Out-of-Plane Electron Transport in Graphite Intercalation Compounds with Applications in Battery Anodes
Authors: Jayaraman Amitesh S. , Kateris Nikolaos , Wang Hai 
Published: August 2024

Graphite intercalation compounds (GICs) are commonly used as anode materials for alkali metal-ion batteries, such as Li-ion and K-ion batteries. Although typically prepared as a low-stage intercalation compound (with a high concentration of the intercalating metal), over several electrochemical cycles, the distribution of intercalate within the graphite sample is expected to be non-uniform with domains of high-stage regions where the intercalant fraction is low [1]. The mechanism of interlayer electron transport in GICs strongly depends on the intercalation staging and temperature, and is expected to vary over the lifetime of a battery.

High-stage GICs and highly oriented pyrolytic graphite (HOPG), which is the upper limit of infinite-stage GIC, have an out-of-plane electrical conductivity that exponentially increases with temperature, whereas low-stage GICs have a conductivity that decreases as a function of temperature [2, 3, 4]. Although out-of-plane electron transport in low-stage GICs can be described by a metallic conduction model, the mechanism of out-of-plane electron transport in HOPG and high-stage GICs is a hitherto unresolved problem [5]. Out-of-plane electrical conductivity for HOPG and high-stage GICs increases exponentially with temperature, which cannot be described by metallic conduction, nor by conventional impurity or defect hopping mechanisms [6].

We propose a new mechanism of electron transport that takes place in HOPG and high-stage GICs at temperatures relevant to battery operation. Electrons are transferred between graphite and intercalant layers through tunneling that is enhanced by large amplitude out-of-plane phonon modes in graphite layers. Due to weak interlayer interactions in adjacent graphite layers, GICs can accommodate large amplitude phonon modes in the out-of-plane direction that locally enhance the interlayer electron tunneling probability. The tunneling enhancement is temperature dependent, and exponentially depends on the population of out-of-plane phonon modes excited at a given temperature. The expression for the conductivity 𝜎 for the phonon amplitude-driven tunneling mechanism as a function of temperature T is shown in Eq. 1; the exponential dependence of conductivity with temperature qualitatively agrees with experimental observations in HOPG and high-stage GICs. On a quantitative level, we also observe from Fig.1 that the theory agrees with experimental values for out-of-plane conductivity in HOPG.

The phonon amplitude-driven tunneling mechanism of electron transport is relevant in describing the kinetic over-potential in batteries that employ layered materials as anodes in ambient temperature operating conditions, and optimally sizing the anode accounting for both electron transport and ion diffusion rates.

References

[1] Weng, Suting, et al. Nanomicro Lett. 15.1 (2023): 1-12.

[2] McRae, E., and J. F. Mareche. J. Mater. Res. 3.1 (1988): 75-86.

[3] Phan, K., C. D. Fuerst, and J. E. Fischer. Solid State Commun. 44.9 (1982): 1351-1355.

[4] Blackman, L. C. F., J. F. Mathews, and Alfred Rene Jean Paul Ubbelohde. Proc. Math. Phys. Eng. Sci. 258.1294 (1960): 339-349.

[5] McRae, Edward, and Bertil Sundqvist. Mol. Cryst. Liq. Cryst. 340.1 (2000): 325-330.

[6] Sugihara, Ko. Phys. Rev. B 37.9 (1988): 4752.

[7] Uher, C., R. L. Hockey, and E. Ben-Jacob. Phys. Rev. B 35.9 (1987): 4483.

[8] Edman, Ludvig, et al. Phys. Rev. B 57.11 (1998): 6227.

Figure 1