For a combined solar cell-battery device classical liquid electrolytes are not able to guarantee long-term stability as temperature rises up to 150°C on the backside of a solar cell. Switching to solid electrolytes with crystalline structure does not only provide thermal stability, long-term cycling stability and safety benefits, but also an improved diffusivity as temperature rises. A promising crystalline solid electrolyte is Li_(5+x)BaLa_2Ta_2O_(11 .5+0.5x), x ∈ [0,2] (1) with a lithium ion conductivity of 10~5 to 5 ?10~5[S ? cm~1]. To gain a better understanding of the limiting processes within the battery cell, a mathematical model which describes the transport of lithium ions in detail, is of great interest. This model has to take into account the flat or non-porous solid electrolyte/electrode interface and the chemical reactions occurring at that interface. Since the interface is quite small compared to porous liquid electrolyte/electrode interfaces, it is important to accurately describe the electrochemical reaction in a mathematical sense. Furthermore, we cannot assume the classical double layer model at the interface, as we have a fixed anion structure which leads to a different ion distribution (2,3) near the interface, as compared to liquid electrolytes.
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