Discharge Model for the Lithium Iron-Phosphate Electrode

Abstract

This paper develops a mathematical model for lithium intercalation and phase change in an iron phosphate-based lithium-ion cell in order to understand the cause for the low power capability of the material. The juxtaposition of the two phases is assumed to be in the form of a shrinking core, where a shell of one phase covers a core of the second phase. Diffusion of lithium through the shell and the movement of the phase interface are described and incorporated into a porous electrode model consisting of two different particle sizes. Open-circuit measurements are used to estimate the composition ranges of the single-phase region. Model-experimental comparisons under constant current show that ohmic drops in the matrix phase, contact resistances between the current collector and the porous matrix, and transport limitations in the iron phosphate particle limit the power capability of the cells. Various design options, consisting of decreasing the ohmic drops, using smaller particles, and substituting the liquid electrolyte by a gel are explored, and their relative importance discussed. The model developed in this paper can be used as a means of optimizing the cell design to suit a particular application.

Current-induced transition from particle-by-particle to concurrent intercalation in phase-separating battery electrodes

“…We obtain good fits, with an of 0.2 and a of 0.6 A m -2 , yielding an average exchange current density of ~ 0.3 A m -2 . The exchange current density is higher than most reported values in literature; however, past work did not consider the active particle fraction and likely overestimated the active reaction area [20][21][22][23] . The fittings may also be affected by departures from Butler-Volmer kinetics at high rates that that lead to curved Tafel plots and small effective values of 27 .…”

“…Dreyer et al proposed that the thermodynamic origin of this behaviour arises from the non-monotonic chemical potential of Li as a function of the particle's composition 17 . On the other hand, a concurrent intercalation pathway, whereby most particles intercalate at once, has also been observed in LFP 18,19 .Despite its crucial importance, the active population has been largely neglected in models describing electrode cycling [20][21][22][23] . Differing approximations in the active population may have contributed to the vast range of experimentally-measured specific exchange current densities, which range from 10 -6 A m -2 to 10 -1 A m -2 in LFP [20][21][22][23] .…”

Toward Low-Cost, High-Energy Density, and High-Power Density Lithium-Ion Batteries

“…Many different designs have been suggested, including graded-porosity and hierarchical architectures, 67,[72][73][74][75][76] and several simulations have shown that smaller active material particles can help decrease the polarization and capacity loss observed at high discharge rates by shortening the Li-ion diffusion path in the particles. 68,71,77 Yet, particle size variations also affect the packing structure of the electrode and can result in different pore sizes and distributions, as well as in differences in the contact resistance between the electrode and the current collector. These variations could be leveraged to improve transport properties and battery performance.…”

In operando tracking phase transformation evolution of lithium iron phosphate with hard X-ray microscopy

“…For example, the domino-cascade model was confirmed experimentally with LiFePO 4 /FePO 4 precession electron diffraction 19 . The shrinking-core mechanism was also developed by a mathematical model 20 . On one hand, the above conflicting mechanisms and disagreement may be attributed to confusion over the specific experimental condition.…”