Mechanics-modified equilibrium potential for linear-elastic electrode materials

Abstract

There is inconsistency in how the mechanics-modified equilibrium potential is constructed in the literature for solid-state batteries; both hydrostatic and surface-normal stresses have been employed. We attempt to resolve this by deriving equilibrium-potential expressions for a linear-elastic electrode material deposited on a solid electrolyte under three different loading conditions: (1) working electrode under out-of-plane uniaxial compression, (2) solid electrolyte under in-plane uniaxial compression, and (3) solid electrolyte under pure shear. Our analysis, which starts from full tensorial stress and strain descriptions specifically at the isothermal electrode/electrolyte interface, indicates that the hydrostatic stress is a more general and widely applicable choice. The deviatoric contribution that the full tensor treatment considers is shown to be practically negligible, making the hydrostatic stress an excellent approximation for battery-modeling purposes. Furthermore, our analytical expressions depend on the mechanical properties of the constituent electrode and electrolyte (i.e., their elastic moduli and Poisson's ratios); no such explicit dependence has been fleshed out previously for experimentally relevant systems. COMSOL simulation results are provided to verify the validity of the analytical expressions, and correction factors are introduced to extend their use to more practical systems. Finally, a cantilever-beam experiment is suggested to help validate our proposed use of the hydrostatic stress more explicitly.