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simulations of innovative cell designs for key operating conditions. However, some parameters of the model are not easily accessible independently and the model must be validated by comparison with experiments. Predicting the distribution of Li is relevant because heterogeneous distribution of Li can have adverse effects on the LiB lifetime and performance (e.g., due to local overpotentials). Also, thicker electrodes are needed to improve the overall energy density, and larger electrical currents are needed for power performances (e.g., fast charging), yet these two effects will typically favour heterogeneous Li distribution.
In this study, simulations were performed and depth- resolved measurements were taken of the Li concentration in a 80-µm-thick electrode made of graphite, the most common anode material (Figure 64). Graphite is a layered material, and Li atoms can be reversibly hosted in the galleries formed between the stacked graphene sheets, forming stages (stage n meaning one gallery filled every n). This numerical model was based on the porous electrode formalism proposed by Newman . Such a model cannot describe phase transitions, yet it has already been shown to suitably simulate the electrochemical behaviour of LiB. In this case, the model predicted a triple succession of homogeneous and heterogeneous Li distribution across the thickness of the graphite electrode (Figure 65).
In order to confirm the predictions experimentally, an operando X-ray diffraction (XRD) electrochemical cell was developed and probed on ID13 (Figure 64a). Combined with the micron-sized beam available on the microfocus end-station, the high photon flux of ID13 and the fast and large 2D detector, the local XRD patterns were measured along the depth of the electrode in real-time. The different stage composition during the delithiation was unambiguously demonstrated. To obtain the local Li concentration, a statistical approach linking the mean distance between consecutive graphene sheets and the mean Li concentration was used.
For the lower concentrations, there was a remarkable match between the simulations and the measurements, with two successive homogeneous/heterogeneous Li distributions clearly observed. However, the heterogeneous Li distribution that was predicted to occur at the transition from stage 1 to stage 2 was not observed experimentally. This implies that the relative weights of transport in the electrolyte, insertion reaction at the graphite/electrolyte interface, and diffusion in the graphite have to be different in that range of Li concentration. The auto-catalytic or auto-inhibitory effect of asymmetrising the usual Butler- Volmer description of the exchange current at the electrode material interface has previously been shown . The exchange current in the high concentration range was thus
Fig. 64: a) Experimental setup at ID13.
b) Measured stage weight showing the successive lithiation stages during
delithiation as a function of depth and time.