On the path-dependence of the open-cell voltage of a galvanic cell involving a ternary or multinary compound with multiple mobile ionic species under multiple chemical potential gradients

It is well known that the open-cell voltage (U) of a galvanic cell involving a binary compound, or a multinary compound with a single kind of mobile ionic species, is a state property under a gradient of chemical potential of the mobile component. It is not so transparent, however, whether U is still a state property when involving a ternary or multinary compound with two or more kinds of mobile ions under multiple chemical potential gradients of those mobile components. We clarify this issue with a multinary oxide that conducts oxide ions, protons and electron holes and is exposed to the chemical potential gradients of both water and oxygen. We show that U is path-and history-dependent, and manifests itself along the diffusion paths of the two mobile components H and O under given boundary conditions.