Threefold Increase in the Young's Modulus of Graphite Negative Electrode during Lithium Intercalation

Density functional theory (DFT) is used to reveal that the polycrystalline Young's modulus (E) of graphite triples as it is lithiated to LiC6. This behavior is captured in a linear relationship between E and lithium concentration suitable for continuum-scale models aimed at predicting diffusion-induced deformation in battery electrode materials. Alternatively, Poisson's ratio is concentration-independent. Charge-transfer analyses suggest simultaneous weakening of carbon-carbon bonds within graphite basal planes and strengthening of interlayer bonding during lithiation. The variation in bond strength is shown to be responsible for the differences between elasticity tensor components, C-ij, of lithium-graphite intercalation (Li-GIC) phases. Strain accumulation during Li intercalation and deintercalation is examined with a core-shell model of a Li-GIC particle assuming two coexisting phases. The requisite force equilibrium uses different Young's moduli computed with DFT. Lithium-poor phases develop tensile strains, whereas Li-rich phases develop compressive strains. Results from the core-shell model suggest that elastic strain should be defined relative to the newest phase that forms during lithiation of graphite, and Li concentration-dependent mechanical properties should be considered in continuum level models.