(286d) Phase Transformation Dynamics in Lithium Iron Phosphate Nanoparticles
Lithium iron phosphate is a promising material for high-rate Li-ion battery cathodes, but its strong tendency for phase separation (into Li-rich and Li-poor regions) poses a significant challenge for mathematical modeling. Battery models focus on diffusion and reactions in dilute solutions, while phase transformation models usually consider closed bulk systems, without coupling to (Faradaic) reaction kinetics at surfaces. We have developed a unified approach to phase transformation dynamics driven by Faradaic insertion/extraction reactions, based on the Cahn-Hilliard equation with (modified) Butler-Volmer boundary conditions. In the limit of strong crystal anisotropy, suitable for LixFePO4 nanoparticles, the model reduces to a nonlinear generalization of the Allen-Cahn equation for phase transformations in an open system, driven by the local overpotential. The theory predicts new phenomena, such as layer-by-layer phase-transformation waves (?domino-cascade?), current-dependent overshoot of the voltage plateau, and nonlinear interactions between phase transforming nanoparticles in composite electrodes, consistent with experiments. The latter effect allows us to fit recent data for ultrafast battery materials with only one parameter (the ?wave resistance?), given the observed particle size distribution. This suggests a new means to enhance rate capability, by optimizing not only the average structure of the porous electrode (porosity, mean pore size, etc.) but also the geometrical fluctuations.