A Conservative and Efficient Model for Grain Boundaries of Solid Electrolytes in a Continuum Model for Solid-State Batteries

A formulation is presented to model ionic conduction efficiently inside, i.e., across and along grain boundaries. Efficiency and accuracy are achieved by reducing it to a two-dimensional manifold while guaranteeing the conservation of mass and charge at the intersection of multiple grain boundaries. The formulation treats the electric field and the electric current as independent solution variables. We elaborate on the numerical challenges this formulation implies and compare the computed solution with results from an analytical solution by quantifying the convergence toward the exact solution. Towards the end of this work, the model is firstly applied to setups with extreme values of crucial parameters of grain boundaries to study the influence of the ionic conduction in the grain boundary on the overall battery cell voltage and, secondly, to a realistic microstructure to show the capabilities of the formulation.