Considering anisotropic diffusion in the active material in charging simulations
Recreating the effect of graphite grain orientation
Microstructure simulations with BatteryDict in GeoDict recreate the micro-resolved ion fluxes and lithium concentration changes within the battery electrode under various charging profiles (constant charging rate, constant current, constant voltage).
Common battery active materials, such as graphite, exhibit a strong directional dependence in lithium ion diffusion due to their atomic structure. For example, in graphite, the diffusion along the graphene planes of covalently bonded carbon atoms (Dpara = 4.4E-10 m²/s) is 6 orders of magnitude higher than perpendicular to the graphene planes (Dperp = 8.7E-16 m²/s) [1].
Thus, lithium ion transport within a single graphite grain practically takes place only along the graphene planes. In fact, ion transport perpendicular to the graphene planes can be neglected.
GeoDict makes it possible to take into account the interaction of anisotropic diffusion properties with the microstructure of the electrode during the charging and discharging process. For this purpose, the graphite grains are simulated with a stripe pattern consisting of two different material IDs. BatteryDict's simulation model automatically ensures that ion exchange between the different material IDs in the active material is prevented, i.e. that an ion flux perpendicular to the stripe pattern cannot occur.
GeoDict's structure generators create such a striped microstructure with just a few mouse clicks. For each elliptical graphite grain, the stripe pattern prevents diffusion along the short axis, i.e. perpendicular to the graphene planes.

The effect of direction-dependent diffusion in graphite is observed in the result of the charging simulation. This example shows lithiation of the graphite electrode shown in Fig. 1 at a charging rate of 2C until a cut-off voltage of 0.01 V.
Taking into account the anisotropic diffusivity of graphite using the striped structure (blue line), the charging simulation shows a faster drop in electrode potential vs. Li/Li+ during lithiation than a comparative simulation in which the diffusivity of graphite is considered isotropic (red line).
![Fig. 4 Line pattern representing anisotropic diffusion in BatteryDict on the scan of a structured graphite electrode from the publication [2].](/fileadmin/_processed_/9/a/csm_Fig4-ResultComparisonScan_adc0163122.webp)
An effect of the anisotropic diffusion on the charging curve is also observed on such a structure. Fig. 4 shows the BatteryDict simulation results, comparing the electrode potentials at a charge rate of 2C. The electrode potential is lower when the anisotropic diffusivity is taken into account (blue line).
As in Example 1, the lithiation of the scanned graphite electrode is more inhomogeneous when the anisotropic diffusivity is considered, which means that the electrode potential drops already at lower transferred capacities compared to isotropic diffusivity.
References:
[1] K. Persson et al., “Lithium Diffusion in Graphitic Carbon,” J. Phys. Chem. Lett., vol. 1, no. 8, pp. 1176–1180, Apr. 2010, doi: 10.1021/jz100188d.
[2] J. Sandherr et al., “Micro embossing of graphite-based anodes for lithium-ion batteries to improve cell performance,” Journal of Energy Storage, vol. 65, p. 107359, Aug. 2023, doi: 10.1016/j.est.2023.107359.