Laplace-Fourier transform solution to the electrochemical kinetics of a symmetric lithium cell affected by interface conformity

Lithium (Li)-metal batteries using solid-state electrolytes (SSEs) have attracted extensive attention owing to their high energy density. However, the interface issues arising from the Li stripping/plating cycles pose a major challenge for the applications of these batteries. This paper reports a three-dimensional (3D) time-dependent electrokinetic model, built based on the Nernst–Planck equation with electroneutrality assumption, to quantify the effects of interface conformity, external pressure, electrolyte Young's modulus, and ionic conductivity on the electrochemical behaviors of symmetric solid-state lithium cells. The evolution of interface morphology is related to the surface roughness, elastoplastic deformation, creep, and plating of the Li metal. The Laplace-Fourier domain solution is analytically derived, and the numerical solution is solved by implementing Talbot's Laplace transform method and the continuous convolution-Fourier transform (CC-FT) algorithm. A number of cases are analyzed, and the results reveal that a non-conformal interface with imperfect contact can induce uneven field distributions and that the nonuniformity increases with contact loss, and that the impact of external pressure on the reduction in ionic conductivity of SSE is similar to its effect on the potential drop. The results also suggest that the external pressure of 12.5 MPa can lead to relatively uniform deposition in a ceramic electrolyte system, while only 2 MPa is required in a polymer electrolyte system. In addition, A pressure of at least 2 MPa is needed to maintain the high ionic conductivity level for polymer composite SSEs of 14–16% volume LLZO particles.