Intercalation Pathway in Graphite Particles Analyzed with a Multi-Layer Phase Field Model
Authors: Cordoba Antoine , Chandesris Marion , Plapp Mathis 
Published: February 2024

Graphite is today the most common negative electrode material in commercial cells, alone or blended with silicon, thanks to its relatively high specific capacity of 372 mAh·g−1, its excellent cycling stability, its low thermodynamic potential, and relatively low cost compared to alternative materials. The increase in the energy densities, power capabilities, and durability of lithium-ion batteries using this conventional cost-effective active material is possible through an optimization of the electrode and material designs. Such optimization requires, however, knowledge of the fundamental mechanisms that govern both the lithium transport inside graphite particles and the electrochemical transfer at the electrolyte / active material interface.
Graphite has an ideal lamellar structure made of graphene sheets. During intercalation, the lithium atoms insert between the graphene planes, with almost no lithium transport across the graphene sheets. The interactions between lithium atoms in adjacent galleries leads to the formation of structures with filled layers separated by a number of empty layers, known as stages. Given this phenomenon, graphite active material undergoes phase separation between successions of several stable phases during lithium intercalation. This staging phenomenon influences the critical properties of graphite like its equilibrium potential, lithium diffusion or lithium insertion kinetics.
In the present work, we use a Cahn-Hilliard type model, adapted to multi-layered materials1 and study the influence of the parameters in the underlying free-energy models. We focus first on the intra-layer and inter-layer lithium interaction contributions. Free-energy models with increasing complexity of inter-layer interactions are introduced and discussed based on their corresponding phase diagrams. In particular, we show that occurrence of fractional 3/2 stage, observed for potassium or rubidium intercalation in graphite at high pressure, requires an interlayer interaction effective at second neighbor, while a continuous screening effect of the intercalant is necessary to predict the occurrence of stages greater than 2 without the occurrence of the fractional 3/2 stage, as observed for lithium2.
The kinetics of stage formation and evolution is also greatly affected by the interaction parameters of the free-energy model. A linear stability analysis (LSA) is performed to investigate the impact of the free energy model parameters on the stage formation dynamics and growth rates. In particular, the LSA shows that stage 2 grows the fastest, even for low lithium filling fraction. In accordance with this result, simulations of spinodal decomposition from moderate homogeneous lithium filling fraction (c=0.3) shows the formation of stage 2 at early times before an evolution towards stage 3 (See figure 1). This higher growth rate of stage 2 seems to have an impact on lithium intercalation pathway. Indeed, during simulations of lithium intercalation in a graphite particle at different C-rates, stage 2 tends to form very early at the electrolyte/particle interface, even when stage 3 and dilute stage 1 dominates inside the particle. The simulation of lithium intercalation also provides access to the effective exchange current density as function of the averaged surface concentration. The presence of the stages at the surface of the particles directly affects this averaged exchange current density. It results in non-symmetric exchange current density profiles, in coherence with operando X-ray micro-diffraction measurement in thick graphite electrodes3.
Figure 1: Snapshots of a spinodal decomposition at different times. The initial average filling fraction is c=0.3 and the system has six layers. For each subfigure, top: lithium content in each layer, bottom: coefficients of the Fourier transform used to track the stages

Smith, R. B. et al. Intercalation Kinetics in Multiphase-Layered Materials. J. Phys. Chem. C 121, 12505–12523 (2017).

Chandesris, M., et al. Thermodynamics and Related Kinetics of Staging in Intercalation Compounds. J. Phys. Chem. C 123, 23711–23720 (2019)

Tardif, S. et al. Combining operando X-ray experiments and modelling to understand the heterogeneous lithiation of graphite electrodes. J. Mater. A 9, 4281–4290 (2021)

Figure 1