Mechanical behaviour of inorganic solid-state batteries: can we model the ionic mobility in the electrolyte with Nernst-Einstein's relation?

Inorganic solid-state lithium-metal batteries could be the next-generation batteries owing to their non-flammability and higher specific energy density. Many research efforts have been devoted to improving the ionic conductivity of inorganic solid electrolytes. For a wide range of electrolytes including liquid and solid polymer electrolytes, an independent measurement or calculation of both electrolyte conductivity and diffusion coefficient is often time-consuming and challenging. As a result, Nernst-Einstein's relation has been used to relate the ionic conductivity to ionic diffusivity after the determination of either parameter. Although Nernst-Einstein's relation has been used for different electrolytes, we demonstrate in this perspective that this relation is not directly transferable to describe the ionic mobility for many inorganic solid electrolytes. The fundamental physics of Nernst-Einstein's relation shows that the relationship between the diffusion coefficient and electrolyte conductivity is derived for ionic mobility in a viscous or a gaseous medium. This postulation contradicts state-of-the-art experimental studies measuring the mechanical behaviour of inorganic solid electrolytes, which show that inorganic solid electrolytes are usually brittle rather than viscoelastic at ambient room temperature. The measurement of loss tangent is required to justify the use of Nernst-Einstein's relation. The outcome of such measurement has two implications. First, if the loss tangent of inorganic solid electrolytes is less than unity in the range of batteries operating temperatures, the impacts of using Nernst-Einstein's relation in modelling the ionic mobility should be quantified. Secondly, if the measured loss tangent is comparable to that of solid polymers and lithium metal, inorganic solid electrolytes may behave in a viscoelastic manner as opposed to the brittle behaviour usually suggested. The fundamental physics of Nernst-Einstein's relation assumes that the electric force is in equilibrium with the viscous force, which is not necessarily compatible with the mechanical properties of a brittle inorganic solid electrolyte.