Electrochemical diffusion signatures of solid-solution and phase-separating active materials in Li-ion batteries

The working principle of lithium-ion batteries lies in the intercalation of lithium ions in electrode active materials, which exhibit either solid-solution or phase-separating behaviour. This study presents a comparative analysis of the electrochemical responses of these two classes of active materials using a multi-particle phase-field model, the structure and description of which are designed to promote easy interpretation by non-modelling experts. Current pulses and open-circuit relaxations, such as those in the galvanostatic intermittent titration technique (GITT), are simulated for different solid-state diffusion coefficients and particle size distributions. The distinct electrode potential responses are explained through the dynamic intra- and inter-particle lithium distributions and their interplay with active material thermodynamics. In solid-solution active materials, numerical results indicate that the solid-state diffusion coefficient tends to be underestimated by the GITT. In phase-separating active materials, current pulses instead generate a shrinking-core lithium distribution along the particle radius (e.g. the Li-rich phase at the particle surface and the Li-poor phase at the particle centre), so that only the phase nucleated at the particle surface can be electrochemically probed in terms of its diffusion and kinetic properties. Such a shrinking-core distribution represents a quasi-equilibrium configuration for a phase-separating active material, resulting in fast electrode potential relaxation upon current interruption and impeding any inter-particle lithium exchange. In fact, while small particles lithiate faster for both active materials during current pulses, the rest phases enable lithium homogenisation among the particles of a solid-solution active material, which can be adequately simulated using a single equivalent particle radius. In contrast, the absence of inter-particle lithium exchange at open circuit in phase-separating active materials may result in over-lithiation of small particles. This poses limitations to single-particle modelling for phase-separating active materials and highlights the need for carefully calibrated rest phases in pulse fast-charging protocols to facilitate inter-particle lithium exchange when the electrode is in an out-of-equilibrium configuration.