4/graphite chemistry
Lithium-ion battery schematic (a). Electrodes are composed of multiple particles which differ in shape and size. The physics-based model is formulated by approximating the battery’s positive and negative electrodes as two spherical particles (b). x and r indicate the Cartesian and radial coordinates, respectively. The thicknesses of negative particle, separator, and positive particle domains are Ln, Ls, and Lp, respectively. Phase transitions experienced by the positive particle during a discharge from 100% to 0% SOC are shown in c. The positive particle is first initialized at a concentration \({\theta }_{{{{\rm{p}}}}}^{{{{\rm{bulk}}}}} \,<\, {\theta }_{{{{\rm{p}}}}}^{\alpha }\) (one-phase), then, it transitions to a two-phase region where the lithium solid phase concentration is described by the core-shell paradigm, and finally, the particle returns to one-phase for \({\theta }_{{{{\rm{p}}}}}^{{{{\rm{bulk}}}}} \,>\, {\theta }_{{{{\rm{p}}}}}^{\beta }\) and stays in this phase until 0% SOC is reached.
