Thermodynamics, stress, and Stefan-Maxwell diffusion in solids: application to small-strain materials used in commercial lithium-ion batteries

The life and performance of lithium-ion batteries are related to the mechanical expansion and contraction of the active materials. We develop a theory and commensurate equations to describe how lithium diffuses within host materials; our focus is clarifying the influence of stress on solid-state diffusion processes. Small-strain mechanics are combined with diffusion processes described by the Stefan-Maxwell equations. For the first time, to our knowledge, we compare host materials in which (a) both the host and lithium guest species diffuse with (b) the conventional approach based on guest (lithium) diffusion only. We describe the merits and weaknesses of our treatment with those that exist today, and we outline improvements to be addressed in subsequent work.