Graphite, serving as the lithium host structure, is still the main component of the anode active material in today's commercial lithium-ion batteries [1]. Yet, the determination of solid diffusion coefficient of lithium in graphite has so far proved difficult, which is reflected by the observation that the values published in the literature vary over several orders of magnitude, which is likely due to the structural and phase-related complexity of the lithium intercalation kinetics in graphite, as well as the heterogeneity of the samples studied [2, 3].

To address the latter point, our study aims to examine the lithiation of a highly oriented pyrolytic carbon (HOPG) disk, in which the basal planes are oriented normal to the disk height. In a first approach, we followed the lithiation of an HOPG disk by in‑situ optical monitoring of the radial movement of the golden LiC₆ phase in top-view images of the HOPG crystal (see left panel of Figure 1a), as was done previously by Guo et al. [3]. This was compared to a subsequent post-mortem analysis by splitting the HOPG disk along its height (see right panel of Figure 1a), clearly illustrating that the apparent LiC₆ phase movement suggested by top-view images is mostly an artefact caused by HOPG crystal imperfections and that the LiC₆ phase front position can only be quantified from the post-mortem analysis of split crystals. Based on the latter analysis approach, we show that the LiC₆ phase ring thickness for different intercalation times and temperatures can be well described using a model based on Fickian diffusion in cylindrical geometry by defining a concentration ratio c/c₀ for the appearance of the golden phase between 0.7-0.8, as shown in Fig. 1b [4]. Within this model framework, an apparent diffusion coefficient of the LiC₆ phase of D₀=0.7-1.4×10^-13 [m²/s] at 25°C can be determined, with an activation energy of E_a=36.5-37.1 [kJ/mol]_.

References:

[1] J. Asenbauer, T. Eisenmann, M. Kuenzel, A. Kazzazi, Z. Chen, D. Bresser, Sustainable Energy & Fuels 2020 4(11), 5387-5416.

[2] K. Persson, V. A. Sethuraman, L. J. Hardwick, Y. Hinuma, Y. S. Meng, A. Van Der Ven, V. Srinivasan, R. Kostecki, G. Ceder, J. Phys. Chem. Lett. 2010, 1(8), 1176-1180.

[3] Y. Guo, R. B. Smith, Z. Yu, D. K. Efetov, J. Wang, P. Kim, M. Z. Bazant, L. E. Brus, J. Phys. Chem. Lett. 2016, 7(11), 2151-2156.

[4] J. Crank, The Mathematics of Diffusion, Oxford university press, 1979.

Figure 1 a) Lithiation of an HOPG disk, in which the basal planes are oriented normal to the disk height. Comparison of top view (left, obtained during in-situ lithiation experiment), vs bulk view (right, obtained after splitting it open during post-mortem) of the same HOPG disk, demonstrate the need to do post-mortem analysis of split crystal to have artefact-free penetration depth of the LiC₆ phase front into the HOPG b) graph comparing the growth of golden ring (LiC₆ phase) using Fickian diffusion in cylinder (lines) to experimental data (denoted by ×) at different intercalation times and temperatures.