Modelling inhomogeneous lithium plating with a distributed equivalent circuit network

In lithium-ion batteries, lithium metal plating on graphite electrodes can be a significant problem. The metal can form dendrites that go through the separator and cause a short circuit, creating a safety hazard. Some of the plated lithium cannot be recovered and is permanently lost, reducing the capacity of the battery.

Many models of lithium plating already exist. However, most of these models assume that lithium plating can be completely prevented by keeping the graphite half-cell potential above 0 V, which experiments have shown to be incorrect [1]. Even those models that explicitly calculate how much lithium is plated do not account for inhomogeneities within the cell.

Distributed equivalent circuit network (DECN) models have been used before to predict thermal gradients within a cell [2]. However, they are normally parameterized using experimental measurements that do not track the internal variables required to predict lithium plating.

In this work, we parameterize a DECN model with the predictions of a validated pseudo-2D model computed using PyBaMM [3]. The pseudo-2D model tracks the graphite half-cell voltage and the changing stoichiometry of the graphite in addition to the full cell voltage and current. These two additional variables allow separate half-cell equivalent circuit network models to be parameterised. This has been done before, [4] but inhomogeneities in the cell were not considered.

The capability of observing the graphite half-cell potential allows this model to identify conditions where lithium plating is thermodynamically possible. While the graphite half-cell potential alone is not sufficient to predict the onset of lithium plating [1], the spatial resolution of the DECN allows high-risk regions of the cell to be located. These are found to be in regions of high current density near the tabs and low temperature regions. This is qualitatively in line with results from a distributed pseudo-2D model of cylindrical cells in the literature [5]. Our results show an average variation in graphite half-cell potential of 23 mV across the cell during a 2C charge under 10°C ambient conditions.

[1] Tao Gao et al., Joule, vol. 5 pp. 393-414, 2021.

[2] Shen Li et al., Journal of Power Sources, vol. 492, pp. 229594, 2021.

[3] Valentin Sulzer et al., Journal of Open Research Software, vol. 9, pp. 14, 2021.

[4] Tongzheng Zhao et al., International Journal of Energy Research, vol. 45, pp. 4155-4169, 2020.

[5] Johannes Sturm et al., Journal of the Electrochemical Society, vol. 167, pp. 130505, 2020.