Investigation of charge transfer models on the evolution of phases in lithium iron phosphate batteries using phase-field simulations

Abstract

Charge transfer is essential for all electrochemical processes, such as in batteries where it is facilitated through the incorporation of ion–electron pairs into solid crystals. The low solubility of lithium (Li) in some of these host lattices cause phase changes, which for example happens in FePO₄. This results in the growth of interfacial patterns at the mesoscale between a Li-poor and Li-rich phase, FePO₄ and LiFePO₄ respectively. Conventionally, the effect of charge transfer on the evolution of these phases is usually modelled using the Butler–Volmer equation. However, the exponentially increasing current–overpotential relation in this formalism becomes problematic for battery systems operating under high currents. In this study, we implement a phase-field model to investigate two electrochemical reaction models: the Butler–Volmer and the Marcus–Hush–Chidsey formulation. We assess their effect on the spatial and temporal evolution of the FePO₄ and LiFePO₄ phases. Both reaction models demonstrate similar microstructural patterns in equilibrium. Nevertheless, a significant increase in current density is caused by using the Butler–Volmer expression, leading to an accelerated reaction rate at high overpotentials and an exaggerated delithiation. Furthermore, we show that including anisotropic elastic strain fields in the phase-field model accelerates the delithiation process, reaching the bulk mass transport limitation faster. These elastic effects, when included in the overpotential, can cause the current density to exceed its limits, a problem inherently mitigated by the Marcus–Hush–Chidsey model.