Intercalation in Li-ion batteries: thermodynamics and its relation to non-ideal solid-state diffusion

Abstract

Intercalation is the key phenomenon taking place in lithium-ion batteries: while its thermodynamics sets the equilibrium voltage of active materials, solid-state diffusion of intercalated lithium determines the rate at which the battery can operate. This study revisits the thermodynamics of intercalation by treating the active material as a binary mixture of filled and empty sites, thus relating the equilibrium potential to the chemical potential difference of intercalated lithium. By setting a reference to unitary activity at half state-of-lithiation, the non-ideal behaviour of the active material is quantified via a revisited form of the thermodynamic enhancement factor, revealing that common solid-solution cathode materials as LiNixMnyCo1-x-yO2, LiNi0.8Co0.15Al0.05O2, and LiCoO2 show strong super-ideal behaviour. The latter is related to the thermodynamic enhancement of the diffusion coefficient of intercalated lithium. A comprehensive overview of the functional forms of Li diffusion flux according to linear irreversible thermodynamics is provided and related to the chemical diffusion coefficient obtained by conventional characterisation techniques. A literature analysis made on solid-solution cathode active materials reveals that while the chemical diffusion coefficient varies significantly with state-of-lithiation, there exists a convenient functional form of diffusion flux according to linear irreversible thermodynamics that enables a fairly stable diffusion coefficient with state-of-lithiation. This has clear benefits from both modelling and experimental viewpoints and potentially sheds light on the mechanistic fundamentals of solid-state diffusion.